Measurement of ${}^{39}\mathrm{K}(p,\gamma ){}^{40}\mathrm{Ca}$ resonance strengths below 900 keV for nucleosynthesis in classical novae

Classical novae are one of the most frequent explosive nucleosynthesis events in our universe but are still not sufficiently understood. To this day, nuclear astrophysics cannot explain the endpoint of the nucleosynthesis networks that drive them. This is mainly due to a scarce experimental database of nuclear reaction rates for proton induced reactions in the mass region above silicon at temperatures between 0.1 and 0.4 GK. Because some nova ejecta hint at the production of elements in the calcium range (Centauri V1065), and some possibly even up to the iron region (Cygni V1974), it is of utmost interest to investigate possible paths towards heavier elements. Here we report on new measurements of resonance strengths for the ${}^{39}\mathrm{K}(p,\gamma ){}^{40}\mathrm{Ca}$ reaction below 900 keV. Measurements were performed at the 5U accelerator at the University of Notre Dame. The implications of these new strengths for the ${}^{39}\mathrm{K}(p,\gamma ){}^{40}\mathrm{Ca}$ reaction rate are discussed.

Figure 1

The figure illustrates the energy dependence of the Gamow peak for $T=0.3$ GK for the reaction ${}^{39}\mathrm{K}(p,\gamma ){}^{40}\mathrm{Ca}$ (solid line) as defined by the Maxwell-Boltzmann distribution of the interacting particles (dotted line) and the proton penetrability through the Coulomb barrier (dashed line) with the single-particle strength distributions of the observed proton unbound states in ${}^{40}\mathrm{Ca}$. Directly observed and candidate states [22] are indicated by green Breit-Wigner shapes and red vertical lines, respectively.

Figure 2

During long measurements, on top of the known resonances, the stability of the thin targets was monitored by scanning the $E_p=828$ keV resonance of the ${}^{39}\mathrm{K}(p,\gamma ){}^{40}\mathrm{K}$ reaction. The scans revealed no measurable degradation.

Figure 3

The top panel shows the measured efficiencies of standard calibration sources ${}^{152}\mathrm{Eu}$ and ${}^{137}$ Cs together with scaled relative efficiencies from an in-house produced ${}^{56}$ Co source and the decay transitions of the 992 keV resonance of the ${}^{27}$ Al($p,\gamma$)${}^{28}$ Si reaction. The calculated efficiencies were fitted by a double exponential function, which was later used for interpolation. The bottom-panel shows the residuals of the measured values to the obtained fit function. The red bands indicate the 68% confidence limits of the fit.

Figure 4

Spectrum for the $E_r=1347$ keV resonance in the ${}^{39}\mathrm{K}(p,\gamma ){}^{40}\mathrm{Ca}$ reaction using a thin target ($\mathrm{\Delta }E\approx 25$ keV). The spectrum shown is for a measurement in the “close geometry” setup; for high statistics, branching ratios and strengths were calculated with “far geometry” measurements to avoid summing contributions. Background lines from proton induced reactions on Na and F contamination in the target material and backings are clearly visible. Many of the weak lines result from proton capture on ${}^{41}\mathrm{K}$ (6.730%) that is present in the natural target material. Single escape (SEP) and double escape (DEP) peaks are also indicated.

Figure 5

Thick target yield for the second excited state to the ground state $\gamma$-ray line in ${}^{40}\mathrm{Ca}$ at $E_{\gamma }=3736$ keV. Steps in the yield curve as a function of increasing proton energy are indicative of new, strong, resonance contributions. The $\gamma$-ray spectra from three of the lowest energy measurements at $E_p=484$, 555, and 616 keV are given in Fig. 7.

Figure 6

Thin target energy scan in the region of the newly identified resonance candidates. Plateaus were clearly visible for the candidates at $E_r=536$ and 596 keV. However, no plateaus were observed at lower energies.

Figure 7

Thick-target $\gamma$-ray spectra taken at three different proton beam energies: (a) 616, (b) 555, (c) 484 keV. Note the split in the spectra energy scales made to highlight the important low and high energy regions. Primary $\gamma$-ray transitions for four of the predicted resonances at $E_r=596$, 536, 431, and 346 keV are indicated, corresponding to characteristic $\gamma$-rays at $E_{\gamma }=5003$, 8858, 8755, and 8671 keV, respectively (see Table 1). The two strong secondary $\gamma$-ray transitions from the 3736 and 3904 keV second and third final states to ground state, respectively, are always clearly visible. The secondary transition from the first excited state at 3353 keV to the ground state is forbidden as it is a $0^{+}\to 0^{+}$ transition. The inset in (a) highlights the clearly visible $E_{\gamma }=5003$ keV line from the $E_r=596$ keV resonance, where no primary ground state transition was observed. Many weaker $\gamma$-ray lines are also present from reactions on ${}^{41}\mathrm{K}(p,\gamma ){}^{42}\mathrm{Ca}$ from the natural abundance potassium target material.

Figure 8

Reaction rate components for the ${}^{39}\mathrm{K}(p,\gamma ){}^{40}\mathrm{Ca}$ reaction over the temperature range applicable for a novae environment. An estimate of the direct capture (DC) contribution is also shown for comparison. The model parameters are given in the text.

Figure 9

Fractional contribution of the strongest narrow resonances that dominate the ${}^{39}\mathrm{K}(p,\gamma ){}^{40}\mathrm{Ca}$ reaction rate. The total rate and the individual resonance contributions are taken relative to the total rate of Longland et al. [22]. The uncertainty of Longland et al. [22] is also indicated for comparison.

Figure 10

Ratio the ${}^{39}\mathrm{K}(p,\gamma ){}^{40}\mathrm{Ca}$ reaction rate of the present work (blue dashed line) as well as from statistical model predictions using sapphire [33] (red dashed line) and non-smoker [34, 35] relative to the rate of Longland et al. [22].

Figure 11

Comparison of the lifetime of ${}^{39}\mathrm{K}$ under novae conditions as a function of temperature using either the present rate (red solid line) or that of Longland et al. [22] (black dashed line).