Zemach radii and nuclear structure effects in hyperfine splitting of Lithium

Abstract

Nuclear structure effects are essential for describing hyperfine splittings from high-precision atomic spectroscopy measurements. These effects are often parametrized by the effective or elastic Zemach radii, with their difference poorly understood. We solve the longstanding discrepancy between the effective and elastic Zemach radii in ${}^6$Li and ${}^7$Li by performing \emph{ab initio} nuclear structure calculations that take into account nuclear polarizability effects. Our results demonstrate that nuclear polarizability effects, negligible in ${}^7$Li, dominate in ${}^6$Li and explain the observed significant deviation between the effective and elastic Zemach radii. Furthermore, we show that the ratios between the nuclear polarizability contributions in different nuclei are universal in the limit of closure and SU(4) symmetry of nuclear forces. In particular, the nuclear polarizability contribution in an odd-odd nucleus is enhanced by a factor of $μ_p/(μ_p+μ_n)\simeq 3$, with $μ_{n,p}$ denoting the nucleon magnetic moments, compared to its odd-$A$ isotopes. The same mechanism also explains the Zemach radius deviations observed in ${}^2$H and ${}^3$He. These findings establish nuclear polarizability as the dominant source of isotope-dependent nuclear corrections to hyperfine splitting in light atoms.