$M_F$-dependent Hyperfine Induced Transition Rates in an External Magnetic Field for Be-like $^{47}$Ti$^{18+}$

TL;DR

This study calculates hyperfine induced transition rates in Be-like $^{47}$Ti$^{18+}$ ions under external magnetic fields, revealing dependence on magnetic quantum number and clarifying discrepancies between experimental and theoretical results.

Contribution

It introduces a multiconfiguration Dirac-Fock calculation of transition rates considering magnetic quantum number dependence in external fields, addressing previous experimental-theoretical discrepancies.

Findings

Transition probability depends on magnetic quantum number $M_F$ even in weak fields.

The difference between experimental and theoretical rates is not due to external magnetic field effects.

The study clarifies the role of magnetic quantum number dependence in hyperfine transitions.

Abstract

Hyperfine induced $2s2p~^3P_0 \rightarrow 2s^2~^1S_0$ transition rates in an external magnetic field for Be-like $^{47}$Ti were calculated based on the multiconfiguration Dirac-Fock method. It was found that the transition probability is dependent on the magnetic quantum number $M_F$ of the excited state, even in the weak field. The present investigation clarified that the difference of the hyperfine induced transition rate of Be-like Ti ions between experiment [Schippers {\sl et al.}, Phys Rev Lett {\bf 98}, (2007) 033001(4)] and theory does not result from the influence of external magnetic field.