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Register a new userAsymptotic normalization coefficient method for two-proton radiative capture
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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 capture $^{15}$O+$p$+$p rightarrow ^{,17}$Ne+$gamma$ is considered as an illustration.
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The astrophysical $S$-factor for the radiative capture $d(p,gamma)^3$He in the energy-range of interest for Big Bang Nucleosynthesis (BBN) is calculated using an {it ab-initio} approach. The nuclear Hamiltonian retains both two- and three-nucleon interactions - the Argonne $v_{18}$ and the Urbana IX, respectively. Both one- and many-body contributions to the nuclear current operator are included. The former retain for the first time, besides the $1/m$ leading order contribution ($m$ is the nucleon mass), also the next-to-leading order term, proportional to $1/m^3$. The many-body currents are constructed in order to satisfy the current conservation relation with the adopted Hamiltonian model. The hyperspherical harmonics technique is applied to solve the $A=3$ bound and scattering states. A particular attention is used in this second case in order to obtain, in the energy range of BBN, an uncertainty on the astrophysical $S$-factor of the order or below $sim$1 %. Then, in this energy range, the $S$-factor is found to be $sim$10 % larger than the currently adopted values.Part of this increase (1-3 %) is due to the $1/m^3$ one-body operator, while the remaining is due to the new more accurate scattering wave functions. We have studied the implication of this new determination for the $d(p,gamma)^3$He $S$-factor on deuterium primordial abundance. We find that the predicted theoretical value for $^2$H/H is in excellent agreement with its experimental determination, using the most recent determination of baryon density of Planck experiment, and with a standard number of relativistic degrees of freedom $N_{rm eff}=3.046$ during primordial nucleosynthesis.
pd capture processes at various energies have been analyzed based on solutions of 3N-Faddeev equations and using modern NN forces. The application of the Siegert theorem is compared to the explicit use of $pi$- and $rho$-like exchange currents connected to the AV18 NN interaction. Overall good agreement with cross sections and spin observables has been obtained but leaving room for improvement in some cases. Feasibility studies for 3NFs consistently included in the 3N continuum and the 3N bound state have been performed as well.
The formalism that describes radiative-capture reactions at low energies within an extended two-cluster potential model is presented. Construction of the operator of single-photon emission is based on a generalisation of the Siegert theorem with which the amplitude of the electromagnetic process is constructed in an explicitly gauge-independent way. While the starting point for this construction is a microscopic (single-nucleon) current model, the resulting operator of low-energy photon emission by a two-cluster system is expressed in terms of macroscopic quantities for the clusters and does not depend directly on their intrinsic coordinates and momenta. The multichannel algebraic scattering (MCAS) approach has been used to construct the initial- and final-state wave functions. We present a general expression for the scattering wave function obtained from the MCAS T matrix taking into account inelastic channels and Coulomb distortion. The developed formalism has been tested on the 3He(alpha,gamma)7Be reaction cross section at astrophysical energies. The energy dependence of the evaluated cross section and S factor agrees well with that extracted from measurement though the calculated quantities slightly overestimate data.
The differential cross section for radiative capture of protons by deuterons is calculated using different realistic NN interactions. We compare our results with the available experimental data below $E_x = 20 MeV$. Excellent agreement is found when taking into account meson exchange currents, dipole and quadrupole contributions, and the full initial state interaction. There is only a small difference between the magnitudes of the cross sections for the different potentials considered. The angular distributions, however, are practically potential independent.
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 $alpha$+$n$+$n rightarrow ^6$He+$gamma$ is calculated. Comparison with the previous calculations is performed.
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