Cross section measurements of proton capture reactions on Se isotopes relevant to the astrophysical $p$ process

Cross sections of proton capture reactions on ${}^{74}\mathrm{Se}$, ${}^{78}\mathrm{Se}$, and ${}^{80}\mathrm{Se}$ have been measured at incident beam energies from 2 to 6 MeV, 1.7 to 3 MeV, and 1.5 to 3.5 MeV, respectively. In the case of ${}^{78,80}\mathrm{Se}$, cross sections were obtained from in-beam $\gamma$-angular distribution measurements, whereas for the ${}^{74}\mathrm{Se}$ isotope they were derived from off-beam activity measurements. The measured cross sections were compared with calculations performed with the nuclear reaction code talys (version 1.6). A good agreement between theory and experiment was found. Astrophysical $S$ factors and reaction rates deduced from the experimental and calculated cross sections were also compared and the impact of different nuclear ingredients in the calculations on the reaction rates was investigated. It was found that, for certain combinations of nuclear input models, the reaction rates obtained at temperatures relevant to $p$-process nucleosynthesis differ by a factor 2 at the most, differences that are well within the acceptable deviations of calculated $p$-nuclei abundances and observations.

Figure 1

Typical low gain $\gamma$ spectrum of the ${}^{78}\mathrm{Se}(p,\gamma ){}^{79}\mathrm{Br}$ reaction measured at $E_p=3\mathrm{MeV}$. The accumulated charge was 10.5 mC (see Sec. 2a for details).

Figure 2

Same as in Fig. 1 but for the ${}^{80}\mathrm{Se}(p,\gamma ){}^{81}\mathrm{Br}$ reaction measured at $E_p=1.7\mathrm{MeV}$. The accumulated charge was $Q=22.6$ mC (see Sec. 2a for details).

Figure 3

Drawing of the scattering chamber employed in the activation measurements (see Sec. 2b for details).

Figure 4

Typical Rutherford backscattering spectrum (RBS) measured with a 2.5-MeV proton beam impinging on a 484-$\mu \mathrm{g}/{\mathrm{cm}}^2$-thick ${}^{nat}\mathrm{Se}$ layer evaporated on a 0.3-mm-thick Si wafer. The black solid curve is the corresponding simulation performed using the code simnra [17].

Figure 5

Typical $\gamma$-activity spectrum taken at $E_p=4$ MeV (see Sec. 2b for details).

Figure 6

Level scheme of the ${}^{79}\mathrm{Br}$ nucleus containing all the $\gamma$ transitions (dashed arrows) observed in the present work to populate its ground state. These transitions were used to determine the total cross section of the ${}^{78}\mathrm{Se}(p,\gamma ){}^{79}\mathrm{Br}$ reaction as described in Sec. 3a.

Figure 7

Same as in Fig. 6 but for ${}^{81}\mathrm{Br}$.

Figure 8

Typical angular distributions of $\gamma$ transitions of ${}^{79}\mathrm{Br}$ measured at $E_p=3$ MeV (see Sec. 3a for details).

Figure 9

Same as in Fig. 8 but for the ${}^{81}\mathrm{Br}$. The corresponding ${\gamma }_0$ transition is plotted in panel (a).

Figure 10

Screening-corrected total cross sections (a), and corresponding $S$ factors (b) of the ${}^{74}\mathrm{Se}(p,\gamma ){}^{75}\mathrm{Br}$ reaction (see Sec. 4b1 for details).

Figure 11

Total cross sections (solid triangles) of the (a) ${}^{74}\mathrm{Se}(p,\gamma ){}^{75}\mathrm{Br}$ and (b) ${}^{77}\mathrm{Se}(p,\gamma ){}^{78}\mathrm{Br}$ reactions reported by Krivonosov et al. [46]. Open triangles indicate the same data divided by a factor 2.5. For comparison, in panel (a), our present results and those of Gyürky et al. [16] are also plotted as solid and open circles, respectively. All plotted cross sections are corrected for screening effects (see Sec. 4b1 for details).

Figure 12

Weighted sum ${\sigma }_{\mathrm{\Sigma }}$ of the screening-corrected total cross sections ${\sigma }_{(p,\gamma )}$ and ${\sigma }_{(p,n)}$ of ${}^{76}\mathrm{Se}(p,\gamma ){}^{77}\mathrm{Br}$ and ${}^{77}\mathrm{Se}(p,n){}^{77}\mathrm{Br}$, respectively (see Sec. 4b1 for details).

Figure 13

Same as in Fig. 10 for the ${}^{78}\mathrm{Se}(p,\gamma ){}^{79}\mathrm{Br}$ reaction (see Sec. 4b1 for details).

Figure 14

Same as in Fig. 10 for the ${}^{80}\mathrm{Se}(p,\gamma ){}^{81}\mathrm{Br}$ reaction (see Sec. 4b1 for details).

Figure 15

Ratios ${\sigma }_m/{\sigma }_{\mathrm{T}}$ for ${}^{78}\mathrm{Se}(p,\gamma ){}^{79}\mathrm{Br}$ and ${}^{80}\mathrm{Se}(p,\gamma ){}^{81}\mathrm{Br}$, in panels (a) and (b), respectively. The talys “optimal” model calculations depicted in both panels with dashed-dotted curves correspond to those explained in Sec. 4b1.

Figure 16

Same as in Fig. 10 but for ${}^{82}\mathrm{Se}(p,\gamma ){}^{83}\mathrm{Br}$ [47].

Figure 17

Comparison of the experimental screening-corrected total cross sections ${\sigma }_{\mathrm{T}}$ from the literature [48, 50, 52] and the present work (solid circles) with our talys calculations for the ${}^{80}\mathrm{Se}(p,n){}^{80}\mathrm{Br}$ reaction (see Sec. 4b3 for details).

Figure 18

Comparison of the experimental screening-corrected total cross sections ${\sigma }_{\mathrm{T}}$ existing in literature [16, 49, 53] and those of the present work (solid circles) with our talys calculations for the ${}^{82}\mathrm{Se}(p,n){}^{82}\mathrm{Br}$ reaction (see also Sec. 4b3).

Figure 19

Total cross sections from [50, 51] for the (a) ${}^{77}\mathrm{Se}(p,n){}^{77}\mathrm{Br}$ and (b) ${}^{78}\mathrm{Se}(p,n){}^{78}\mathrm{Br}$ reactions compared with our talys calculations (see Sec. 4b2 for details).

Figure 20

Experimental ratios ${\sigma }_m$/(${\sigma }_m+{\sigma }_g$) from Ref. [54] compared in panel (a) and (b) with our talys calculations for the ${}^{77}\mathrm{Se}(p,n){}^{77}\mathrm{Br}$ and ${}^{80}\mathrm{Se}(p,n){}^{80}\mathrm{Br}$ reactions, respectively (see Sec. 4b3 for details).

Figure 21

Comparison of our talys calculations with the experimental ratios ${\sigma }_g/{\sigma }_m$ reported in [53, 56] for the ${}^{80}\mathrm{Se}(p,n){}^{80}\mathrm{Br}$ reaction and ${\sigma }_g/({\sigma }_m+{\sigma }_g)$ reported in [55] for ${}^{82}\mathrm{Se}(p,n){}^{82}\mathrm{Br}$ (see Sec. 4b3 for details).

Figure 22

Ratios of the ground-state reaction rates ${\mathrm{RR}}_{\mathrm{O}}$ over ${\mathrm{RR}}_3$ for ${}^{74}\mathrm{Se}(p,\gamma ){}^{75}\mathrm{Br}$ (solid curve), ${}^{78}\mathrm{Se}(p,\gamma ){}^{79}\mathrm{Br}$ (dashed curve), and ${}^{80}\mathrm{Se}(p,\gamma ){}^{81}\mathrm{Br}$ (dashed-dotted curve). ${\mathrm{RR}}_{\mathrm{O}}$ have been derived from the talys “optimal” combinations. ${\mathrm{RR}}_3$ are the reaction rates deduced from the talys-3 calculations.

Figure 23

Stellar reaction rates of the ${}^{74}\mathrm{Se}(p,\gamma ){}^{75}\mathrm{Br}$, ${}^{78}\mathrm{Se}(p,\gamma ){}^{79}\mathrm{Br}$, and ${}^{80}\mathrm{Se}(p,\gamma ){}^{81}\mathrm{Br}$ reactions at temperatures relevant to $p$ process. The shaded areas and talys-3 calculations (solid curves) are explained in the caption of Fig. 10 and in Sec. 4b. The corresponding REACLIB [57] and BRUSLIB [58] rates are indicated by the dashed and dotted curves, respectively.

Figure 24

Ratios ${\mathrm{r}}_{i3}$ of the upper and lower calculated stellar reaction rates over the global talys-3 combination of the $n\mathrm{OMP}$, $\alpha \mathrm{OMP}$, NLD, and $\gamma \mathrm{SF}$ models (see text for details). The solid and dashed curves indicate the stellar reaction-rate ratios of those given in the BRUSLIB [58] and REACLIB [57] databases, respectively, over the corresponding ones calculated using the global talys-3 combination.