Exploratory study on the masses of odd-$Z$ nuclei and $r$-process simulation based on the deformed relativistic Hartree-Bogoliubov theory in continuum

TL;DR

This work addresses the need for reliable nuclear masses of neutron-rich, odd-$Z$ nuclei to fuel $r$-process studies. It extends the deformed relativistic Hartree-Bogoliubov in continuum framework (DRHBc) to odd-$Z$ nuclei by estimating their masses from neighboring even-$Z$ results and microscopic pairing gaps, producing a pseudo DRHBc mass table with $8 \le Z \le 120$ and rms deviations near $1.5$ MeV when rotation is included. Using this mass table in a classical $r$-process model, the authors show that deformation effects can shift the $r$-process path and abundances, introducing a notable trough around $A\approx170$ associated with rapid shape transitions; pairing-gap details are less decisive. The results highlight the importance of deformation and potentially beyond-mean-field effects (e.g., triaxiality) for accurate $r$-process predictions and provide a practical mass input for future dynamical network calculations.

Abstract

Nuclear masses of exotic nuclei are important for both nuclear physics and astrophysics. The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) is capable of providing proper descriptions for exotic nuclei by simultaneously including deformation, pairing correlation and continuum effects, and a mass table of even-$Z$ nuclei with $8 \leqslant Z \leqslant 120$ has been developed based on the DRHBc theory. This work employs a methodology to estimate the masses of odd nuclei using neighboring even nuclei's masses and microscopic pairing gaps, and the performance of microscopic pairing gaps are validated by comparing with empirical ones. Combining the DRHBc masses of even-$Z$ nuclei and the estimated masses of odd-$Z$ nuclei, a pseudo DRHBc mass table is developed, with the root-mean-square (rms) deviation from available mass data $σ=1.47$ MeV. Then this mass table is employed in the $r$-process simulation; results show that the differences in the details of pairing gaps do not yield qualitative discrepancy in $r$-process abundances, while the deformation effects can influence the $r$-process path and thus affect the $r$-process abundance. In particular, the nuclear shape transitions can even lead to the discontinuity of the $r$-process path, suggesting that incorporating triaxiality or beyond-mean-field effects would be valuable for further improvement.

Figures (12)

• Figure 1: Average pairing gaps of even-even nuclei with $8\leqslant Z \leqslant 120$ in DRHBc theory for (a) neutron and (b) proton, in comparison with the empirical pairing gaps $\Delta=12A^{-1/2}$ and $\Delta=34A^{-3/4}$Ring1980NMBPBohr1998book, respectively.
• Figure 2: The differences between the pseudo and real DRHBc results for the binding energies of even-odd nuclei with $8 \leqslant Z \leqslant 120$ scaled by colors. (a) The rotational correction is not considered. (b) The rotational correction is included.
• Figure 3: The same as Fig. \ref{['mass_exam']}, but the pairing gaps are estimated with the empirical formulas (a) $\Delta=12A^{-1/2}$ ("emp-1/2" for short) and (b) $\Delta=34A^{-3/4}$ ("emp-3/4" for short). The rotational correction is included.
• Figure 4: The differences between the pseudo DRHBc binding energies and the available data Wang2021CPC for the nuclei with $8 \leqslant Z \leqslant 120$ scaled by colors. The details about the pseudo DRHBc results can be found in the text. (a) The rotational correction is not considered. (b) The rotational correction is included.
• Figure 5: The differences between the pseudo DRHBc results of one-neutron separation energy and the available data Wang2021CPC for the nuclei with $8 \leqslant Z \leqslant 120$ scaled by colors. (a) The rotational correction is not considered. (b) The rotational correction is included.