Resolving anomalous collectivity in the $4_1^+$ to $2_1^+$ transition of $^{58}$Fe

Abstract

The low-excitation states of atomic nuclei in the region around the $N = Z = 28$ shell closure are generally well described by the shell model. Most experimental observables in the iron isotopes $^{56}$Fe, $^{58}$Fe, and $^{60}$Fe ($Z = 26$; $N=30$, $32$, $34$) support a shell-model description. However, the lifetimes of the $4_1^+$ state in $^{58}$Fe in the literature result in a reduced transition strength that deviates markedly from shell-model predictions. There are three independent measurements, all in agreement and all based on the Doppler Shift Attenuation Method (DSAM) or Doppler-Broadened Line Shape method (DBLS). In this work, Coulomb-excitation measurements were performed on $^{56}$Fe and $^{58}$Fe beams to determine the ratios $B(E2; 4_1^+ \to 2_1^+)/B(E2; 2_1^+ \to 0_1^+)$. Thus, $B(E2; 4_1^+ \to 2_1^+)$ is determined relative to the known $B(E2; 2_1^+ \to 0_1^+)$ values. For $^{56}$Fe, $B(E2; 4_1^+ \to 2_1^+) = 23(4)$ W.u., agreeing with the adopted value. However, for $^{58}$Fe, the $B(E2; 4_1^+ \to 2_1^+)$ values obtained (for the various combinations of matrix element signs that could not be firmly established) are all significantly lower than the value derived from the previous lifetime measurements, and are in accord with shell-model calculations. The 1978 DSAM measurement of Bolotin et al., Nucl. Phys. A 311, 75 (1978), has been re-examined. The discrepancy between that measurement and the Coulomb-excitation measurement can be ascribed to the Lindhard-Scharff-Schi{\o}tt (LSS) electronic stopping powers adopted for the DSAM analysis, which considerably overestimate contemporary values. Evidently, lifetime measurements from that era that are based on LSS stopping powers should be used with caution. The revised lifetime data, incorporating current stopping powers, are compared with shell-model calculations.