The astrophysical S-factor of the 12 C（p,γ 0 ） 13 N reaction at energies from 25 keV to 5 MeV within the framework of a modified potential cluster model with forbidden states is considered.The experimental phase shifts resonant δ_(2_(S 1/2 )),δ_(2_(P 3/2 )),and non-resonant δ_(2_(D 3/2 )) at the energies up to E c.m. =3 MeV are reproduced with high accuracy,which provides the appropriate agreement with the experimental data for the S-factor of 1950-2023 years.Two sets of asymptotic constant are used:Set Ⅰ refers to C w =1.30（2）,and Set Ⅱ refers to C w =1.37（1）.Set Ⅰ leads to the astrophysical factor S（25）=1.34 ± 0.02 keV·b,which is in agreement with data by Skowronski et al.,2023-1.34 ±0.09 keV·b;Set Ⅱ gives S（25）=1.49 ± 0.02 keV·b,which is in agreement with data by Kettner et al.,2023-1.48 ±0.09 keV·b.The reaction rates of 12 C（p,γ 0 ） 13 N at temperatures T 9 from 0.001 to 10 are calculated The detailed comparison with some models,the R-matrix approach,and NACRE Ⅱ data for reaction rates is considered.

We present our brief response and some comments to the article [Phys. Rev. C 108. 065801 (2023)]. In [Phys. Rev. C 108. 065801 (2023)] contains at least one unfounded and false statement, and our answer illuminates this explicitly. We made a graphical comparison of our results [Phys. Rev. Phys. Rev. C 105, 065806 (2022)] with the [Phys. Rev. C 108. 065801 (2023)]. Since in [Phys. Rev. C 108. 065801 (2023)] our potentials from [Phys. Rev. C 105, 065806 (2022)] with the slight modification were used, the results of these works are almost identical but in [Phys. Rev. C 108. 065801 (2023)] the opposite was stated.

We explicitly present the comparison of the results for the astrophysical S-factor and reaction rate for the ^6Li(p,γ)^7Be capture process at astrophysical energies, presented in Phys. Rev. Phys. Rev. C 105, 065806 (2022) and Phys. Rev. C 108. 065801 (2023) obtained within the famework of potential models. We demonstrate that both potential model approaches describe successfully the astrophysical S-factor and reaction rate simultaneously and reproduce the LUNA Collaboration [Phys. Rev. C 102, 052802(R) (2020)] results.

We study a radiative $p^{15}$N capture on the ground state of $^{16}$O at stellar energies within the framework of a modified potential cluster model (MPCM) with forbidden states, including low-lying resonances. The investigation of the $^{15}$N($p,\gamma _{0}$)$^{16}$O reaction includes the consideration of $^{3}S_{1}$ resonances due to $E1$ transitions and the contribution of $^{3}P_{1}$ scattering wave in $p$ + $^{15}$N channel due to $^{3}P_{1}\longrightarrow $ $^{3}P_{0}$ $M1$ transition. We calculated the astrophysical low-energy $S-$factor, and extrapolated $S(0)$ turned out to be within $34.7-40.4$ keV$\cdot $b. The important role of the asymptotic constant (AC) for the $^{15}$N($p,\gamma _{0}$)$^{16}$O process with interfering $^{3}S_{1}$(312) and $^{3}S_{1}$(962) resonances is elucidated. A comparison of our calculation for $S-$factor with existing experimental and theoretical data is addressed, and a reasonable agreement is found. The reaction rate is calculated and compared with the existing rates. It has negligible dependence on the variation of AC, but shows a strong impact of the interference of $^{3}S_{1}$(312) and $^{3}S_{1}$(962) resonances, especially at temperatures, referring to the CNO Gamow windows. We estimate the contribution of cascade transitions to the reaction rate based on the exclusive experimental data by \textit{Imbriani, et al. 2012}. The reaction rate enhancement due to the cascade transitions is observed from $T_{9} > 0.3 $ and reaches the maximum factor $\sim $\ 1.3 at $T_{9}=1.3$. We present the Gamow energy window and a comparison of rates for radiative proton capture reactions $^{12}$N($p,\gamma $)$^{13}$O, $^{13}$N($p,\gamma $) $^{14}$O, $^{14}$N($p,\gamma $)$^{15}$O, and $^{15}$N($p,\gamma $)$^{16}$O obtained in the framework of the MPCM and give temperature windows, prevalence, and significance of each process.

The C-14(p,gamma)N-15 reaction is of considerable interest in nuclear astrophysics. This reaction is one of the reactions of N-15 production in the stars. The rate of the C-14(p,gamma) N-15 reaction plays an important role in the formation of nuclei with an atomic mass of more than 14. Currently, this reaction at low energies has not been studied well enough, both experimentally and theoretically. Therefore, in this work, within the framework of a modified potential cluster model with a classification of orbital states according to Young's diagrams and taking into account allowed and forbidden states, we examined the possibility of describing the available experimental data for the total cross sections of the radiative p(14)C capture to the ground state of the N-15 nucleus. The calculations carried out take into account the wide resonance at 1.4 MeV in c.m. and performed at energies up to 5 MeV. It is shown that only on the basis of the E1 transition from the p(14)C scattering state, it is quite possible to explain the magnitude and shape of the experimental astrophysical S-factor. The work presents comparisons of the astrophysical S-factors of the radiative p(14)C capture to the ground state of the N-15 nucleus found by us with the experimental data available in the literature. Based on the obtained total cross sections, the rate of this reaction was calculated in the temperature range from 0.01 to 10.0 T-9. The calculated results for rates are approximated by a simple expression, which simplifies their use in applied thermonuclear and astrophysical research.

We discuss current attempts to employ the modified potential cluster model to describe the available experimental data on the B-13(n, gamma(0+1))B-14 total cross-sections. The estimated results of the M1 and E1 transitions from the n B-13 scattering states to the ground and first excited states of B-14 are presented. The 1(st) resonance at E-x = 1. 275 MeV (1(+)) is revealed in both the cross-section and reaction rate. Within the variation in the asymptotic constant, a thermal cross-section interval of 5.1 - 8.9 mb is proposed. Based on the theoretical total cross-sections at energies of 0.01 eV to 5 MeV, we calculate the reaction rate in the temperature range of 0.01 to 10T (9). The ignition T 9 values of the B-13(n, gamma(0+1))B-14 reaction depending on a neutron number density of n(overbar)(n) similar to 10(22) cm(-3) are determined. The radiative neutron capture reaction rates on the boron B10-13 and carbon C12-14 isotopes are compared.

Within the modified potential cluster model (MPCM) with forbidden states, the total cross sections are calculated for capture in the ground and first excited states of the 9 Li nucleus in the n 8 Li channel in the energy range from 10 −5 eV to 5 MeV based on Е 1 and M 1 transitions. The experimentally proved resonance at E c.m. = 0.232 MeV in the 4 P 5/2 wave and ab initio -predicted 4 P 3/2 resonance at 1.32 MeV [Phys. Rev. C 103, 035801 (2021)] are considered. The strong impact of the asymptotic constant and channel spectroscopic factors on the total capture cross sections are responsible for the variation in the absolute values within factor two. As a consequence, the thermal cross sections are σtherm= 24–46.8 mb. The evaluation of σtherm based on the extrapolation of ab initio cross sections yields ∼85 mb. The reaction rate is calculated in the temperature range from 0.01 to 10 T 9 . The reported reaction rates are compared at the benchmark point 1 T 9 . The comparison of two datasets [Phys. Rev. C 103, 035801 (2021) and Phys. Rev. C 105, 064608 (2022)] on reaction rates recently calculated in microscopic models in extended temperature intervals shows the essential quantitative and qualitative differences. The comparative joint analysis of the reaction rates of radiative neutron capture on the lithium isotopes 6,7,8 Li is suggested for the choice of an optimal interval for the asymptotic constants.

The B-11(p,gamma)C-12 reaction is of considerable interest in the field of controlled thermonuclear fusion and in nuclear astrophysics. In thermonuclear reactors, structural elements containing boron can be used as neutron absorbers. This reaction is one of the reactions of B-11 production in the stars (sic). The rate of the B-11(p,gamma)C-12 reaction (occurring in the interiors of first-generation stars) can be of great importance for the amount of B-11 and B-10 observed today in the Earth's crust and in the interstellar medium. Therefore, in this work, within the framework of a modified potential cluster model with a classification of orbital states according to Young's diagrams and taking into account allowed and forbidden states, we examined the possibility of describing the available experimental data for the total cross sections of the radiative p(11)B capture to the ground state of the C-12 nucleus at energies up to 1.5 MeV. It is shown that only on the basis of E1 and M1 transitions from the p(11)B scattering states, taking into account the first resonance for the ground state of the C-12 nucleus, it is quite possible to explain the magnitude and shape of the experimental astrophysical S-factor. The work presents comparisons the astrophysical S-factors of the radiative p(11)B capture to the ground state of the C-12 nucleus found by us with the experimental data available in the literature. Based on the obtained theoretical S-factor, the rate of this reaction was calculated in the temperature range from 0.01 to 1 T-9. The calculated results for rates are approximated by a simple expression, which simplifies their use in applied thermonuclear and astrophysical research.

Within the framework of the modified potential cluster model with forbidden states, the total cross-sections of radiative n Be-9 capture to the ground and five low-lying excited states are calculated at energies from 10(-2) eV up to 5 MeV. The thermal cross-section E ( x ) from 7.371 MeV up to 10.570 MeV corresponding to the following states with x , MeV): 9Be(n,? (0+1+2+3+4+5))Be-10 reaction rates are calculated at temperatures from 0.001 to 10 T-9. Contrary to the available data, we propose that the rise in the reaction rate near factor five at T-9 > 1 is mainly due to the first 3(-)(E-R = 0.559 MeV) resonance. We foresee this contrast as arising from different model approaches.

The 10B(p,γ)11C reaction is of significant interest in nuclear astrophysics and in the field of controlled thermonuclear fusion. This reaction is one of the reactions of 11B production, which is carried out through the 10B(p,γ)11C(e̱ṯa̱+ν)11B chain. The rate of the 10B(p,γ)11C reaction (occurring in the interiors of first-generation stars) can be of great importance for the amount of 10B and 11B observed today in the interstellar medium and in the Earth's crust. In thermonuclear reactors, structural elements containing boron can be used as neutron absorbers, etc. Therefore, in this work, within the framework of a modified potential cluster model with a classification of orbital states according to Young's diagrams and taking into account allowed and forbidden states, we examined the possibility of describing the available experimental data for the total cross sections of the radiative p10B capture to the ground state of the 11C nucleus at energies up to 1 MeV. It is shown that only on the basis of E1 and M1 transitions from the p10B scattering states, taking into account the first resonance for the ground state of the 11C nucleus, it is quite possible to explain the magnitude and shape of the experimental astrophysical S-factor. The work presents comparisons the astrophysical S-factors of the radiative p10B capture to the ground state of the 11C nucleus found by us with the experimental data available in the literature. Based on the obtained theoretical S-factor, the rate of this reaction was calculated in the temperature range from 0.01 to 1 T9. The calculated results for rates are approximated by a simple expression, which simplifies their use in applied thermonuclear and astrophysical research.

We present new calculations of the astrophysical S factor and reaction rate for the Li-6(p, gamma) Be-7 reaction at energies of 10 keV to 5 MeV in the framework of a modified potential cluster model with forbidden states, including low lying resonances. The astrophysical S(E) factor is compared with the available experimental data and calculations done within different models. The results for the S factor are in good agreement with the data set (for E < 0.3 MeV) and calculations (for E < 0.6 MeV) of the LUNA Collaboration [Phys. Rev. C 102, 052802(R) (2020)]. The recommended extrapolated zero value S(0) turned out to be 101 eV b. Using the theoretical total cross sections, the Li-6(p, gamma) Be-7 capture reaction rate is calculated at temperatures ranging from 0.01T(9) to 10T(9) and compared with NACRE and NACRE II. Analytical expressions for the S factor and reaction rate are given, and the effect of low-lying resonances on the reaction rate is estimated. We suggest updating the NACRE and NACRE II databases in light of the new LUNA data and present calculations.

Within the framework of the modified potential cluster model with the classification of orbital states according to Young’s diagrams, the possibility of describing the experimental data for the total cross sections of radiative n13C capture to the ground and first excited states of the 14C nucleus at energies from 10 meV (1 meV = 10–3 eV) to 5 MeV is considered. It is shown that it is quite possible to explain values of the known experimental cross sections only based on E1 transitions from some n13C scattering states, taking into account the first resonance at 153 keV. Based on theoretical total cross sections, the capture reaction rate has been calculated in the temperature range from 0.01 to 10.0 Т9, and its analytical parameterization has been performed.

Within the framework of the modified potential cluster model with a classification of orbital states according to Young’s diagrams, the possibility of predicting the missing experimental data for the total cross sections of radiative n 11 B capture on the first excited state of the 12 B nucleus at 0.95 MeV (2 + ) for the reaction energies from 10 meV (1 meV = 10 -3 eV) to 7 MeV is considered. Based on the obtained total cross sections that take into account resonances up to 5 eV, the reaction rate is calculated at temperatures from 0.01 to 10.0 Т 9 . It is shown that low-lying resonances have a significant effect on the capture reaction rate.

We consider the rate of radiative n6Li capture reaction in the temperature range from 0.01 to 10 T9 within the framework of the modified potential cluster model with forbidden states. The total cross sections are calculated for capture to the ground, and the first excited states of the 7Li nucleus in the n6Li channel in the energy range from 10 meV to 5 MeV. Analytical expressions approximate the total cross-section at low energies and the reaction rate over the entire considered temperature range.

We present new calculations of the astrophysical $S-$factor and reaction rate for the $^{6}$Li$(p,\gamma )^{7}$Be reaction at energies of 10 keV to 5 MeV in the framework of a modified potential cluster model with forbidden states, including low lying resonances. The astrophysical $S(E)-$factor is compared with the available experimental data and calculations done within different models. The results for the $S-$factor are in good agreement with the data set (for $E<0.3$ MeV) and calculations (for $E<0.6$ MeV) of LUNA collaboration (Phys. Rev. C 102$,$ 052802, 2020). The recommended extrapolated zero value $S(0)$ turned out to be 101 eV $\cdot $ b. Using the theoretical total cross-sections$,$ the $^{6}$Li$(p,\gamma)^{7} $Be capture reaction rate is calculated at temperatures ranging from 0.01 to 10 $T_{9}$ and compared with NACRE and NACRE II. Analytical expressions for the $S-$factor and reaction rate are given, and the effect of low-lying resonances on the reaction rate is estimated. We suggest to update the NACRE and NACRE II databases in light of the new LUNA data and present calculations.

Within the framework of the modified potential cluster model with a classification of orbital states according to Young's diagrams, the possibility of predicting the missing experimental data for the total cross sections of radiative n(11)B capture on the first excited state of the B-12 nucleus at 0.95 MeV (2(+)) for the reaction energies from 10 meV (1 meV = 10(-3) eV) to 7 MeV is considered. Based on the obtained total cross sections that take into account resonances up to 5 eV, the reaction rate is calculated at temperatures from 0.01 to 10.0 T-9. It is shown that low-lying resonances have a significant effect on the capture reaction rate.