Global systematics and theoretical interpretation of $l$-forbidden $M1$ transitions in odd-$A$ nuclei

Abstract

The $l$-forbidden magnetic dipole ($M1$) transitions, characterized by a change in orbital angular momentum ($Δ\ell = 2$), serve as sensitive probes of higher-order effects, including configuration mixing and meson-exchange currents. In this work, we present a comprehensive systematic study of all experimentally known $l$-forbidden $M1$ transitions, covering odd-$A$ nuclei with neutron numbers $27 \leq N \leq 126$. To interpret these global systematics, we apply a theoretical framework based on the relativistic Dirac wave function. This approach directly links the $l$-forbidden $M1$ transition amplitudes between pseudospin-partner orbitals to experimental single-particle magnetic moments. We perform a global comparison across isotopic chains by substituting unknown magnetic moments with rescaled Schmidt estimates. Focusing on dominant transition groups, including $p_{3/2} \rightarrow f_{5/2}$, $s_{1/2} \rightarrow d_{3/2}$, and $d_{5/2} \rightarrow g_{7/2}$, our analysis establishes a robust linear correlation between the transition amplitudes $\sqrt{B(M1)}$ and the corresponding empirical single-particle matrix elements $M_{\mathrm{sp}}$. The proportionality coefficient $ρ$ serves as an empirical measure of single-particle strength fragmentation and quantifies the role of configuration mixing in driving $l$-forbidden transitions across the nuclear chart.