Gamow-Teller transitions toCa45via theSc45(t,He3+γ)reaction at115 MeV/uand its application to stellar electron-capture rates

Background: Stellar electron-capture reactions on medium-heavy nuclei are important for many astrophysical phenomena, including core-collapse and thermonuclear supernov\ae{} and neutron stars. Estimates of electron-capture rates rely on accurate estimates of Gamow-Teller strength distributions, which can be extracted from charge-exchange reactions at intermediate beam energies. Measured Gamow-Teller transition strength distributions for stable pf-shell nuclei are reasonably well reproduced by theoretical calculations in the shell model, except for lower mass nuclei where admixtures from the sd shell can become important.Purpose: This paper presents a ${\ensuremath{\beta}}^{+}$ charge-exchange experiment on $^{45}\mathrm{Sc}$, one of the lightest pf-shell nuclei. The focus was on Gamow-Teller transitions to final states at low excitation energies, which are particularly important for accurate estimations of electron-capture rates at relatively low stellar densities. The experimental results are compared with various theoretical models.Method: The double-differential cross section for the $^{45}\mathrm{Sc}(t,^{3}\mathrm{He}+\ensuremath{\gamma})$ reaction was measured using the NSCL Coupled-Cyclotron Facility at $115\phantom{\rule{4pt}{0ex}}\mathrm{MeV}/u$. Gamow-Teller contributions to the excitation-energy spectra were extracted by means of a multipole-decomposition analysis. $\ensuremath{\gamma}$ rays emitted due to the deexcitation of $^{45}\mathrm{Ca}$ were measured using GRETINA to allow for the extraction of Gamow-Teller strengths from very weak transitions at low excitation energies.Results: Gamow-Teller transition strengths to $^{45}\mathrm{Ca}$ were extracted up to an excitation energy of 20 MeV, and that to the first excited state in $^{45}\mathrm{Ca}$ at 174 keV was extracted from the $\ensuremath{\gamma}$-ray measurement, which, even though weak, is important for the astrophysical applications and dominates under certain stellar conditions. Shell-model calculations performed in the pf shell-model space with the GXPF1A, KB3G, and FPD6 interactions did not reproduce the experimental Gamow-Teller strength distribution, and a calculation using the quasiparticle random phase approximation that is often used in astrophysical simulations also could not reproduce the experimental strength distribution.Conclusions: Theoretical models aimed at describing Gamow-Teller transition strengths from nuclei in the lower pf shell for the purpose of estimating electron-capture rates for astrophysical simulations require further development. The likely cause for the relatively poor performance of the shell-model theory is the influence of intruder configurations from the sd shell. The combination of charge-exchange experiments at intermediate beam energy and high-resolution $\ensuremath{\gamma}$-ray detection provides a powerful technique to identify weak transitions to low-lying final states that are nearly impossible to identify without the coincidences. Identification of these weak low-lying transitions is important for providing accurate electron-capture rates for astrophysical simulations.