$\gamma$-ray spectroscopy of astrophysically important states in ${}^{39}\mathrm{Ca}$

Background: Nova explosions synthesize elements up to $A\simeq 40$, and discrepancies exist between calculated and observed abundances of Ar and Ca created in the explosion. The ${}^{38}\mathrm{K}(p,\gamma ){}^{39}\mathrm{Ca}$ reaction rate has been shown to be influential on these isotopic abundances at the endpoint of nova nucleosynthesis. The energies of the three most important resonances, corresponding to $J^{\pi }=5/2^{+}$ excited states in the ${}^{39}\mathrm{Ca}$ nucleus above the proton separation threshold, are uncertain and one has been measured with conflicting values [$E_r=679\left(2\right)$ versus $E_r=701\left(2\right)$ keV] in previous experiments.

Purpose: Reducing the uncertainties on the resonance energies would allow for a better understanding of the reaction rate. To improve these uncertainties, we searched for $\gamma$ rays from the depopulation of the corresponding excited states in ${}^{39}\mathrm{Ca}$.

Methods: We report a new measurement of these resonance energies via the observation of previously unobserved $\gamma$-ray transitions. These transitions were observed by studying the ${}^{40}\mathrm{Ca}{(}^3\mathrm{He},\alpha \gamma ){}^{39}\mathrm{Ca}$ reaction with Gammasphere ORRUBA Dual Detectors for Experimental Structure Studies (GODDESS). The updated resonance energies were then used to calculate the ${}^{38}\mathrm{K}(p,\gamma ){}^{39}\mathrm{Ca}$ reaction rate and assess its uncertainties.

Results: In total, 23 new transitions were found, including three $\gamma$-ray transitions corresponding to the three $J^{\pi }=5/2^{+}$ states of astrophysical interest at energies of 6156.2(16), 6268.8(22), and 6470.8(19) keV. These correspond to resonance energies in the ${}^{38}\mathrm{K}(p,\gamma ){}^{39}\mathrm{Ca}$ reaction of 386(2), 498(2), and 701(2) keV.

Conclusions: Updated ${}^{38}\mathrm{K}(p,\gamma ){}^{39}\mathrm{Ca}$ reaction rate calculations show a reduced upper limit at nova temperatures. However, the lower-than-previously-measured energy of the 498-keV resonance and uncertainty in its resonance strength increases the upper limit of the rate close to previous estimates at 0.4 GK.

Figure 1

Particle identification spectrum plotting the particle energy detected in one strip of the BB10 ($y$ axis) and Super X3 detectors ($x$ axis) at ${\theta }_{\mathrm{lab}}\approx {50}^{\circ }$. The reaction channel of interest was selected by gating on the ${}^4\mathrm{He}$ nuclei in this spectrum.

Figure 2

Summed, Doppler-corrected Gammasphere spectrum gated on the detected ${}^4\mathrm{He}$ nuclei, timing between the silicon and germanium detectors, and a $\gamma$-ray multiplicity of 1. Single-escape peaks (s) and direct ground state transitions are shown in the spectrum, with the transitions labeled by their energies.

Figure 3

The ratios of the individual contribution of the 386-keV resonance to the mean value of the contribution calculated from Refs. [7, 10] (Lotay 2016). The $1\sigma$ upper limit of the contribution is reduced to less than a factor of 1.3 with the resonance strength held constant in the present study.

Figure 4

The fractional contribution of the 498-keV resonance to the overall reaction rate. The resonance strengths used in the present work were estimated theoretically with assumed proton spectroscopic factors of 0.01 and 0.1. The upper limit of the fractional contribution from this resonance is much higher than shown in Refs. [7, 10] (Lotay 2016).

Figure 5

Upper limits of the total ${}^{38}\mathrm{K}(p,\gamma ){}^{39}\mathrm{Ca}$ reaction rate from the present work and Refs. [7, 10] (Lotay 2016) and [11] (Setoodehnia 2018). Energy uncertainties that were previously neglected were included in the calculation of the upper limits. Also shown are the mean rate from Ref. [7] and Hauser-Feshbach rate uncertainty band [6] (Iliadis 2001) as presented in Refs. [7, 10], for comparison.

Figure 6

Ratios of the $1\sigma$ upper limits from Fig. 5 to the mean value presented in Refs. [7, 10]. The upper limit from the present work is smaller than previous measurements due to the reduction in uncertainty on energy of the 386-keV resonance. However, at higher temperatures the current upper limit approaches the previous limits due to the lower energy of the 498-keV resonance and resonance-strength uncertainty.