Calculation of Francium Hyperfine Anomaly

Elena Konovalova,Yuriy Demidov,Mikhail Kozlov,Anatoly Barzakh

doi:10.3390/atoms6030039

Abstract

The Dirac–Hartree–Fock plus many-body perturbation theory (DHF + MBPT) method has been used to calculate hyperfine structure constants for Fr. Calculated hyperfine structure anomaly for hydrogen-like ion is in good agreement with analytical expressions. It has been shown that the ratio of the anomalies for s and p1/2 states is weakly dependent on the principal quantum number. Finally, we estimate Bohr–Weisskopf corrections for several Fr isotopes. Our results may be used to improve experimental accuracy for the nuclear g factors of short-lived isotopes.

Highlights

The hyperfine structure constants (HFS) and isotope shifts are highly sensitive to the changes of charge and magnetization distributions inside the nucleus
It follows from Equations (1) and (3) that, if we calculate the HFS constant for different R and dnuc, we should get in the first order in δ and e the following dependence on the nuclear radius: A( g I, dnuc, R) = g I A0 1 − (b N + b M dnuc ) R2γ−1
The hyperfine anomaly (HFA) in this method can be parameterized by coefficients b N and b M

Summary

Introduction

The hyperfine structure constants (HFS) and isotope shifts are highly sensitive to the changes of charge and magnetization distributions inside the nucleus. The ratio of magnetic hyperfine constants A for different isotopes is usually assumed to be μ equal to the ratio of their nuclear g factors g I = μ N I , where μ and I are magnetic moment and spin of the nucleus, μ N is nuclear magneton. This is true only for the point-like nucleus. Changes of the nuclear charge radii in the Fr isotopic series were calculated from the isotope shift measurements [23,24]

Theory and Methods

HFS Anomaly for H-Like Francium Ion

HFS Anomaly of Neutral Francium Atom

Conclusions