FROM THE CURRENT LITERATURE

ALPHA RADIOACTIVITY

IN THE REGION OF NUCLEI WITH 82 NEUTRONS

In nuclei of medium mass, the first $\alpha$-radioactivity to be discovered was that of the isotope $\mathrm{Sm}^{147}$. Using a semiempirical mass formula corrected in accordance with the latest measurements of the masses of medium nuclei, one can approximately calculate the energy released when an $\alpha$ particle is detached from the nucleus. Already in work 1 it was shown in this way that many rare-earth elements are $\alpha$-radioactive, for upon detachment of an $\alpha$ particle a small positive energy—of the order of $2\ \mathrm{MeV}$—must be released. As is known from the theory of $\alpha$ decay, the half-life increases rapidly as the energy of the $\alpha$ particle decreases. An $\alpha$-decay energy of $2\ \mathrm{MeV}$ corresponds to an $\alpha$-decay period of more than $10^{16}$ years. $\alpha$-radioactivity with such a large half-life cannot be detected.

From the systematics of $\alpha$ decay of heavy nuclei 2 it follows that the $\alpha$-decay energy increases as the number of neutrons decreases and that, in heavy nuclei near the closed shell of 126 neutrons, namely in nuclei with 128 neutrons, the $\alpha$-decay energy reaches a maximum. A similar increase of $\alpha$-decay energy should be expected in the region of the rare earths near the closed shell of 82 neutrons. Higher $\alpha$-decay energies must also lead to higher decay rates. By analogy with heavy nuclei, the maximum $\alpha$-decay energy in this region should be expected for nuclei with 84 neutrons.

The reviewed papers 3, 4, 5 give experimental data on $\alpha$-radioactive nuclei of medium mass obtained in recent years.

Two of the isotopes of medium mass have natural $\alpha$-radioactivity; the others were obtained by bombardment of medium nuclei with high-energy particles.

A brief bombardment with 200-MeV protons of tungsten, silver, tantalum, palladium, samarium oxide, and the oxide of the tellurium isotope $\mathrm{Te}^{122}$ did not lead to the production of $\alpha$-radioactive nuclei.

Table I presents data on all presently known $\alpha$-radioactive nuclei lighter than lead.

In none of the nuclei of medium mass has a fine structure of $\alpha$ decay been detected, i.e., all the nuclei listed in Table I emit $\alpha$ particles of only one energy. The energies of the $\alpha$ particles were measured by pulse-height analysis with proportional counters, except for the data for $\mathrm{Tb}^{149}$, marked a. The energy of the $\alpha$ particle of $\mathrm{Tb}^{149}$ was measured with a magnetic spectrograph; the standard used was the energy of the $\alpha$ particle of $\mathrm{Ra}^{226}$, with energy $4.777\ \mathrm{MeV}$ 6. The errors given with $\pm$ signs are estimates of their limits, not probable errors.

Table 1

Alpha radioactivity of isotopes of elements lighter than lead

Continuation of Table 1

Neodymium. The previously predicted \(1\ \alpha\)-radioactivity of the natural isotope of neodymium \(Nd^{144}\) was recently discovered \(^{5}\). The energy of the \(\alpha\)-particles was found by studying their tracks in photographic plates impregnated with compounds of neodymium mixed with samarium. Comparison of the tracks of the \(\alpha\)-particles of \(Nd^{144}\) with the tracks of the \(\alpha\)-particles of \(Sm^{147}\) showed that the energy of the \(\alpha\)-particles of \(Nd^{144}\) is \(1.9 \pm 0.1\) MeV. The half-life is a rough estimate.

Samarium. The energy of the \(\alpha\)-particles of \(Sm^{147}\) is taken from the most accurate data of work \(^{7}\); according to measurements of pulses of a counter with argon, this energy is \(2.18\) MeV. But in accordance with the data of work \(^{9}\), this value must be corrected for the nonlinearity of the dependence of the ionization of argon on the energy of the \(\alpha\)-particle. With this correction, the energy of the \(\alpha\)-particles of \(Sm^{147}\) will be \(2.21\) MeV. The half-life of \(Sm^{147}\) is given according to the tables \(^{8}\).

Europium. Bombardment of samarium with protons of energy \(200\) MeV, lasting less than an hour, did not give \(\alpha\)-radioactivity. Only prolonged bombardments with protons and deuterons of the isotope \(Sm^{147}\) gave \(\alpha\)-activity. The assignment of the \(\alpha\)-particles to europium was confirmed by chemical separation of europium. It was established that all neutron-deficient europium isotopes with mass numbers from 144 to 150, except \(Eu^{147}\), do not have appreciable \(\alpha\)-activity.

Gadolinium. Activity with \(\alpha\)-particle energy \(3.18\) MeV is obtained by bombarding samarium oxide enriched in the isotope \(Sm^{147}\) with \(\alpha\)-particles of energy \(38\) MeV. The same activity can be obtained by bombarding europium oxide with protons of energy \(50\) MeV. The assignment of this activity to gadolinium was confirmed by chemical separation.

The mass number was determined from the threshold of the reactions found experimentally. For the reaction \(Sm^{147}(\alpha, xn)\) it is \(28\)—\(30\) MeV, and for the reaction \(Eu^{151}(p, yn)\) it proved to be \(\sim 30\) MeV. Comparison of these experimental data with the threshold calculated from the semiempirical formula for masses at various \(x\) and \(y\) leads to the conclusion that \(x = 3\) and \(y = 4\), and the product of the reaction is \(Gd^{148}\).

An estimate of the half-life was made from the yield of the reaction \(Sm^{147}(\alpha, 3n)\), obtained from the excitation curve by comparison with an analogous reaction for \(Bi^{209}\).

The assignment of the activities with \(\alpha\)-particle energies \(3.0\) MeV and \(2.7\) MeV to gadolinium was confirmed by chemical separation. The mass numbers were established tentatively with the aid of semiempirical relations for the energies of \(\alpha\)-decay.

The six-hour \(\alpha\)-activity mentioned in communication \(^{10}\) and attributed to gadolinium does not belong to it.

Terbium. The assignment of the activity with \(\alpha\)-particle energy \(3.95\) MeV to terbium was confirmed by chemical separation. The mass number was established mass-spectrographically. The lower limit of the ratio of \(\alpha\)-activity to electron capture is \(1\%\).

The assignment of the activity with \(\alpha\)-particle energy \(3.45\) MeV to terbium was also confirmed chemically. The mass number was established tentatively from the excitation function for the reaction \(Eu(\alpha, xn)\), which leads to the probable product of the reaction \(Tb^{151}\) and possible \(Tb^{150}\). Decay proceeds predominantly by electron capture, with the lower limit of the ratio \(\alpha\)-decay/electron capture \(> 4 \cdot 10^{-6}\). This value is possibly underestimated.

Dysprosium. An approximate theoretical calculation, analogous to the calculation given in book \(^{11}\), makes it possible to establish that in the reaction \(Tb^{159}(p, xn)\) the probable number of evaporated neutrons is from 7 to 11, which leads to the conclusion that the product of the reaction is an isotope of dysprosium with mass number \(A\) from 149 to 153. The tentative ordinal number of the active elements with \(\alpha\)-particle energies \(4.2\) MeV and \(4.06\) MeV was established from consideration of the reactions leading to the formation of these activities.

For the activity with \(\alpha\)-particle energy \(3.6\) MeV, its belonging to dysprosium was established by chemical separation.

Short bombardment of dysprosium oxide with protons of energy 200 MeV gives, among other activities, an \(\alpha\)-activity with energy \(4.2 \pm 0.15\) MeV and a half-life of 4 min. It is possible that this is an isotope of holmium.

Short bombardment of samarium oxide with \(C^{12}\) ions of energy 100 MeV produces a 3.5-minute \(\alpha\)-activity, the energy of whose \(\alpha\)-particles could not be measured. It is possible that this \(\alpha\)-activity belongs to isotopes of holmium or erbium.

Gold. The assignment of the activity with \(\alpha\)-particle energy 5.1 MeV to gold was confirmed by chemical separation. The limits of the mass number values are based on an estimate of the energy of the bombarding particles needed to obtain this activity. These limits are very approximate.

Table II

Energies of \(\alpha\)-decay of nuclei of rare-earth elements

* Parentheses mean that the mass number is unknown and has been adopted tentatively for the calculations.

Mercury. The assignment of \(\alpha\)-particles with energy 5.6 MeV to mercury isotopes was confirmed by chemical separation.

Calculation of the \(\alpha\)-decay energy from cycles in the region of the rare earths is possible only for \(\mathrm{Pm}^{147}\) and \(\mathrm{Nd}^{147}\) from the \(\alpha\)-decay energy of \(\mathrm{Sm}^{147}\); by

following scheme:

\[ \begin{array}{cccccc} & E_{\beta}=0.223\ \text{MeV} & & E_{\beta+\gamma}=0.915\ \text{MeV} & & \\ \mathrm{Sm}^{147} & \xleftarrow{\ \beta^-\ } & \mathrm{Pm}^{147} & \xleftarrow{\ \beta^-\ } & \mathrm{Nd}^{147} & \\ \alpha \downarrow & & \vdots & & \vdots & \\ E_{\alpha}=2.26\ \text{MeV} & & E_{\alpha 1}=1.56\ \text{MeV (calc.)} & & E_{\alpha 2}=1.04\ \text{MeV (calc.)} & \\ \mathrm{Nd}^{143} & \xleftarrow{\ \beta^-\ } & \mathrm{Pr}^{143} & \xleftarrow{\ \beta^-\ } & \mathrm{Ce}^{143} & \\ & E_{\beta}=0.932\ \text{MeV} & & E_{\beta+\gamma}=1.44\ \text{MeV} & & \end{array} \]

The scheme gives the total energies of α-decay, including corrections for the recoil energy of the nucleus and for the electrostatic potential energy of the α-particle relative to the electron cloud (the screening correction).

Dependence of the α-decay energy on the number of neutrons in nuclei. The dashed lines with long strokes show lines calculated from the semiempirical mass formula. \(a\)—the mass number is known, \(b\)—the mass number is known approximately, \(v\)—only the limit of the α-decay energy is known, \(g\)—the mass number is unknown and has been assumed tentatively.

screening). The latter correction, in accordance with work \(^{12}\), in the region of the rare earths is equal to 20 keV and must be added to the energy of the α-particle. The energies

The values for the $\beta$-decay of $\mathrm{Pm}^{147}$ and $\mathrm{Pr}^{143}$ are taken from Table 8, the decay energy of $\mathrm{Nd}^{147}$ is taken from work 13, and for the decay of $\mathrm{Ce}^{143}$, from 14.

Table II presents the total $\alpha$-decay energies of rare-earth isotopes. Along with the experimental data, the table also gives limiting values of the $\alpha$-decay energies of the isotopes $\mathrm{Sm}^{144}$ and $\mathrm{Sm}^{148}$, found theoretically on the basis that their half-life is greater than $10^{14}$ years; otherwise their activity would have been detected.

The figure shows the dependence of the energies given in Table II on the number of neutrons $N$ in the nuclei. As should be expected, the greatest $\alpha$-decay energy occurs for the nucleus with 84 neutrons, which confirms, by analogy with the $\alpha$-systematics for heavy nuclei, the presence of a shell of 82 neutrons.

When the atomic number changes from 64 to 65, the increase in the $\alpha$-decay energy is much greater than in the transition from 63 to 64. This may mean that 64 is a “magic” number for protons. Such a “subshell” of 64 protons can be explained in the shell model with strong spin-orbit coupling,^15 if one takes into account a certain splitting of the $2d_{5/2}$ and $2d_{3/2}$ levels.

V. K.

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