Hyperfine anomalies in Fr: boundaries of the spherical single particle model

TL;DR

This study measures hyperfine splittings in francium isotopes to explore nuclear magnetization distribution, comparing results with a simple shell model, and identifies isotopes suitable for weak interaction research.

Contribution

It provides new high-precision hyperfine measurements in francium isotopes and evaluates the validity of the spherical single-particle model for these nuclei.

Findings

Good agreement between measurements and the shell model for neutron-deficient isotopes.

Near-constant proton anomalies observed in several even-N isotopes.

Identification of isotopes suitable for parity non-conservation studies.

Abstract

We have measured the hyperfine splitting of the $7P_{1/2}$ state at the 100 ppm level in Fr isotopes ($^{206g,206m, 207, 209, 213, 221}$Fr) near the closed neutron shell ($N$ = 126 in $^{213}$Fr). The measurements in five isotopes and a nuclear isomeric state of francium, combined with previous determinations of the $7S_{1/2}$ splittings, reveal the spatial distribution of the nuclear magnetization, i.e. the Bohr-Weisskopf effect. We compare our results with a simple shell model consisting of unpaired single valence nucleons orbiting a spherical nucleus, and find good agreement over a range of neutron-deficient isotopes ($^{207-213}$Fr). Also, we find near-constant proton anomalies for several even-$ N$ isotopes. This identifies a set of Fr isotopes whose nuclear structure can be understood well enough for the extraction of weak interaction parameters from parity non-conservation studies.