Energy levels of A = 21−44 nuclei (V)

The mass of the nucleus, through its binding energy, continues to be of capital importance not only for various aspects of nuclear physics, but also for other branches of physics, notably weak-interaction studies and astrophysics. The authors first describe the modern experimental techniques dedicated to the particularly challenging task of measuring the mass of exotic nuclides and make detailed comparisons. Though tremendous progress in these and the associated production techniques has been made, allowing access to nuclides very far from stability, it is still not yet possible to produce many nuclides involved in stellar nucleosynthesis, especially the $r$ process, leaving no choice but to resort to theory. The review thus goes on to describe and critically compare the various modern mass formulas that may be used to extrapolate from the data towards the neutron drip line. Special attention is devoted to the crucial interplay between theory and experiment, showing how new measurements far from stability can considerably reduce the ambiguity in extrapolations to nuclides even further away.

Recent trends in the determination of nuclear masses

A semiempirical shell-model formula

Development of the semiempirical droplet model

We discuss the systematics of ground-state quadrupole correlations of binding energies and mean-square charge radii for all even-even nuclei, from ${}^{16}$O up to the superheavies, for which data are available. To that aim we calculate their correlated $J=0$ ground state by means of the angular-momentum and particle-number projected generator coordinate method, using the axial mass quadrupole moment as the generator coordinate and self-consistent mean-field states restricted only by axial, parity, and time-reversal symmetries. The calculation is performed within the framework of a nonrelativistic self-consistent mean-field model by use of the same Skyrme interaction SLy4 and to a density-dependent pairing force to generate the mean-field configurations and to mix them. These are the main conclusions of our study: (i) The quadrupole correlation energy varies between a few 100 keV and about 5.5 MeV. It is affected by shell closures, but varies only slightly with mass and asymmetry. (ii) Projection on angular momentum $J=0$ provides the major part of the energy gain of up to about 4 MeV; all nuclei in the study, including doubly magic ones, gain energy by deformation. (iii) The mixing of projected states with different intrinsic axial deformations adds a few 100 keV up to 1.5 MeV to the correlation energy. (iv) Typically nuclei below mass $A\ensuremath{\le}60$ have a larger correlation energy than static deformation energy whereas the heavier deformed nuclei have larger static deformation energy than correlation energy. (v) Inclusion of the quadrupole correlation energy improves the description of mass systematics, particularly around shell closures, and of differential quantities, namely two-nucleon separation energies and two-nucleon gaps. The correlation energy provides an explanation of ``mutually enhanced magicity.'' (vi) The correlation energy tends to decrease the shell effect on binding energies around magic numbers, but the magnitude of the suppression is not large enough to explain the relative overbinding at $N=82$ and $N=126$ neutron-shell closures in mean-field models. (vii) Charge radii are also found to be sensitive to the quadrupole correlations. Static quadrupole deformations lead to a significant improvement of the overall systematics of charge radii. The dynamical correlations improve the local systematics of radii, in particular around shell closures. Although the dynamical correlations might reduce the charge radii for specific nuclei, they lead to an overall increase of radii when included, in particular in light nuclei.

Global study of quadrupole correlation effects

Two new independent mass relations are derived and are shown to be consistent with several existing nuclear models. The most general functional dependence on proton number, neutron number, and mass number (or isospin value) of masses which satisfy these relations exactly is discussed, and a procedure for determining the values of these functions which give a best least-squares fit to the body of known masses is developed. The functions which give the best over-all fit are listed together with the resulting theoretical mass table which shows the discrepancies to known masses and the theoretical values for proton, neutron, and alpha-particle decay energies.

I. Kelson

Papers

Set of Nuclear-Mass Relations and a Resultant Mass Table