Relativistic description of magnetic moments in nuclei with doubly closed shells plus or minus one nucleon

TL;DR

This paper employs a relativistic density functional approach to accurately calculate magnetic moments in nuclei near doubly closed shells, highlighting the importance of pion exchange effects for improved agreement with experimental data.

Contribution

It introduces a relativistic model incorporating pion exchange currents and residual interactions, providing more precise magnetic moment calculations than previous non-relativistic methods.

Findings

Relativistic calculations match experimental data within 6.1% deviation.

Pion exchange plays a crucial role in magnetic moment description.

Relativistic approach outperforms earlier non-relativistic models.

Abstract

Using the relativistic point-coupling model with density functional PC-PK1, the magnetic moments of the nuclei $^{207}$Pb, $^{209}$Pb, $^{207}$Tl and $^{209}$Bi with a $jj$ closed-shell core $^{208}$Pb are studied on the basis of relativistic mean field (RMF) theory. The corresponding time-odd fields, the one-pion exchange currents, and the first- and second-order corrections are taken into account. The present relativistic results reproduce the data well. The relative deviation between theory and experiment for these four nuclei is 6.1% for the relativistic calculations and somewhat smaller than the value of 13.2% found in earlier non-relativistic investigations. It turns out that the $\pi$ meson is important for the description of magnetic moments, first by means of one-pion exchange currents and second by the residual interaction provided by the $\pi$ exchange.