Feasibility of studying astrophysically important charged-particle emission with the variable energy $\gamma$-ray system at the Extreme Light Infrastructure–Nuclear Physics facility

In the environment of a hot plasma, as achieved in stellar explosions, capture and photodisintegration reactions proceeding on excited states in the nucleus can considerably contribute to the astrophysical reaction rate. Usually, such reaction rates including the excited-state contribution are obtained from theoretical calculations as the direct experimental determination of these astrophysical rates is currently unfeasible. Future experiments could provide constraining information on the current reaction models which would improve the predictive power of the theoretical reaction rates. In the present study, experiments of photodisintegration with charged-particle emission leading to specific excited states in the residual nucleus are proposed. The expected experimental results can be used to determine the particle-transmission coefficients in the model calculations of photodisintegration and capture reactions. With such constrained transmission coefficients, the astrophysical reaction rates especially involving the excited-state contributions can be better predicted and implemented in astrophysical simulations. In particular, ($\gamma ,p$) and ($\gamma ,\alpha$) reactions in the mass and energy range relevant to the astrophysical $p$ process are considered and the feasibility of measuring them with the ELISSA detector system at the future Variable Energy $\gamma$-ray (VEGA) facility at Extreme Light Infrastructure–Nuclear Physics is investigated. To this end, in a first step 17 reactions with proton emission and 17 reactions with $\alpha$ emission are selected and the dependence of calculated partial cross sections on the variation of nuclear property input is tested. The simulation results reveal that, for the ($\gamma ,p$) reaction on 12 targets of ${}^{29}\mathrm{Si}$, ${}^{56}\mathrm{Fe},{}^{74}\mathrm{Se},{}^{84}\mathrm{Sr},{}^{91}\mathrm{Zr},{}^{96,98}\mathrm{Ru},{}^{102}\mathrm{Pd},{}^{106}\mathrm{Cd}$, and ${}^{115,117,119}\mathrm{Sn}$, and the ($\gamma ,\alpha$) reaction on five targets of ${}^{50}\mathrm{V},{}^{87}\mathrm{Sr},{}^{123,125}\mathrm{Te}$, and ${}^{149}\mathrm{Sm}$, the yields of the reaction channels with the transitions to the excited states in the residual nucleus, namely ($\gamma ,X_i$) with $i\ne 0$, are relevant and even dominant. Therefore, these 17 reactions are considered in the further feasibility study. For each of the 17 photon-induced reactions, in order to attain the detectable limit of 100 counts per day for the total proton or $\alpha$-particle yields, the minimum required $\gamma$-beam energies $E_{\mathrm{low}}$ for the measurements are estimated. It is further found that for each considered reaction, the total yields of the charged-particle $X$ may be dominantly contributed from one, two, or three ($\gamma ,X_i$) channels within a specific, narrow energy range of the incident $\gamma$ beam. If the actual measurements of these photon-induced reactions are performed in this energy range, the sum of the yields of the dominant ($\gamma ,X_i$) channels can be approximated by the measured yields of the charged particle $X$ within acceptable uncertainty. This allows to experimentally obtain the yields of the ($\gamma ,X_i$) channels which dominantly contribute to the total yields of $X$. Using the simulated yields, these energy ranges for each of the 17 photon-induced reactions are derived. Furthermore, the energy spectra of the ($\gamma ,X_i$) channels with $0\le i\le 10$ are simulated for each considered reaction, with the incident $\gamma$-beam energies in the respective energy range as derived before. Based on the energy spectra, the identification of the individual dominant ($\gamma ,X_i$) channels is discussed. It becomes evident that measurements of the photon-induced reactions with charged-particle emissions considered in this work are feasible with the VEGA+ELISSA system and will provide knowledge useful for nuclear astrophysics.

Figure 1

The cross sections of the ($\gamma ,p_i$) channels with $0\le i\le 10$ and the ($\gamma ,np$) channel on 17 targets of ${}^{29}\mathrm{Si},{}^{47}\mathrm{Ti},{}^{56}\mathrm{Fe},{}^{73}\mathrm{Ge},{}^{74}\mathrm{Se},{}^{84}\mathrm{Sr},{}^{91}\mathrm{Zr},{}^{95}\mathrm{Mo},{}^{96,98}\mathrm{Ru}$, ${}^{102}\mathrm{Pd},{}^{106}\mathrm{Cd},{}^{115,117,119}\mathrm{Sn},{}^{132}\mathrm{Ba}$, and ${}^{142}\mathrm{Nd}$. The ($\gamma ,p_i$) indicates the reaction with proton emission proceeding on the $i\mathrm{th}$ final state ($i$=0 for the ground state) in the residual nucleus. All the results are calculated by TALYS 1.9.

Figure 2

The cross sections of the ($\gamma ,{\alpha }_i$) channels with $0\le i\le 10$ and the ($\gamma ,n\alpha$) channel on 17 targets of ${}^{50}\mathrm{V}$, ${}^{67}\mathrm{Zn},{}^{87}\mathrm{Sr},{}^{107}\mathrm{Ag},{}^{113,115}\mathrm{In},{}^{119}\mathrm{Sn},{}^{123,125}\mathrm{Te},{}^{149,154}\mathrm{Sm},{}^{155,156,157,158,160}\mathrm{Gd}$, and ${}^{207}\mathrm{Pd}$. The ($\gamma ,{\alpha }_i$) indicates the reaction with $\alpha$-particle emission proceeding on the $i\mathrm{th}$ final state ($i=0$ for the ground state) in the residual nucleus. All the results are calculated by TALYS 1.9.

Figure 3

The ratios of the ($\gamma ,p_1$) cross section to the ($\gamma ,p_{\mathrm{tot}.}$) cross section for ${}^{96}\mathrm{Ru}$ calculated with six sets of NLDs (a), four sets of OMPs (b), and eight sets of SFs (c) available in TALYS 1.9, and the ratios of the ($\gamma ,{\alpha }_0$) cross section to the ($\gamma ,{\alpha }_{\mathrm{tot}.}$) cross section for ${}^{123}\mathrm{Te}$ calculated with six sets of NLDs (d), eight sets of OMPs (e), and eight sets of SFs (f) available in TALYS 1.9. The nuclear structure ingredients used for the calculations are indexed by numbers and described in the main text.

Figure 4

(a) The simulated yields $Y_i^p$ for ${}^{96}\mathrm{Ru}(\gamma ,p_i$) with $0\le i\le 10,Y^{np}$ for ${}^{96}\mathrm{Ru}(\gamma$,np), and $Y_{\mathrm{total}}^p$ for ${}^{96}\mathrm{Ru}(\gamma ,p_{\mathrm{tot}.}$). (b) The simulated yields $Y_i^{\alpha }$ for ${}^{123}\mathrm{Te}(\gamma ,{\alpha }_i$) with $0\le i\le 10,Y^{n\alpha }$ for ${}^{123}\mathrm{Te}(\gamma ,n\alpha$), and $Y_{\mathrm{total}}^{\alpha }$ for ${}^{123}\mathrm{Te}(\gamma ,{\alpha }_{\mathrm{tot}.}$).

Figure 5

The relative contributions of the ($\gamma ,X_i$) channels ($X=p$ or $\alpha$) for each $i\mathrm{th}$ final state ($0\le i\le 10$) in the residual nucleus to the total yields of the charged particle $X$, $Y_i^X/Y_{\mathrm{total}}^X$, for the considered 17 photo-induced reactions. The blue, yellow, and purple bands illustrate the energy ranges of the incident $\gamma$ beam for performing the measurements, in which one, the sum of two, and the sum of three ($\gamma ,X_i$) channels respectively contribute more than $90\%$ to the total yield of $X$. See the text for more details.

Figure 6

Energy spectra of the protons emitted from ($\gamma ,p_1$) and ($\gamma ,p_{\mathrm{tot}.}$) channels, indexed by “L01” and “Total” respectively, on ${}^{96}\mathrm{Ru}$ target (a) and ${}^{98}\mathrm{Ru}$ target (b) at $E_{\gamma }$ = 10.0 MeV. The results of ($\gamma ,p_{\mathrm{tot}.}$) include the contributions from all the ($\gamma ,p_i$) channels with $0\le i\le 10$.

Figure 7

Energy spectra of the protons emitted from ($\gamma ,p_0$), ($\gamma ,p_1$), and ($\gamma ,p_{\mathrm{tot}.}$) channels on ${}^{29}\mathrm{Si}$ at $E_{\gamma }$ = 14.5 MeV (a) and ${}^{91}\mathrm{Zr}$ at $E_{\gamma }$ = 12.0 MeV (b), and energy spectra of the $\alpha$ particles emitted from ($\gamma ,{\alpha }_0$), ($\gamma ,{\alpha }_1$), and ($\gamma ,{\alpha }_{\mathrm{tot}.}$) channels on ${}^{87}\mathrm{Sr}$ at $E_{\gamma }$ = 13.5 MeV (c) and ${}^{123}\mathrm{Te}$ at $E_{\gamma }$ = 11.5 MeV (d). The results of ($\gamma ,X_{\mathrm{tot}.}$) ($X$ = p or $\alpha$) include the contributions from all the ($\gamma ,X_i$) channels with $0\le i\le 10$.

Figure 8

Energy spectra of the protons emitted from ($\gamma ,p_0$), ($\gamma ,p_2$), and ($\gamma ,p_{\mathrm{tot}.}$) channels on ${}^{119}\mathrm{Sn}$ at $E_{\gamma }$ = 14.5 MeV (a), and energy spectra of the $\alpha$ particles emitted from ($\gamma ,{\alpha }_0$), ($\gamma ,{\alpha }_2$), and ($\gamma ,{\alpha }_{\mathrm{tot}.}$) channels on ${}^{125}\mathrm{Te}$ at $E_{\gamma }$ = 12.5 MeV (b). The results of ($\gamma ,X_{\mathrm{tot}.}$) ($X=p$ or $\alpha$) include the contributions from all the ($\gamma ,X_i$) channels with $0\le i\le 10$.

Figure 9

Energy spectra of the protons emitted from ($\gamma ,p_0$), ($\gamma ,p_3$), and ($\gamma ,p_{\mathrm{tot}.}$) channels on ${}^{102}\mathrm{Pd}$ (a) and ${}^{106}\mathrm{Cd}$ (b) at $E_{\gamma }$ = 10.0 MeV, and ${}^{115}\mathrm{Sn}$ (c) and ${}^{117}\mathrm{Sn}$ (d) at $E_{\gamma }$ = 12.5 MeV. The results of ($\gamma ,p_{\mathrm{tot}.}$) include the contributions from all the ($\gamma ,X_i$) channels with $0\le i\le 10$.

Figure 10

Energy spectra of the protons emitted from ($\gamma ,p_0$), ($\gamma ,p_1$), ($\gamma ,p_2$), and ($\gamma ,p_{\mathrm{tot}.}$) channels on ${}^{74}\mathrm{Se}$ at $E_{\gamma }$ = 10.0 MeV (a), and from ($\gamma ,p_0$), ($\gamma ,p_1$), ($\gamma ,p_3$), and ($\gamma ,p_{\mathrm{tot}.}$) on ${}^{84}\mathrm{Sr}$ at $E_{\gamma }$ = 13.0 MeV (b). Energy spectra of the $\alpha$ particles emitted from ($\gamma ,{\alpha }_0$), ($\gamma ,{\alpha }_1$), ($\gamma ,{\alpha }_4$), and ($\gamma ,{\alpha }_{\mathrm{tot}.}$) on ${}^{50}\mathrm{V}$ at $E_{\gamma }$ = 14.5 MeV (c), and ($\gamma ,{\alpha }_0$), ($\gamma ,{\alpha }_1$), ($\gamma ,{\alpha }_2$), and ($\gamma ,{\alpha }_{\mathrm{tot}.}$) on ${}^{149}\mathrm{Sm}+\gamma$ at $E_{\gamma }$ = 11.0 MeV (d). The results of ($\gamma ,X_{\mathrm{tot}.}$) (X = p or $\alpha$) include the contributions from all the ($\gamma ,X_i$) channels with $0\le i\le 10$.

Figure 11

The energy spectra of the proton from ${}^{117}\mathrm{Sn}+\gamma$ reaction and the $\alpha$ particle from ${}^{123}\mathrm{Te}+\gamma$ reaction at $E_{\gamma }$ = 19.0 MeV. The results of ($\gamma ,X_i$) channels are indexed by “L0i” for $0\le i\le 10$, and the results of ($\gamma ,np$) and ($\gamma ,n\alpha$) channels are indexed by “($\gamma ,np$)” and “($\gamma ,n\alpha$),” respectively. The label “Total” denotes the results counting all these considered contributions.