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-Schiøtt (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.

Figures (13)

• Figure 1: Experimental and calculated yrast-band (a) energies and (b) reduced $E2$ transition strengths in even-even iron isotopes above the $N = 28$ closed shell. Data are taken from Refs. Junde2011Nesaraja2010Browne2013. Shell-model calculations are shown for the HO Horie1971Horie1973 basis space and interactions, which have a $^{48}$Ca core, and for the larger $fp$ basis, which has a $^{40}$Ca core, and uses the GXPF1A Honma2004Honma2005 interaction (denoted GX1A in the figure). The recommended core-polarization charges are used, $\delta e = 1.0$ for the HO calculations and $\delta e = 0.5$ for the GXPF1A calculations (thus the effective charges for protons and neutrons are $e_{\pi}=1+\delta e$ and $e_{\nu}=\delta e$.) The experimental $B{\left(E2; 4_1^+ \to 2_1^+\right)}$ value for $^{58}$Fe ($N = 32$) from the literature Nesaraja2010 is significantly enhanced in comparison to neighboring isotopes, and in strong disagreement with both shell-model calculations.
• Figure 2: A representative photodiode energy spectrum from the $^{58}$Fe measurement. The peak shape corresponds to that of Rutherford backscattering of the $^{58}$Fe beam nuclei from the $^{197}$Au target.
• Figure 3: The particle-gated $\gamma$-ray spectrum collected during the measurement with the $^{56}$Fe beam, summed over all detectors. Transitions detected following decay of Coulomb-excited $^{56}$Fe are labeled by their energies in keV and $I_i^{\pi} \to I_f^{\pi}$. Both transitions can be seen in (a) for comparison, with (b) expanded to show the much weaker $4_1^+ \to 2_1^+$ transition.
• Figure 4: The particle-gated $\gamma$-ray spectrum collected during the measurement with the $^{58}$Fe beam, summed over all detectors. Transitions detected following decay of Coulomb-excited $^{58}$Fe are labeled, along with $^{58}$Ni, which is present as a beam contaminant, and a line from the $^{197}$Au target. Transitions from $^{58}$Fe are labeled by their energies in keV and $I_i^{\pi} \to I_f^{\pi}$. The two lower-energy transitions can be seen in (a), along with a line from the target, with (b) expanded to show the $2_2^+ \to 2_1^+$ transition. The two higher-energy transitions in $^{58}$Fe can be seen in (c), along with the 1454-keV $2^+_1 \rightarrow 0^+_1$ line from the $^{58}$Ni beam contaminant.
• Figure 5: Partial level scheme of $^{56}$Fe, showing the observed transitions. Dashed lines represent additional buffer states included in the analysis. Level properties and transition energies are taken from Ref. Junde2011, with energies given to the nearest keV.