Primary γ -ray intensities and γ -strength functions from discrete two-step γ -ray cascades in radiative proton-capture experiments

Abstract

Background: Reaction rates of radiative capture reactions can play a crucial role in the nucleosynthesis of heavy nuclei in explosive stellar environments. These reaction rates depend strongly on $\ensuremath{\gamma}$-ray decay widths in the reaction products, which are, for nonresonant capture reactions at high excitation energies, derived from the $\ensuremath{\gamma}$-ray strength function and the nuclear level density. Recently, the ratio method was applied to primary $\ensuremath{\gamma}$ rays observed from ($d,p$) reactions and nuclear resonance fluorescence measurements to extract the dipole strength in atomic nuclei and to test the generalized Brink-Axel hypothesis.Purpose: The purpose of this work is to apply the ratio method to primary $\ensuremath{\gamma}$-ray intensities of the $^{63,65}\mathrm{Cu}(p,\ensuremath{\gamma})$ reactions to extract $\ensuremath{\gamma}$-ray strength information on the nuclei $^{64,66}\mathrm{Zn}$. The impact of spin distribution, total $\ensuremath{\gamma}$-ray decay widths, level densities, and width fluctuations on the application of the ratio method will be discussed. Additionally, by comparing the relative $\ensuremath{\gamma}$-ray strength at different excitation energies, conclusions on the validity of the generalized Brink-Axel hypothesis can be made.Method: The radiative proton capture reaction measurements have been performed at the HORUS $\ensuremath{\gamma}$-ray spectrometer of the University of Cologne at one excitation energy for each reaction. Primary $\ensuremath{\gamma}$-ray intensities have been determined by normalizing secondary $\ensuremath{\gamma}$-ray transitions in two-step cascades using their absolute branching ratio. The ratio method was applied to the measured primary $\ensuremath{\gamma}$-ray intensities as well as to previous measurements by Erlandsson $et$ $al.$ at different excitation energies.Results: The relative strength function curve for $^{64}\mathrm{Zn}$ from our measurement shows no significant deviation from the previous measurement at a different excitation energy. The same is true for $^{66}\mathrm{Zn}$ where both measurements were at almost the same excitation energy. Absolute $\ensuremath{\gamma}$-strength function values have been obtained by normalizing the relative curves to quasiparticle random phase approximation calculations because of the absence of experimental data in the respective energy region.Conclusion: The generalized Brink-Axel hypothesis, i.e., the independence of the strength function on the excitation energy, seems to hold in the studied energy region and nuclei. The method to obtain primary $\ensuremath{\gamma}$-ray intensities from two-step cascade spectra was shown to be a valuable and sensitive tool although its uncertainties are connected to the knowledge of the low-energy level scheme of the investigated nucleus. The scaling in the ratio method should be taken with care, because the relative strength is not a simple sum of ${f}_{E1}$ and ${f}_{M1}$ but a somewhat complex linear combination dependent on the excitation energy of the nucleus.