TABLE OF NUCLEAR MOMENTS*)

J. E. Mack

I. GENERAL DESCRIPTION OF THE TABLE

Below is given a table of nuclear moments according to data as of January 1950. The table is furnished with a number of explanations, which, however, are not intended to be a general review of the question of nuclear moments.

Definitive tables can be compiled only in those areas whose study has been completed. With regard to nuclear moments, which continue to be actively studied, this cannot be done. Therefore any table of moments becomes obsolete before it reaches the reader. On the other hand, however, at the present time such a table is especially useful. Earlier tables of this type\(^{1–14}\) testify to the steady growth in the number of nuclei studied. This is clearly seen from the following table (ω). A transitional period has now begun: experimental information is available on the nuclear moments of all 109 stable isotopes (with the exception of 15) with odd mass number. The main attention is now being devoted to increasing the accuracy of the determination of moments. Nevertheless, several of the spin values given already require redetermination; many stable even-even isotopes and a large number of radioactive nuclei remain unstudied; the study of quadrupole and higher multipole moments has only begun.

Table I (see pp. 396–411), compiled at the beginning of 1950, contains the values of the mechanical or spin moments \(I\) and the most probable values of the magnetic dipole moments \(\mu\) and electric quadrupole moments \(Q\) for each nucleus in the normal state. Here the spin \(I\) is expressed in units of \(\hbar\), the moment \(\mu\) in units of the nuclear magneton \(e\hbar/2M_p c\), and \(Q\) in units equal to \(e \cdot 10^{-24}\ \mathrm{cm}^2\), where \(e\) is the magnitude of the electronic charge in CGSE, \(M_p\) is the rest mass of the proton, and \(c\) is the speed of light in vacuum. A positive value of \(Q\) denotes an elongated, and a negative value of \(Q\) a flattened, nonspherical distribution of charge,

) J. E. Mack, Rev. Mod. Phys. 22*, 64 (1950).

Table a

Evolution of Tables of Nuclear Moments

since \(Q=\int\!\!\int \rho_I(3z^2-r^2)\,d\tau\), where \(\rho_I\) is the charge density in the state with \(m_I=I\), and the remaining notation has its usual meaning.

Each column of the tables respectively denotes:

1. \(N\) — number of neutrons (odd \(N\) in boldface).
2. \(Z\) — number of protons, or atomic number (odd \(Z\) in boldface).
3. Chemical symbol of the element.
4. \(A=N+Z\), mass number (radioactive nuclei are marked with an asterisk).
5. \(I\) (in units of \(\hbar\)).
6. \(\mu\) (in units of \(e\hbar/2M_pc\)).
7. \(Q\) (in units of \(e\cdot10^{-24}\ \mathrm{cm}^2\)).
8. References to the literature concerning the values of \(I\).
9. References to the literature concerning \(\mu\) (articles used in the calculations are indicated in italics).
10. References to the literature concerning \(Q\) (articles used in the calculations are indicated in italics).
11. Chemical symbols of the elements (second time).
12. Mass number (second time).

Quantities that may be regarded as doubtful are enclosed in parentheses (when, in addition to the quantity enclosed in parentheses, a quantity not enclosed in parentheses is given, the latter is presumed to be more probable). A question mark inside parentheses indicates strong doubt and the absence of any rigorous and final proofs. For nuclei with odd nuclear numbers for which data have not yet been obtained, blank spaces have been left in the table.

At the end of the article a bibliography is given, the four columns of which respectively denote: 1) the symbol indicating the author and year; 2) the reference to the article; 3) the chemical symbols of the elements to which the given article is devoted; and 4) the symbol indicating the character of the experimental data, according to the following designations, borrowed from earlier tables\(^{3,13,14}\):

\(A\) — magnetic-resonance method with an atomic beam,
\(B\) — band spectrum,
\(C\) — spectrum of combinational scattering,
\(H\) — heat capacity,
\(M\) — magnetic-resonance method with a molecular beam,
\(N\) — nuclear scattering,
\(O\) — ortho-para conversion,
\(P\) — polarization of resonance radiation,
\(R\) — resonance absorption or induction,
\(S\) — hyperfine structure in line spectra,
\(W\) — absorption of microwaves,
\(Z\) — deflection of an atomic beam.

MOMENTS

Table I

TABLE OF NUCLEAR MOMENTS

Table I (continued)

TABLE OF NUCLEAR MOMENTS

Table I (Continuation)

TABLE OF NUCLEAR MOMENTS

Table 1 (Continued)

TABLE OF NUCLEAR MOMENTS

Table I (continued)

TABLE OF NUCLEAR MOMENTS

Table I (continued)

TABLE OF NUCLEAR MOMENTS

Table I (Continuation)

Table of Nuclear Moments

Table 1 (Conclusion)

II. Mechanical Moment \(I\)

In contrast to the moments \(\mu\) and \(Q\), the values of the mechanical moments contain no small errors, since according to the quantum-mechanical commutation rules \(I\) is strictly an integer for even \(A\) and strictly a half-integer for odd \(A\) \(^{15}\).

Below are listed all cases in which there are discrepancies in the values of \(I\) that are not based on new data and that occur among the postwar tables.

Table b

Discrepancies in the values of \(I\) in postwar tables

\({}^{9}_{4}\mathrm{Be}\).—The theoretically indicated \(^{15}\) and usually accepted value \(3/2\) for \(I(\mathrm{Be}^{9})\) is not experimentally substantiated. The exclusion of the value \(1/2\) was based on plausible arguments of KU\(^{39}\), and the exclusion of values greater than \(3/2\) on the considerations that, for the known gyromagnetic ratio, such a spin would lead to partial resolution of the hyperfine structure \(\mathrm{PD}^{41}\).

\({}^{25}_{12}\mathrm{Mg}\).—Crawford CR\(^{50}\) estimates the possibility that \(I(\mathrm{Mg}^{25})\) differs from \(5/2\) as \(1:10\).

\({}^{77}_{34}\mathrm{Se}\).—Both values \(I = 7/2 \pm 1\) were obtained by using the interval rule for a partially resolved hyperfine structure MA\(^{49}\). The value \(|Q| < 2 \cdot 10^{-3}\) OO\(^{50}\), TW\(^{50}\) appears to be well established for \(\mathrm{Se}^{77}\). These values do not absolutely exclude one another, although the unusually low value of \(Q\), smaller than in the deuteron, naturally leads to the assumption that \(I\) must be equal to \(1/2\). Experiments SA\(^{50}\) were carried out for an independent determination of the spin.

III. MAGNETIC DIPOLE MOMENT \(\mu\)

A. The proton moment

Immediately before the publication of this table, important new data became known on the first direct measurement of the magnetic moment of the proton in nuclear magnetons—n.m. (i.e. proton magnetons), carried out by Hippel, Sommer, and Thomas \(^{\mathrm{HP}49}\). The ratio of the nuclear-resonance frequency for the proton \(\nu_p\) to the cyclotron frequency of the proton \(\nu_c\), measured in the same magnetic field, gives directly (without the diamagnetic correction; see Section III C.1) the value \(\mu({}^{0}_{1}\mathrm{H}^{1})\) in special units (n.m.), independently of any other measurements. Thus one obtains the value \(\mu({}^{0}_{1}\mathrm{H}^{1}\), without correction) \(= 2.792469 \pm 0.000078\) n.m., which is only preliminary, since the authors have not yet clarified the question of possible systematic errors. Nevertheless, I prefer this method (with the diamagnetic correction introduced) to any other, because it is the most direct. Introducing the diamagnetic correction \([1 - (3 \pm 2)\cdot 10^{-5}]\) increases the original value by \((8 \pm 6)\cdot 10^{-5}\) magnetons, so that after rounding the last digit the best value used in the table is at present as follows:

\[ \mu({}^{0}_{1}\mathrm{H}^{1},\ \text{with diamagnetic correction}) = +2.79255 \pm 0.00010\ \text{n.m.} \]

All the other values of \(\mu\) in the table have been obtained from their ratios to \(\mu({}^{0}_{1}\mathrm{H}^{1}\), without correction), and if the value adopted for \(\mu({}^{0}_{1}\mathrm{H}^{1})\) is changed, then all the other quantities in the 6th column must be changed correspondingly.

B. Ratio of the moments of the deuteron and the proton

Of all the ratios between nuclear magnetic moments, the most thoroughly studied is the ratio between the moments of the deuteron and the proton. In view of the special interest shown in this ratio, we shall consider it in greater detail. Although the abundance and accuracy of the available data are far from typical, the averaging operation described below may be regarded as a characteristic method for obtaining values of \(\mu\) for the table.

For the reasons discussed below (Section III C.2), only measurements by the nuclear-resonance method were used for calculating \(\mu({}^{0}_{1}\mathrm{H}^{2})\). The results are given in Table II (see p. 414). In the absence of sufficient information, the weight of each measurement, indicated in the last column of Table II, was taken inversely proportional to the errors stated by the corresponding author. The mean value is \(0.3070150\); as the uncertainty (see Section III D) we adopt the value \(0.000003\), which is greater than the uncertainties indicated in most individual determinations (this was done with

for the purpose of covering the inaccuracies of all determinations). Bitter (see B 150) recommends taking the errors (inaccuracies) to be three times larger than here. In view of certain physical considerations indicated in Section III, it does not seem expedient to estimate the error in greater detail.

Table II

RATIO OF THE DEUTERON AND PROTON MOMENTS

The measurements B I 47 and W J 49 were performed in one laboratory, as were also the measurements S N 49 and L M 50. In the latter group of experiments, an especially high field homogeneity of the order of \(10^{-5}\) was achieved.

It would be premature to discard any values from Table II, since different chemical compounds were studied. Moreover, in view of the “chemical effect” (see Section III C. 2) and the appreciable difference in the physical and chemical

properties between light and heavy hydrogen, in principle objections may arise against comparing uncorrected deuteron-proton ratios obtained for different chemical samples. And indeed, Lindström showed in LM50 that two investigated compounds gave a difference in the ratio equal to \((7 \pm 3)\cdot 10^{-6}\). In gaseous samples, where the correction can be calculated, the ratio \(\mu(\mathrm{H}^2)/\mu(\mathrm{H}^1)\) needs a new determination.

Recently the study of deuteron and proton moments and, especially, their ratio has begun on the basis of new methods \(^{16-18}\).

C. Corrections

At present the moments are calculated with such great accuracy that discussion of certain small corrections becomes inevitable.

For the purpose of understanding the following arguments it is necessary to remember that, in contrast to nuclear-resonance methods, magnetic-resonance methods with atomic and molecular beams, the method of microwave absorption, and the method of hyperfine structure in optical line spectra are based, in essence, on measurements of hyperfine structure, i.e. on the measurement of the energy difference between the two lowest levels, from which the magnetic dipole moment of the nucleus can be approximately calculated \(^{19-25}\). In discussing corrections it is convenient to consider together all methods falling into the category of hyperfine-structure measurements. Below in this article they will all be called hyperfine-structure methods. In the table itself the moments obtained by nuclear-resonance methods are distinguished from those obtained by hyperfine-structure methods in the following way. A value obtained by the nuclear-resonance method is always accompanied by an indication of the error following the sign \(\pm\) without special symbols; values obtained by hyperfine-structure methods are either given without an indication of error, or are marked after the error by the letter \(h\). Values entered in the table are given without corrections, except for the diamagnetic correction. Values obtained by hyperfine-structure methods are indicated only for the convenience of readers wishing to apply other corrections (Section III C. 3—6).

Among the data suitable for calculations of nuclear dipole moments, measurements of most well-known samples were carried out, on the one hand, by methods of nuclear induction or nuclear resonance and, on the other hand, by methods of magnetic resonance of atomic or molecular beams (the hyperfine-structure method). But in each case of application of both measurement methods

by the method of nuclear resonance or nuclear induction give higher accuracy. In those cases where measurements of both types are available, in order to avoid confusion I completely neglect hyperfine-structure methods. In doing so, in principle one has to neglect some independent data, but the relatively small weight of these data, together with possible inaccuracies in the corrections, led me to take this course.

C. 1. Diamagnetic correction

The diamagnetic correction is the correction for the interaction between the nuclei and the diamagnetic moment of the atomic electrons. The diamagnetic interaction has the same effect on the measurement of the nuclear moment as if the nuclear moment (the true one, as opposed to the observed one) were multiplied by a coefficient equal to unity minus a quantity approximately proportional to the atomic number to the power \(4/3\). This correction reduces to dividing the observed nuclear \(g\)-factor by \(1 - DZ^{4/3}\), where \(D\) in the Fermi–Thomas model is \(3.19 \cdot 10^{-5}\). In the more exact Hartree model \(D\) is somewhat smaller and is a slowly increasing function of \(Z\), which was calculated by Lamb\(^{26}\). Ramsey (Phys. Rev. 77, 567 (1950)) pointed out that neither Lamb’s diamagnetic correction coefficient (see \(^{26}\), formula (6)), equal for hydrogen to 0.9999822, nor Anderson’s\(^{AN48}\) helium-like approximation, giving the coefficient 0.9999676, is suitable in the case of experiments with molecules. Ramsey proposes a theoretical coefficient, taking into account the spin-rotational interaction of the molecule and equal for \(H_2\) gas to 0.9999729. Unfortunately, up to the present time the experiments have been performed only with other substances (see Table II), although one was made with \(H_2\) gas\(^{HP50}\). The important but difficult case of the “boomerang-shaped” water molecule has not yet been considered. Thus, at the present time the chief significance of Ramsey’s remark lies in the warning against expecting too high an accuracy when applying diamagnetic corrections. In the present article Anderson’s value is used for helium, and a value approximately the same as Ramsey’s for hydrogen. The remaining values are taken from Lamb’s article\(^{26}\) or obtained by means of linear interpolation (for \(_{81}\mathrm{Tl}\) and \(_{82}\mathrm{Pb}\) the values are extrapolated from \(_{74}\mathrm{W}\) and \(_{80}\mathrm{Hg}\)). The notation in parentheses indicates that the diamagnetically corrected value was taken from PR\(^{50}\). Interpolation over the wide interval between \(Z = 1\) and \(Z = 19\) is, undoubtedly, a crude procedure, but it leads to corrections that are small in comparison with the corrections for heavier atoms. Throughout the table, for the sake of uniformity, the correction is sometimes given to a greater number of places than is justified by our knowledge of its magnitude.

Table c

Diatomic corrections used in Table I

Table c (Continued)

Table c (Continued)

Table c (Conclusion)

According to Lamb, the diamagnetic correction is applicable in measurements by the hyperfine-structure method and is usually also applied in all measurements of $\mu$ in atoms, i.e., in nuclei surrounded by electrons, regardless of the method by which this moment is measured. Whereas the effect itself depends on the degree of ionization of the atom, the correction is usually regarded only as a function of $Z$, i.e., it is introduced under the assumption that all atoms are neutral.

C. 2. Chemical Effects

In recent papers devoted to the most accurate measurements, there are a number of indications of lines of unusual shape and, in particular, of asymmetry of some singlet lines. The extensive literature devoted to relaxation time will not be discussed here.

will not be. The question arises whether the nature of the chemical compound can influence the nuclear-resonance frequency (see, for example, SN49). Peake discoveredPA48 a doubling of the proton resonance in crystals, while Knight foundKG49 that the nuclear frequency in a metal is several tens of percent higher than the frequency of the same nucleus in a salt. Quite recently some asymmetric lines were resolved into groups, and workers in several laboratories independently arrived at the conviction that this effect arises not from imperfections of the apparatus, but is connected with the nature of the chemical bonding of the atoms whose nuclei are being observed (see BL50, XX50, BJ50). The splittings discovered so far have relative values from \(10^{-5}\) to \(5 \cdot 10^{-3}\) and, at least in first approximation, are proportional to the strength of the external field. The largest of the indicated values was found (see PR50) in \(N\): an aqueous solution of \(\mathrm{NH_4NO_3}\) gives two signals separated by 5.3 gauss at a field strength of \(1.05 \cdot 10^4\) gauss, and experiments with other compounds show that the ammonium group gives values for \(\mu_r(N)\) higher than the nitrate group*). Ramsey emphasizes that separating the chemical effect from the diamagnetic one is artificial. A higher-order chemical effect, the dependence of the ratio of the resonance frequencies of two isotopes of one and the same element on the chemical compound, appears in the data of LM50 (see the last two lines in Table II).

C.3. Radiation correction

The introduction of the radiation correction is necessary because the mass of the electron depends on the field in which it is located. Schwinger^27 and Luttinger^28 eliminated the observed discrepancy between the ratio of hyperfine-structure splitting and the ratio of magnetic dipole moments for the isotopes of hydrogen and some—

*) Because of the presence of the chemical effect, it is important to indicate the compounds on which the measurements were made. In the case of the measurements indicated in PR50, the following compounds were used, predominantly in the form of aqueous solutions:

\[ {}_{7}\mathrm{N}^{14}:\mathrm{HNO_3} \qquad {}_{48}\mathrm{Cd}:\mathrm{CdCl_2} \]

\[ {}_{7}\mathrm{N}^{15}:\mathrm{NH_3} \qquad {}_{50}\mathrm{Sn}:\mathrm{SnCl_2} \]

\[ {}_{17}\mathrm{Cl}:\mathrm{HCl} \qquad {}_{78}\mathrm{Pt}:\mathrm{H_2PtCl_6} \]

\[ {}_{23}\mathrm{V}:\mathrm{NaVO_3} \qquad {}_{80}\mathrm{Hg}:\mathrm{HgNO_3} \]

\[ {}_{25}\mathrm{Mn}:\mathrm{LiMnO_4},\ \mathrm{KMnO_4} \qquad {}_{81}\mathrm{Tl}:\mathrm{Tl(C_2H_3O_2)} \]

\[ {}_{27}\mathrm{Co}:\mathrm{K_3Co(CN)_6} \qquad {}_{82}\mathrm{Pb}:\mathrm{Pb(C_2H_3O_2)_2} \]

other elements \(^{29-31}\)*) by introducing into the magnetic moment associated with the electron spin the radiative correction \((1+\alpha/2\pi)=1.001162\). Here \(\alpha\) is the fine-structure constant, approximately equal to \(1/137\). Division by this factor of the magnitude of the hyperfine splitting, which is determined by the interaction between the nucleus and the magnetic moment of the extranuclear electrons, should, according to the interpretation, make this magnitude compatible with the values obtained by nuclear-resonance methods.

C. 4. Relativistic effects

An electron moving rapidly in a force field has, owing to relativistic effects, a slightly different moment, which leads to some change in the hyperfine structure of the atom. The question of the magnetic moment of a heavy atom was discussed by Breit \(^{32}\). Margenau \(^{33}\) found a correction associated with the rapid motion of charged particles in a central field. This correction for an \(S\)-electron is equal to

\[ \left(1-\frac{Z_0^2\alpha^2}{3n_{\mathrm{eff}}^2}\right), \]

where \(-Z_0^2/n_{\mathrm{eff}}^2\) is the ionization potential of the atom in Rydberg units. This effect in typical cases has a relative magnitude of the order of \(10^{-5}\). The values of the corrections for individual non-\(S\)-electrons may be found in Margenau.

C. 5. Reduced-mass effect

Breit and his collaborators \(^{34-35}\) showed that the motion of the nucleus gives a contribution to the hyperfine structure of order \(\left(1+\frac{m}{M}\right)^{-3}\), which quantitatively corresponds to \(10^{-8}\) of the fine structure of hydrogen. Here \(m\) and \(M\) are, respectively, the masses of the electron and the nucleus. The introduction of the factor \(\left(1+\frac{m}{M}\right)^{-3}\) in application to isotope pairs of heavier atoms, although formal and not justified, has come into use and helps to reconcile measurements of hyperfine structure with measurements by nuclear-resonance methods. The factor \(\left(1+\frac{m}{M}\right)^{-3}\) gives a correction of \(8\cdot10^{-4}\) between \(\mathrm{H}^1\) and \(\mathrm{H}^2\), a correction of \(4\cdot10^{-4}\) between \(\mathrm{Li}^6\) and \(\mathrm{Li}^7\), and a correction of \(2\cdot10^{-6}\) between \(\mathrm{K}^{39}\) and \(\mathrm{K}^{41}\).

*) The corresponding measurements were carried out for the following elements:

C. 6. Effects of the size and structure of the nucleus.

Rosenthal and Breit \(^{36}\) found that the energy levels of an atom depend appreciably on the dimensions of the nucleus, even when the nucleus is spherically symmetric. In contrast to this size effect, which is significant mainly for heavy nuclei, Bohr \(^{37}\) drew attention to a structural effect which may also be significant for light nuclei. This effect is connected with the spatial distribution of the nuclear magnetic moment and depends on how this moment is distributed among the nuclear particles. For Rb, two odd isotopes, \({}^{50}_{37}\mathrm{Rb}^{87}\) and \({}^{52}_{37}\mathrm{Rb}^{89}\), have ground states with different spins, and there are indications of the presence of a closed shell \(^{38—40}\). For this case, Bitter \(^{41}\) calls attention to the existence of an anomaly in the hyperfine structure, despite the fact that here an explanation of this anomaly by the size effect is highly improbable. It is thereby emphasized that the structural effect, i.e. the distribution of the moment, exerts an influence at least comparable with the size effect. In rubidium the magnitude of the anomaly is of the order of \(3 \cdot 10^{-3}\).

D. Errors in the values of \(\mu\)

The magnitude of the error indicated in Table I for each dipole moment is by no means the total error in determining the value of \(\mu\). Usually this error coincides with that given by the author, but in those cases where the data of different authors differ beyond the limits of the errors, the value of the error in the table has been increased. The increases in the errors made are small, except for the case of \(\mathrm{Be}^{9}\), where an error of \(\pm 8 \cdot 10^{-4}\) is given, although one of the two authors gave a value equal to about \(1/50\) of this quantity. No systematic errors have been taken into account in the table and, in particular, although the diamagnetic correction was introduced according to Section III C. 1, other effects (Section III C. 2—III C. 6) were not taken into consideration. At present, for the best measurements, a relative error of less than \(10^{-3}\) can hardly be accepted with confidence solely because of the presence of one chemical effect. In cases where a quantity is given without an indication of the error, it may probably be considered correct to the last digit.

For two quantities marked by braces with the sign \(r\) at the top of the brace, the ratio is known better than the individual values themselves; this ratio can usually be found in the reference common to both quantities, and always in the reference given at least for one of the quantities. In the case of Hg, when the brace is given without the sign \(r\), the ratio was used to determine the moment of one of the isotopes. The sign \(r > 0\) in the case of Ir means that the moments have the same sign.

IV. QUADRUPOLE MOMENT \(Q\)

The values of the quadrupole moments indicated in the table can hardly be regarded as anything other than approximate, although some of them are given with errors of the order of one percent.

In those cases where the ratio of quadrupole moments is known, parentheses and the symbol \(r\) are used analogously to the way this was done for the moment \(\mu\).

The proofs for the existence of octupole and magnetic quadrupole moments are not convincing (see BG48, DJ49s), despite certain contrary assertions by Tolansky2.

V. LITERATURE

The literature indicated in the table is not complete. However, at least the first paper in which the value of the “correct” spin was published is cited. A sufficient number of recent papers are also given. In the main, references to literature concerning spin moments are not given in italics, and papers giving manifestly erroneous spin values are not indicated. Literature concerning dipole and quadrupole moments is given in italics in those cases when it contains values that appear preferable.

References marked with the index \(c\) indicate the use of the corresponding paper in calculating the moment, although the paper itself does not contain the value of the moment.

LITERATURE FOR THE EXPLANATIONS TO THE TABLE

1. L. Pauling and S. Goudsmit, The Structure of Line Spectra (1930).
2. K. Murakawa, Sci Pap. Tokyo JPCR 17, 6 (1931).
3. H. Kallman and H. Schüler, Ergeb. d. exakt. Naturwiss. 11, 134 (1932).
4. E. Marx, Handbuch der Radiologie (Leipzig, 1933).
5. H. E. White, Introduction to Atomic Spectra (New York, 1934).
6. See SH35, in Table I (only quadrupole moments).
7. H. A. Bethe and R. F. Bacher, Rev. Mod. Phys. 8, 82 (1936).
8. G. Herzberg, Atomic Spectra and Atomic Structure (New York, 1937).
9. R. Gregoire, Tables Annuelles des Constantes, etc., Physique Nucléaire (Paris, 1938), No. 26.
10. See SH38, in Table I (only quadrupole moments).
11. J. Mattauch and S. Flügge, Nuclear Physics Tables, 1941 (New York, 1946), English translation.
12. W. F. Meggers, J. Opt. Soc. Am. 36, 431 (1946).
13. H. H. Goldsmith and D. Inglis, Brookhaven report BNL—1—5 (1948).
14. H. L. Poss, Brookhaven report BNL26 (T.—10) (1949).
15. M. Rose and H. A. Bethe, Phys. Rev. 61, 205; correction, p. 993 (1937).
16. J. M. Luttinger, Helv. Phys. Acta 21, 483 (1948); Phys. Rev. 75, 309 (1949); 75, 1277 (1949).

1. M. Slotnick and W. Heitler, Phys. Rev. 75, 1645 (1949).
2. K. M. Case, Phys. Rev. 76, 1 (1949).
3. S. Goudsmit and R. F. Bacher, Phys. Rev. 34, 1501 (1929).
4. S. Goudsmit, Phys. Rev. 43, 636 (1933).
5. See GU31.
6. G. Racah, Zeits. f. Physik 71, 431 (1931).
7. G. Breit and L. A. Wills, Phys. Rev. 44, 470 (1933).
8. E. Fermi and E. Segrè, Zeits. f. Physik 82, 729 (1933).
9. M. F. Crawford, Phys. Rev. 47, 768 (1935); M. F. Crawford and L. A. Wills, Phys. Rev. 48, 69 (1935); M. F. Crawford and A. L. Schawlow, Phys. Rev. 76, 1310 (1949).
10. W. E. Lamb, Phys. Rev. 60, 817 (1941).
11. J. Schwinger, Phys. Rev. 73, 416 (1948); 76, 790 (1949).
12. J. M. Luttinger, Phys. Rev. 74, 893 (1948).
13. Nafe, Nelson and Rabi, Phys. Rev. 71, 914 (1947); J. E. Nafe and E. B. Nelson, Phys. Rev. 73, 718 (1948).
14. Nagle, Julian and Zacharias, Phys. Rev. 72, 971 (1947).
15. P. Kusch and H. M. Foley, Phys. Rev. 72, 1256 (1947); H. M. Foley and P. Kusch, 73, 412 (1928). Calculations to accuracy \(x^3\) give the value \(\left(1+\dfrac{a}{2\pi}-\dfrac{2.97a^2}{\pi^2}\right)=1.001147\). (R. Karplus and N. M. Kroll, Phys. Rev. 77, 536 (1950)).
16. G. Breit, Nature 122, 649 (1928).
17. H. Margenau, Phys. Rev. 57, 383 (1940).
18. G. Breit and R. E. Meyerott, Phys. Rev. 72, 1023 (1947); 75, 1447 (1949).
19. G. Breit and G. E. Brown, Phys. Rev. 74, 1278 (1948); Breit, Brown and Arfken, Phys. Rev. 76, 1299 (1949).
20. J. E. Rosental and G. Breit, Phys. Rev. 41, 459 (1932).
21. A. Bohr, V. F. Weisskopf, Phys. Rev. 77, 94 (1950).
22. M. G. Mayer, Phys. Rev. 74, 235 (1948); 75, 1969 (1949).
23. E. P. Wigner and E. Feenberg, Reports on Progress in Physics, London 8, 274 (1942); E. Feenberg and K. C. Hammack, Phys. Rev. 75, 1877 (1949); Feenberg, Hammack and Nordheim, Phys. Rev. 75, 1968 (1949).
24. L. W. Nordheim, Phys. Rev. 75, 1894 (1949).
25. F. Bitter, Phys. Rev. 76, 150 (1949).
26. S. Tolansky, Proc. Roy. Soc. London A170, 205 (1939).

Literature for Table I

Literature for Table I (Continued)

J. E. Mack

Literature for Table I (continued)

TABLE OF NUCLEAR MOMENTS

Literature for Table I (Continued)

J. E. Mack

Literature for Table I (continued)

Literature for Table I (Continued)

Literature for Table I (Continued)

Literature for Table I (Continued)

Literature for Table I (continued)

TABLE OF NUCLEAR MOMENTS

Literature for Table I (continued)

J. E. MACK

Literature to Table I (Conclusion)