The Bohr-Weisskopf effect in the potassium isotopes

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.