Astrophysical S-factors of radiative capture reactions on light nuclei have been calculated in a two-cluster potential model, taking into account the separation of orbital states by the use of Young schemes. The local two-body potentials describing the interaction of the clusters were determined by fitting scattering data and properties of bound states. The many-body character of the problem is approximatively accounted for by Pauli forbidden states. An important feature of the approach is the consideration of the dependence of the interaction potential between the clusters on the orbital Young schemes, which determine the permutation symmetry of the nucleon system. Proton capture on 2H, 6Li, 7Li, 12C, and 13C was analyzed in this approach. Experimental data at low energies were described reasonably well when the phase shifts for cluster-cluster scattering, extracted from precise data, were used. This shows that decreasing the experimental error on differential elastic scattering cross sections of light nuclei at astrophysical energies is very important also to allow a more accurate phase shift analysis. A future increase in precision will allow more definite conclusions regarding the reaction mechanisms and astrophysical conditions of thermonuclear reactions.
Within the potential cluster model with Pauli forbidden states the possibility of description of the experimental data on the total radiative n12C- and n13C-capture cross sections in the astrophysical energy range from 25 meV to 1.0 MeV is presented. The E1-transition covers the capture data from the scattering states to the ground one of 13C and 14C nuclei. Capture on the three low laying excited states 1/2+, 3/2- and 5/2+ of 13C was calculated.
In the framework of the modified potential cluster model with forbidden states the possibility of describing the available experimental data on the total cross sections and astrophysical S-factor for p11B radiative capture to the ground state of 12C was treated at astrophysical energies.
Within the framework of the modified potential cluster model with the forbidden states and the classification of states according to Young tableaux the possibility of describing the available experimental data for the total reaction cross sections of the neutron radiative capture on 10Be at thermal and astrophysical energies was shown.
The possibility of the description of the available experimental data for cross sections of the neutron capture reaction on 10B at thermal and astrophysical energies, taking into account the resonance at 475 keV, was considered within the framework of the modified potential cluster model with forbidden states and accounting for the resonance behavior of the scattering phase shifts.
The possibility to describe the astrophysical S-factor of the 4He12C radiative capture is considered in the potential cluster model at the energy range 0.1-4.0 MeV. It is shown that the approach used, which takes into account E2 transitions only, gives a good description of the new experimental data for adjusted parameters of potentials and leads to the value S(300) = 16.0$\cdotp$keV b.
Fine-tunings in radiative $α$-particle capture on $^{12}$C at astrophysical energies
Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn（波恩大学亥姆霍兹辐射与核物理研究所及贝特理论物理中心）；Institute for Advanced Simulation (IAS-4), Forschungszentrum Jülich（于利希研究中心先进模拟研究所（IAS-4））；Peng Huanwu Collaborative Center for Research and Education, International Institute for Interdisciplinary and Frontiers, Beihang University（北京航空航天大学交叉前沿国际学院彭桓武教研协同中心）
The continued interest to the study of the radiative neutron capture on atomic nuclei is caused, on the one hand, by the important role of this process in the analysis of many fundamental properties of nuclei and nuclear reactions, and, on the other hand, by the wide use of the capture cross section data in the various applications of nuclear physics and nuclear astrophysics, and, also, by the analysis of the processes of primordial nucleosynthesis in the Universe. This review is devoted to description of the results obtained for the processes of the radiative neutron capture at thermal and as…
The possibility of description of the experimental data for the astrophysical S-factor of the proton radiative capture on 16O to the ground and first excited states of 17F was considered in the frame of the modified potential cluster model with forbidden states and classification of the states according to Young tableaux. It was shown that on the basis of the E1 transitions from the P states of p16O scattering to the bound states of 17F in the p16O channel, it generally succeed to explain the value of measured astrophysical S-factors and reaction rates at astrophysical energies.
The astrophysical S-factor of p2H radiative capture in the energy range down to 1 keV is considered in the potential cluster model with the classification of orbital states according to Young's scheme symmetry. It is shown that the approach used, which takes into account E1 transition only, gives a good description of the new experimental data for two potentials of the bound state of 3He nucleus and leads to the value S=1.35(5) \cdot 10-4 keVb and 1.65(5)\cdot 10-4 keVb.
The phase shift analysis for position location of the 2S1/2 resonance at 1,5 MeV was carried out on the basis of the known experimental measurements. Also, the possibility to describe the available experimental data on the astrophysical S-factor for the proton capture reaction on 14C to the ground state of 15N at astrophysical energies was considered in the frame of modified potential cluster model.
The symmetry energy and its density dependence are pivotal for many nuclear physics and astrophysics applications, as they determine properties ranging from the neutron-skin thickness of nuclei to the crust thickness and the radius of neutron stars. Recently, PREX-II reported a value of $0.283\pm0.071$ fm for the neutron-skin thickness of $^{208}$Pb, $R_{\rm skin}^{^{208}\text{Pb}}$, implying a symmetry-energy slope parameter $L$ of $106\pm37$ MeV, larger than most ranges obtained from microscopic calculations and other nuclear experiments. We use a nonparametric equation of state representati…
The possibility of description of the experimental data for the astrophysical S-factor of the radiative proton capture on 15N at the energies from 50 to 1500 keV was considered in the framework of the modified potential cluster model with the classification of the orbital states according to Young tableaux. It was shown that, on the basis of the M1 and the E1 transitions from different states of the p15N scattering to the ground state of 16O in the p15N channel, it is quite succeed to explain general behavior of the S-factor in the considered energy range in the presence of two resonances.
We have studied the neutron-capture reactions 8Li(n,gamma)9Li and its role in the primordial nucleosynthesis. The n + 8Li --> 9Li + gamma reaction has a significant astrophysical interest because it includes one of the variants of chain of primordial nucleosynthesis processes of the Universe and thermonuclear reactions in type II supernova.
In the frame of modified potential cluster model based on the classification of orbital states by Young diagrams and revised interaction potential parameters for the bound states of 7Be in 3He4He cluster model with forbidden states the astrophysical S-factor for the radiative capture reaction has been calculated from the 10 keV. Obtained results S(23 keV) = 0.561 keV b reproduce the latest experimental data at 23 keV. Calculated and parametrized reaction rate is compared to some results known in the range of temperatures from 0.05 to 5 T9.
Radiative capture of nucleons at energies of astrophysical interest is one of the most important processes for nucleosynthesis. The nucleon capture can occur either by a compound nucleus reaction or by a direct process. The compound reaction cross sections are usually very small, specially for light nuclei. The direct capture proceeds either via the formation of a single-particle resonance, or a non-resonant capture process. In this work we calculate radiative capture cross sections and astrophysical S-factors for nuclei in the mass region A<20 using single-particle states. We carefully discus…
We have considered the possibility to describe the astrophysical S-factors of some light atomic nuclei on the basis of the potential cluster model by taking into account the supermultiplet symmetry of wave functions and splitting the orbital states according to Young's schemes. Such an approach allows analyzing the structure of inter-cluster interactions, to determine the presence of allowed and forbidden states in the interaction potential and so the number of nodes of the orbital wave function of cluster relative motion.
The phase shift analysis, done on the basis of the known measurements of the differential cross-sections of the p13C elastic scattering at the energy range 250-750 keV, shows that it is enough to take into account only 3S1 wave in the considered energy region. The potential for the triplet 3S1 state in p13C system at the resonance energy 0.55 MeV corresponding to quantum numbers JpT = 1-1 as well as the potential for the 3P1 bound state of 14N were constructed on the basis of the obtained scattering phase shifts. The possibility to describe the experimental data of the astrophysical S-factor o…
The total cross sections of the 16O(n,gamma)17O radiative capture process is described in the framework of the modified potential cluster model with the classification of orbital states according to Young tableaux. The possibility to describe the experimental data for the total cross sections of the neutron radiative capture on 16O at the energies from 0.025 eV to 1.5 MeV is shown on the basis of E1 and M1 processes. The transitions to the bound states of 17O in the n16O channel from 2S1/2, 2P3/2 and 2D3/2 waves of the n16O scattering have been considered. These transitions have been considere…
The variants of intercluster interaction potentials were constructed for description of the resonance nature of some phase shifts of the n7Li elastic scattering at low energies and the P2 ground state of 8Li in the n7Li cluster channel. The possibility of describing the total cross sections of 7Li(n,g)8Li in the region from 5 meV (5 10-3 eV) to 1 MeV including resonance at 0.25 MeV was shown with the potentials obtained in the potential cluster model taking into account forbidden states.
Radiative capture reactions play a crucial role in stellar nucleosynthesis but have proved challenging to determine experimentally. In particular, the large uncertainty ($\sim$100%) in the measured rate of the $^{12}$C$(α,γ)^{16}$O reaction is the largest source of uncertainty in any stellar evolution model. With development of new high current energy-recovery linear accelerators (ERLs) and high density gas targets, measurement of the $^{16}$O$(e,e^\prime α)^{12}$C reaction close to threshold using detailed balance opens up a new approach to determine the $^{12}$C$(α,γ)^{16}$O reaction rate wi…
The total cross sections of the radiative neutron capture processes on 9Be, 14C, 14N, 15N, and 16O are described in the framework of the modified potential cluster model with the classification of orbital states according to Young tableaux. The continued interest in the study of these reactions is due, on the one hand, to the important role played by this process in the analysis of many fundamental properties of nuclei and nuclear reactions, and, on the other hand, to the wide use of the capture cross section data in the various applications of nuclear physics and nuclear astrophysics, and, al…
A relationship between the Coulomb inclusive break-up probability and the radiative capture reaction rate for weakly-bound three-body systems is established. This direct link provides a robust procedure to estimate the reaction rate for nuclei of astrophysical interest by measuring inclusive break-up processes at different energies and angles. This might be an advantageous alternative to the determination of reaction rates from the measurement of $B(E1)$ distributions through exclusive Coulomb break-up experiments. In addition, it provides a reference to assess the validity of different theore…
In this review we have considered the possibility to describe the astrophysical S-factors of radiative capture reactions with light atomic nuclei on the basis of the potential two-cluster model by taking into account the splitting the orbital states according to Young's schemes. Within this model, interaction of the nucleon clusters is described by local two-particle potential determined by fit to the scattering data and properties of bound states of these clusters. Many-body character of the problem is taken into account under some approximation, in terms of the allowed or forbidden by the Pa…
Big Bang Nucleosynthesis (BBN) relevance reactions 3He(2H,γ)5Li, 3H(3He,γ)6Li, 5Li(n,γ)6Li as a key to approach for scenario of 6Li formation are treated. The rates of reaction for these processes are analyzed. Comparison of the reactions rates and the prevalence of light elements leads to the assumption that the two-step process 2H + 3He --> 5Li + γ and n + 5Li --> 6Li + γ can make a significant contribution to the formation of 6Li at the BBN at least at temperatures T9 of the order of unity. Calculations of the total cross sections, astrophysical S-factor, and reaction rates have been perfor…
We present a new calculation of the ${}^6{\rm Li}(p,γ){}^7{\rm Be}$ radiative capture astrophysical $S$-factor in a cluster model framework. We consider several intercluster potentials, adjusted to reproduce the ${}^7{\rm Be}$ bound state properties and the $p-{}^6{\rm Li}$ elastic scattering phase shifts. Using these potentials, we calculate the astrophysical $S$-factor, obtaining a good agreement with available data, and the photon angular distribution. Finally, we discuss the consequences of a hypothetical resonance-like structure on the $S$-factor.
The astrophysical S-factor of the 4He-12C radiative capture is calculated in the potential model at the energy range 0.1-2.0 MeV. Radiative capture 12C(α,γ)16O is extremely relevant for the fate of massive stars and determines if the remnant of a supernova explosion becomes a black hole or a neutron star. Because this reaction occurs at low-energies the experimental measurements is very difficult and perhaps impossible. In this paper, radiative capture of the 12C(α,γ)16O reaction at very low-energies is taken as a case study. In comparison with other theoretical methods and available experimen…
Study of radiative proton capture by the 7Be nucleus with the use of ab initio approaches
Dukhov Research Institute for Automatics（杜霍夫自动技术研究研究所）；Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University（莫斯科国立大学索博列金核物理研究所）；RUDN University（俄罗斯人民友谊大学）
The total cross sections of the n9Be --> gamma10Be radiative capture are described in the framework of the modified potential cluster model (MPCM) with the classification of orbital states according to Young tableaux at thermal and astrophysical energies.
Proton capture cross sections in the energy range of astrophysical interest for mass region 40-54 have been calculated in the Hauser-Feshbach formalism with reaction code TALYS1.6. The density dependent M3Y effective nucleon-nucleon interaction folded with target radial matter densities from relativistic mean field approach is used to obtain the semi-microscopic optical potential. A definite normalization of potential-well depths has been used over the entire mass region. The $(p,γ)$ rates of some reactions, important in the astrophysical scenario, are calculated using the potential in the rel…
We have studied the neutron-capture reactions 10,11B(n, g) and the role of the 11B(n, g) reaction in seeding r-process nucleosynthesis. The possibility of the description of the available experimental data for cross sections of the neutron capture reaction on 10B at thermal and astrophysical energies, taking into account the resonance at 475 keV, was considered within the framework of the modified potential cluster model (MPCM) with forbidden states and accounting for the resonance behavior of the scattering phase shifts. In the framework of the same model the possibility of describing the ava…
We have studied the proton-capture reaction 3H(p,γ)4He. It plays a role in the nucleosynthesis of primordial elements in the early Universe leading to the pre-stellar formation of 4He nuclei. All results of our researches and more new data from works show that the contribution of the 3H(p,γ)4He capture reaction into the processes of primordial nucleosynthesis is relatively small. However, it makes sense to consider this process for making the picture complete of the formation of prestellar 4He and clearing of mechanisms of this reaction. Furthermore, we have considered the 3He(2H,γ)5Li reactio…
The radiative thermal neutron capture cross sections over the range of thermal energies from 1 keV to 1 MeV are studied in statistical Hauser-Feshbach formalism. The optical model potential is constructed by folding the density dependent M3Y nucleon-nucleon interaction with radial matter densities of target nuclei obtained from relativistic-mean-field (RMF) theory. The standard nuclear reaction code TALYS1.8 is used for calculation of cross sections. The nuclei studied in the present work reside near the $Z=28$ proton shell closure and are of astrophysical interests taking part in p-, s-, and …
The low-energy behavior of the astrophysical S-factor for E1 direct radiative captures a(p,gamma)b leading to loosely bound final states (b=a+p) is investigated. We derive a first-order integral representation for S(E) and focus on the properties around zero energy. We show that it is the competition between various effects, namely the remnant Coulomb barrier, the initial and final centrifugal barriers and the binding energy, that defines the behavior of the S(E->0). Contrary to previous findings, we prove that S(E->0) is not determined by the pole corresponding to the bound state. The derivat…
In the framework of the modified potential cluster model the possibility of describing the available experimental data for the total cross sections for n11B radiative capture at thermal and astrophysical energies were considered with taking into account the 21 and 430 keV resonances.
The results are presented on the total cross sections, astrophysical S-factor, reaction rate of the deuteron radiative capture on 3He at the temperatures from 0.03 up to 3 T9 calculated in the framework of the potential cluster model with the forbidden states coming from the classification of the orbital states by the Young diagrams. Within the used model and exploited Young diagram classification made it possible to reproduce the general features of the available experimental data on the cross section and reconstructed astrophysical S-factor in the energy range from 200 keV up to 1.4 MeV. The…
The neutron capture cross sections have been studied near the $Z=50$ closed shell for a number of nuclei those take part in heavy element nucleosynthesis, the slow and the rapid neutron capture processes and the proton capture process. An optical model potential is constructed in theoretical approach by folding the density dependent M3y purely real nucleon-nucleon interaction with the target radial matter density in relativistic mean field (RMF) approach. The standard code TALYS1.8 is used for cross-section calculation. We have presented the Maxwellian-averaged capture cross-section (MACS) val…
Radiative capture reaction rates for $^6$He, $^9$Be and $^{17}$Ne formation at astrophysical conditions are studied within a three-body model using the analytical transformed harmonic oscillator method to calculate their states. An alternative procedure to estimate these rates from experimental data on low-energy breakup is also discussed
We summarize recent ab initio studies of low-energy electroweak reactions of astrophysical interest, relevant for both big bang nucleosynthesis and solar neutrino production. The calculational methods include direct integration for np radiative and pp weak capture, correlated hyperspherical harmonics for reactions of A=3,4 nuclei, and variational Monte Carlo for A=6,7 nuclei. Realistic nucleon-nucleon and three-nucleon interactions and consistent current operators are used as input.
Radiative capture processes in 4He12C channel of 16O nucleus are considered on the basis of potential two-cluster model with intercluster interactions which contain forbidden states and reproduce phase shifts of elastic scattering and some characteristics of bound states. Astrophysical S-factors are calculated at low energies. It was shown that the model used enables to describe the total cross-sections of the photoprocesses.
We consider the astrophysical reaction rates for radiative neutron capture reactions ($n,γ$) in the crust of a neutron star. The presence of degenerate neutrons at high densities (mainly in the inner crust) can drastically affect the reaction rates. Standard rates assuming a Maxwell-Boltzmann distribution for neutrons can underestimate the rates by several orders of magnitude. We derive simple analytical expressions for reaction rates at a variety of conditions with account for neutron degeneracy. We also discuss the plasma effects on the outgoing radiative transition channel in neutron radiat…
The ${^3{\rm He}}(α,γ){^7{\rm Be}}$ and ${^3{\rm H}}(α,γ){^7{\rm Li}}$ astrophysical $S$ factors are evaluated at low collision energies (less than 2.5 MeV in the centre-of-mass frame) within the no-core shell model with continuum approach using a renormalized chiral nucleon-nucleon interaction.
The method of asymptotic normalization coefficients is a standard approach for studies of two-body non-resonant radiative capture processes in nuclear astrophysics. This method suggests a fully analytical description of the radiative capture cross section in the low-energy region of the astrophysical interest. We demonstrate how this method can be generalized to the case of three-body $2p$ radiative captures. It was found that an essential feature of this process is the highly correlated nature of the capture. This reflects the complexity of three-body Coulomb continuum problem. Radiative capt…
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 …
We propose a new computational method for astrophysical reaction rate of radiative capture process. In the method, an evolution of a wave function is calculated along the imaginary-time axis which is identified as the inverse temperature. It enables direct evaluation of reaction rate as a function of temperature without solving any scattering problem. The method is tested for two-body radiative capture reaction, ${^{16}{\rm O}}(α,γ){^{20}{\rm Ne}}$, showing that it gives identical results to that calculated by the ordinary procedure. The new method will be suited for calculation of triple-alph…
Folding model approach to the elastic $p+^{12,13}$C scattering at low energies and radiative capture $^{12,13}$C$(p,γ)$ reactions
Ho Chi Minh City University of Education（胡志明市教育大学）；Institute of Nuclear Science and Technology, VINATOM（核科学技术研究所，越南原子能研究所）；University of Science, VNU-HCM（胡志明市国家大学所属科学大学）
The nucleon radiative capture reactions are important in pure and applied nuclear physics, especially in nuclear astrophysics. The keV-nucleon radiative capture reactions are studied with $^{12}$C and $^{16}$O targets using the bound-to-continuum potential model in which both scattering and bound states are treated simultaneously and based on the Skyrme Hartree-Fock approximation. The obtained results are shown to be in good agreement with the available experimental data. Alongside astrophysical aspects, the nuclear structure features were revisited for enlarging the prospect of adopting the n…
It is shown that in the framework of the modified potential cluster model we succeeded in correct describing the available experimental data for neutron radiative capture on 10Be total cross-sections at low, astrophysical and thermal energies. All interaction potentials for different partial waves are constructed by describing the basic characteristics of the bound states and spectra of final nucleus. Experimental data for the total cross-sections of the neutron radiative capture on 10Be were obtained by using known data for reduced probabilities of 11Be Coulomb dissociation.
The low-energy behavior of the strength function for the $1^-$ soft dipole excitation in $^{6}$He is studied theoretically. Use of very large basis sizes and well-grounded extrapolation procedures allows to move to energies as small as 1 keV, at which the low-energy asymptotic behavior of the E1 strength function seems to be achieved. It is found that the low-energy behavior of the strength function is well described in the effective three-body "dynamical dineutron model". The astrophysical rate for the $α$+$n$+$n \rightarrow ^6$He+$γ$ is calculated. Comparison with the previous calculations i…
We have applied the Gamow shell model (GSM) in the coupled-channel representation to study the astrophysical $S$-factor for the proton radiative capture reaction of $^6$Li. Reaction channels are built by coupling the proton wave function expanded in different partial waves with the GSM wave functions of the ground state ($1^+$) and the excited states ($3^+_1$, $0^+_1$ and $2^+_1$) of $^6$Li. All relevant $E1$, $M1$, and $E2$ transitions from the initial continuum states in $^7$Be to the final bound states (${3/2}^-_1$ and ${1/2}^-_1$) states are included. It is found that the calculated total …
Within the potential cluster model with the forbidden states and an orbital states classification according to the Young diagrams the possibility of description of experimental data for the total cross-sections of radiative n15N-capture at energies from 25 to 370 keV was considered. It was shown that only on basis of the E1-transitions from the different states of n15N-scattering to the ground state of 16N nucleus in n15N-channel it is well succeed to explain the value of the total cross-sections in the considered energy range and to prognosticate its behavior at energy E 1 eV. These cross-sec…
The shell model embedded in the continuum is applied to calculate the astrophysical S-factor and the reaction rate for the radiative proton capture reaction 17F(p,gamma)18Ne. The dominant contribution to the cross-section at very low energies is due to M1 transitions J_i^pi = 2^+ --> J_f^pi = 2_1^+ whose magnitude is controlled by a weakly bound 2_2^+ state at the excitation energy E_x = 3.62 MeV.
The total cross sections of the radiative proton capture on 8Li at astrophysical energies were considered in the framework of the modified potential cluster model with forbidden states, with the classification of the orbital cluster states according to Young diagrams. The recalculation of total cross sections for the 9Be(γ,p0)8Li photodisintegration was used as experimental data. In whole, it is possible to obtain the available data on cross sections at energies to 7.0 MeV. Astrophysical S-factors and reaction rates at the temperature range of 0.01 to 10 T9 were calculated. It was shown that t…
The structure of the Borromean nucleus $^9$Be ($α+α+n$) is addressed within a three-body approach using the analytical transformed harmonic oscillator method. The three-body formalism provides an accurate description of the radiative capture reaction rate for the entire temperature range relevant in Astrophysics. At high temperatures, results match the calculations based on two-step sequential processes. At low temperatures, where the particles have no access to intermediate two-body resonances, the three-body direct capture leads to reaction rates larger than the sequential processes. These r…
The radiative neutron capture reaction rates have been studied at very low energies which are of interest for nuclear astrophysics. The rates for many of these reactions have remained independent of temperature so far. The temperature dependence of the thermonuclear reaction rates have been explored within the statistical model. Apart from the compound nuclear contribution, the pre-equilibrium as well as the direct effects have been taken into account. The corresponding Maxwellian-averaged thermonuclear reaction rates of relevance in astrophysical plasmas at temperatures in the range from 10$^…
