Phonon contributions to ab initio double mass differences of magic nuclei

TL;DR

This paper investigates how phonon interactions influence double mass differences in magic nuclei using ab initio methods, highlighting the importance of particle-phonon coupling effects for accurate nuclear mass predictions.

Contribution

It introduces a comprehensive approach incorporating particle-phonon coupling effects into ab initio calculations of double mass differences in magic nuclei, improving agreement with experimental data.

Findings

PC corrections improve DMD predictions for heavy nuclei like $^{132}$Sn and $^{208}$Pb.

For lighter nuclei, PC corrections sometimes worsen the agreement, indicating limits of perturbation theory.

The approach accounts for three PC effects: induced interaction, Z-factor renormalization, and single-particle energy shifts.

Abstract

Odd-even double mass differences (DMD) of magic nuclei are found within the approach starting from the free $NN$ interaction with account for particle-phonon coupling (PC) effects. We consider three PC effects: the phonon induced effective interaction, the renormalization of the "ends" due to the $Z$-factor corresponding to the pole PC contribution to the nucleon mass operator and the change of the single-particle energies. The perturbation theory in $g^2_L$, where $g_L$ is the vertex of the $L$-phonon creation, is used for PC calculations. PC corrections to single-particle energies are found self-consistently with an approximate account for the tadpole diagram. Results for magic $^{40,48}$Ca, $^{56,78}$Ni, $^{100,132}$Sn and $^{208}$Pb nuclei are presented. For lighter part of this set of nuclei, from $^{40}$Ca till $^{56}$Ni, the cases divide approximately in half between those where the PC corrections to DMD values make agreement with the data better and the ones with the opposite result. In the major part of the cases of worsening of description of DMD, a poor applicability of the perturbation theory for the induced interaction is the most probable reason of the phenomenon. For intermediate nuclei, $^{78}$Ni and $^{100}$Sn, there is no sufficiently accurate data on masses of nuclei necessary for finding DMD values. Finally, for heavier nuclei, $^{132}$Sn and $^{208}$Pb, PC corrections always make agreement with the experiment better.