Revised ${}^3$He nuclear charge radius due to electronic hyperfine mixing

Abstract

The significant discrepancy in the difference of squared nuclear charge radii $\Delta R^2$ of ${}^{3,4}$He obtained from electronic-atom or muonic-atom energy levels is a puzzle. In this paper, we show that the tension is resolved by including off-diagonal mixing effects due to the hyperfine interaction. Our findings indicate that the hyperfine mixing effect from the $n{}^{3}S$ and $n{}^{1}S$ states ($n>2$) of ${}^3$He leads to a $-1.37$ kHz adjustment in the isotope shift of the $2{}^{1}S-2{}^{3}S$ transition, surpassing the current uncertainty by a factor of $7$. This results in a change of $-0.0064{\mathrm{fm}}^2$ in $\Delta R^2$, shifting from $1.0757(15){\mathrm{fm}}^2$ to $1.0693(15){\mathrm{fm}}^2$ as determined by Werf {\it et al.}, significantly reducing the discrepancy with the value of $1.0636(31){\mathrm{fm}}^2$ determined by $\mu {\mathrm{He}}^{+}$, and aligning with the result of $1.069(3)$ ${\mathrm{fm}}^2$ obtained from the $2{}^{3}S-2{}^{3}P$ transition. This adjustment will result in a noticeable change in the absolute nuclear charge radius of ${}^3$He by $-0.0017\mathrm{fm}$, aligning the revised value of $1.9715(11)\mathrm{fm}$ with the value of $1.97007(94)\mathrm{fm}$ determined by ${\mu }^3{\mathrm{He}}^{+}$ within $1\sigma$. Our results offer crucial insights into resolving discrepancy in $\Delta R^2$ for ${}^{3,4}$He and determining the charge radius of ${}^3$He.

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Cited by in corpus (2)

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