The Bohr-Weisskopf effect in the potassium isotopes

TL;DR

This study calculates hyperfine structure constants in potassium isotopes, revealing the 4p_{1/2} state is unaffected by certain corrections, and refines nuclear magnetic moments using these findings.

Contribution

It provides new calculations of hyperfine constants considering BW and BR effects and clarifies the nuclear model applicability for potassium isotopes.

Findings

The 4p_{1/2} state is free from BW and BR corrections.

Nuclear magnetic moments were corrected using atomic and nuclear factors.

The atomic factor for K I ground state was calculated.

Abstract

The magnetic hyperfine structure constants have been calculated for low-lying levels in neutral potassium atom taking into account the Bohr--Weisskopf (BW) and Breit--Rosenthal (BR) effects. According to our results the $4p_{1/2}$ state of K~I is free from both BR and BW corrections on the level of the current theoretical uncertainties. Using this finding and the measured values of the $A(4p_{1/2})$ constants, we corrected the nuclear magnetic moments for several short-lived potassium isotopes. The BW correction is represented as a product of atomic and nuclear factors. We calculated the atomic factor for the ground state of K I, which allowed us to extract nuclear factors for potassium $I^\pi = 3/2^+$ isotopes from the experimental data. In this way the application range of the single-particle nuclear model for nuclear-factor calculation in these isotopes has been clarified.