The $2_1^+ \to 3_1^+$ gamma width in $^{22}$Na and second class currents

TL;DR

This paper measures the gamma decay branch in $^{22}$Na and uses it to determine the weak magnetism form factor, revealing discrepancies with theoretical models and suggesting the presence of second class currents.

Contribution

First unambiguous measurement of the $2_1^+ o 3_1^+$ gamma branch in $^{22}$Na, enabling a new determination of the weak magnetism form factor.

Findings

The gamma branch in $^{22}$Na is 0.45(8)%

The weak magnetism form factor is |b/Ac_1| = 8.7(1.1)

Discrepancy between observed form factors and theoretical predictions

Abstract

A previous measurement of the $\beta-\gamma$ directional coefficient in $^{22}$Na $\beta$ decay was used to extract recoil-order form factors. The data indicate the requirement of a significant induced-tensor matrix element for the decay.This conclusion largely relies on a Standard-Model-allowed weak magnetism form factor which was determined using an unpublished value of the analog $2_1^+\to3_1^+$ $\gamma$ branch in $^{22}$Na, with the further assumption that the transition is dominated by its isovector $M1$ component. We obtain for the first time an unambiguous determination of the $2_1^+ \to 3_1^+$ branch in $^{22}$Na to be $0.45(8)\%$. Using the Conserved Vector Current (CVC) hypothesis, our branch determines the weak magnetism form factor for $^{22}$Na $\beta$ decay to be $|b/Ac_1| = 8.7(1.1)$. Together with the $\beta-\gamma$ angular correlation coefficient, we obtain a large induced-tensor form factor for the decay that continues to disagree with theoretical predictions. Two plausible explanations are suggested.