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From Current Literature
Nuclear Masses in the Region of Mass Number 40
In the paper under review¹, measurements were made of a number of doublets with a double-focusing mass spectrometer; these made it possible to determine the masses of atoms with mass numbers close to 40 and the masses of H¹ and C¹². Table I gives the mean values of the doublets measured for this purpose.
Table I
Doublets for measuring the masses of light atoms
| Doublet | Number of measurements | Mean value in \(10^{-4}\) atomic mass units |
|---|---|---|
| \(C_4 — SO\) | 5 | \(331,32 \pm 0,13\) |
| \(O_2 — S\) | 6 | \(177,64 \pm 0,07\) |
| \(C_3H_8 — CO_2\) | 6 | \(728,54 \pm 0,15\) |
| \(C_4 — S^{33}O\) | 4 | \(413,85 \pm 0,46\) |
| \(C_4H_2 — S^{34}O\) | 5 | \(529,00 \pm 0,40\) |
| \(C_3 — HCl^{35}\) | 5 | \(233,41 \pm 0,44\) |
| \(C_3H_2 — HCl^{37}\) | 5 | \(420,14 \pm 0,46\) |
| \(C_3 — A^{36}\) | 4 | \(325,01 \pm 0,33\) |
| \(H_2O — A^{36}/2\) | 6 | \(268,19 \pm 0,28\) |
| \(C_3H_2 — A^{38}\) | 5 | \(529,10 \pm 0,40\) |
| \(C_3H_3 — K^{39}\) | 6 | \(599,05 \pm 0,26\) |
| \(C_3H_5 — K^{41}\) | 5 | \(773,61 \pm 0,33\) |
| \(C_3H_6 — Ca^{42}\) | 3 | \(882,47 \pm 0,34\) |
| \(C_3H_7 — Ca^{43}\) | 4 | \(960,40 \pm 0,52\) |
| \(CO_2 — Ca^{44}\) | 7 | \(346,07 \pm 0,59\) |
| \(C_4 — Ca^{48}\) | 5 | \(475,90 \pm 1,0\) |
| \(C_2O_2H_5 — Sc^{45}O\) | 4 | \(783,17 \pm 0,41\) |
These doublet values lead to the following values for the masses of the atoms of hydrogen and carbon:
\[ \mathrm{H}^{1} - 1.008146(\pm 3), \]
\[ \mathrm{C}^{12} - 12.003842(\pm 4). \]
The calculation of the masses of the remaining atoms listed in Table II was carried out
Table II
Masses of atoms from sulfur to scandium, measured mass-spectrographically
| Isotope | $\mathrm{H}^{1}\ 1.008142 \pm 3$ $\mathrm{C}^{12}\ 12.003804 \pm 17$ |
$\mathrm{H}^{1}\ 1.008146 \pm 3$ $\mathrm{C}^{12}\ 12.003842 \pm 4$ |
|---|---|---|
| $\mathrm{S}^{32}$ | $31.982236 \pm 7$ | $31.982236 \pm 7$ |
| $\mathrm{S}^{33}$ | $32.98197 \pm 8$ | $32.98213 \pm 5$ |
| $\mathrm{S}^{34}$ | $33.97860 \pm 8$ | $33.97876 \pm 5$ |
| $\mathrm{Cl}^{35}$ | $34.97993 \pm 7$ | $34.98004 \pm 5$ |
| $\mathrm{Cl}^{37}$ | $36.97754 \pm 7$ | $36.97766 \pm 5$ |
| $\mathrm{A}^{36}$ | $35.97892 \pm 4^{a}$ | $35.97900 \pm 3^{a}$ |
| $\mathrm{A}^{38}$ | $37.97479 \pm 7$ | $37.97491 \pm 4$ |
| $^{40}$ | $39.97502 \pm 4^{b}$ | $39.97513 \pm 3^{b}$ |
| $\mathrm{K}^{39}$ | $38.97593 \pm 6$ | $38.97606 \pm 3$ |
| $\mathrm{K}^{41}$ | $40.97476 \pm 6$ | $40.97490 \pm 4$ |
| $\mathrm{Ca}^{40}$ | $39.97534 \pm 9^{c}$ | $39.97545 \pm 9^{c}$ |
| $\mathrm{Ca}^{42}$ | $41.97202 \pm 6$ | $41.97216 \pm 4$ |
| $\mathrm{Ca}^{43}$ | $42.97237 \pm 8$ | $42.97251 \pm 6$ |
| $\mathrm{Ca}^{44}$ | $43.96920 \pm 6$ | $43.96924 \pm 6$ |
| $\mathrm{Ca}^{48}$ | $47.96763 \pm 12$ | $47.96778 \pm 10$ |
| $\mathrm{Sc}^{45}$ | $44.97000 \pm 6$ | $44.97010 \pm 5$ |
a — weighted mean of two doublets of $\mathrm{A}^{36}$;
b — weighted mean of the doublets $\mathrm{C}_{3}\mathrm{H}_{4} - \mathrm{A}^{40}$, $\mathrm{D}_{2}\mathrm{O} - \mathrm{A}^{40}/2$, $\mathrm{Ne}^{20} - \mathrm{A}^{40}/2$ and $\mathrm{D}_{2}\mathrm{O} - \mathrm{Ne}^{20}$ (4);
c — from the doublet $\mathrm{Ca}^{40} - \mathrm{A}^{40} = 3.2 \pm 0.8$.
by two methods: from these values of the masses of $\mathrm{H}^{1}$ and $\mathrm{C}^{12}$ (third column of Table II) and from the mass values calculated from the energies of nuclear reactions in the work of Li and coauthors$^{2}$ (second column of Table II); the errors are expressed in units of the last decimal place. Table III gives a comparison of the differences of the measured masses with the same differences calculated from nuclear reactions. The agreement of the data is satisfactory.
From Current Literature
Table III
Comparison with certain nuclear reactions
| From Table II (atomic mass units) |
From nuclear reactions (atomic mass units) |
Reactions used | |
|---|---|---|---|
| \(S^{33} - S^{32}\) | \(0,99989 \pm 5\) | \(0,9970 \pm 2\) | \(S^{32}\ (d,p)\ S^{33}\) |
| \(Cl^{37} - A^{36}\) | \(0,99866 \pm 6\) | \(0,99864 \pm 3\) | \(Cl^{37}\ (pn)\ A^{37}\) \(A^{36}\ (dp)\ A^{37}\) |
| \(A^{38} - Cl^{37}\) | \(0,99725 \pm 6\) | \(0,99705\) | \(Cl^{37}\ (n\gamma)\ Cl^{38}\) \(Cl^{38}\ (\beta)\ A^{38}\) |
| \(Ca^{42} - K^{41}\) | \(0,99726 \pm 6\) | \(0,99720\) | \(K^{41}\ (n\gamma)\ K^{42}\) \(K^{42}\ (\beta)\ Ca^{42}\) |
An attempt has been made to compare the mass values obtained from experiment with the theoretically calculated masses, using the semiempirical formula (see, for example, \(^{8}\)). This comparison is presented graphically in the figure.
[Figure: vertical axis — “packing coefficient \(\times 10^{-4}\)”; horizontal axis — “mass number.” The plotted mass-number range is approximately \(32\) to \(48\), with labels for elements \(S\), \(Cl\), \(A\), \(K\), \(Ca\), \(Sc\).]
The dashed line represents the curve constructed from points calculated by the semiempirical mass formula. The solid curve connects the experimental points (from the last column of Table II). The agreement is very good—one curve repeats the oscillations of the other. Deviations occur only at mass numbers 40 and 48.
V. Kravtsov
References
- T. Collins, A. Nier and W. Johnson Jr., Phys. Rev. 84, 717 (1951).
- UFZh 46 (1952).
- E. Fermi, Nuclear Physics. IL, 1951, pp. 13–16.
- A. Nier and T. Roberts, Phys. Rev. 81, 507 (1951).