arXiv subjects

S. A. Turakulov

Publications and source records attributed to S. A. Turakulov.

15 recordsLinked to original sources

arXiv2026

Structure of the $^8$B and $^8$Li nuclei and the astrophysical $S_{17}(0)$-factor of the $^7$Be($p,γ$)$^8$B direct capture process within a three-body model

The structure of the ground $(2^+)$ and excited $(1^+)$ bound states of the $^8$B and $^8$Li nuclei is studied within the framework of the $α+^3$He($^3$H)+$p(n)$ three-body potential cluster model based on the hyperspherical Lagrange-mesh method. The two-body realistic potentials have been applied from the literature. Convergent theoretical estimates for the three-body binding energy and matter radius have been obtained with the maximal hypermomentum $K_{max}=22$ and 28 for the ground and excited $1^+$ states, respectively. The ANC value of the virtual transition of the $^8$B nucleus is estimated self-consistently by matching the overlap integral of the $^8$B three-body and the $^7$Be two-body wave functions with it's asymptotics. The obtained values are $0.211$~fm$^{-1/2}$ and $0.739$~fm$^{-1/2}$ in the spin 1 and spin 2 channels, respectively. For the ANC values of the $^8$Li nucleus the estimates $0.220$~fm$^{-1/2}$ and $0.774$~fm$^{-1/2}$ are extracted. The ratio $C^2(^8 {\rm B})/C^2(^8 {\rm Li})=0.912$ implies a breaking of the mirror symmetry of the strong nuclear forces of order 27\% due to the Coulomb interaction and the dynamical three-body effects. For the $S_{17}(0)$ -factor an estimate $22.492\pm0.014$ eV b was obtained based on the asymptotic theory developed by D. Baye [Phys. Rev. C {\bf 62},065803 (2000)]. The spin 2 channel contributes with $S^{(2)}_{17}(0)=20.838 \pm 0.014$ eV b, while the spin 1 channel yields $S^{(1)}_{17}(0)=1.654 \pm 0.003$ eV b. These results for $S_{17}(0)$ are in a good agreement with the estimate $20.8\pm0.7{\rm(th)}\pm1.4{\rm(exp)}$ eV b of the SF II, but larger than the recommended value $20.5\pm0.70$ eV b of the SF III. At the same time, our estimate is very close to the value 22.4 eV b used in the most successful Solar Model BAR2M [W.~Yang and Z.~Tian, AJ {\bf 970} (2024), 38].

nucl-th↗

arXiv2025

Astrophysical $S$ factor and reaction rate of the direct $^{12}{\rm C}(p, γ)^{13}{\rm N}$ capture process within a potential model approach

The astrophysical direct nuclear capture reaction $^{12}{\rm C}(p, γ)^{13}{\rm N}$ is studied within the framework of a potential model. Parameters of the nuclear $p-^{12}$C interaction potentials of the Woods-Saxon form are adjusted to reproduce experimental $p-^{12}$C scattering phase shifts, as well as the binding energies and empirical values of the asymptotic normalization coefficient (ANC) for the $^{13}$N(1/2$^-$) ground state from the literature. The reaction rates are found to be very sensitive to the description of the value of the ANC of the $^{13}$N($1/2^{-}$) ground state and width of the $^{13}$N($1/2^+$) resonance at the $E_x=2.365$ MeV excitation energy. The potential model, which yields the ANC value of 1.63 fm$^{-1/2}$ for the $^{13}$N($1/2^{-}$) ground state and a value $Γ$=39 keV for the $^{13}$N($1/2^+$) resonance width, is able to reproduce the astrophysical $S$ factor in the energy interval up to 2 MeV, the empirical values of the reaction rates in the temperature region up to $T=10^{10}$ K of the LUNA Collaboration and the results of the R-matrix fit. The astrophysical factor $S(0)=1.35$ keV b is found using the asymptotic expansion method of D. Baye. The obtained value is in a good agreement with the Solar Fusion II result. At the same time, the calculated value of 1.44 keV b of the astrophysical $S$ factor at the Solar Gamow energy is consistent with the result of the R-matrix fit of $S(25~\rm{keV})=1.48 \pm 0.09$ keV b by Kettner {\it et al.}, but slightly less than the result of $S(25~\rm{keV})=1.53 \pm 0.06$ keV b the LUNA Collaboration.

nucl-th↗

arXiv2024

Reply to the "Comments to the paper "Detailed study of the astrophysical direct capture reaction $^{6}{\rm Li}(p, γ)^{7}{\rm Be}$ in ..." " by S.B. Dubovichenko, A.S. Tkachenko, R. Ya. Kezerashvili, arXiv:2401.04281 (2024)

The differences in potential models used in our work and in the original paper of the authors of the Comment are discussed. The neglecting of simple rules of reaction calculations is shown as a possible origin of the defect in the temperature dependence of the reaction rates in the work of the authors of the Comment.

nucl-th↗

arXiv2024

Study of the direct $^{16}{\rm O}(p, γ)^{17}{\rm F}$ astrophysical capture reaction within a potential model approach

A potential model is applied for the analysis of the astrophysical direct nuclear capture process $^{16}$O(p,$γ)^{17}$F. The phase-equivalent potentials of the Woods-Saxon form for the p$-^{16}$O interaction are examined which reproduce the binding energies and the empirical values of ANC for the $^{17}$F(5/2$^+$) ground and $^{17}$F(1/2$^+$) ($E^*$=0.495 MeV) excited bound states from different sources. The best description of the experimental data for the astrophysical $S$ factor is obtained within the potential model which yields the ANC values of 1.043 fm$^{-1/2}$ and 75.484 fm$^{-1/2}$ for the $^{17}$F($5/2^{+}$) ground and $^{17}$F($1/2^{+}$) excited bound states, respectively. The zero-energy astrophysical factor $S(0)=9.321$ KeV b is obtained by using the asymptotic expansion method of D. Baye. The calculated reaction rates within the region up to 10$^{10}$ K are in good agreement with those from the R-matrix approach and the Bayesian model in both absolute values and temperature dependence.

nucl-th↗

arXiv2023

Detailed study of the astrophysical direct capture reaction $^{6}{\rm Li}(p, γ)^{7}{\rm Be}$ in a potential model approach

The astrophysical $S$ factor and reaction rates of the direct capture process $^{6}$Li(p,$γ)^{7}$Be are estimated within a two-body single-channel potential model approach. Central potentials of the Gaussian-form in the $^2P_{3/2}$ and $^2P_{1/2}$ waves are adjusted to reproduce the binding energies and the empirical values of the asymptotic normalization coefficients (ANC) for the $^7$Be(3/2$^-$) ground and $^7$Be(1/2$^-$) excited bound states, respectively. The parameters of the potential in the most important $^2S_{1/2}$ scattering channel were fitted to reproduce the empirical phase shifts from the literature and the low-energy astrophysical $S$ factor of the LUNA collaboration. The obtained results for the astrophysical $S$ factor and the reaction rates are in a very good agreement with available experimental data sets. The numerical estimates reproduce not only the absolute values, but also the energy and temperature dependence of the $S$ factor and reaction rates of the LUNA collaboration, respectively. The estimated $^{7}{\rm Li/H}$ primordial abundance ratio $(4.67\pm 0.04 )\times 10^{-10}$ is well consistent with recent BBN result of $(4.72\pm 0.72) \times 10^{-10}$ after the Planck observation.

nucl-th↗

arXiv2022

ASTROPHYSICAL S(0)-FACTORS FOR THE $^{3}{\rm He}(α, γ)^{7}{\rm Be}$, $^{3}{\rm H}(α, γ)^{7}{\rm Li}$ and $^{7}{\rm Be}(p, γ)^{8}{\rm B}$ DIRECT CAPTURE PROCESSES IN A POTENTIAL MODEL

Astrophysical S-factors at zero energy for the direct nuclear capture reactions $^{3}{\rm He}(α, γ)^{7}{\rm Be}$, $^{3}{\rm H}(α, γ)^{7}{\rm Li}$ and $^{7}{\rm Be}(p, γ)^{8}{\rm B}$ are estimated within the framework of two-body potential cluster model on the basis of extranuclear capture approximation of D. Baye and E. Brainis. The values of S(0)-factors have been calculated using two different potential models for each process, which were adjusted to the binding energies and empirical values of the asymptotical normalization coefficients from the literature. New values of S(0)-factors have been obtained.

nucl-th↗

arXiv2021

Astrophysical S factor and rate of $^{7}{\rm Be}(p, γ)^{8}{\rm B}$ direct capture reaction in a potential model

The astrophysical $^7{\rm Be}(p, γ)^8{\rm B}$ direct capture process is studied in the framework of a two-body single-channel model with potentials of the Gaussian form. A modified potential is constructed to reproduce the new experimental value of the $S$-wave scattering length and the known astrophysical $S$ factor at the Gamow energy, extracted from the solar neutrino flux. The resulting potential is consistent with the theory developed by Baye [Phys. Rev. C {\bf 62} (2000) 065803] according to which the $S$-wave scattering length and the astrophysical $S$ factor at zero energy divided by the square of ANC are related. The obtained results for the astrophysical $S$ factor at intermediate energies are in good agreement with the two data sets of Hammache {\it et al.} [Phys. Rev. Lett. {\bf 86}, 3985 (2001); {\it ibid.} {\bf 80}, 928 (1998)]. Linear extrapolation to zero energy yields $ S_{17}(0) \approx (20.5 \pm 0.5) \, \rm eV \, b $, consistent with the Solar Fusion II estimate. The calculated reaction rates are substantially lower than the results of the NACRE II collaboration.

nucl-th↗

arXiv2020

Analysis of the $^{3}{\rm He}(α, γ)^{7}{\rm Be}$ and $^{3}{\rm H}(α,γ)^{7}{\rm Li}$ astrophysical direct capture reactions in a modified potential-model approach

Astrophysical $S$ factors and reaction rates of the direct radiative capture processes $^{3}{\rm He}(α, γ)^{7}{\rm Be}$ and $^{3}{\rm H}(α,γ)^{7}{\rm Li}$, as well as the primordial abundance of the $^{7}{\rm Li}$ element, are estimated in the framework of a modified two-body potential model. It is shown that suitable modification of phase-equivalent $α-^{3}{\rm He}$ potentials in the $d$ waves can improve the description of the astrophysical $S$ factor for the direct $^{3}{\rm He}(α, γ)^{7}{\rm Be}$ radiative capture reaction at energies above 0.5 MeV. An estimated $^{7}{\rm Li/H}$ abundance ratio of $(4.89\pm 0.18 )\times 10^{-10}$ is in very good agreement with the recent measurement of $(5.0\pm 0.3) \times 10^{-10}$ by the LUNA collaboration.

nucl-th↗

arXiv2019

Comparative study of the direct $α+d$ $\rightarrow$ $^6$Li + $γ$ astrophysical capture reaction in few-body models

A comparative analysis of the astrophysical S factor and the reaction rate for the direct $ α(d,γ)^{6}{\rm Li}$ capture reaction, and the primordial abundance of the $^6$Li element, resulting from two-body, three-body and combined cluster models is presented. It is shown that the two-body model, based on the exact-mass prescription, can not correctly describe the dependence of the isospin-forbidden E1 S factor on energy and does not reproduce the temperature dependence of the reaction rate from the direct LUNA data. It is demonstrated that the isospin-forbidden E1 astrophysical S factor is very sensitive to the orthogonalization procedure of Pauli-forbidden states within the three-body model. On the other hand, the E2 S factor does not depend on the orthogonalization method. This insures that the orthogonolizing pseudopotentials method yields a very good description of the LUNA collaboration's low-energy direct data. At the same time, the SUSY transformation significantly underestimates the data from the LUNA collaboration. On the other hand, the energy dependence of the E1 S factor are the same in both methods. The best description of the LUNA data for the astrophysical S factor and the reaction rates is obtained within the combined E1(three-body OPP)+E2(two-body) model. It yields a value of $(0.72 \pm 0.01) \times 10^{-14}$ for the $^6$Li/H primordial abundance ratio, consistent with the estimation $(0.80 \pm 0.18) \times 10^{-14}$ of the LUNA collaboration. For the $^6{\rm Li}/^7{\rm Li}$ abundance ratio an estimation $(1.40\pm 0.12)\times 10^{-5}$ is obtained in good agreement with the Standard Model prediction.

nucl-th↗

arXiv2019

Astrophysical $S$-factor of the direct $α(d,γ)^6$Li capture reaction in a three-body model

At the long-wavelength approximation, electric dipole transitions are forbidden between isospin-zero states. In an $α+n+p$ model with $T = 1$ contributions, the $α(d,γ)^6$Li astrophysical $S$-factor is in agreement with the experimental data of the LUNA collaboration, without adjustable parameter. The exact-masses prescription used to avoid the disappearance of $E1$ transitions in potential models is not founded at the microscopic level.

nucl-th↗

arXiv2019

$^{3}{\rm He}(α, γ)^{7}{\rm Be}$ and $^{3}{\rm H}(α,γ)^{7}{\rm Li}$ reaction rates and the implication for Big Bang nucleosynthesis in the potential model

The reaction rates of the direct astrophysical capture processes $^{3}{\rm He}(α, γ)^{7}{\rm Be}$ and $^{3}{\rm H}(α,γ)^{7}{\rm Li}$, as well as the abundance of the $^{7}{\rm Li}$ element are estimated in the framework of a two-body potential model. The estimated $^{7}{\rm Li/H}$ abundance ratio of $^{7}{\rm Li/H}=(5.07\pm 0.14 )\times 10^{-10}$ is in a very good agreement with the recent measurement $^{7}{\rm Li/H}=(5.0\pm 0.3) \times 10^{-10}$ of the LUNA collaboration.

nucl-th↗

arXiv2018

Theoretical study of the direct $α+d$ $\rightarrow$ $^6$Li + $γ$ astrophysical capture process in a three-body model II. Reaction rates and primordial abundance

The astrophysical S-factor and reaction rate of the direct capture process $α+d$ $\rightarrow$ $^6$Li + $γ$, as well as the abundance of the $^6$Li element are estimated in a three-body model. The initial state is factorized into the deuteron bound state and the $α+d$ scattering state. The final nucleus $^6$Li(1+) is described as a three-body bound state $α+n+p$ in the hyperspherical Lagrange-mesh method. Corrections to the asymptotics of the overlap integral in the S- and D-waves have been done for the E2 S-factor. The isospin forbidden E1 S-factor is calculated from the initial isosinglet states to the small isotriplet components of the final $^6$Li(1+) bound state. It is shown that the three-body model is able to reproduce the newest experimental data of the LUNA collaboration for the astrophysical S-factor and the reaction rates within the experimental error bars. The estimated $^6$Li/H abundance ratio of $(0.67 \pm 0.01)\times 10^{-14}$ is in a very good agreement with the recent measurement $(0.80 \pm 0.18)\times 10^{-14}$ of the LUNA collaboration.

nucl-th↗

arXiv2018

Astrophysical $^{3}{\rm He}(α, γ)^{7}{\rm Be}$ and $^{3}{\rm H}(α,γ)^{7}{\rm Li}$ direct capture reactions in a potential model approach

The astrophysical $^{3}{\rm He}(α, γ)^{7}{\rm Be}$ and $^{3}{\rm H}(α, γ)^{7}{\rm Li}$ direct capture processes are studied in the framework of the two-body model with the potentials of a simple Gaussian form, which describe correctly the phase-shifts in the s-, p-, d-, and f-waves, as well as the binding energy and the asymptotic normalization constant of the ground $p_{3/2}$ and the first excited $p_{1/2}$ bound states. It is shown that the E1-transition from the initial s-wave to the final p-waves is strongly dominant in both capture reactions. On this basis the s-wave potential parameters are adjusted to reproduce the new data of the LUNA collaboration around 100 keV and the newest data at the Gamov peak estimated with the help of the observed neutrino fluxes from the Sun, $S_{34}$(23$^{+6}_{-5}$ keV)=0.548$\pm$0.054 keV b for the astrophysical S-factor of the capture process $^{3}{\rm He}(α, γ)^{7}{\rm Be}$. The resulting model describes well the astrophysical S-factor in low-energy Big Bang nucleosynthesis region of 180-400 keV, however has a tendency to underestimate the data above 0.5 MeV. Two-body potentials, adjusted on the properties of the $^7$Be nucleus, $^3{\rm He}+α$ elastic scattering data and the astrophysical S-factor of the $^{3}{\rm He}(α, γ)^{7}{\rm Be}$ direct capture reaction, are able to reproduce the properties of the $^7$Li nucleus, the binding energies of the ground 3/2$^-$ and first excited 1/2$^-$ states, and phase shifts of the $^3 {\rm H}+α$ elastic scattering in partial waves. Most importantly, these potential models can successfully describe both absolute value and energy dependence of the existing experimental data for the mirror astrophysical $^{3}{\rm H}(α, γ)^{7}{\rm Li}$ capture reaction without any additional adjustment of the parameters.

nucl-th↗

arXiv2016

Theoretical study of the $α+d$ $\rightarrow$ $^6$Li + $γ$ astrophysical capture process in a three-body model

The astrophysical capture process $α+d$ $\rightarrow$ $^6$Li + $γ$ is studied in a three-body model. The initial state is factorized into the deuteron bound state and the $α+d$ scattering state. The final nucleus $^6$Li(1+) is described as a three-body bound state $α+n+p$ in the hyperspherical Lagrange-mesh method. The contribution of the E1 transition operator from the initial isosinglet states to the isotriplet components of the final state is estimated to be negligible. An estimation of the forbidden E1 transition to the isosinglet components of the final state is comparable with the corresponding results of the two-body model. However, the contribution of the E2 transition operator is found to be much smaller than the corresponding estimations of the two-body model. The three-body model perfectly matches the new experimental data of the LUNA collaboration with the spectroscopic factor 2.586 estimated from the bound-state wave functions of $^6$Li and deuteron.

nucl-th↗

arXiv2014

Theoretical analysis of the astrophysical S-factor for the alpha+d -->6Li + gamma capture reaction in the two body model

Theoretical estimations for the astrophysical S-factor and the d(alpha,gamma)6Li reaction rates are obtained on the base of the two-body model with the alpha-d potential of a simple Gaussian form, which describes correctly the phase-shifts in the S-, P-, and D-waves, the binding energy and the asymptotic normalization constant in the final S-state. Wave functions of the bound and continuum states are calculated by using the Numerov algorithm of a high accuracy. A good convergence of the results for the E1- and E2- components of the transition is shown when increasing the upper limit of effective integrals up to 40 fm. The obtained results for the S-factor and reaction rates in the temperature interval 10E+6 K < T < 10E+10 K are in a good agreement with the results of Ref. A.M. Mukhamedzhanov, et.al., Phys. Rev., C 83, 055805 (2011), where the authors used the known asymptotical form of wave function at low energies and a complicated potential at higher energies.

nucl-th↗