Gamow-Teller transition strengths from ${}^{56}\mathrm{Fe}$ extracted from the ${}^{56}\mathrm{Fe}(t,{}^3\mathrm{He})$ reaction

Background: Gamow-Teller (GT) transition strengths are key inputs for estimating weak reaction rates of importance for a wide variety of astrophysical applications. $\left(n,p\right)$-type charge-exchange reactions, such as the $(t,{}^3\mathrm{He})$ reaction used in this work, are commonly used for extracting the GT strength distribution in the ${\beta }^{+}$ (electron-capture) direction. Such studies are important for testing theoretical models used to estimate weak rates for a large number of nuclei for simulations of astrophysical phenomena.

Purpose: The ${}^{56}\mathrm{Fe}(t,{}^3\mathrm{He})$ reaction at 115 $A$MeV was measured in order to extract GT strengths for transitions to ${}^{56}\mathrm{Mn}$. The extracted strength distributions were compared with shell-model calculations in the $pf$-shell model space using the KB3G and GXPF1a interactions, and with calculations in the quasi-particle random-phase approximation (QRPA).

Method: Differential cross sections and excitation-energy spectra for the ${}^{56}\mathrm{Fe}(t,{}^3\mathrm{He})$ reaction were determined by measuring the trajectories of ${}^3\mathrm{He}$ ejectiles through the S800 magnetic spectrograph and deducing their momenta. Contributions corresponding to GT transitions were isolated by using a multipole decomposition analysis. A well-established proportionality between GT strength and differential cross section at zero-linear-momentum transfer was utilized to convert extracted cross sections to GT strengths.

Results and Conclusions: GT transition strengths from ${}^{56}\mathrm{Fe}$ to ${}^{56}\mathrm{Mn}$ were extracted up to an excitation energy of 10 MeV. Shell-model calculations with the GXPF1a interaction reproduced the observed GT strength distribution slightly better than calculations with the KB3G interaction. The calculated strength distribution in the QRPA did not reproduce the observed strength distribution. The new experimental data have an improved precision at low excitation energies compared to previous results obtained from an ${}^{56}\mathrm{Fe}\left(n,p\right)$ experiment. Electron-capture rates based on the experimental and theoretical Gamow-Teller strengths were compared and deviations were included in an assessment of the validity of electron-capture rates based on theoretical models for nuclei in the $pf$ shell.

Figure 1

Differential cross section for the ${}^{56}\mathrm{Fe}(t,{}^3\mathrm{He})$ reaction, plotted as a function of excitation energy in ${}^{56}\mathrm{Mn}$. The spectrum is plotted for angular bins observed in the laboratory frame (in millirads). The observed spectrum is shown as the data points, with the hatched regions containing the results of the MDA.

Figure 2

Differential cross section for the peak observed at 1.17 MeV in the ${}^{56}\mathrm{Mn}$ spectrum, with the results from the MDA superimposed. The cross section is dominated by a $\Delta L=0$ component associated with the excitation of a known $1^{+}$ state. The error bars only represent the statistical uncertainty associated with the number of events measured in each angular bin.

Figure 3

GT strength distributions from ${}^{56}\mathrm{Fe}$ to ${}^{56}\mathrm{Mn}$ (a) extracted from the ${}^{56}\mathrm{Fe}(t,{}^3\mathrm{He})$ data (with horizontal bars indicating the 250-keV-wide energy bins, except for the peaks at 0.1 and 1.17 MeV, for which they indicate the accuracy with which the peak locations could be identified in the current data), (b) extracted from the ${}^{56}\mathrm{Fe}\left(n,p\right)$ data (in 1-MeV bins, as indicated by the horizontal bars), (c) from calculations in the QRPA (divided by 3), (d) from shell-model calculations using the KB3G interaction, and (e) from shell-model calculations using the GXPF1a interaction. In (f), running sums of the GT strengths as a function of excitation energies are plotted. The hatched regions of the data represent the statistical and systematic uncertainties in the $(t,{}^3\mathrm{He})$ data and the statistical uncertainty in the $\left(n,p\right)$ data.

Figure 4

Electron-capture rates on ${}^{56}\mathrm{Fe}$ derived from the experimental and theoretical GT strength distributions of Fig. 3 (a) at $\rho Y_e={10}^7$ $\text{g}/{\mathrm{cm}}^3$ and (b) at $\rho Y_e={10}^9$ $\text{g}/{\mathrm{cm}}^3$.