Tables of Binding Energies and the Energy Surface of Heavy Nuclei

V. A. Kravtsov

Tables of binding energies of the nucleons of heavy nuclei are of great interest. Experimentalists need them for predicting the properties of new, as yet undiscovered nuclei. For questions in the theory of nuclear structure, such tables provide material that makes it possible to establish new regularities and to check previously stated propositions. In particular, in the region of heavy nuclei they make it possible to ascertain how sharply the neutron shell of 126 neutrons and the proton shell of 82 protons are expressed.

Tables of nucleon binding energies, or tables of mass defects of heavy nuclei, have more than once been compiled by calculating differences of binding energies from the energies of alpha and beta decays determined experimentally. In this way Sterns compiled tables of mass defects of heavy nuclei.S1 By the same method WayW1 calculated tables of binding energies of the last neutrons and protons in the lead region. Tables of binding energies of nuclei of heavy elements, published by WapstraW2 in 1950, were also compiled. The first version of Wapstra’s tables was published in an appendix to Rosenfeld’s bookR1 as early as 1948. We do not list here still older tables of this type, since they are very out of date and have by now completely lost their significance.

Stern’s tables contain the greatest amount of material—namely, 126 mass defects of heavy nuclei—but they give rise to rather many doubts. First of all, some decay energies used in the calculations of the mass defects differ from the generally accepted values (for example, the decay energies of Tl207, Pb212, Th235, Pa233, etc.). In calculating mass defects from electron captures, the energy presumably carried away by the neutrino was not taken into account. Stern’s tables do not contain sufficiently detailed indications of the order of calculation of the mass defects presented.

in the tables, as well as about the decay energies adopted in these calculations. The insufficiency of these indications makes it very difficult to correct them on the basis of new experimental data. Since Stern’s tables appeared in 1949 and use experimental data published only up to and including 1948, they are at present obsolete.

Wei’s work contains very little data—only 37 binding energies of the last protons and neutrons—and is also obsolete, since it was published in 1949.

The most well-founded and most recent work is represented by Wapstra’s tables, published in 1950.^W2 They contain differences of nucleon binding energies for 102 heavy nuclei—somewhat fewer than in Stern, since in this work Wapstra refrained from calculations connected with estimating the energies of electron captures. A great merit of these tables is the detailed indication of the order of the calculations, given in the diagrams and in the text, with an enumeration of all decay energies and other experimental data used in the calculations. This facilitates the possibility of correcting and supplementing the tables when new experimental data appear in print. A very important advantage of Wapstra’s tables is the presence of checks on the calculations and on the correctness of the experimental data adopted, according to the position of the points on smooth curves. This check is especially necessary for choosing proposed beta-decay schemes, which often give rise to doubts.

The most significant shortcoming of all the cited tables is that the differences of nucleon binding energies of nuclei belonging to different radioactive families were determined from unreliable semiempirical formulas for binding energies (see, for example, G^3, p. 69, formula (2.5), or P^3, p. 13).

At the present time it has become possible to avoid these questionable paths for determining differences of nucleon binding energies of nuclei of different radioactive families and, using for this purpose experimental data from measurements of neutron binding energies, to obtain differences of binding energies of nuclei of different radioactive families from experiment. In a number of works published in recent years, M^1, H^1, K^2, H^3, P^2, P^4, H^6, H^7, K^6, results are given for measurements of neutron binding energies for heavy nuclei by various methods. The accuracy of these measurements has begun to approach the accuracy of measurements of alpha- and beta-decay energies. Thus, experimental data on neutron binding energies can be used analogously to alpha- and beta-decay energies, but already for finding differences of binding energies of nuclei of different radioactive families.

Quite recently, new tables of masses and mass defects of light nuclei^L4, and new tables of atomic constants^D5, have also appeared in print. All these refined quantities are

basis of any nuclear tables. The number of heavy nuclei known to us has also increased considerably. All this made it possible once again to calculate more accurately the binding energies of nucleons in a larger number of heavy nuclei, without the use of semiempirical formulas, on the basis solely of experimental data. The first version of such refined tables of binding energies of the nucleons of heavy nuclei was compiled by the author at the beginning of 1951. The differences of these energies, which are the binding energies of the last protons and neutrons, were published in the form of graphs illustrating work K5 on the shells of heavy nuclei and the binding energies of nucleons.

In June 1951 a second paper by Wapstra W3 was published on the surface of binding energies near \(Z = 82\) and \(Z = 126\). This paper gives 67 differences of the binding energies of nucleons in heavy nuclei from mercury to emanation. In Wapstra’s 1951 paper, the differences of the binding energies of nucleons in various nuclei were obtained from experimental data: from the energies of alpha and beta decays and from neutron binding energies. The binding energies of some nuclei were obtained by extrapolation and interpolation of the binding-energy curves.

The table presented in the present article contains 233 masses of isotopes and the binding energies of the nucleons of their nuclei, beginning with the platinum isotopes \(Z = 78\) and ending with the californium isotope \(Z = 98\), i.e., practically all known nuclei, both natural and obtained artificially, as well as a number of nuclei still unknown, but whose energy it was possible to find. In compiling this table, all published experimental data were used: alpha- and beta-decay energies, neutron binding energies, and mass-spectrographic measurements. To check the correctness of the calculations and to expand the table, certain regularities established for heavy nuclei were used, namely: the dependence of the electron-capture energy on the half-life, the presence of smooth curves on which lie the binding energies of nucleons of even-odd, odd-odd, and even-even nuclei, etc. Below are given the principal formulas, regularities, and procedure for calculating the energies used in the table. Then the tables themselves are given, with the necessary notes and calculations of the errors of these tables. In the conclusion of the article an image is given of the energy surface of heavy nuclei, some of its sections, and the most general conclusions from the tables and the energy surface.

1. DIFFERENCES OF THE BINDING ENERGIES OF NUCLEI OF ONE RADIOACTIVE FAMILY

To derive the formulas for the differences of the binding energies of nucleons in a nucleus, let us introduce the following notation.

\(M(Z,A)\)—the mass of an atom with atomic number \(Z\) and mass number \(A\).

\(E(Z,A)\) is the binding energy of the nucleons of a nucleus with atomic number \(Z\) and mass number \(A\).

By the definition of the binding energy of the nucleons of a nucleus, given, for example, in Shpolsky’s book (\(S^4\), p. 340), we have:

\[ E(Z,A)=Zm_{\mathrm H}+(A-Z)m_n-M(Z,A), \tag{1} \]

where \(m_{\mathrm H}\) is the mass of the hydrogen atom, and \(m_n\) is the mass of the neutron.

If we denote by \(e_\alpha\) the kinetic energy of the alpha particle emitted as a result of the decay of the initial radioactive nucleus with mass number \(A\), then the alpha-decay energy \(E_\alpha\), equal to the sum of the kinetic energies of the alpha particle and the recoil nucleus, is expressed as follows:

\[ E_\alpha=e_\alpha\left(\frac{A}{A-4}\right). \tag{2} \]

In the case of alpha decay of an initial nucleus with mass \(M(Z,A)\), we can write the following equation expressing the law of conservation of mass in the process of alpha decay:

\[ M(Z,A)=M(Z-2,A-4)+M_\alpha+E_\alpha, \tag{3} \]

where \(M_\alpha\) is the mass of the alpha particle. Expressing the binding energies of the initial nucleus and of the daughter nucleus with mass \(M(Z-2,A-4)\) by formula (1), we obtain from equation (3)

\[ E(Z,A)-E(Z-2,A-4)=E(\alpha)-E_\alpha, \tag{4} \]

where \(E(\alpha)=E(2,4)\) is the binding energy of the nucleons of the alpha particle. Formula (4) makes it possible to calculate the difference of the binding energies of the nucleons of the initial and daughter nuclei in alpha decay from the known alpha-decay energy \(E_\alpha\).

For the formula for the differences of the binding energies of the nucleons of nuclei in the case of beta decay, we additionally introduce the following notation: \(E_\beta\) is the maximum energy of the beta particles (the end point of the beta spectrum); \(E_\gamma\) is the energy of the gamma rays accompanying beta decay, if the daughter nucleus in beta decay is formed in an excited state.

If beta decay of an initial nucleus with binding energy \(E(Z,A)\) takes place and a daughter nucleus with energy \(E(Z+1,A)\) is formed, then, analogously to the case of alpha decay, from the law of conservation of energy and formula (1) we obtain:

\[ E(Z,A)-E(Z+1,A)=(m_n-m_{\mathrm H})-E_\beta-E_\gamma. \tag{5} \]

Formula (5) makes it possible to calculate the difference of the binding energies of the initial and daughter nuclei in beta decay from the sum of the energy of the beta-spectrum end point \(E_\beta\) and the energy of the gamma rays \(E_\gamma\) following the beta decay.

Serious difficulties arise when beta decay is accompanied by gamma radiation. For the correct choice of the sum of the quantities \(E_\beta+E_\gamma\), it is necessary to know precisely the beta-decay scheme of the given nucleus and the difference between the levels of the parent and daughter nuclei (see, for example, \(K^1\)). Beta-decay schemes may be regarded as reliably known if observations have been made of coincidences of beta-particle emissions with gamma photons and of gamma photons with gamma photons (\(K^1\), pp. 161–165).

In positron decay, when calculating the differences of the energies of the parent and daughter nuclei, one must also introduce into the formula the energy equivalent of the electron mass \(m_e\) (see \(G^1\)). From the law of conservation of energy and formula (1), taking into account not only the masses of the nuclei but also the mass of the electron and of the positron that is produced, we obtain:

\[ E(Z,A)-E(Z-1,A)=-(m_{\mathrm{n}}-m_{\mathrm{H}})-E_{\beta^+}^{\,\max}-E_\gamma-2m_e, \tag{6} \]

where \(E_{\beta^+}^{\max}\) is the maximum energy of the positrons (the end point of the positron spectrum).

\(E_\gamma\) is the energy of the gamma rays accompanying positron decay, if the daughter nucleus is formed in an excited state.

Formula (6) makes it possible to calculate the difference in binding energies of the parent and daughter nuclei from the sum of the energies \(E_{\beta^+}\)—the end point of the positron spectrum—and \(E_\gamma\)—the energy of the gamma rays.

Just as in the case of beta decay, in positron decay there are difficulties in the correct choice of the sum \(E_{\beta^+}+E_\gamma\) when gamma rays are present. The correct choice is possible only when there is an experimentally verified decay scheme.

It should be noted that all the formulas given above make it possible to calculate differences in the binding energy of nucleons of nuclei belonging to one of the four known radioactive families of heavy nuclei.

All values \(E_\alpha\), \(E_\beta+E_\gamma\) accepted for the calculations of binding energies are given in Table II with references to the literature.

2. DIFFERENCES IN THE BINDING ENERGIES OF NUCLEONS OF NUCLEI OF DIFFERENT RADIOACTIVE FAMILIES

The difference in the binding energies of the nucleons of nuclei of isotopes of one element that differ by one neutron and belong to different radioactive families is expressed by the formula

\[ e_n(Z,A)=E(Z,A)-E(Z,A-1), \tag{7} \]

where \(e_n(Z,A)\) is the binding energy of the “last” neutron in the nucleus \((Z,A)\).

Table I

Measured binding energies of the last neutrons in heavy nuclei
(compiled using papers published before January 1, 1952)

Nucleus	Binding energies of the last neutron (MeV), measured in reactions: $(\gamma,\mathrm n)$	Binding energies of the last neutron (MeV), measured in reactions: $(\mathrm n,\gamma)$	Binding energies of the last neutron (MeV), measured in reactions: $(\mathrm d,\mathrm p)$	Binding energies of the last neutron (MeV), measured in reactions: $(\mathrm d,\mathrm t)$	Adopted in Table II (MeV)
1	2	3	4	5	6
$\mathrm{Pt}^{194}$	$9,5 \pm 0,2\;(\mathrm{S}10)$				$9,5 \pm 0,2$
$\mathrm{Pt}^{195}$	$6,1 \pm 0,1\;(\mathrm{P}2)$		$6,14 \pm 0,2\;(\mathrm{H}6)$		$6,1 \pm 0,15$
$\mathrm{Pt}^{196}$	$8,2 \pm 0,2\;(\mathrm{S}10)$		$8,0 \pm 0,2\;(\mathrm{H}6)$		$8,1 \pm 0,15$
$\mathrm{Au}^{197}$	$7,9 \pm 0,2\;(\mathrm{S}10)$				$8,1 \pm 0,1$
$\mathrm{Au}^{197}$	$8,0 \pm 0,15\;(\mathrm{H}1)$				$8,1 \pm 0,1$
$\mathrm{Au}^{197}$	$8,1 \pm 0,1\;(\mathrm{P}2)$				$8,1 \pm 0,1$
$\mathrm{Au}^{198}$		$6,54\;(\mathrm{H}6)$	$6,35 \pm 0,15\;(\mathrm{H}6)$		$6,4 \pm 0,2$
$\mathrm{Hg}^{201}$	$6,25 \pm 0,2\;(\mathrm{H}1)$				$6,4 \pm 0,2$
$\mathrm{Hg}^{201}$	$6,6 \pm 0,2\;(\mathrm{P}2)$				$6,4 \pm 0,2$
$\mathrm{Tl}^{203}$	$8,8 \pm 0,2\;(\mathrm{S}10)$				not suitable
$\mathrm{Tl}^{204}$		$6,54\;(\mathrm{H}6)$	$6,52 \pm 0,15\;(\mathrm{H}6)$		$6,53 \pm 0,15$
$\mathrm{Tl}^{205}$	$7,5 \pm 0,2\;(\mathrm{S}10)$			$7,7 \pm 0,2\;(\mathrm{H}6)$	$7,48 \pm 0,15$
$\mathrm{Tl}^{205}$	$7,48 \pm 0,15\;(\mathrm{H}1)$			$7,7 \pm 0,2\;(\mathrm{H}6)$	$7,48 \pm 0,15$
$\mathrm{Tl}^{205}$	$7,3 \pm 0,25\;(\mathrm{P}2)$			$7,7 \pm 0,2\;(\mathrm{H}6)$	$7,48 \pm 0,15$

Nucleus	Binding energies of the last neutron (MeV), measured in reactions: (γ, n)	Binding energies of the last neutron (MeV), measured in reactions: (n, γ)	Binding energies of the last neutron (MeV), measured in reactions: (d, p)	Binding energies of the last neutron (MeV), measured in reactions: (d, t)	Adopted in Table II (MeV)
1	2	3	4	5	6
Tl206		6,23 ± 0,05 (K6)	6,16 ± 0,15 (H6)		6,20 ± 0,10
Pb206	8,25 ± 0,10 (P4) 6,75 ± 0,2 (S10)			8,10 ± 0,10 (H6)	8,12 ± 0,10
Pb207	6,95 ± 0,1 (P4) 6,9 ± 0,1 (P2)	6,734 ± 0,008 (K6)	6,71 ± 0,03 (H6)	6,70 ± 0,05 (H6)	6,71 ± 0,01
Pb208	7,3 ± 0,2 (S10) 7,44 ± 0,10 (P4)	7,380 ± 0,008 (K6)	7,37 ± 0,03 (H6)	7,37 ± 0,05 (H6)	7,38 ± 0,01
Pb209			3,87 ± 0,05 (H6)		3,87 ± 0,05
Bi209	7,40 ± 0,2 (S10) 7,45 ± 0,2 (M1) 7,2 ± 0,1 (P2)			7,44 ± 0,05 (H6)	7,44 ± 0,05
Bi210		4,170 ± 0,015 (K6)	4,14 ± 0,03 (H6)		4,22 ± 0,05
Th232	6,35 ± 0,04 (M7) 6,0 ± 0,15 (P2)				6,35 ± 0,04
Th233			4,9 ± 0,2 (H6)		4,9 ± 0,2
U238	5,8 ± 0,15 (P2) 5,97 ± 0,10 (H7)		5,9 ± 0,2 (H6)		5,9 ± 0,1
U239			4,63 ± 0,15 (H6)		4,6 ± 0,15

Experimental determination of the binding energy of a neutron in a nucleus can be carried out in four different ways, namely by measuring the energy balance in the following four reactions: \((d,p)\), \((d,t)\), \((\gamma,n)\), and \((n,\gamma)\). In determining \(e_n\) from the reaction \((d,p)\), if the target nucleus is \((Z,A-1)\), the binding energy of the “last” neutron in the daughter nucleus \((Z,A)\) is found from the formula

\[ e_n = Q_R + E(d) + E_\gamma, \]

where \(Q_R\) is the reaction energy, \(E(d)\) is the binding energy of the deuteron, and \(E_\gamma\) is the total energy of the gamma rays if the daughter nucleus was formed in an excited state. Since it is not always possible to register gamma photons, especially if their energy is small, for example of the order of \(0.1\) MeV, an error in the measurement of \(e_n\) is possible. If the gamma energy is not included, then \(e_n\), determined from the reaction \((d,p)\), will be less than or equal to (if the daughter nucleus is not excited) the true binding energy of the last neutron of the daughter nucleus.

If measurements are made using the reaction \((d,t)\), then the neutron binding energy of the target nucleus \((Z,A)\) will be found from the formula

\[ e_n = E(t) - E(d) - Q_R - E_\gamma, \]

where the notation is as before and \(E(t)\) is the binding energy of the triton. If the gamma energy is not included, then \(e_n\) determined from the reaction \((d,t)\) will be greater than or equal to the true binding energy of the last neutron of the target nucleus.

Considering similarly the reaction \((\gamma,n)\), where the neutron binding energy \(e_n\) is equal to its threshold, it can be shown that the obtained value of the threshold is greater than or equal to the true neutron binding energy of the target nucleus. The result of measuring \(e_n\) by the reaction \((n,\gamma)\) is ambiguous if the gamma-decay scheme is not known.

Table I (see pp. 346–347) gives all neutron binding energies published by the time the table was compiled, with references to the cited literature, listed in alphabetical order at the end of the article. In the last column of Table I are given the experimental mean values \(e_n\) selected for Table II.

In selecting the values of \(e_n\), attention was paid to the cycles that can be formed from \(e_n\), \(E_\alpha\), and \(E_\beta\), and to the arrangement of the binding energies of the nucleons of nuclei on smooth curves (see § 4).

3. DIFFERENCES OF NUCLEAR BINDING ENERGIES FROM ELECTRON CAPTURES

Applying the law of conservation of energy to the capture of an electron by a nucleus from some atomic level, one can find the difference between the binding energies of the nucleons of the initial nucleus \((Z,A)\) and the daughter nucleus \((Z-1,A)\). Using formula (1), we obtain:

\[ E(Z,A) - E(Z-1,A) = -(m_n - m_h) - E_x - E_k - E_\gamma, \tag{8} \]

TABLES OF BINDING ENERGIES

where \(E_x\) is the energy of the X-rays emitted upon capture of an electron by the daughter nucleus. If electron capture occurs from the \(K\)-level, and this is the most frequently encountered case,

\[ E_x=hR(Z-1)^2=13.6(Z-1)^2\ \text{eV}, \tag{9} \]

where \(h\) is Planck’s constant, \(R\) is Rydberg’s constant; \(E_k\) is the energy of electron capture, carried off, as is assumed, by the neutrino; \(E_\gamma\) is the energy of the gamma rays accompanying electron capture, if the daughter nucleus is formed in an excited state.

The greatest difficulty is posed by the determination of the electron-capture energy \(E_k\), which cannot be measured directly. In the region of heavy nuclei, where most nuclei are radioactive and the magnitudes of the energies of alpha decays and beta decays have been measured, one can calculate electron-capture energies from closed cycles. For example, in this way one can calculate the energy of electron capture of the nucleus \(\mathrm{Np}^{235}\) from the cycle:

\[ \begin{array}{ccccc} & & K & & \\ & \mathrm{U}^{235} & \longleftarrow & \mathrm{Np}^{235} & \\ E_\alpha=4.66\ \text{MeV} & \downarrow\alpha & & \alpha\downarrow & E_\alpha=5.15\ \text{MeV} \\ & \mathrm{Th}^{231} & \xrightarrow{\ \beta\ } & \mathrm{Pa}^{231} & \\ & & E_\beta+E_\gamma=0.32\ \text{MeV}. & & \end{array} \]

From the scheme and from formulas (4), (5), and (8), taking into account that in the alpha decays of the cycle there are no gamma rays, while the beta decay \(\mathrm{Th}^{231}\) according to the scheme (see \(J^1\)) has a transition energy to the ground state \(E_\beta+E_\gamma=0.324\ \text{MeV}\), it is not difficult to show that

\[ E_k=E_\alpha(\mathrm{Np}^{235})-E_\alpha(\mathrm{U}^{235})-(E_\beta+E_\gamma)-E_x. \]

The best available measurements, with the correction for recoil-nucleus energy according to formula (2), give for \(E_\alpha(\mathrm{Np}^{235})=5.15\ \text{MeV}\) \(P^1\) and for \(E_\alpha(\mathrm{U}^{235})=4.66\ \text{MeV}\) \(G^7\). By formula (9), for \(Z=93\), \(E_x=0.11\ \text{MeV}\). Thus, for electron capture of \(\mathrm{Np}^{235}\),

\[ E_k=0.06\ \text{MeV}^*). \]

Similar calculations were carried out by \(T^1\), and the energies were compared with the half-life period of electron capture. In particular, the half-life period for \(\mathrm{Np}^{235}\), according to the tables of Dzhelepov and Petrovich \(D^2\), is equal to 435 days, with the branching ratio of electron

\(^*)\) In Thomson’s paper \(T^1\), the value \(E_k=0.14\ \text{MeV}\) for \(\mathrm{Np}^{235}\), since for the beta decay of \(\mathrm{Th}^{231}\) the value \(E_\beta+E_\gamma=0.24\ \text{MeV}\) was adopted there; this is now obsolete and is refuted by the data of \(J^1\).

of capture relative to alpha decay, equal to 0.999. Thus, the period of the partial electron-capture half-life will be:

\[ \tau_k=\frac{435\ \text{days}}{0.999}=435\ \text{days}=6.3\cdot 10^5\ \text{min}. \]

In this way 15 electron-capture energies were calculated and a graph was constructed of the dependence of the logarithm of \(E_k\) on the logarithm of \(\tau_k\), presented in Fig. 1. As is seen from Fig. 1, the points for odd-even (odd \(Z\) and even \(N\)) nuclei and even-odd (even \(Z\) and odd \(N\)) nuclei, i.e. for nuclei with an odd mass number, lie satisfactorily on a straight line of the logarithmic plot. The electron-capture energies for odd-odd nuclei are too few in number (only 5) for it to be possible to determine the position of a second curve. It can only be noted that for odd-odd nuclei the electron-capture energies are considerably larger. A small number of additional data for electron captures of even-even nuclei shows that their electron-capture energy is smaller than that of nuclei with an odd mass number. Three dependences of \(E_k\) on the half-life period separately for even-even nuclei, for nuclei with an odd mass number, and for odd-odd nuclei correspond to the existing theoretical ideas, in particular to the semiempirical formulas for nuclear energies (\(G^2\), p. 69 or \(F^3\), p. 13). Also in accordance with theory, the electron-capture energies increase as the half-life period decreases. Comparing the nuclei of isobars, we see that the half-life period for electron capture decreases rapidly with increasing distance from stable isobaric nuclei or mono-alpha-radioactive nuclei. This distance corresponds to the rise along the isobaric energy parabolas (\(B^1\), p. 36) and to the increase in their steepness and, consequently, to an increase in the decay energy.

Fig. 1. Graph of the dependence of the electron-capture half-life period on the decay energy. All quantities are plotted on the axes on a logarithmic scale.

All these theoretical considerations indicate that the graph (Fig. 1) best represents reality far from especially stable nuclei in the region around \({}_{82}\mathrm{Pb}^{208}\), since here we have the largest deviations from semi-empirical formulas for binding energies (see, for example, P³).

Thus, the graph (Fig. 1) and the additional considerations set out above make it possible to estimate, at least approximately, electron-capture energies from the magnitude of the half-life period. It is clear that such an estimate is very approximate, but nevertheless the error of this estimate far from \(Z = 82\) and \(N = 126\) should not exceed \(\pm 0.5\) MeV. The possibility of estimating \(E_k\) makes it possible to considerably enlarge the number of nuclei in the table of binding energies and to check extrapolation and interpolation along curves, as indicated below.

4. SECTIONS OF ENERGY SURFACES AND THEIR USE FOR CHECKING AND INTERPOLATION

As is known, the binding energy of nucleons in nuclei depends not only on the atomic number \(Z\) and the mass number \(A\), but also on the parity of the atomic number \(Z\) and of the number of neutrons \(N\). It has been established that, considering the nuclear binding energy \(E(Z,A)\) as a function of \(Z\) and \(A\), it can be represented in the form of three smooth surfaces, not intersecting in the space \((E,Z,A)\), separately for even-even nuclei, nuclei with odd \(A\), and odd-odd nuclei. In this case it turns out that the binding energies \(E(Z,A)\) are largest for even-even nuclei and smallest for odd-odd nuclei. The energy surface for nuclei with odd \(A\), i.e. for even-odd and odd-even nuclei, is located approximately midway between the even-even surface and the odd-odd surface (see B¹, G² and F³). The fact that each of these surfaces is smooth and has no inflections provides a good method for checking calculations and interpolating binding energies when the number of nuclei under study is large. For these purposes it is most convenient to study sections of the energy surfaces. These sections may be taken in different directions, for example in the planes \(A = \mathrm{const}\), \(Z = \mathrm{const}\), \(N = A - Z = \mathrm{const}\), \(I = N - Z = A - 2Z = \mathrm{const}\), etc. The largest number of points will be in the sections \(Z = \mathrm{const}\); second in number of points is the section \(I = \mathrm{const}\), third \(N = \mathrm{const}\), etc. Therefore the most convenient for checking and interpolation will be isotopic sections \(Z = \mathrm{const}\), i.e. sections on which the binding energies of nucleons in the nuclei of isotopes of one and the same element are represented. Sections \(I = \mathrm{const}\), although they also contain a sufficient number of points, are not of interest for checking, since they contain nuclei connected with one another by alpha decays, whose energies

are known most accurately. This makes the curves of the sections \(I=\mathrm{const}\) always smooth, since the main sources of errors—the beta-decay energies—do not affect their course. The curves of the sections \(N=\mathrm{const}\) can also be used for checking, but the number of points on them is somewhat smaller. The principal method of checking and interpolation is provided by the curves of isotopic sections \(Z=\mathrm{const}\). Here one must distinguish two cases: even \(Z\) and odd \(Z\). For even \(Z\), with odd \(A\) we have even-odd nuclei, and with even \(A\), even-even nuclei. Thus, constructing the binding energies of nucleons \(E\) for even \(Z\) as a function of \(A\), we obtain two curves: one for even-even nuclei with larger \(E\), and another for even-odd nuclei with smaller \(E\). In the case of odd \(Z\), we shall likewise have two curves: for odd-even nuclei (odd \(A\)) with larger \(E\), and for odd-odd nuclei (even \(A\)) with smaller \(E\). In Figs. 2, 3, and 4 three sections are presented: \(Z=82\) (Pb), \(Z=83\) (Bi), and \(Z=92\) (U). In order to reduce the steepness of the curves, here, as in many other cases, the graphs show not the values \(E(Z,A)\) themselves, but the differences \(E_0(A)-E(Z,A)\), where \(E_0(A)\) is the following auxiliary linear function:

\[ E_0(A)=1600.6+5.5(A-200)\ \text{Mev}. \tag{10} \]

This function increases by \(5.5\ \text{Mev}\) per nucleon, i.e., on the average somewhat more slowly than the binding energy in the region of heavy nuclei.

In Fig. 2 we see that the curve for the even-odd isotopes of lead lies higher than that for the even-even ones. All the points fall well on a smooth curve. If for \(\mathrm{Pb}^{214}\) (RaB) it is assumed that beta decay (spectrum limit \(0.65\ \text{Mev}\)) \(\mathrm{S}^{11}\) leads to the ground state of \(\mathrm{Bi}^{214}\) (RaC), then on the curve we obtain the point marked by a triangle. The curve for even-even nuclei then begins to move away from the curve of even-odd nuclei (in Fig. 2 it is shown by a dotted line). If, however, it is considered that the beta transition leads to an excited state of \(\mathrm{Bi}^{214}\) and that in the subsequent cascade gamma rays of energy \(0.35\ \text{Mev}\) follow, then the curve will pass through the point marked by a cross (in Fig. 2, the solid line). The second variant, as is seen from Fig. 2, is better, and therefore for \(\mathrm{Pb}^{214}\) it is accepted that \(E_\beta+E_\gamma=0.65+0.35=1.00\ \text{Mev}\).

In Fig. 3 we see that the curve for the bismuth isotopes of the odd-odd nuclei lies higher than that of the odd-even nuclei. All the points fall well on a smooth curve, except for the value marked by an asterisk \(*\) for \(A=211\) (\(\mathrm{Bi}^{211}\)); this point unquestionably falls outside the curve for odd-even nuclei. A study of the curves for \(Z=85\), \(Z=87\), etc. (not given here) shows that on them the corresponding points for \(A=215\), \(A=219\)

Fig. 2. Isotopic sections of the energy surfaces \(E_0(A) - E(Z,A)\): a—for even-even nuclei, b—for even-odd nuclei, c—a variant for an even-even nucleus that fits the curve poorly. The extrapolated curve is indicated by a coarse dashed line; the rejected variant of the curve by a fine dashed line.

Fig. 3. Isotopic cross section of the energy surfaces \(E_0(A)-E(Z,A)\) for bismuth \((Z=83)\): \(a\)—for odd-even nuclei, \(b\)—for odd-odd nuclei, \(c\)—for the isomeric nucleus. The extrapolated curve is indicated by a dashed line.

and so on, i.e., for nuclei whose alpha-decay product is \(Bi^{211}\), also deviate upward from the smooth curve by approximately \(0.30\)—\(0.40\) MeV. If, in calculating the binding energy of \(Bi^{211}\), one takes the alpha-decay energy to be not \(6.746\) MeV, but \(6.393\) MeV, i.e., not according to the longest-range group but according to the second group of alpha particles, we obtain a value for the binding energy of the nucleons of \(Bi^{211}\) that lies on the smooth curve (in Fig. 3 this value is indicated by a cross).

Fig. 4. Isotopic section of the energy surfaces \(E_0(A) - E(Z,A)\) for uranium \((Z=92)\). Designation of points: \(a\)—for even-even nuclei, \(b\)—for odd-odd nuclei, \(v\)—a variant of values for odd-even nuclei not lying on the curve of the section. The rejected variant of the curve is indicated by a dashed line.

Having adopted such a binding energy for \(Bi^{211}\) and, from it, calculated the binding energies of \(At^{215}\), \(Fr^{219}\), and other nuclei connected with \(Bi^{211}\) by a chain of alpha decays, we obtain values that lie well on the smooth curves. Together with Wapstra \(^{3}\), one may suppose that the long-range group of alpha particles of \(Bi^{211}\) is obtained by the decay of the isomer \(Bi^{211m}\). This supposition is quite convincing, since it has recently been established \(^{1}\) that the neighboring bismuth isotope \(Bi^{210}\) also has an isomeric state.

In Fig. 4, where the section curves for uranium isotopes \((Z=92)\) are presented, the curve for \(E_0 - E\) of even-odd nuclei lies higher, i.e., corresponds to smaller binding energies, than for even-even nuclei, just as in lead. These curves made it possible to improve the values of the binding energies of the \(U^{237}\) nuclei. If the value of the beta-decay energy of this nucleus is taken to be the same as in Wapstra \(^{2}\), i.e., \(E_\beta = 0.49\) MeV, then as a result we obtain

the value \(E\), represented on the graph by a triangle. This value leads to the odd-even surface intersecting the even-even one near \(A = 237\) (dashed line in Fig. 4), which is unlikely. Comparing the experimental data from the tables of atomic nuclei by Dzhelepov and Petrovich \(^{\mathrm{D}2}\), one may assume that the beta-decay energy for \(\mathrm{U}^{237}\) may be equal to \(E_\beta = 0.70\) MeV, if it is considered that after the beta transition \(0.24\) MeV are emitted successively in a cascade, \(E_{\gamma 1} = 0.204\) MeV and \(E_{\gamma 2} = 0.260\) MeV. These values lead to the binding energies of the nucleons of the nucleus \(\mathrm{U}^{237}\), shown on the curve by circles, which fit the curve well and do not lead to an intersection of the odd-even and even-even curves.

The cross-section curves of the energy surfaces were used both to check the correctness of the choice of decay schemes and to find intermediate values of the binding energies of nuclei not yet observed experimentally, for example \(\mathrm{Em}^{213}\), \(\mathrm{Em}^{214}\), \(\mathrm{Em}^{215}\), \(\mathrm{Fr}^{213}\), \(\mathrm{Fr}^{214}\), etc., and to find the binding energies of extrapolated nuclei. Extrapolation was allowed only when it was possible to verify the data obtained with its aid by other methods. More detailed information on this is given in § 6.

5. USE OF DATA ON THE MEASUREMENT OF NUCLEAR MASSES

Not only relative but also absolute values of binding energies are of interest. To enter absolute values of binding energies into the tables, it was necessary to use direct measurements of atomic masses. In all subsequent calculations the adopted values were the mass of the neutron \(m_n\), the neutral hydrogen atom \(m_{\mathrm H}\), and the mass of the helium atom from the work of Li et al. \(^{\mathrm{L}4}\), where all these quantities were calculated from the energies of nuclear reactions, taking the mass of the isotope \(\mathrm{O}^{16}\) to be equal to 16.00000. According to the data of Li et al., these values are as follows:

\[ m_n = 1.008982 \pm 0.000003 \ \text{atomic mass units}, \]

\[ m_{\mathrm H} = 1.008142 \pm 0.000003 \ \text{” ” ”}, \]

\[ m(\mathrm{He}^4) = 4.003873 \pm 0.000015 \ \text{” ” ”}. \]

In addition, for calculating binding energies the following quantities are necessary:

\[ (m_n - m_{\mathrm H}) = 0.782 \pm 0.001 \ \text{MeV}; \]

\[ 1 \ \mathrm{AEM} \ (\text{atomic mass unit}) = 931.152 \pm 0.008 \ \text{MeV}^{\mathrm{D}5}. \]

The most recent data on measurements of the masses of heavy atoms were published by Duckworth and co-workers \(^{\mathrm{D}3,\mathrm{D}4 \text{ and } \mathrm{S}7}\). In these works the following were obtained from mass-spectrographic comparisons ...

masses, corrected for the mass values of light nuclei, published by Li et al.:

\[ \begin{aligned} \mathrm{Pt}^{194} &— 194.0248 \pm 0.0014 \quad (\mathrm{D}4),\\ \mathrm{Pt}^{195} &— 195.02593 \pm 0.00078 \quad (\mathrm{D}3),\\ \mathrm{Pt}^{196} &— 196.02658 \pm 0.00060 \quad (\mathrm{D}4),\\ \mathrm{Pb}^{208} &— 208.0416 \pm 0.0015 \quad (\mathrm{D}4),\\ \mathrm{Th}^{232} &— 232.1064 \pm 0.0012 \quad (\mathrm{S}7),\\ \mathrm{U}^{238} &— 238.1291 \pm 0.0014 \quad (\mathrm{S}7). \end{aligned} \]

Using these data, one can calculate, by formula (1), the following binding energies of nucleons in nuclei:

\[ \begin{aligned} {}_{2}\mathrm{He}^{4}: E(\alpha) &= 28.28 \pm 0.02\ \text{MeV}\\ {}_{78}\mathrm{Pt}^{194}: E(78,194) &= 1538.4 \pm 1.3 \quad »\\ {}_{78}\mathrm{Pt}^{195}: E(78,195) &= 1545.7 \pm 0.7 \quad »\\ {}_{78}\mathrm{Pt}^{196}: E(78,196) &= 1553.5 \pm 0.6 \quad »\\ {}_{80}\mathrm{Pb}^{208}: E(82,208) &= 1636.8 \pm 1.4 \quad » \end{aligned} \]

\[ \begin{aligned} {}_{90}\mathrm{Th}^{232}: E(90,232) &= 1771.0 \pm 1.1\ \text{MeV}\\ {}_{92}\mathrm{U}^{238}: E(92,238) &= 1798.5 \pm 1.5 \quad » \end{aligned} \]

The binding energy of nucleons in the alpha particle is used to calculate the differences of the energies of nuclei connected by alpha decays, according to formula (4). The binding energy of the nucleus \({}_{82}\mathrm{Pb}^{208}\) is taken as the basis for the binding-energy values of the entire table. All energies, except for the binding energies of certain light isotopes of Pt, Au, and Hg, are calculated from the binding energy of \(\mathrm{Pb}^{208}\). The remaining energies are calculated from the binding energies of \(\mathrm{Pt}^{194}\), \(\mathrm{Pt}^{195}\), and \(\mathrm{Pt}^{196}\), computed from mass-spectrographic data.

The binding energies of \(\mathrm{Th}^{232}\) and \(\mathrm{U}^{238}\), obtained from mass-spectrographic data, are not used, since they differ greatly from the energies calculated from the binding energy of \(\mathrm{Pb}^{208}\) according to radioactive-decay data and neutron binding energies. The magnitude of this discrepancy will be discussed in § 8.

6. PROCEDURE FOR CALCULATING THE BINDING ENERGIES OF NUCLEONS OF NUCLEI AND DESCRIPTION OF TABLE II

As was indicated in the preceding paragraph, the calculation of the binding energies of nucleons of most nuclei began with the binding energy of the nucleus \({}_{82}\mathrm{Pb}^{208}\), determined from mass-spectrographic data. The binding energies of most other nuclei were found from the binding energy

nucleus ${}_{82}\mathrm{Pb}^{208}$ from energy differences, which were calculated from the energies of alpha or beta decays according to formulas (4), (5), or (6); from the measured neutron binding energies according to formula (7), and sometimes from an estimate of the electron-capture energy according to formulas (8) and (9) and the graph in Fig. 1.

Initially, the binding energies of nuclei were calculated only from alpha and beta decays and from nucleon binding energies obtained experimentally. From these data, $E_0 - E$ (see formula (10), § 4) were calculated, and isotopic sections were constructed for all $Z$, similar to those shown in Figs. 2, 3, and 4. The curves of these sections for Tl and Pb were continued toward small $A$, and the values of the binding energies of the light isotopes of thallium ($A$ from 202 to 197) and lead ($A$ from 202 to 196) were found by graphical extrapolation. These extrapolated energies were checked in the following ways. The thallium curves are connected with the bismuth alpha decays $\mathrm{Bi}^{201}$ and $\mathrm{Bi}^{203}$. It turned out that the energies of $\mathrm{Bi}^{201}$ and $\mathrm{Bi}^{203}$, calculated from the energies of $\mathrm{Tl}^{197}$ and $\mathrm{Tl}^{199}$, fit well on the continued curves of the bismuth sections (see Fig. 2, dashed curves). The use of the measured alpha-decay energies of $\mathrm{At}^{203}$, $\mathrm{At}^{205}$, $\mathrm{At}^{207}$, and $\mathrm{At}^{209}$ makes it possible, from the bismuth curves, to construct curves for the isotopic section of astatine. The curves of the light astatine isotopes obtained in this way agree well with their continuation carried out from the data of alpha and beta decays and measurements of neutron binding energies. All this, taken together, gives great confidence in the correctness of the binding-energy values of the light thallium isotopes found by extrapolation. In the same way, from the alpha-decay energies of the light polonium isotopes ($A$ from 207 to 200) and the smoothness of the curves of the polonium sections obtained in this way, the extrapolation of the curves of the lead section was checked.

Toward smaller $Z$, the energies were calculated using the estimate of electron-capture energies from the graph in Fig. 1, with subsequent checking against the curves of the isotopic sections. The graph in Fig. 1 was used for $Z \leqslant 81$ and $N \leqslant 121$, i.e., where the shell $Z = 82$, $N = 126$ already has little effect. And indeed, with small corrections (less than 0.4 MeV), all points fit well on the section curves of the isotopes of mercury, gold, and platinum. Still greater confidence in the correctness of these calculations is given by the fact that the mass-spectrographic binding energies of $\mathrm{Pt}^{194}$, $\mathrm{Pt}^{195}$, and $\mathrm{Pt}^{196}$ fit well on the section curves of the platinum isotopes. It should be noted that the binding energies of these platinum isotopes were taken not as exactly equal to the mass-spectrographic values, but as linked with the neutron binding energies obtained experimentally and listed in Table I. Corrections to the experimental mass-spectrographic data for platinum were made within the limits of their errors.

The masses of isotope atoms are calculated from the binding energies by the formula

\[ M(Z,A)=Zm_{\mathrm{H}}+(A-Z)m_n-E(Z,A). \]

Table II contains the following columns.

The 1st column contains the atomic number and the symbol of the element.

The 2nd column contains the mass number of the given isotope of the element. A mass number given in parentheses means that this isotope had not been obtained by the time the tables were compiled.

The 3rd column gives the number of neutrons in the given nucleus.

The 4th column contains indications of the type of radioactivity inherent in the given isotope:

\[ \begin{aligned} \beta^- &\text{— beta radioactivity,}\\ \alpha &\text{— alpha radioactivity,}\\ K &\text{— electron capture from the K level,}\\ \beta^+ &\text{— positron decay,}\\ \text{st.} &\text{— stable isotope.} \end{aligned} \]

A symbol in parentheses means that the type of radioactivity is presumed and has not been precisely established.

The 5th column contains indications of the energy of which isotope was used to calculate the mass and energy of the given isotope. “M. S.” denotes that the energy of the given isotope was obtained from mass-spectrographic data; “interp.” means that the energy of the given isotope was obtained by interpolation or extrapolation along the curves of isotopic sections (see § 4).

If the symbol of the isotope from which the energy was calculated is supplied on the left with an asterisk, this means that the original source for the calculation of the energies of these isotopes is the mass-spectrographic data for one of the platinum isotopes. The absence of an asterisk shows that the initial quantities in the chain of calculations of the mass and binding energy of these isotopes were the mass and binding energy of \({}_{82}\mathrm{Pb}^{208}\), obtained mass-spectrographically.

The 6th column contains the mass of the isotope, calculated from the binding energy. The mass is expressed in atomic mass units (physical scale); the relative error is expressed in units of the last decimal place (see § 8).

The 7th column contains the binding energies of the nucleons of the given isotope, expressed (in MeV) with the relative error (see § 8).

The 8th column contains the differences of the binding energies of neighboring isotopes. These differences are numerically equal to the binding energies of the last neutron \(e_n\).

In those cases when \(e_n\) coincides with the average value obtained from experiment, a reference to Table I is given under the number, where this value and its error are presented.

V. A. KRAVTSOV

Masses of isotopes and
(Compiled using articles,

Atomic number \(Z\) and symbol of element	Mass number \(A\)	Number of neutrons \(N\)	Type of radioactivity	Isotope from which the given mass was calculated	Mass of isotope atom \(M(Z,A)\) (atomic mass units)	Binding energy of the nucleons of the isotope nucleus \(E(Z,A)\) (MeV)
78—Pt	193	115	stable	\(*\mathrm{Pt}^{194}\)	\(193,0250\pm9\)	\(1529,9\pm0,9\)
78—Pt	194	116	stable	M. S. (see § 7,1)	\(194,0238\pm8\)	\(1539,4\pm0,8\)
78—Pt	195	117	stable	M. S. (see § 7,2)	\(195,0262\pm8\)	\(1545,5\pm0,8\)
78—Pt	196	118	stable	M. S. (see § 7,1)	\(196,0265\pm8\)	\(1553,6\pm0,8\)
78—Pt	197	119	\(\beta^{-}\)	\(*\mathrm{Au}^{197}\)	\(197,0291\pm7\)	\(1559,5\pm0,7\)
78—Pt	198	120	stable	interp.	\(198,0301\pm8\)	\(1567,0\pm0,8\)
78—Pt	199	121	\(\beta^{-}\)	\(\mathrm{Au}^{199}\)	\(199,0330\pm7\)	\(1572,6\pm0,7\)
79—Au	194	115	\(\beta^{+}\)	\(*\mathrm{Pt}^{194}\)	\(194,0271\pm9\)	\(1535,5\pm0,9\)
79—Au	195	116	K	\(*\mathrm{Pt}^{195}\)	\(195,0264\pm7\)	\(1544,5\pm0,7\)
79—Au	196	117	K; \(\beta^{-}\)	\(*\mathrm{Pt}^{196}\)	\(196,0281\pm8\)	\(1551,3\pm0,8\)
79—Au	197	118	stable	\(*\mathrm{Au}^{196}\)	\(197,0284\pm7\)	\(1559,4\pm0,7\)
79—Au	198	119	\(\beta^{-}\)	\(*\mathrm{Au}^{197}\)	\(198,0305\pm8\)	\(1565,8\pm0,8\)
79—Au	199	120	\(\beta^{-}\)	\(\mathrm{Hg}^{199}\)	\(199,0310\pm6\)	\(1573,7\pm0,6\)
79—Au	200	121	\(\beta^{-}\)	\(\mathrm{Hg}^{200}\)	\(200,0335\pm7\)	\(1579,7\pm0,7\)
80—Hg	195	115	K	\(*\mathrm{Au}^{195}\)	\(195,0282\pm9\)	\(1542,1\pm0,9\)
80—Hg	196	116	stable	\(*\mathrm{Au}^{193}\)	\(196,0276\pm9\)	\(1551,0\pm0,9\)
80—Hg	197	117	K	\(*\mathrm{Au}^{197}\)	\(197,0287\pm9\)	\(1558,3\pm0,9\)
80—Hg	198	118	stable	\(\mathrm{Tl}^{198}\)	\(198,0290\pm6\)	\(1566,4\pm0,6\)

Table of Binding Energies

binding energies of nucleons
published before January 1, 1952.)

Table II

Binding energy of the last neutron \(e_n\) (Mev)	Binding energy of the last proton \(e_p\) (Mev)	Binding energy of the last pair of neutrons \(e_{2n}\) (Mev)	Binding energy of the last pair of protons \(e_{2p}\) (Mev)	Energy of radioactive transformation (Mev)	Half-life of electron capture
9.5 (Table I)
6.1 (Table I)
8.1 (Table I)		14.2
5.9				\(0.67 \pm 0.05\) (H10)
7.5		13.8
5.6				\(1.8 \pm 0.1\) (D2)
	5.6			\(1.8 \pm 0.2\) (D2)
9.0	5.1			0.1	185 days (S11)
6.8	5.8			0.8 \(0.47 \pm 0.05\) (S2)	5.6 days (S11)
8.1 (Table I)	5.8	14.9
6.4 (Table I)	6.3			\(1.37 \pm 0.02\) (E2, D1, L2)
7.9	6.7	14.4		\(0.46 \pm 0.01\) (S8)
6.0	7.1			\(2.5 \pm 0.2\) (D2)
	6.6		12.2	1.3	38 hours (M6)
8.9	6.7		11.6
7.3	7.0		12.8	0.2	64 hours (S11)
8.1	7.1	15.4	12.8

Atomic number \(Z\) and element symbol	Mass number \(A\)	Number of neutrons \(N\)	Type of radioactivity	Isotope by which the mass of this isotope was determined	Isotopic atomic mass \(M(Z,A)\) (atomic mass units)	Binding energy of the nucleons of the isotope nucleus \(E(Z,A)\) (\(Mэв\))
1	2	3	4	5	6	7
80—Hg	199	119	stable	Tl\(^{199}\)	199,0305±6	1573,4±0,6
80—Hg	200	120	stable	Tl\(^{200}\)	200,0309±6	1581,4±0,6
80—Hg	201	121	stable	Tl\(^{201}\)	201,0330±6	1587,8±0,6
80—Hg	202	122	stable	Tl\(^{202}\)	202,0336±6	1595,6±0,6
80—Hg	203	123	\(\beta^{-}\)	Tl\(^{203}\)	203,0358±3	1601,9±0,3
80—Hg	204	124	stable	interpol.	204,0369±4	1609,2±0,4
80—Hg	205	125	\(\beta^{-}\)	Tl\(^{205}\)	205,0400±2	1614,7±0,2
80—Hg	(206)	126	\((\beta^{-})\)	interpol.	206,0418±3	1621,4±0,3
81—Tl	(196)	115	(K)	interpol.	196,0314±6	1546,7±0,6
81—Tl	197	116	K	interpol.	197,0304±4	1556,0±0,4
81—Tl	198	117	K	interpol.	198,0313±4	1563,5±0,4
81—Tl	199	118	K	interpol.	199,0311±4	1572,0±0,4
81—Tl	200	119	K	interpol.	200,0328±4	1578,8±0,4
81—Tl	201	120	K	interpol.	201,0331±3	1586,9±0,3
81—Tl	202	121	K	interpol.	202,0348±3	1593,7±0,3
81—Tl	203	122	stable	Tl\(^{204}\)	203,0352±2	1601,7±0,3
81—Tl	204	123	\(\beta^{-}\)	Tl\(^{205}\)	204,0372±2	1608,2±0,2
81—Tl	205	124	stable	Tl\(^{205}\)	205,0381±1	1615,7±0,2
81—Tl	206	125	\(\beta^{-}\)	Pb\(^{206}\)	206,0404±1	1621,9±0,1
81—Tl	207	126	\(\beta^{-}\)	Pb\(^{207}\)	207,04204±1	1628,76±0,01

TABLES OF BINDING ENERGIES

Continuation of Table II

Binding energy of the last neutron $e_n$ (MeV)	Binding energy of the last proton $e_p$ (MeV)	Binding energy of the last neutron pair $e_{2n}$ (MeV)	Binding energy of the last proton pair $e_{2p}$ (MeV)	Energy of radioactive transformation (MeV)	Half-life of electron capture
8	9	10	11	12	13
7,0	7,6		13,9
8,0	7,7	15,0	14,4
6,4 (Table I)	8,1		15,2
7,8		14,2
6,3
7,3		13,6		$0,487 \pm 0,006$ (S4, M2)
5,4
6,7		12,2		$1,75 \pm 0,05$ (L3)
				(1,2)
	4,6			(3,4)
9,3	5,0			(1,4)
7,5	5,2			2,0	1,8 hr. (N2)
8,5	5,6	15,8		0,5	7 hr. (N2)
6,8	5,4			1,6	27 hr. (N2)
8,1	5,5	14,9		0	72 hr. (N2)
6,8	5,9			1,0	12 days (N2)
8,0	6,0	14,8
6,5 (Table I)	6,3			$0,783 \pm 0,010$ (S3)
7,5 (Table I)	6,5	14,0
6,2 (Table I)	7,2			$1,63 \pm 0,10$ (N1)
6,9	7,4	13,1		$1,442 \pm 0,008$ (E1)
3,82

Atomic number \(Z\) and element symbol	Mass number \(A\)	Number of neutrons \(N\)	Type of radioactivity	Isotope into which this nuclide decays	Mass of isotope atom \(M(Z,A)\) (atomic mass units)	Binding energy of the nucleons of the isotope nucleus \(E(Z,A)\) (MeV)
81—Tl	208	127	\(\beta^-\)	Pb\(^{208}\)	208,04692±1	1632,58±0,01
81—Tl	209	128	\(\beta^-\)	Bi\(^{213}\)	209,05044±10	1637,67±0,11
81—Tl	210	129	\(\beta^-\)	Bi\(^{214}\)	210,0558±3	1641,0±0,3
82—Pb	196	114	(K)	internal	196,0335±5	1543,9±0,5
82—Pb	197	115	(K)	internal	197,0341±7	1551,7±0,7
82—Pb	198	116	K	internal	198,0336±4	1560,6±0,4
82—Pb	199	117	K	internal	199,0344±6	1568,2±0,6
82—Pb	200	118	K	internal	200,0340±3	1576,9±0,3
82—Pb	201	119	K	internal	201,0352±6	1584,2±0,6
82—Pb	202	120	K	internal	202,0350±3	1592,7±0,3
82—Pb	203	121	K	Tl\(^{203}\)	203,0364±6	1599,8±0,6
82—Pb	204	122	stable	Tl\(^{204}\)	204,0363±2	1608,2±0,2
82—Pb	205	123	(K)	Pb\(^{206}\)	205,03846±5	1614,59±0,05
82—Pb	206	124	stable	Pb\(^{207}\)	206,03872±2	1622,71±0,02
82—Pb	207	125	stable	Pb\(^{208}\)	207,04050±1	1629,42±0,01
82—Pb	208	126	stable	M. S.	208,04160	1636,80
82—Pb	209	127	\(\beta^-\)	Pb\(^{208}\)	209,04638±5	1640,67±0,05
82—Pb	210	128	\(\beta^-\)	Bi\(^{210}\)	210,04973±4	1645,91±0,04
82—Pb	211	129	\(\beta^-\)	Bi\(^{211}\)	211,05467±6	1649,68±0,06
82—Pb	212	130	\(\beta^-\)	Bi\(^{212}\)	212,05808±1	1654,86±0,01

TABLES OF BINDING ENERGIES

Continuation of Table II

Binding energy of the last neutron \(e_n\) (MeV)	Binding energy of the last proton \(e_p\) (MeV)	Binding energy of the last neutron pair \(e_{2n}\) (MeV)	Binding energy of the last proton pair \(e_{2p}\) (MeV)	Energy of radioactive transformation (MeV)	Half-life of electron capture
8	9	10	11	12	13
6,09				\(4,997 \pm 0,007\) (N4)
3,3
7,8				· (1,9)
8,9	5,0		9,6	(3,4)
7,6	4,6	16,7	9,6	(2,0)	25 min. (N2)
8,7	4,7		9,9	(2,9)	80 min. (N2)
7,3	4,9	16,3	10,5	(1,0)	18 hours (N2)
8,5	5,4		10,8	(1,8)	8 hours (N2)
7,1	5,8	15,8	11,3	(0,1)	\(> 500\) years (N2)
8,4	6,1		12,0	(1,0)	52 hours (N2)
6,4	6,5	15,5	12,5
8,12 (Table I)	6,4		12,7	(0,2)
6,71 (Table I)	7,0	14,5	13,5
7,38 (Table I)	7,5		14,7
3,87 (Table I)	8,04	14,09	15,4
5,24	8,09			(1,09) (§ 7, 1)
3,77	8,24	9,11		\(0,073 \pm 0,025\) (W3)
5,18	8,7			\(1,39 \pm 0,06\) (W2)
3,5		8,95		\(0,589 \pm 0,004\) (N4)

Atomic number \(Z\) and element symbol	Mass number \(A\)	Number of neutrons \(N\)	Type of radioactivity	Isotope by which the mass of this one is calculated	Mass of isotope atom \(M(Z,A)\) (atomic mass units)	Binding energy of nucleons of the isotope nucleus \(E(Z,A)\) (MeV)
82—Pb	(213)	131	\((\beta^-)\)	interpol.	\(213,0633 \pm 4\)	\(1658,4 \pm 0,4\)
82—Pb	214	132	\(\beta^-\)	Bi\(^{214}\)	\(214,0669 \pm 3\)	\(1663,4 \pm 0,3\)
83—Bi	198	115	K	interpol.	\(198,0404 \pm 5\)	\(1553,5 \pm 0,5\)
83—Bi	199	116	K	interpol.	\(199,0397 \pm 5\)	\(1562,5 \pm 0,5\)
83—Bi	200	117	K	interpol.	\(200,0404 \pm 5\)	\(1570,2 \pm 0,5\)
83—Bi	201	118	K; \(\alpha\)	Tl\(^{197}\)	\(201,0399 \pm 4\)	\(1579,0 \pm 0,4\)
83—Bi	202	119	K	interpol.	\(202,0407 \pm 4\)	\(1586,6 \pm 0,4\)
83—Bi	203	120	K; \(\alpha\)	Tl\(^{199}\)	\(203,0404 \pm 4\)	\(1595,3 \pm 0,4\)
83—Bi	204	121	K	interpol.	\(204,0414 \pm 3\)	\(1602,7 \pm 0,3\)
83—Bi	205	122	K	interpol.	\(205,0412 \pm 3\)	\(1611,3 \pm 0,3\)
83—Bi	206	123	K	interpol.	\(206,0425 \pm 2\)	\(1618,4 \pm 0,2\)
83—Bi	207	124	K	interpol.	\(207,0126 \pm 3\)	\(1626,7 \pm 0,3\)
83—Bi	208	125		Bi\(^{209}\)	\(208,04421 \pm 8\)	\(1633,54 \pm 0,08\)
83—Bi	209	126	stable	Bi\(^{210}\)	\(209,04521 \pm 6\)	\(1640,98 \pm 0,06\)
83—Bi	210	127	\(\alpha\); \(\beta^-\)	Po\(^{210}\)	\(210,04966 \pm 3\)	\(1645,20 \pm 0,03\)
83—Bi	211	128	\(\alpha\)	Tl\(^{207}\)	\(211,05278 \pm 1\)	\(1650,65 \pm 0,01\)
83—Bi	212	129	\(\alpha\); \(\beta^-\)	Po\(^{212}\)	\(212,05745 \pm 1\)	\(1654,67 \pm 0,01\)

Binding Energy Tables

Continuation of Table II

Binding energy of the last neutron, $e_n$ (MeV) 8	Binding energy of the last proton, $e_p$ (MeV) 9	Binding energy of the last pair of neutrons, $e_{2n}$ (MeV) 10	Binding energy of the last pair of protons, $e_{2p}$ (MeV) 11	Energy of radioactive transformation (MeV) 12	Half-life of electron capture 13
5,0				(2,4) 1,00±0,05 (W3) (§ 4)
9,0	1,8			(6,2)	7 min. (N2)
7,7	1,9			(4,8)	25 min. (N2)
8,8	2,0			(5,8)	35 min. (N2)
7,6	2,1	16,5		{ (4,3) 5,25±0,06 (N2)	110 min. (N2)
8,7	2,4			(5,2)	95 min. (K4)
7,4	2,6	16,3		{ (3,6) 4,95±0,06 (N2, D6)	12 hr. (N2)
8,6	2,9			(4,6)	12 hr. (D2)
7,1	3,1	15,9		(2,5)	14,5 days (K4)
8,3	3,8			(3,4)	6,3 days (S11)
6,8	4,0	15,4		(1,8)	50 years (N3, G8)
7,44 (Table I)	4,12
4,22 (Table I)	4,18	14,2
5,45	4,53			{ 4,94±0,10 1,17±0,02 } (W3)
4,02	4,74	9,67		6,393±0,010 (§ 4)
5,3	4,99			{ 6,200±0,001 (G3) 2,250±0,003 (N4)

Atomic number \(Z\) and element symbol	Mass number \(A\)	Number of neutrons \(N\)	Types of radioactivity	Isotope by which the mass of the given one was calculated	Mass of an atom of the isotope \(M(Z,A)\) (atomic mass units)	Binding energy of the nucleons of the isotope nucleus \(E(Z,A)\) (MeV)
1	2	3	4	5	6	7
83—Bi	213	130	\(\alpha\) \(\beta^{-}\)	Po\(^{213}\)	\(213{,}0607 \pm 1\)	\(1660{,}0 \pm 0{,}1\)
83—Bi	214	131	\(\alpha\) \(\beta^{-}\)	Po\(^{214}\)	\(214{,}0658 \pm 3\)	\(1663{,}6 \pm 0{,}3\)
84—Po	200	116	K \(\alpha\)	Pb\(^{196}\)	\(200{,}0438 \pm 5\)	\(1566{,}2 \pm 0{,}5\)
84—Po	201	117	K \(\alpha\)	Pb\(^{197}\)	\(201{,}0442 \pm 7\)	\(1574{,}2 \pm 0{,}7\)
84—Po	202	118	K \(\alpha\)	Pb\(^{198}\)	\(202{,}0435 \pm 4\)	\(1583{,}2 \pm 0{,}4\)
84—Po	203	119	K \(\alpha\)	Pb\(^{199}\)	\(203{,}0444 \pm 6\)	\(1590{,}8 \pm 0{,}6\)
84—Po	204	120	K \(\alpha\)	Pb\(^{200}\)	\(204{,}0438 \pm 4\)	\(1599{,}7 \pm 0{,}4\)
84—Po	205	121	K \(\alpha\)	Pb\(^{201}\)	\(205{,}0447 \pm 6\)	\(1607{,}2 \pm 0{,}6\)
84—Po	206	122	K \(\alpha\)	Pb\(^{202}\)	\(206{,}0446 \pm 3\)	\(1615{,}7 \pm 0{,}3\)
84—Po	207	123	K \(\alpha\)	Pb\(^{203}\)	\(207{,}0458 \pm 6\)	\(1622{,}9 \pm 0{,}6\)
84—Po	208	124	\(\alpha\)	Pb\(^{204}\)	\(208{,}0458 \pm 2\)	\(1631{,}3 \pm 0{,}2\)
84—Po	209	125	\(\alpha\)	Pb\(^{205}\)	\(209{,}04765 \pm 5\)	\(1637{,}92 \pm 0{,}05\)
84—Po	210	126	\(\alpha\)	Pb\(^{206}\)	\(210{,}04840 \pm 1\)	\(1645{,}59 \pm 0{,}015\)
84—Po	211	127	\(\alpha\)	Pb\(^{207}\)	\(211{,}05251 \pm 6\)	\(1650{,}12 \pm 0{,}06\)
84—Po	212	128	\(\alpha\)	Pb\(^{208}\)	\(212{,}05503 \pm 1\)	\(1656{,}14 \pm 0{,}01\)

Continuation of Table II

Binding energy of the last neutron \(e_{1n}\) (MeV)	Binding energy of the last proton \(e_{1p}\) (MeV)	Binding energy of the last pair of neutrons \(e_{2n}\) (MeV)	Binding energy of the last pair of protons \(e_{2p}\) (MeV)	Energy of radioactive transformation (MeV)	Electron-capture half-life
3.6	5.1	9.33		\(\left\{\begin{array}{l}5.97 \pm 0.03\\ 1.25 \pm 0.10\end{array}\right.\) (W3)
3.6	5.2			\(\left\{\begin{array}{l}5.610 \pm 0.003\ \text{(W3)}\\ 3.50 \pm 0.3\ \text{(C1)}\end{array}\right.\)
8.0	3.7		5.6	\(\left\{\begin{array}{l}(3.1)\\ 5.96 \pm 0.03\ \text{(K7)}\end{array}\right.\)	11 min. (K7)
9.0	4.0		6.0	\(\left\{\begin{array}{l}(3.9)\\ 5.82 \pm 0.03\ \text{(K7)}\end{array}\right.\)	18 min. (K7)
7.6	4.2	17.0	6.3	\(\left\{\begin{array}{l}(2.5)\\ 5.70 \pm 0.03\ \text{(K7)}\end{array}\right.\)	52 min. (K7)
8.9	4.2		6.6	\(\left\{\begin{array}{l}(3.6)\\ 5.67 \pm 0.04\ \text{(P1)}\end{array}\right.\)	47 min. (S11)
7.5	4.4	16.5	6.9	\(\left\{\begin{array}{l}(2.1)\\ 5.48 \pm 0.02\ \text{(K7)}\end{array}\right.\)	3.8 hr. (K7)
8.5	4.5		7.4	\(\left\{\begin{array}{l}(3.2)\\ 5.31 \pm 0.02\ \text{(K7)}\end{array}\right.\)	1.5 hr. (K7)
7.2	4.4	16.0	7.5	\(\left\{\begin{array}{l}(1.8)\\ 5.31 \pm 0.02\ \text{(K7)}\end{array}\right.\)	9 days (K7)
8.4	4.5		8.3	\(\left\{\begin{array}{l}(2.9)\\ 5.20 \pm 0.02\ \text{(K7)}\end{array}\right.\)	5.7 hr. (K7)
6.6	4.6	15.6	8.5	\(5.20 \pm 0.02\) (K7)
7.67	4.38		8.50	\(4.95 \pm 0.02\) (K7)
4.53	4.61	14.3	8.79	\(5.402 \pm 0.003\) (W3)
6.02	4.92		9.45	\(7.577 \pm 0.015\) (N3)
4.31	5.49	10.55	10.23	\(8.945 \pm 0.001\) (W3)

Ordinal number $Z$ and symbol of the element	Mass number $A$	Number of neutrons $N$	Type of radioactivity	Isotope from which the mass of this one was calculated	Mass of the isotope atom $M(Z,A)$ (atomic mass units)	Binding energy of the nucleons of the isotope nucleus $E(Z,A)$ ($Mэв$)
1	2	3	4	5	6	7
84—Po	213	129	$\alpha$	Pb$^{209}$	213,05938±5	1660,45±0,05
84—Po	214	130	$\alpha$	Pb$^{210}$	214,06202±4	1666,36±0,04
84—Po	215	131	$\alpha$	Pb$^{211}$	215,06661±6	1670,45±0,06
84—Po	216	132	$\alpha$	Pb$^{212}$	216,06937±1	1676,24±0,01
84—Po	(217)	133		intermediate	217,0742±3	1680,1±0,3
84—Po	218	134	$\alpha$	Pb$^{214}$	218,0773±3	1685,6±0,3
85—At	202	117	K	intermediate	202,0511±6	1575,4±0,6
85—At	203	118	K $\alpha$	Bi$^{199}$	203,0502±5	1584,6±0,5
85—At	204	119	K	intermediate	204,0509±5	1592,3±0,5
85—At	205	120	K $\alpha$	Bi$^{201}$	205,0502±5	1601,3±0,5
85—At	206	121	K	intermediate	206,0510±5	1608,9±0,5
85—At	207	122	K $\alpha$	Bi$^{203}$	207,0506±4	1617,7±0,4
85—At	208	123	K	intermediate	208,0516±5	1625,1±0,5
85—At	209	124	K $\alpha$	Bi$^{205}$	209,0512±3	1633,8±0,3
85—At	210	125	K	intermediate	210,0526±4	1640,9±0,4
85—At	211	126	K $\alpha$	Bi$^{207}$	211,0529±3	1649,0±0,3
85—At	212	127	$\alpha$	Bi$^{208}$	212,0564±3	1654,1±0,3

*) (§ 7, 2).

Continuation of Table II

8	9	10	11	12	13
Binding energy of the last neutron $e_n$ (MeV)	Binding energy of the last proton $e_p$ (MeV)	Binding energy of the last pair of neutrons $e_{2n}$ (MeV)	Binding energy of the last pair of protons $e_{2p}$ (MeV)	Energy of radioactive transformation (MeV)	Half-period of electron capture decay
5,91	5,78		10,77	8,496±0,005 (W3)
	6,4	10,22	11,50	7,827±0,001 (W3)
4,09	6,8		12,0	7,510±0,015 (W3)
5,79		9,88	12,8	6,903±0,001 (W3)
3,9
5,5		9,4		6,1105±0,0006 (W2)
	1,2			(6,9)	2 min. (B2)
9,2	1,4			(5,3) 6,22±0,04 (B2)	7 min. (B2)
7,7	1,5			(6,5)	25 min. (B2)
9,0	1,6	16,7		(4,8) 6,02±0,04 (B2)	25 min. (B2)
7,6	1,7			(5,9)	2,6 hr. (B2)
8,8	2,0	16,4		(4,3) 5,86±0,04 (B2)	2 hr. (B2)
7,4	2,2			(5,3)	6,3 hr. (B2)
8,7	2,5	16,1		(3,2) 5,76±0,04 (B2)	5,5 hr.
7,1	3,0			(3,7)	8,3 hr. (S11)
8,1	3,4	15,2		(0,2) 6,00±0,04 (P1)	18 hr. (S11)
5,1	4,0			7,7±0,2 estimate (P1)*)
6,1

Atomic number \(Z\) and element symbol	Mass number \(A\)	Number of neutrons	Type of radioactivity	Isotope by which mass was calculated	Mass of isotope \(M(Z,A)\) (atomic mass units)	Binding energy of the nucleons of the isotope nucleus \(E(Z,A)\) (MeV)
85—At	213	128	\(\alpha\)	Bi\(^{209}\)	\(213,0588\pm2\)	\(1660,2\pm0,2\)
85—At	214	129	\(\alpha\)	Bi\(^{210}\)	\(214,06314\pm5\)	\(1664,53\pm0,05\)
85—At	215	130	\(\alpha\)	Bi\(^{211}\)	\(215,06541\pm5\)	\(1670,78\pm0,05\)
85—At	216	131	\(\alpha\)	Bi\(^{212}\)	\(216,06985\pm4\)	\(1675,01\pm0,04\)
85—At	217	132	\(\alpha\)	Bi\(^{213}\)	\(217,0723\pm1\)	\(1681,1\pm0,1\)
85—At	218	133	\(\alpha\)	Bi\(^{214}\)	\(218,0769\pm\)	\(1685,2\pm0,3\)
86—Em	211	125	K	inter.	\(211,0562\pm4\)	\(1645,1\pm0,4\)
86—Em	212	126	\(\begin{cases}\text{EC}\\ \alpha\end{cases}\)	Po\(^{208}\)	\(212,0565\pm2\)	\(1653,2\pm0,2\)
86—Em	(213)	127		inter.	\(213,0602\pm3\)	\(1658,1\pm0,3\)
86—Em	(214)	128		inter.	\(214,0619\pm3\)	\(1664,9\pm0,3\)
86—Em	(215)	129		inter.	\(215,0658\pm3\)	\(1669,6\pm0,3\)
86—Em	216	130	\(\alpha\)	Po\(^{212}\)	\(216,06767\pm5\)	\(1676,26\pm0,05\)
86—Em	217	131	\(\alpha\)	Po\(^{213}\)	\(217,07173\pm6\)	\(1680,84\pm0,06\)
86—Em	218	132	\(\alpha\)	Po\(^{214}\)	\(218,07368\pm6\)	\(1687,39\pm0,05\)
86—Em	219	133	\(\alpha\)	Po\(^{215}\)	\(219,07795\pm6\)	\(1691,78\pm0,06\)
86—Em	220	134	\(\alpha\)	Po\(^{216}\)	\(220,08012\pm1\)	\(1698,12\pm0,01\)
86—Em	(221)	135		inter.	\(221,0847\pm3\)	\(1702,2\pm0,3\)
86—Em	222	136	\(\alpha\)	Po\(^{218}\)	\(222,0872\pm\)	\(1708,3\pm0,3\)

*) (§ 7, 2).

Table of Binding Energies

Continuation of Table II

Binding energy of the last neutron $e_n$ (MeV) 8	Binding energy of the last proton $e_p$ (MeV) 9	Binding energy of the last neutron pair $e_{2n}$ (MeV) 10	Binding energy of the last proton pair $e_{2p}$ (MeV) 11	Energy of radioactive transformation (MeV) 12	Half-life period of electron capture 13
	4,1	11,2		9,3±0,2 estimate (P1)*)
4,3	4,08			8,95±0,04 (D2)
6,25	4,42	10,6		8,15±0,04 (D2)
4,23	4,56			7,94±0,04 (D2)
6,1	4,9	10,3		7,155±0,010 (D2)
4,1	5,1			6,75±0,10 (P1)
	4,2		7,2	3,0	> 8 min. (H2)
8,1	4,2		7,6	{ (0) 6,29±0,03 (H2)
4,9	4,0		8,0
6,8	4,7	11,7	8,8
4,7	5,1		9,2
6,7	5,48	11,4	9,90	8,16±0,04 (M5)
4,58	5,83		10,39	7,89±0,04 (P1)
6,55	6,3	11,13	11,15	7,25±0,025 (P1)
4,39	6,6		11,7	6,95±0,014 (P1)
6,34		10,73	12,5	6,398±0,001 (W2)
4,1
6,1		10,2		5,587±0,001 (W2)

Atomic number \(Z\) and element symbol	Mass number \(A\)	Number of neutrons, \(N\)	Type of radioactivity	Isotope, by which mass is calculated	Mass of the isotope atom \(M(Z,A)\) (atomic mass units)	Binding energy of the nucleons of the isotope nucleus \(E(Z,A)\) (MeV)
87—Fr	211	124	K	inter.	\(211{,}0610\pm5\)	\(1639{,}9\pm0{,}5\)
87—Fr	212	125	K, \(\alpha\)	\(At^{208}\)	\(212{,}0622\pm5\)	\(1647{,}1\pm0{,}5\)
87—Fr	(213)	126		inter.	\(213{,}0624\pm5\)	\(1655{,}3\pm0{,}5\)
87—Fr	(214)	127		inter.	\(214{,}0656\pm5\)	\(1660{,}7\pm0{,}5\)
87—Fr	(215)	128		inter.	\(215{,}0668\pm4\)	\(1667{,}9\pm0{,}4\)
87—Fr	(216)	129		inter.	\(216{,}0704\pm2\)	\(1672{,}9\pm0{,}2\)
87—Fr	(217)	130		inter.	\(217{,}0719\pm2\)	\(1679{,}9\pm0{,}2\)
87—Fr	218	131	\(\alpha\)	\(At^{214}\)	\(218{,}07560\pm6\)	\(1684{,}82\pm0{,}06\)
87—Fr	219	132	\(\alpha\)	\(At^{215}\)	\(219{,}07728\pm6\)	\(1691{,}62\pm0{,}06\)
87—Fr	220	133	\(\alpha\)	\(At^{216}\)	\(220{,}08104\pm6\)	\(1696{,}48\pm0{,}06\)
87—Fr	221	134	\(\alpha\)	\(At^{217}\)	\(221{,}0830\pm1\)	\(1703{,}0\pm0{,}1\)
87—Fr	222	135	\(\beta^{-}\)	inter.	\(222{,}0871\pm3\)	\(1707{,}6\pm0{,}3\)
87—Fr	223	136	\(\beta^{-}\)	\(Ra^{223}\)	\(223{,}0894\pm2\)	\(1713{,}8\pm0{,}2\)
87—Fr	224	137	\((\beta^{-})\)	\(Ac^{228}\)	\(224{,}0939\pm1\)	\(1718{,}0\pm0{,}1\)
88—Ra	220	132	\(\alpha\)	\(Em^{216}\)	\(220{,}07968\pm6\)	\(1696{,}97\pm0{,}06\)
88—Ra	221	133	\(\alpha\)	\(Em^{217}\)	\(221{,}08295\pm7\)	\(1702{,}29\pm0{,}07\)
88—Ra	222	134	\(\alpha\)	\(Em^{218}\)	\(222{,}08467\pm6\)	\(1709{,}05\pm0{,}06\)
88—Ra	223	135	\(\alpha\)	\(Em^{219}\)	\(223{,}08808\pm6\)	\(1714{,}24\pm0{,}06\)
88—Ra	224	136	\(\alpha\)	\(Em^{220}\)	\(224{,}09021\pm1\)	\(1720{,}62\pm0{,}01\)

BINDING-ENERGY TABLES

Continuation of Table II

Binding energy of the last neutron $e_n$ (MeV)	Binding energy of the last proton $e_p$ (MeV)	Binding energy of the last pair of neutrons $e_{2n}$ (MeV)	Binding energy of the last pair of protons $e_{2p}$ (MeV)	Energy of radioactive transformation (MeV)	Half-life period of electron capture
8	9	10	11	12	13
				4,3	8 min. (H2)
7,2	2,0			$\left\{\begin{array}{c}(5,2)\\6,37\pm0,03\ \text{(H2)}\end{array}\right.$	34 min. (H2)
8,2	2,1	15,4
5,5	2,6
7,2	3,0	12,7
5,0	3,3
7,0	3,6	12,0
4,9	3,98			$7,99\pm0,04$ (W2)
6,80	4,23	11,7		$7,44\pm0,04$ (P1)
4,86	4,70			$6,81\pm0,04$ (H2)
6,5		11,4		$6,42\pm0,01$ (H2)
4,6				(2,2)
6,2		10,8		$1,20\pm0,2$ (W2)
4,2				(3,4)
	5,35		9,58	$7,57\pm0,02$ (M5)
5,32	5,81		10,51	$6,83\pm0,04$ (P1)
6,76	6,0	12,08	10,93	$6,62\pm0,03$ (P1)
5,19	6,6		12,0	$5,82\pm0,015$ (P1)
6,38	6,8	11,57	12,3	$5,785\pm0,001$ (W2)
5,0

Atomic number \(Z\) and symbol of the element	Mass number \(A\)	Number of neutrons \(N\)	Type of radioactivity	Isotope by which the mass of this isotope was calculated	Mass of the isotope atom \(M(Z,A)\) (atomic mass units)	Binding energy of the nucleons of the isotope nucleus \(E(Z,A)\) (MeV)
1	2	3	4	5	6	7
88—Ra	225	137	\(\beta^{-}\)	\(\mathrm{Ac}^{225}\)	\(225,0938 \pm 2\)	\(1725,6 \pm 0,2\)
88—Ra	226	138	\(\alpha\)	\(\mathrm{Em}^{222}\)	\(226,0963 \pm 3\)	\(1731,7 \pm 0,3\)
88—Ra	227	139		interpol.	\(227,0999 \pm 5\)	\(1736,7 \pm 0,5\)
88—Ra	228	140	\(\beta^{-}\)	\(\mathrm{Ac}^{228}\)	\(228,10278 \pm 8\)	\(1742,37 \pm 0,08\)
88—Ra	229	141		interpol.	\(229,1062 \pm 5\)	\(1747,5 \pm 0,5\)
88—Ra	230	142	\(\beta^{-}\)	\(\mathrm{Ac}^{230}\)	\(230,1089 \pm 5\)	\(1753,4 \pm 0,5\)
89—Ac	222	133	\(\alpha\)	\(\mathrm{Fr}^{218}\)	\(222,08709 \pm 8\)	\(1706,01 \pm 0,08\)
89—Ac	223	134	\(\alpha\)	\(\mathrm{Fr}^{219}\)	\(223,08842 \pm 8\)	\(1713,14 \pm 0,08\)
89—Ac	224	135	\(\alpha\)	\(\mathrm{Fr}^{220}\)	\(224,09166 \pm 7\)	\(1718,48 \pm 0,07\)
89—Ac	225	136	\(\alpha\)	\(\mathrm{Fr}^{221}\)	\(225,0933 \pm 1\)	\(1725,3 \pm 0,12\)
89—Ac	226	137	\(\beta^{-}\)	interpol.	\(226,0968 \pm 3\)	\(1730,4 \pm 0,3\)
89—Ac	227	138	\(\alpha\)	\(\mathrm{Fr}^{223}\)	\(227,0986 \pm 2\)	\(1737,1 \pm 0,2\)
89—Ac	228	139	\(\alpha\); \(\beta^{-}\)	\(\mathrm{Th}^{228}\)	\(228,10272 \pm 8\)	\(1741,64 \pm 0,08\)
89—Ac	229	140	\((\beta^{-})\)	interpol.	\(229,1044 \pm 5\)	\(1748,4 \pm 0,5\)
89—Ac	230	141	\(\beta^{-}\)	\(\mathrm{Th}^{230}\)	\(230,1076 \pm 5\)	\(1753,8 \pm 0,5\)
90—Th	224	134	\(\alpha\)	\(\mathrm{Ra}^{220}\)	\(224,09135 \pm 6\)	\(1717,99 \pm 0,06\)
90—Th	225	135	\(\alpha\)	\(\mathrm{Ra}^{221}\)	\(225,09401 \pm 8\)	\(1723,88 \pm 0,08\)
90—Th	226	136	\(\alpha\)	\(\mathrm{Ra}^{222}\)	\(226,09543 \pm 6\)	\(1730,92 \pm 0,06\)

BINDING-ENERGY TABLES

Continuation of Table II

Binding energy of the last neutron $e_n$ (MeV) 8	Binding energy of the last proton $e_p$ (MeV) 9	Binding energy of the last neutron pair $e_{2n}$ (MeV) 10	Binding energy of the last proton pair $e_{2p}$ (MeV) 11	Energy of radioactive transformation (MeV) 12	Half-life period of electron capture 13
	7,6			0,20+(0,35)±0,2 (W2, D2, § 7, 3)
6,1		11,1		4,88±0,01 (P1)
5,0
5,7				0,05±0,01 (D2)
5,1
5,9				1,2±0,1 (J3)
	3,72			7,09±0,04 (D2)
7,13	4,09			6,76±0,04 (P1)
5,34	4,24			6,28±0,04 (P1)
6,8	4,7	12,2		5,91±0,01 (P1)
5,1	4,8			(1,3)
6,7	5,4	11,8		5,04±0,02 (P1)
4,5	4,9			{ 4,62±0,08 (P1) 2,52±0,07 (N4)
6,8	6,0	11,3		(1,1)
5,4	6,3			2,2±0,1 (J3)
	4,85		8,94	7,26±0,02 (M5)
5,89	5,40		9,64	6,69±0,04 (P1)
7,04	5,6	12,93	10,30	6,41±0,025 (P1)
5,45

1. Atomic number \(Z\) and symbol of the element	2. Mass number \(A\)	3. Number of neutrons \(N\)	4. Type of radioactivity	5. Isotope from which the mass of the given isotope was calculated	6. Atomic mass of the isotope \(M(Z,A)\) (atomic mass units)	7. Nuclear binding energy of the isotope \(E(Z,A)\) (MeV)
90—Th	227	137	\(\alpha\)	\(\mathrm{Ra}^{223}\)	\(227,09856 \pm 6\)	\(1736,37 \pm 0,06\)
90—Th	228	138	\(\alpha\)	\(\mathrm{Ra}^{224}\)	\(228,10001 \pm 1\)	\(1743,38 \pm 0,01\)
90—Th	229	139	\(\alpha\)	\(\mathrm{Ra}^{225}\)	\(229,1033 \pm 2\)	\(1748,7 \pm 0,2\)
90—Th	230	140	\(\alpha\)	\(\mathrm{Ra}^{226}\)	\(230,1053 \pm 3\)	\(1755,2 \pm 0,3\)
90—Th	231	141	\(\beta^{-}\)	\(\mathrm{Pa}^{231}\)	\(231,1084 \pm 2\)	\(1760,7 \pm 0,2\)
90—Th	232	142	\(\alpha\)	\(\mathrm{Rd}^{225}\)	\(232,1100 \pm 8\)	\(1766,60 \pm 0,08\)
90—Th	233	143	\(\beta^{-}\)	\(\mathrm{Pa}^{233}\)	\(233,1144 \pm 2\)	\(1771,8 \pm 0,2\)
90—Th	234	144	\(\beta^{-}\)	\(\mathrm{Pa}^{234}\)	\(234,1175 \pm 4\)	\(1777,3 \pm 0,4\)
90—Th	235	145	\((\beta^{-})\)	\(\mathrm{Pa}^{235}\)	\(235,1207 \pm 5\)	\(1782,7 \pm 0,5\)
91—Pa	226	135	\(\alpha\)	\(\mathrm{Ac}^{222}\)	\(226,09841 \pm 6\)	\(1727,36 \pm 0,09\)
91—Pa	227	136	\(\alpha\)	\(\mathrm{Ac}^{223}\)	\(227,09936 \pm 9\)	\(1734,84 \pm 0,09\)
91—Pa	228	137	\(\alpha\)	\(\mathrm{Ac}^{224}\)	\(228,10220 \pm 7\)	\(1740,56 \pm 0,08\)
91—Pa	229	138	\(\alpha\)	\(\mathrm{Ac}^{225}\)	\(229,1036 \pm 1\)	\(1747,6 \pm 0,1\)
91—Pa	230	139	\(\alpha\)	\(\mathrm{Ac}^{226}\)	\(230,1066 \pm 3\)	\(1753,2 \pm 0,3\)
91—Pa	231	140	\(\alpha\)	\(\mathrm{Ac}^{227}\)	\(231,1081 \pm 2\)	\(1760,2 \pm 0,2\)
91—Pa	232	141	\(\beta^{-}\)	\(\mathrm{U}^{232}\)	\(232,1114 \pm 6\)	\(1765,69 \pm 0,06\)
91—Pa	233	142	\(\beta^{-}\)	\(\mathrm{U}^{233}\)	\(233,1131 \pm 2\)	\(1772,2 \pm 0,2\)

\((*)\) experimental, \(e_n = 6,35 \pm 0,04\) (Table 1).
\((**)\) experimental, \(e_n = 4,9 \pm 0,2\) (Table 1).
\((***)\) (§ 7,4).
\((****)\) (§ 7,2).

Continuation of Table II

8. Binding energy of the last neutron, $\varepsilon_n$ (MeV)	9. Binding energy of the last proton, $\varepsilon_p$ (MeV)	10. Binding energy of the last pair of neutrons, $\varepsilon_{2n}$ (MeV)	11. Binding energy of the last pair of protons, $\varepsilon_{2p}$ (MeV)	12. Energy of radioactive transformation (MeV)	13. Half-life of electron capture
7,01	6,0		10,8	6,15±0,015 (P1)
5,3	6,3	12,46	11,7	5,520±0,004 (P1)
6,5	7,1		12,0	5,14±0,04 (P1)
5,5	6,8	11,8	12,8	4,76±0,01 (P1)
5,9*)	6,9		13,2	0,32±0,04 (J1)
5,2**)		11,4	13,2	4,05±0,02 (P1)
5,5				1,23±0,01 (B1)
5,4		10,7		0,205±0,010 (D2)
				1,8±0,4 (cycle) ***)
7,48	3,48			6,93±0,04 (P1)
5,72	3,92			6,58±0,04 (P1)
7,0	4,19			6,20±0,04 (P1)
5,6	4,2	12,7		5,78±0,04 (W2)
7,0	4,5			5,5±0,1 estimate (P1) ****)
5,5	5,0	12,6		5,136±0,006 (W2)
6,5	5,0			1,35±0,05 (O1)
5,3	5,6	12,0		0,618±0,020 (K3)

1 Atomic number \(Z\) and element symbol	2 Mass number \(A\)	3 Number of neutrons \(N\)	4 Type of radioactivity	5 Isotope from which the mass of the given one was calculated	6 Atomic mass of the isotope \(M(Z,A)\) (atomic mass units)	7 Binding energy of the isotope’s nucleons \(E(Z,A)\) (MeV)
91—Pa	234	143	\(\beta^{-}\)	U\(^{234}\)	234,1164±4	1777,5±0,4
91—Pa	235	144	\(\beta^{-}\)	U\(^{235}\)	235,1187±3	1783,7±0,3
92—U	228	136	\(\alpha\)	Th\(^{224}\)	228,10252±6	1739,48±0,06
92—U	229	137	\(\alpha\)	Th\(^{225}\)	229,10490±9	1745,63±0,09
92—U	230	138	\(\alpha\)	Th\(^{226}\)	230,10571±7	1753,24±0,07
92—U	231	139	\(\alpha\)	Th\(^{227}\)	231,1084±1	1759,1±0,12
92—U	232	140	\(\alpha\)	Th\(^{228}\)	232,10969±4	1766,26±0,04
92—U	233	141	\(\alpha\)	Th\(^{229}\)	233,1124±2	1772,1±0,2
93—Np	234	142	\(\alpha\)	Th\(^{230}\)	234,1144±3	1778,6±0,3
93—Np	235	143	\(\alpha\)	Th\(^{231}\)	235,1173±2	1784,3±0,2
93—Np	236	144	\(\alpha\)	Th\(^{232}\)	236,11980±9	1790,30±0,09
93—Np	237	145	\(\beta^{-}\)	Np\(^{237}\)	237,1230±3	1795,7±0,3
93—Np	238	146	\(\alpha\)	Th\(^{234}\)	238,1260±3	1801,3±0,3
93—Np	239	147	\(\beta^{-}\)	Np\(^{239}\)	239,1289±6	1806,9±0,6
93—Np	231	138	\(\alpha\)	Pa\(^{227}\)	231,1101±1	1756,7±0,1
93—Np	232	139	K	U\(^{232}\)	232,1129±5	1762,5±0,5
93—Np	233	140	\(\alpha\)	Pa\(^{229}\)	233,1136±1	1770,2±0,14

*) (§ 7, 2).
*) experimental, \(e_a = 5,9 \pm 0,1\) (Table 1).
**) experimental, \(e_a = 4,6 \pm 0,15\) (Table 1).

TABLES OF BINDING ENERGIES

Continuation of Table II

Binding energy of last neutron $\varepsilon_n$ (MeV) 8	Binding energy of last proton $\varepsilon_p$ (MeV) 9	Binding energy of last pair of neutrons $\varepsilon_{2n}$ (MeV) 10	Binding energy of last pair of protons $\varepsilon_{2p}$ (MeV) 11	Energy of radioactive transformation (MeV) 12	Half-life of electron capture 13
	5,7			1,93±0,05 (W2)
6,2	6,4	11,5		1,4±0,1 (M4)
6,15	4,64		8,56	6,79±0,01 (M5)
	5,07		9,26	6,53±0,04 (P1)
7,61	5,6	13,76	9,86	5,96±0,04 (P1)
5,9	5,9		10,4	5,6±0,1 estimate (P1) *)
7,2	6,1	13,02	11,1	5,40±0,04 (P1)
5,8	6,4		11,4	4,908±0,003 (W2)
6,5	6,4	12,3	12,0	4,84±0,02 (P1)
5,7	6,8		12,5	4,66±0,03 (G7)
6,0	6,6	11,7	13,0	4,577±0,004 (O1,G6,J2)
5,4			13,0	0,70±0,10 (D2, S11)
5,6 **)		11,0		4,25±0,01 (P1)
5,6 ***)				1,295±0,010 (H9)]
	3,5			6,39±0,05 (M3)
5,8	3,4			2,9	13 min. (M3)
7,7	3,9	13,5		5,65±0,05 (M3)
5,7

Atomic number \(Z\) and element symbol	Mass number \(A\)	Number of neutrons \(N\)	Type of radioactivity	Isotope from which the mass of the given one was calculated	Mass of isotope \(M(Z,A)\) (atomic mass units)	Binding energy of the nucleons of the isotope nucleus \(E(Z,A)\) (MeV)
93—Np	234	141	K	\(\mathrm{U}^{234}\)	\(234,1165 \pm 6\)	\(1775,9 \pm 0,6\)
93—Np	235	142	\(\alpha\)	\(\mathrm{Pa}^{231}\)	\(235,1175 \pm 3\)	\(1783,3 \pm 0,3\)
93—Np	236	143	\(\beta^{-}\)	\(\mathrm{Pu}^{236}\)	\(236,12040 \pm 9\)	\(1788,96 \pm 0,09\)
93—Np	237	144	\(\alpha\)	\(\mathrm{Pa}^{233}\)	\(237,1221 \pm 3\)	\(1795,7 \pm 0,3\)
93—Np	238	145	\(\beta^{-}\)	\(\mathrm{Pu}^{238}\)	\(238,1258 \pm 3\)	\(1800,7 \pm 0,3\)
93—Np	239	146	\(\beta^{-}\)	\(\mathrm{Pu}^{239}\)	\(239,1275 \pm 6\)	\(1807,4 \pm 0,6\)
93—Np	(240)	147	\((\beta^{-})\)	interp.	\(240,1313 \pm 7\)	\(1812,3 \pm 0,7\)
94—Pu	232	138	\(\alpha\)	\(\mathrm{U}^{228}\)	\(232,1136 \pm 3\)	\(1761,1 \pm 0,3\)
94—Pu	(233)	139	(K)	interp.	\(233,1158 \pm 3\)	\(1767,4 \pm 0,3\)
94—Pu	234	140	\(\alpha\)	\(\mathrm{U}^{230}\)	\(234,11631 \pm 8\)	\(1775,26 \pm 0,08\)
94—Pu	(235)	141	(K)	interp.	\(235,1187 \pm 3\)	\(1781,4 \pm 0,3\)
94—Pu	236	142	\(\alpha\)	\(\mathrm{U}^{232}\)	\(236,11985 \pm 6\)	\(1788,69 \pm 0,06\)
94—Pu	237	143	K	\(\mathrm{Np}^{237}\)	\(237,1224 \pm 2\)	\(1794,7 \pm 0,2\)
94—Pu	238	144	\(\alpha\)	\(\mathrm{U}^{234}\)	\(238,1243 \pm 3\)	\(1801,3 \pm 0,3\)
94—Pu	239	145	\(\alpha\)	\(\mathrm{U}^{235}\)	\(239,1268 \pm 2\)	\(1807,3 \pm 0,2\)
94—Pu	240	146	\(\alpha\)	\(\mathrm{U}^{236}\)	\(240,12931 \pm 9\)	\(1813,33 \pm 0,09\)
94—Pu	241	147	\(\alpha\), \(\beta^{-}\)	\(\mathrm{U}^{237}\)	\(241,1323 \pm 3\)	\(1818,9 \pm 0,3\)
94—Pu	242	148	\(\alpha\)	\(\mathrm{U}^{238}\)	\(242,1352 \pm 4\)	\(1824,6 \pm 0,4\)
94—Pu	243	149	\(\beta^{-}\)	interp.	\(243,1384 \pm 6\)	\(1830,0 \pm 0,6\)

BINDING-ENERGY TABLES

Continuation of Table II

Binding energy of the last neutron $e_n$ (MeV) 8	Binding energy of the last proton $e_p$ (MeV) 9	Binding energy of the last pair: neutrons $e_{2n}$ (MeV) 10	Binding energy of the last pair: protons $e_{2p}$ (MeV) 11	Energy of radioactive transformation (MeV) 12	Half-life of electron capture 13
	3,8			1,8	4,4 days (D2)
7,4	4,7	13,1		5,15±0,04 (P1)
5,7	4,7			0,51±0,07 (O1)
6,7	5,4	12,4		4,85±0,04 (P1)
5,0	5,0			1,375±0,020 (F1)
6,7	6,1	11,7		0,715±0,015 (G5, H9)
4,9	5,4			(1,8)
6,3	4,4		7,9	6,7±0,2 (P1)
7,9	4,9		8,3	(1,9)
6,1	5,1	14,2	9,00	6,26±0,04 (P1)
7,3	5,5		9,3	(1,0)
6,0	5,4	13,43	10,1	5,85±0,04 (P1)
6,6	5,7		10,4	0,1	40 days (S11)
6,0	5,6	12,6	11,0	5,587±0,006 (W2)
6,0	6,6		11,6	5,24±0,01 (P1)
		12,0	12,0	5,25±0,02 (T4)
5,6			12,0	{ 4,99±0,01 (T4) 0,01±0,01
5,7		11,3		4,96±0,04 (S9, T6)
5,4				1,0

Periodic number \(Z\) and element symbol	Mass number \(A\)	Number of neutrons \(N\)	Type of radioactivity	Isotope from which the mass of the given one was calculated	Mass of isotope \(M(Z,A)\) (atomic mass units)	Binding energy of nucleons of the isotope nucleus \(E(Z,A)\) (MeV)
1	2	3	4	5	6	7
95—Am	238	143	K	Pu\(^{238}\)	238,1268±6	1798,2±0,6
95—Am	239	144	\(\alpha\)	Np\(^{235}\)	239,1277±3	1805,7±0,3
95—Am	240	145	K	Pu\(^{240}\)	240,1306±5	1811,4±0,5
95—Am	241	146	\(\alpha\)	Np\(^{237}\)	241,1321±2	1818,3±0,2
95—Am	242	147	\(\beta^{-}\)	Cm\(^{242}\)	242,1354±3	1823,6±0,3
95—Am	243	148	\(\alpha\)	Np\(^{239}\)	243,1373±2	1830,2±0,2
95—Am	(244)	149	(\(\beta^{-}\))	interpol.	244,1408±3	1835,3±0,3
96—Cm	238	142	\(\alpha\)	Pu\(^{234}\)	238,12728±9	1796,93±0,09
96—Cm	239	143	(K)	interpol.	239,1294±3	1803,3±0,3
96—Cm	240	144	\(\alpha\)	Pu\(^{236}\)	240,13057±7	1810,60±0,07
96—Cm	241	145	K	Am\(^{241}\)	241,1329±6	1816,8±0,6
96—Cm	242	146	\(\alpha\)	Pu\(^{238}\)	242,1348±3	1823,4±0,3
96—Cm	243	147	\(\alpha\)	Pu\(^{239}\)	243,1371±2	1829,6±0,2
96—Cm	244	148	\(\alpha\)	Pu\(^{240}\)	244,1395±1	1835,7±0,1
97—Bk	243	146	\(\alpha\)	Am\(^{239}\)	243,1388±4	1827,2±0,4
97—Bk	245	148	\(\alpha\)	Am\(^{241}\)	245,1428±3	1840,2±0,3
98—Cf	244	146	\(\alpha\)	Cm\(^{240}\)	244,14225±9	1831,61±0,09
98—Cf	246	148	\(\alpha\)	Cm\(^{242}\)	246,1460±4	1844,8±0,4

Continuation of Table II

Binding energy of the last neutron $e_n$ (MeV)	Binding energy of the last proton $e_p$ (MeV)	Binding energy of the last pair of neutrons $e_{2n}$ (MeV)	Binding energy of the last pair of protons $e_{2p}$ (MeV)	Energy of radioactive transformation (MeV)	Half-life period of electron capture
8	9	10	11	12	13
	3.5			2.2	1.2 h (S6)
7.5	4.4			$5.87 \pm 0.05$ (S6)
5.7	4.1			1.2	50 h (S6)
6.9	5.0	12.6		$5.638 \pm 0.005$ (S6, A1)
5.3	4.7			$0.575 \pm 0.010$ (S6)
6.6	5.6	11.9		$5.30 \pm 0.03$ (S6)
5.1				(1,2)
—
6.4			8.24	$6.61 \pm 0.04$ (P1)
	5.1		8.6	(1,5)
7.3	4.9	13.67	9.3	$6.37 \pm 0.04$ (P1)
6.2	5.4		9.5	0.6	55 d (S11)
6.6	5.1	12.8	10.1	$6.213 \pm 0.003$ (T3, A1)
6.2	6.0		10.7	$5.99 \pm 0.04$ (T2)
6.1	5.5	12.3	11.1	$5.88 \pm 0.04$ (P1)
	3.8			$6.83 \pm 0.05$ (T2)
	4.5	13.0		$6.43 \pm 0.05$ (H8)
	4.4		8.2	$7.27 \pm 0.05$ (G4)
	4.6	13.2	9.1	$6.87 \pm 0.05$ (G4)

In the following 9th, 10th, and 11th columns are given the binding energies of the last proton \(e_p\) and the binding energies of the last pairs of neutrons \(e_{2n}\) and pairs of protons \(e_{2p}\). These quantities were calculated from the binding energies of the nuclear nucleons, given in the 7th column, by the formulas

\[ e_p(Z,A)=E(Z,A)-E(Z-1,A-1), \tag{11} \]

\[ e_{2n}(Z,A)=E(Z,A)-E(Z,A-2), \tag{12} \]

\[ e_{2p}(Z,A)=E(Z,A)-E(Z-2,A-2). \tag{13} \]

The 12th column contains, expressed in MeV, the energy of the given type of decay, listed in column 4, corresponding to the transition from the ground state of the initial nucleus to the ground state of the daughter nucleus. The experimental data are given with the error; alongside, in brackets, is given a reference to the cited literature, listed in alphabetical order at the end of the article. References are also given here to the paragraphs in which explanations are given concerning the choice of experimental data. The numbers in brackets are obtained from the binding energies (from column 7).

The 13th column contains half-lives for electron capture, with references to the cited literature.

7. NOTES TO TABLE II

1. It is assumed that in the beta decay of \({}_{82}\mathrm{Pb}^{209}\) the daughter nucleus is formed in an excited state with subsequent emission of gamma rays of total energy \(E_\gamma = 0.40\) MeV, which have not yet been observed (see W3, H6).

2. The alpha-decay energies of the nuclei \(\mathrm{At}^{212}\), \(\mathrm{At}^{213}\), \(\mathrm{Pa}^{230}\), and \(\mathrm{U}^{231}\) were estimated from the graph given in paper P1.

3. The binding energy of the nucleus \(\mathrm{Ra}^{235}\) does not lie on the secant curve for radium isotopes if the measured value \(E_\beta = 0.20\) MeV is adopted. The binding energies of the nuclei \(\mathrm{Th}^{239}\), \(\mathrm{U}^{239}\), \(\mathrm{Pa}^{233}\), etc., calculated from this value also fall off the corresponding curves. In order for all these energies to lie on smooth curves, it is necessary to assume that the beta decay of \(\mathrm{Ra}^{235}\) is accompanied by gamma rays of total energy \(E_\gamma = 0.35\) MeV, which have not yet been observed (see W2).

4. In one of the recent articles H4, an allegedly obtained isotope \(\mathrm{Th}^{235}\) is mentioned; the energy of its beta spectrum, 1.8 MeV, is determined from a cycle; in this cycle the beta-decay energy of \(\mathrm{U}^{239}\) is taken to be 1.8 MeV. The alpha-decay energies of \(\mathrm{Np}^{239}\) and \(\mathrm{U}^{239}\) are determined from the graph of paper P1 and are considered equal, respectively, to 4.6 MeV and 4.1 MeV. This value, obtained from the cycle, gives the binding energy of \(\mathrm{Th}^{235}\), fitting well on the even-odd secant curve, which confirms the correctness of the assump-

of this value of the beta-decay energy of \( \mathrm{Th}^{235} \), which has still not been measured because of the short half-life.

Concerning the nuclei \( \mathrm{Pb}^{214} \), \( \mathrm{Bi}^{211} \), and \( \mathrm{U}^{237} \), see the explanations in § 4.

Table III

Binding energies of some isomers of heavy nuclei

Nucleus	Energy computed from the energies of Table II	Type of radioactivity	Energy of radioactive transformation (MeV)	Binding energy of the nuclear isomer (MeV)	Energy of the isomeric transition (MeV)	Literature and notes
\( \mathrm{Bi}^{210m} \)	\( \mathrm{Tl}^{206} \)	\( \alpha \)	\( 5.12 \pm 0.05 \)	\( 1645.02 \pm 0.03 \)	\( 0.18 \)	N1
\( \mathrm{Bi}^{211m} \)	\( \mathrm{Tl}^{207} \)	\( \alpha \)	\( 6.748 \pm 0.006 \)	\( 1650.29 \pm 0.01 \)	\( 0.35 \)	W3 and (§ 4)
\( \mathrm{Pa}^{234m} \)	\( \mathrm{U}^{234} \)	\( \beta \)	\( 2.32 \pm 0.05 \)	\( 1777.1 \pm 0.4 \)	\( 0.394 \)	D2

Table III contains the binding energies of nucleons of three isomers of heavy nuclei with atomic numbers greater than 82. In the penultimate column the energy of the isomeric transition is given, i.e., the difference between the energies of the isomeric level and the ground level of the given nucleus.

All the tables have been compiled using journal literature published up to January 1, 1952.

8. ACCURACY OF THE TABULAR DATA

Two approaches should be distinguished in determining the accuracy of the binding energies given in Table II—namely, one may consider the absolute accuracy and the accuracy of the relative values of the binding energies. The absolute accuracy is determined mainly by the error of the mass-spectrographic data for \( {}_{82}\mathrm{Pb}^{208} \), which underlie the table, which is large relative to the other data and has already been given in § 5. Absolute accuracy is not so essential, since for elucidating the properties of nuclei the relative binding energies of nuclei and isotope masses are of greatest importance, and therefore it is especially important to know the relative accuracy of the binding energies of nuclei and isotope masses, which are given in Table II (columns 6 and 7).

Since the relative binding energies of nuclei are calculated from formulas (4), (5), (6), (7), and (8), into which the experimental data enter in the form of algebraic sums, the calculation of relative

errors should be carried out according to the formula for errors of an algebraic sum (see, for example, \(L^1\)):

\[ \sigma_E=\sqrt{\sigma_1^2+\sigma_2^2+\ldots+\sigma_i^2}, \tag{14} \]

where \(\sigma_1, \sigma_2, \ldots, \sigma_i\) are the errors of the experimental data (decay energies and neutron binding energies), given in the 12th column of Table II and in Table I, beginning with the initial nucleus \({}_{82}\mathrm{Pb}^{208}\) along all \(i\) links of the calculation chain leading to the energy of the given nucleus.

Somewhat more complicated is the calculation of the relative errors of the binding energies of those nuclei in whose calculation extrapolation and an estimate of electron capture were used, since it is very difficult to establish the errors arising in the extrapolation and estimate. In § 3 it was indicated that the greatest possible error in estimating the energy of electron capture is \(\pm 0.5\) MeV. An estimate of the error in determining the energy by graphical extrapolation gives about \(0.2\) MeV per two nucleons, i.e. per one “step” along the even or odd curve. Allowing for such errors, the relative errors of the nuclear binding energies given in Table II were calculated by formula (14).

The accuracy of the figures given in the tables is confirmed, in particular, by the quite satisfactory agreement of the calculated \(\varepsilon_n\), given in column 8, and the measured values placed in the notes, for the nuclei \(\mathrm{Th}^{233}\), \(\mathrm{Th}^{239}\), \(\mathrm{U}^{238}\), and \(\mathrm{U}^{239}\).

The deviations of points from the curves of the sections (see § 4) of the energy surfaces are considerably smaller than the errors given in Table II.

The only substantial discrepancies are the binding energies of the nuclei \(\mathrm{Th}^{232}\) and \(\mathrm{U}^{238}\), obtained from mass-spectrographic data (see § 5).

\[ \text{For } \mathrm{Th}^{232}:\ E_{\mathrm{M.S}}-E_{\mathrm{tabl}}=+4.4\ \text{MeV}, \]

\[ \text{For } \mathrm{U}^{238}:\ E_{\mathrm{M.S}}-E_{\mathrm{tabl}}=-2.8\ \text{MeV}, \]

where \(E_{\mathrm{M.S}}\) is the binding energy of the nucleus obtained from mass-spectrogram measurements, and \(E_{\mathrm{tabl}}\) is the same energy taken from Table II. These discrepancies exceed the errors of the measurements and tabular data and cannot be explained either by shortcomings of the beta-decay schemes or by any other irregularities of the calculations. It must be assumed that this discrepancy is most likely caused by errors in the mass-spectrographic data for \({}_{90}\mathrm{Th}^{232}\), \({}_{92}\mathrm{U}^{238}\), and \({}_{82}\mathrm{Pb}^{208}\). This is also confirmed by the fact that the deviations of the mass-spectrographic data from the tabular ones have different signs.

The errors of the binding energies in whose calculation extrapolation and estimates of electron-capture energies were used must be considered ...

Fig. 5. Energy surface of the binding energies of heavy nuclei \(E_0(A)-E(Z,A)\), where \(E_0(A)=1600.6+5.5(A-200)\) MeV. Spacing of isoenergetic curves: \(1\) MeV. Marks on the isoenergetic curves are given only in the region (in small type): \(a\)—nuclei with known energies, \(b\)—line connecting the nuclei most stable with respect to isobaric transformations, \(v\)—boundary of the so-called shells.

are somewhat exaggerated. This can be seen from the fact that these data, with a large degree of accuracy exceeding the accuracy allowed by these errors, fall on the curves of the sections (see, for example, Fig. 2 and Fig. 3—the dotted curve). In addition, the regularity of the first tabular differences, which are \(e_n\) and \(e_p\), given in columns 8 and 9, is considerably better than could be assumed from the errors. This is quite understandable, since in calculating the errors we did not take into account the improvement of the data by “cross” control—the electron-capture energy was checked by the smoothness of the curves, extrapolation by alpha decays, etc. (see § 6).

The absolute error of the tabulated values of the binding energies is the sum of the errors of the mass-spectrographic data for \({}_{82}\mathrm{Pb}^{208}\) and of the relative error calculated by formula (14). Taking into account the serious discrepancy of the data for \(\mathrm{Th}^{233}\) and \(\mathrm{U}^{238}\), which may also be connected with insufficient accuracy of the mass-spectrographic data for \(\mathrm{Pb}^{208}\), it may be considered that the absolute error for all energies is not less than 2 MeV.

A study of the relative errors of the nuclear binding energies given in Table II shows that the relative accuracy considerably exceeds the accuracy of mass spectrography.

9. THE ENERGY SURFACE AND ITS SECTIONS

For studying the properties of nuclei, the energy surface is very convenient, making it possible to compare nuclear energies. We shall consider the binding-energy surface, which geometrically represents the dependence of the binding energy of the nucleons of nuclei \(E\) on the atomic number \(Z\) and the mass number \(A\), i.e. the surface with equation

\[ E=f(Z,A). \]

In order to represent the three-dimensional energy surface on a plane drawing, we use lines of equal binding energies—isoenergets. To reduce the number of isoenergets, we shall consider not the energy surface \(E(Z,A)\) itself, but its relative position under the auxiliary inclined plane defined by the equation

\[ E_0(A)=1600.6+5.5(A-200)\ \text{MeV}, \tag{10} \]

which has already been discussed in § 4, with slope \(5.5\,\dfrac{\text{MeV}}{\text{nucleon}}\).

In Fig. 5 the isoenergets of the binding-energy surface are presented on the \(Z,A\) plane, with all even-odd ...

inequalities with respect to the inclined plane (10), i.e. for the function \(E_0(A)-E(Z,A)\). Since the binding energy of the nucleons of the nucleus \(E(Z,A)\) enters this expression with a minus sign, all points of the surface lying lower usually correspond to more stable nuclei, with exceptions that will be described below. The cross section of the isoenergetics for this surface is given every 1 MeV; the labels of the even isoenergetics (in MeV) are written in small type. The mass numbers \(A\) (increasing from bottom to top) and the atomic numbers \(Z\) (increasing from left to right) are indicated in large type. Nuclei with known energies are indicated by small circles. A double line denotes the line connecting the nuclei most stable with respect to isobaric transitions. Triple lines connect nuclei having either 126 neutrons or 82 protons, i.e. the closing lines of the so-called neutron and proton shells.

Fig. 6. Diagram of the levels of the binding energies of isobars, explaining the possibility of isobaric transformations into the nucleus \((Z,A)\). Energy is plotted from top to bottom.

The energy surface helps to estimate the stability of nuclei, in particular with respect to isobaric transformations, i.e. to beta decay, positron decay, and electron capture. If we plotted along the vertical axis \(E\), downward from the plane \((Z,A)\), the total energy of the nuclei or their mass, then the line of greatest stability with respect to isobaric transformations would be the axis of the “valley,” i.e. the line connecting the lowest points of the energy surface (see, for example, \({}^{61}\)). In the present case we plot not the total energy, but the binding energy of the nucleons of the nuclei \(E(Z,A)\), which leads to somewhat different results. On the basis of equations §§ 1 and 3—(5), (6), and (8)—we can establish the following energy conditions for the possibility of isobaric transitions into the daughter nucleus \((Z,A)\), represented graphically in the diagram of Fig. 6. In Fig. 6, in the form of three columns, the possible levels of the binding energy of the nucleons of three isobaric nuclei, \((Z+1,A)\), \((Z,A)\), and \((Z-1,A)\), are shown, with the binding energies of the nucleons \(E(Z,A)\) plotted from top to bottom along the vertical axis. As follows from formula (5) and the scheme in Fig. 6, the nucleus \((Z-1,A)\) can undergo beta decay and transform into the nucleus \((Z,A)\) if its binding-energy level lies not lower than \((m_n-m_{\mathrm{H}})=0.782\) MeV in comparison with the binding-energy level of the nucleus \((Z,A)\), i.e. in the shaded ...

of the shaded region above the line \(bb\). On the basis of formula (6) one may assert that the nucleus \((Z+1,A)\) is capable of capturing an electron and being transformed into the nucleus \((Z,A)\), if the level of its binding energy is above the line of the level \(E(Z,A)\) by \((m_n-m_H)+E_x\), i.e. in the hatched region above the line \(cc\). \(E_x\) is the energy of the X rays emitted upon electron capture. According to formula (9), the magnitude \(E_x\) for capture of an electron from the \(K\)-orbit in the interval \(Z\) from 78 to 98 varies from \(0.081\) MeV to \(0.127\) MeV. Similarly, the region of levels of the nucleus \((Z+1,A)\) for which positron decay is also possible is indicated by cross-hatching. The nuclei \((Z-1,A)\), whose binding-energy levels lie below the line \(bb\), are stable with respect to beta transformation into the nucleus \((Z,A)\), and the nuclei \((Z+1,A)\) with binding-energy levels lying below the line \(cc\) are stable with respect to electron capture with subsequent transformation into the nucleus \((Z,A)\).

Thus, we see that sometimes a nucleus lying at the bottom of the valley will be stable with respect to isobaric transformations, and sometimes not. If the binding-energy level of the nucleus \((Z-1,A)\) lies even below the binding energy of the isobaric nucleus \((Z,A)\), but by an amount smaller than \(0.782\) MeV, then beta decay of the nucleus \((Z-1,A)\) is energetically possible, as follows from the scheme in Fig. 6. In Figs. 7 and 8 a number of examples of isobaric sections of the energy surface given in Fig. 5 are presented. Fig. 7 represents sections for even mass numbers \(A\); in Fig. 8 are shown sections for isobars with odd mass numbers \(A\). In the case of even \(A\), two curves may be drawn: for even-even nuclei, lying lower, and for odd-odd nuclei, located higher; they are shown in Fig. 7 by dashed lines, and between them runs a wave-like curve representing an even isobaric section. Odd isobaric sections (Fig. 8) have no bends and are smooth curves, sometimes resembling parabolas (see \(B^1\), p. 36 and \(F^3\), pp. 14 and 17). From these curves one can show when nuclei lying at the bottom of the valley are not beta-stable. For example, on the curve \(A=210\) (Fig. 7) we have the nucleus \({}_{82}\mathrm{Pb}^{210}\) (RaD), whose energy lies in a depression and, in spite of this, it is beta-radioactive and transforms into the nucleus \({}_{83}\mathrm{Bi}^{210}\) (RaE), whose binding energy is smaller and, consequently, which lies higher on the graph. Another example may be \({}_{95}\mathrm{Am}^{243}\), whose energy on the curve \(A=243\) (Fig. 8) lies at the very lowest point of the curve. In spite of the greatest binding energy, the nucleus \({}_{95}\mathrm{Am}^{243}\) is beta-radioactive (see §6) and transforms into the nucleus \({}_{96}\mathrm{Cm}^{243}\), which on this curve is the only beta-stable nucleus.

The double line of nuclei most stable with respect to isobaric transitions in Fig. 5 has been drawn taking into account all these features of the energy surface.

Fig. 7. Isobaric sections of the energy surface for several even mass numbers \(A\).

Fig. 8. Selected cross sections of the energy surface for several odd mass numbers \(A\).

In addition to the energy surface in Fig. 5, the slope of which is shown changed, Table IV is given with the true slopes of lines stable with respect to isobaric nuclear transitions on the unchanged energy surface. The largest deviations from the mean slope are found before the mass number 208 and after it. At mass number 208 on this line lies the especially stable nucleus \({}_{82}\mathrm{Pb}^{208}\), at which such a substantial break in the slope occurs. Further changes in the slope are considerably smaller.

Table IV

Slopes of lines stable with respect to isobaric nuclear transitions on the energy surface of heavy nuclei.

Interval of mass numbers	Slope per unit length, \(\dfrac{M\text{эв}}{\text{nucleon}}\)
194—208	6,98
208—216	4,93
216—228	5,59
228—236	5,87
236—244	5,68
Mean 194—244	5,93

If one considers separately the three energy surfaces: even-even, odd-odd, and the surface for odd \(A\), it can be shown that for large \(A\) the even-even surface, within the limits of error, coincides with the surface for odd \(A\). If, for example, in the nuclei \({}_{86}\mathrm{Em}^{218}\) and \({}_{86}\mathrm{Em}^{219}\) the distance between them reaches \(1\ M\text{эв}\), then, as is seen from Fig. 4, in \({}_{92}\mathrm{U}^{236}\), \({}_{92}\mathrm{U}^{239}\) this distance decreases to \(0.1\ M\text{эв}\) or less, as also in \({}_{90}\mathrm{Th}^{239}\), \({}_{94}\mathrm{Pu}^{242}\), and \({}_{96}\mathrm{Cm}^{244}\). The distance between the odd-even surface and the surface for odd \(A\) changes less.

An energy surface based not on exact calculations, but on conclusions from the systematics of the energies of alpha decays alone, was discussed in the work of Perlman and co-workers P¹. The conclusions of the cited work on a number of questions diverge from the results of the study of the figures presented in Table II and of the surface shown in Fig. 5. In particular, along the lines \(N=126\) and \(Z=82\) there are no sharp irregularities, steps, or bends, but only a clearly expressed change of slopes, which is also indicated in W³. It should be noted that the change in slope is gradually smoothed out as one moves away from the especially stable nucleus \({}_{82}\mathrm{Pb}^{208}\), as follows also from K⁵. As can be established from Table IV, there is likewise no tendency toward the formation of a plateau between \(A=224\) and \(A=236\), and even, on the contrary, in this region a secondary maximum of the slope is formed. For \(A\) greater than 236, contrary to the assertions of P¹, we have not an increase but, on the contrary, a decrease in the slope. In the work P¹ no sharply expressed “pit” was found either, in which lie \({}_{82}\mathrm{Pb}^{208}\) and \({}_{83}\mathrm{Bi}^{209}\), and which is clearly visible in Fig. 5.

As we have seen from a number of examples, the table of binding energies and the energy surface constructed from it constitute a valuable means for comparing various experimental

materials relating to heavy nuclei. The methods of compiling the tables, described here in sufficient detail, make it possible to correct and supplement the tables as new experimental materials appear in print.

In conclusion I express my gratitude to A. V. Kravtsov for substantial help in calculating isotope masses from binding energies.

CITED LITERATURE

A1. F. Asaro, F. Reynolds and I. Perlman, Bull. Am. Phys. Soc. 26, No. 8, 10 (1951).

B1. G. Bethe and R. Bacher, Nuclear Physics, Part 1, GNTU, Kharkov (1938).

B2. M. Bunker, L. Langer and R. Moffat, Phys. Rev. 80, 468 (1950).

B3. G. Barton, A. Ghiorso and I. Perlman, Phys. Rev. 82, 13 (1951).

C1. J. Cork, C. Branyan, A. Stoddard, H. Keller, J. Le Blanc and W. Childs, Phys. Rev. 83, 681 (1951).

D1. B. Dzhelepov, A. Bashilov, A. Zolotavin and N. Anton’eva, DAN 64, 803 (1940).

D2. B. Dzhelepov and I. Petrovich, UFN 40, 597 (1950).

D3. H. Duckworth, K. Woodcock and R. Preston, Phys. Rev. 78, 479 (1950).

D4. H. Duckworth and R. Preston, Phys. Rev. 82, 468 (1951).

D5. Dumond and Cohen, UFN 45, 438 (1951).

D6. D. Dunlavey and G. Seaborg, Bull. Am. Phys. Soc. 26, No. 8, 9 (1951).

E1. H. Evans, Proc. Phys. Soc. A63, 575 (1950).

E2. L. Elliot and J. Wolfson, Bull. Am. Phys. Soc. 26, No. 1, 46 (1951).

E3. H. Ewald, ZS. f. Naturforsch. 6a, 293 (1951).

F1. M. Freedman, A. Jaffey and F. Wagner, Phys. Rev. 79, 410 (1950).

F2. Ya. Frenkel, Principles of the Theory of Atomic Nuclei, Publishing House of the Academy of Sciences of the USSR, Moscow (1950).

F3. E. Fermi, Nuclear Physics, IL, Moscow (1951).

G1. A. Grinberg, Uspekhi khimii 11, 141 (1942).

G2. (Edited by) K. Guggenheim et al., Scientific and Technical Foundations of Nuclear Energy, Vol. 1, IL, M. (1948).

G3. L. Groshev, L. Shavtvalov, DAN 68, 257 (1949).

G4. A. Ghiorso, S. Thompson, K. Street and G. Seaborg, Phys. Rev. 81, 154 (1951).

G5. R. Graham and R. Bell, Bull. Am. Phys. Soc. 26, No. 3, 31 (1951).

G6. A. Ghiorso, J. Brittain, W. Manning and G. Seaborg, Phys. Rev. 82, 559 (1951).

G7. A. Ghiorso, Phys. Rev. 82, 979 (1951).

G8. M. Crace and T. Prescott, Phys. Rev. 84, 1059 (1951).

H1. A. Hanson, R. Duffield, J. Knight, B. Diven and H. Palevsky, Phys. Rev. 76, 578 (1949).

H2. E. Hyde, A. Ghiorso and G. Seaborg, Phys. Rev. 77, 765 (1950).

H3. J. Huizenga, L. Magnusson, O. Simpson and G. Winslow, Phys. Rev. 79, 908 (1950).

H4. B. Harvey and B. Parson, Phys. Rev. 80, 1098 (1950).

H5. W. Hornyak, T. Lauritsen, P. Morrison and W. Fowler, Rev. Mod. Phys. 22, 291 (1950).

H6. J. Harvey, Phys. Rev. 81, 353 (1951).

H7. J. Huizenga, L. Magnusson, P. Fields, M. Studier and R. Duffield, Phys. Rev. 82, 561 (1951).
H8. E. Hulet, S. Thompson, A. Ghiorso and K. Street, Jr., Phys. Rev. 84, 366 (1951).
H9. T. Huizenga, L. Magnusson, M. Freedman and F. Wagner, Jr., Phys. Rev. 84, 1264 (1951).
H10. O. Huber, F. Humbel, H. Schneider and A. de-Shalit, Helv. Phys. Acta 24, 629 (1951).
J1. A. Jaffey, J. Lerner and S. Warshaw, Phys. Rev. 82, 498 (1951).
J2. A. Jaffey, H. Diamond, A. Hirsch and T. Mech, Phys. Rev. 84, 785 (1951).
J3. W. Jenkins and G. Seaborg, Bull. Am. Phys. Soc. 26, No. 8, 10 (1951).
K1. V. Kondrat’ev, UFN 38, 153 (1949).
K2. B. Kinsey, G. Bartolomew and W. Walker, Phys. Rev. 78, 77 (1950).
K3. H. Keller and J. Cork, Phys. Rev. 79, 1030 (1950).
K4. D. Karraker and D. Templeton, Phys. Rev. 81, 510 (1951).
K5. V. A. Kravtsov, DAN 77, 43 (1951).
K6. B. Kinsey, G. Bartolomew and W. Walker, Phys. Rev. 82, 380 (1951).
K7. D. Karraker, A. Ghiorso and D. Templeton, Phys. Rev. 83, 390 (1951).

L1. L. Lakhtin, A Course in Probability Theory, Moscow–Leningrad, 1924, pp. 157–162.
L2. P. Levy and E. Greuling, Phys. Rev. 75, 819 (1949).
L3. W. Lyon, Phys. Rev. 82, 276 (1951).
L4. C. Li, W. Whaling, W. Fowler and C. Lauritsen, Phys. Rev. 83, 512 (1951).

M1. J. McElhinney, A. Hanson, R. Bekker, R. Duffield and B. Diven, Phys. Rev. 75, 542 (1949).
M2. A. Mitchell, Rev. Mod. Phys. 22, 36 (1950).
M3. L. Magnusson, S. Thompson and G. Seaborg, Phys. Rev. 78, 363 (1950).
M4. W. Meinke and G. Seaborg, Phys. Rev. 78, 475 (1950).
M5. W. Meinke, A. Ghiorso and G. Seaborg, Phys. Rev. 81, 782 (1951).
M6. J. Moon and A. Thompson, Phys. Rev. 83, 892 (1951).
M7. L. Magnusson, J. Huizenga, P. Fields, M. Studier and R. Duffield, Phys. Rev. 84, 166 (1951).
N1. H. Neumann, J. Howland and I. Perlman, Phys. Rev. 77, 720 (1950).
N2. H. Neumann and I. Perlman, Phys. Rev. 78, 191 (1950).
N3. H. Neumann and I. Perlman, Phys. Rev. 81, 958 (1951).
N4. Nuclear Data, National Bureau of Standards. Circular 499 (1950).
O1. D. Orth and G. O’Kelley, Phys. Rev. 82, 758 (1951).
P1. I. Perlman, A. Ghiorso and G. Seaborg, UFN 42, 220 (1950).
P2. R. Parsons and C. Collie, Proc. Phys. Soc. 63A, 839 (1950).
P3. M. Pryce, Proc. Phys. Soc. 63A, 692 (1950).
P4. H. Palevsky and A. Hanson, Phys. Rev. 79, 242 (1950).
R1. L. Rosenfeld, Nuclear Forces, Amsterdam, 1948.
S1. M. Stern, Rev. Mod. Phys. 21, 316 (1949).
S2. R. Steffen, O. Huber and F. Humbel, Helv. Phys. Acta 22, 167 (1949).
S3. D. Saxon and J. Richards, Phys. Rev. 76, 982 (1949).
S4. H. Stätl and K. Siegbahn, Ark. Mat. Astr. Fys. 36A, No. 21 (1949).
S5. E. V. Shpolsky, Atomic Physics, vol. II, Gostekhizdat, Moscow, 2nd ed. (1950).

S6. K. Street, A. Ghiorso and G. Seaborg, Phys. Rev. 79, 530 (1950).
S7. G. Stanford and H. Duckworth, Bull. Am. Phys. Soc. 26, No. 3, 38 (1951).
S8. P. Sherk and R. Hill, Phys. Rev. 83, 1097 (1951).
S9. J. Sullivan, O. Pyle, M. Studier, P. Fields and F. Manning, Phys. Rev. 83, 1267 (1951).
S10. R. Sher, T. Halpern and A. Mann, Phys. Rev. 84, 387 (1951).
S11. I. P. Selinov, Atomic Nuclei and Nuclear Transformations. Vol. 1. Tables in Atomic-Nucleus Physics. Gostekhizdat, Moscow (1951).
T1. S. Thompson, Phys. Rev. 76, 319 (1949).
T2. S. Thompson, A. Ghiorso and G. Seaborg, Phys. Rev. 80, 781 (1950).
T3. S. Thompson, K. Street, A. Ghiorso and Seaborg, Phys. Rev. 80, 790 (1950).
T4. S. Thompson, K. Street, A. Ghiorso and F. Reynolds, Phys. Rev. 80, 1108 (1950).
T5. E. Tomlinson, H. Fulbright and T. Howland, Jr., Phys. Rev. 83, 223 (1951).
T6. S. Thompson, K. Street, A. Ghiorso and F. Reynolds, Phys. Rev. 84, 165 (1951).
W1. K. Way, Phys. Rev. 75, 1448 (1949).
W2. A. Wapstra, Physica 16, 33 (1950).
W3. A. Wapstra, Physica 17, 628 (1951).