The AME 2020 atomic mass evaluation (II). Tables, graphs and references

In this paper, tables with numerical values and graphs derived from the evaluation of the input data given in Part I [1] are presented.

Firstly, we present a table that contains the values of atomic masses and their uncertainties (Table I), followed by a table containing the influences for primary nuclides (Table II) and a table of twelve reaction and decay energies (Table III).

The tabular information is followed by a series of graphs that include the two-neutron separation energies and total $ \alpha $-decay energies as a function of the neutron number, and the two-proton separation energies as a function of the proton number.

Finally, references of the input data used in the Ame 2020 [1] and the Nubase 2020 [2] evaluations are given at the end of this article.

Table I presents the atomic masses expressed as mass excess in keV, together with the binding energy per nucleon, the beta-decay energy and the total atomic mass in the unified atomic mass unit, similar to those published in the earlier AME editions [3-9]. Traditionally, the masses of nuclides are measured for electrically neutral atoms or single-charged ions. At present, the highest precision masses are measured using Penning traps for a single-charged ion. This is the main reason why atomic masses, rather than nuclear masses, are presented in the Ame.

In general, the nuclear masses $ M_N $ can be calculated from the atomic ones $ M_A $ as:

where $ B_{e} $(Z) is the electron binding energy. The ionization energy is generally (much) smaller than the uncertainty of the mass and, for a small number of very precise mass measurements, corrections for the first- and second-ionization potentials can be applied without much loss of accuracy. The same is true for the electron mass, $ m_e $; see Table A in Part I [1].

Nowadays, several mass measurements are conducted with fully or almost fully ionized atoms. In such cases, a correction must be made for the total binding energy of all the removed electrons $ B_e(Z) $. Unfortunately, the precision of the calculated $ B_e (Z) $ values is not well established, since this quantity (approximately 760 keV for $ _{92}{\rm{U}} $) cannot be easily measured. However, we can state with a high confidence that the precision for $ _{92} {\rm{U}}$ is better compared to that for the best known masses of the uranium isotopes, which is about 1.1 keV. An approximate formula for $ B_{e} $ can be found in the review of Lunney, Pearson and Thibault [10]:

The atomic masses are given in mass units and the derived quantities in energy units. For the atomic mass unit we use the “unified atomic mass unit”, symbol “u”, defined as 1/12 of the atomic mass of one $ ^{12} {\rm{C}}$ atom in its electronic and nuclear ground states and in its rest coordinate system. The energy values are expressed as electron-volt, using the international volt V (see discussion in Part I, Section 2).

Due to the dramatic increase in the mass accuracy for some light nuclides, the printing format of the mass table is not adequate for the most precisely known masses, which require additional digits. Table A gives mass excess and atomic mass values for 16 nuclides, whose masses are known with the highest precision, with an uncertainty below 1 eV.

Table II lists all primary nuclides, together with the main data that contribute to their mass determination (up to the three most important ones) and the influences of these data on their masses. It complements the information given in the main table (Part I, Table I) where the significance (total flux) and the main flux of each datum are displayed. In other words, the flow-of-information matrix $ {\bf F} $, defined in Part I, Section 4.3, is (partly) displayed once along lines and once along columns.

The linear combinations involving neighboring nuclides with small differences in atomic number and mass number, and particles such as n, p, d, t, $ ^3 {\rm{He}}$ and $ \alpha $, are important for studies of the trends in the nuclear energy surface and for Q-values of frequently used reactions and decays. In Table III, values for 12 such combinations and their uncertainties are presented.

With the help of the instructions given in the explanation of Table III, values for 28 additional reactions and their uncertainties can be derived. The derived values will be correct, but in a few cases (when reactions involving light nuclei measured with very high precision) the uncertainties will be slightly larger than those obtained when correlations are taken into account.

In cases where any combination of the most precise mass values are involved, the uncertainties can be obtained with the help of the correlation coefficients given in Table B, where the variances and covariances for the most precisely known light nuclei are listed. As an example, if one considers the mass difference between $ ^3 {\rm{H}}$ and $ ^3 {\rm{He}}$, it can be easily obtained from the values listed in Table A. However, the corresponding uncertainty cannot be simply determined from the square root of the quadratic sum of the individual uncertainties, which would be:

Since there is a strong correlation between these two nuclides, the uncertainty of the mass difference should be calculated using the correlation information provided in Table B. Thus, its uncertainty can be obtained from the square root of the sum of the variances minus twice the covariance:

As a result, the final uncertainty is smaller when the correlations are taken into account.

For all other cases, the correlation coefficients are made available at the AMDC websites [11].

All the information contained in the mass table (Table I) and in the nuclear reaction and separation energy table (Table III) can be displayed in plots of the binding energy (or mass) versus Z, N, or A. The atomic mass surface as a function of Z and N splits into four sheets due to the pairing energy, as discussed in Ref. [3]. The even-even sheet lies lowest, the odd-odd highest, and the other two nearly halfway in-between. These sheets are nearly parallel almost everywhere in this three-dimensional space and have remarkably regular trends, as one may convince oneself by making various cuts (e.g. Z or N or A constant). Any derivative of the binding energies also defines four sheets. In this context, derivative means a specified difference between the masses of two nearby nuclides. For a derivative specified in such a way where the differences are between nuclides in the same mass sheet, the nearly parallelism of these sheets leads to an almost unified surface for the derivative, thus allowing a single display. The derivatives are also smooth and have the advantage of displaying much smaller variations in data. Therefore, in order to illustrate the regular trends in the mass surface, three derivatives of this last type were chosen:

1. the two-neutron separation energies versus N, with lines connecting the isotopes of a given element (Figs. 1–9);

2. the two-proton separation energies versus Z, with lines connecting the isotones (nuclides with the same number of neutrons) (Figs. 10–17);

3. the $ Q_\alpha $ values versus N, with lines connecting the isotopes of a given element (Figs. 18–26).

Clearly showing the trends from the mass surface (TMS), these graphs can be quite useful for checking the quality of any interpolation or extrapolation (if not too far). When some masses deviate from the regular TMS in a specific mass region, there could be a serious physical cause, like a shell or subshell closure or an onset of deformation. However, if only one mass exhibits an irregular pattern, thus violating the general smooth trends, then one may seriously question the correctness of the related input data.

A complete list of references related to the input data used in the AME2020 and the NUBASE2020 evaluations are presented at the end of this paper. The individual references are given using the “Nuclear Science Reference” (NSR) database [12] keynumbers and identified by the corresponding CODEN style [12]. There is only one exception for the Eur. Phys. A journal, where instead of the ‘ZAANE’ identifier [12], we have used ‘EPJAA’.

This work is supported in part by the Strategic Priority Research Program of Chinese Academy of Sciences (CAS, Grant No. XDB34000000), the National Key Research and Development Program of China (Grant No.2016YFA0400504), the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under Contract No. DE-AC02-06CH11357. W.J.H. acknowledges financial support by the Max-Planck-Society. S.N. acknowledges the support of the RIKEN Pioneering Project Funding.