Full Text
MASSES OF LIGHT ATOMS CALCULATED FROM NUCLEAR REACTION ENERGIES
Until now, the masses of light atoms have been calculated using both data from measurements of the energy balance \(Q\) of nuclear reactions and mass-spectrographic measurements; see, for example, \(^{1}\). Thanks to the large number of well-measured nuclear-reaction energies, the referenced work \(^{2}\) carried out a calculation of the masses of light atoms directly from the mass of the atom of the isotope \(O^{16}\), without using mass-spectrographic data. In this work all the newest and most precise measurements of nuclear-reaction energies for light nuclei \(A \le 20\) were collected. From some reactions closed cycles can be formed, which makes it possible to calculate atomic masses in different ways. Since different results may be obtained in this way, it was first necessary to perform an “adjustment” of all the experimental data. In closing the cycles it turned out that the use of some measurements leads to the result that the sum of the energies around the cycle differs from zero by an amount exceeding the error. These measurements were rejected as erroneous. In those cases where the cycles gave deviations from zero within the limits of error, an adjustment of all the energies was performed. The energy adjustment was carried out by the method of least squares, taking into account all the individual experimental data. In doing so, the errors of the adjusted values were also calculated. The adjustment of reaction energies over the whole region of light nuclei led to the result that, after it, the value of the calculated masses no longer depended on the order of the calculations. From the adjusted reaction energies the masses of light atoms were calculated from the mass of the oxygen isotope \(O^{16}\), taken, by convention, to be equal to \(16,000\,000\) atomic mass units (physical scale). The results of these calculations are given in the table. In the first
Table of atomic masses
| Symbol of atom | Mass number \(A\) | Mass defect \(M - A\) (MeV) | Atomic masses \(M\) from nuclear data (in atomic mass units) | Atomic masses \(M\) from mass spectroscopy |
|---|---|---|---|---|
| n | 1 | 8,3638 ± 0,0029 | 1,008 982 (±3) | — |
| H | 1 | 7,5815 ± 0,0027 | 1,008 142 (±3) | 1,008 165 (±4) |
| H | 2 | 13,7203 ± 0,006 | 2,014 735 (±6) | 2,014 778 (±8) |
| H | 3 | 15,8271 ± 0,010 | 3,016 997 (±11) | — |
(Continuation)
| Atomic symbol | Mass number $A$ | Mass defect $M-A$ (MeV) | Atomic masses $M$ from nuclear data (in atomic mass units) | Atomic masses $M$ from mass spectroscopy |
|---|---|---|---|---|
| He | 3 | 15,8086 ± 0,010 | 3,016 977 (±11) | — |
| He | 4 | 3,6066 ± 0,014 | 4,003 873 (±15) | 4,003 944 (±19) |
| He | 6 | 19,065 ± 0,025 | 6,020 474 (±27) | — |
| Li | 6 | 15,850 ± 0,021 | 6,017 021 (±22) | — |
| Li | 7 | 16,969 ± 0,024 | 7,018 223 (±26) | — |
| Li | 8 | 23,296 ± 0,028 | 8,025 018 (±30) | — |
| Be | 7 | 17,832 ± 0,024 | 7,019 150 (±26) | — |
| Be | 8 | 7,309 ± 0,027 | 8,007 850 (±29) | — |
| Be | 9 | 14,007 ± 0,028 | 9,015 043 (±30) | — |
| Be | 10 | 15,560 ± 0,026 | 10,016 711 (±28) | — |
| B | 9 | 15,076 ± 0,029 | 9,016 190 (±31) | — |
| B | 10 | 15,004 ± 0,026 | 10,016 114 (±28) | — |
| B | 11 | 11,909 ± 0,022 | 11,012 789 (±23) | — |
| B | 12 | 16,912 ± 0,020 | 12,018 162 (±22) | — |
| C | 11 | 13,889 ± 0,022 | 11,014 916 (±24) | — |
| C | 12 | 3,542 ± 0,015 | 12,003 804 (±17) | 12,003 842 (±6) |
| C | 13 | 6,958 ± 0,013 | 13,007 473 (±14) | — |
| C | 14 | 7,153 ± 0,010 | 14,007 682 (±11) | — |
| N | 13 | 9,179 ± 0,013 | 13,009 858 (±14) | — |
| N | 14 | 6,998 ± 0,010 | 14,007 515 (±11) | 14,007 564 (±7) |
| N | 15 | 4,528 ± 0,011 | 15,004 863 (±12) | — |
| O | 15 | 7,233 ± 0,012 | 15,007 768 (±13) | — |
| O | 16 | — | 16,000 000 (by convention) | — |
| O | 17 | 4,221 ± 0,006 | 17,004 533 (±7) | — |
| F | 17 | 6,970 ± 0,011 | 17,007 486 (±11) | — |
| F | 19 | 4,149 ± 0,014 | 19,004 456 (±15) | — |
| F | 20 | 5,914 ± 0,017 | 20,006 352 (±19) | — |
In the second column of the table the symbol of the atom and the mass number are given. In the third column the mass defect is given, i.e., the difference between the true mass of the atom and its mass number, expressed in megaelectron-volts. In the fourth column the masses of atoms calculated from nuclear-reaction energies and expressed in atomic mass units (amu) (physical scale) are listed. In doing so it was assumed³ that \(1\) amu \(= 931.152\) MeV. In the fifth (last) column, for comparison, the latest mass-spectrographic data, taken from Nier’s work⁴, are given. The errors in the fourth and fifth columns, given in parentheses, are expressed in units of the last significant digit of the mass values.
As is evident from the table, the mass-spectrographic data are everywhere larger than the masses calculated from nuclear-reaction energies by amounts exceeding the errors. Owing to the mutual dependence of all the values of reaction energies, linked by cycles, they cannot be adjusted independently so that, without violating the closures, the mass values obtained from nuclear data could be brought closer to the mass-spectrographic values. The authors of the work under review indicate that only further, more precise measurements both of nuclear-reaction energies and of mass spectra can bring together the mass values obtained by the different methods.
V. Kravtsov
References
- A. Tollestrup, W. Fowler and C. Lauritsen, Phys. Rev. 78, 372 (1950).
- C. Li, W. Whaling, W. Fowler and C. Lauritsen, Phys. Rev. 83, 512 (1951).
- UFN 45, 458 (1951).
- A. Nier, Phys. Rev. 81, 624 (1950).