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The study of the CNO cycle involves the examination of the proton radiative capture, or the $(p,\ensuremath{\gamma})$ reactions below 2 MeV. The astrophysical $\mathcal{S}$ factor characterizing the $(p,\ensuremath{\gamma})$ reaction is usually reduced to the electric dipole transition $E1$ from the scattering state to the bound state. In this work, the partial scattering and the single-particle bound wave functions in the reduced matrix element of the transition are obtained from the single self-consistent mean-field potential deduced from the Skyrme Hartree-Fock calculation. The astrophysical $\mathcal{S}$ factors of the $(p,\ensuremath{\gamma})$ reactions in the CNO cycle were successfully reproduced. The self-consistent Hartree-Fock calculation from the discrete to the continuum is a promising approach for the microscopic analysis of the nucleon-induced reactions in nuclear astrophysics.

Differential cross sections of $(p,n)$ and $(^{3}\mathrm{He},t)$ charge-exchange reactions leading to the excitation of the isobaric analog state (IAS) of the target nucleus are calculated with the distorted wave Born approximation. The $G$-matrix double-folding method is employed to determine the nucleus-nucleus optical potential within the framework of the Lane model. $G$ matrices are obtained from a Brueckner-Hartree-Fock calculation using the Argonne Av18 nucleon-nucleon potential. Target densities have been taken from Skyrme-Hartree-Fock calculations which predict values for the neutron skin thickness of heavy nuclei compatible with current existing data. Calculations are compared with experimental data of the reactions $(p,n)\mathrm{IAS}$ on $^{14}\mathrm{C}$ at ${E}_{\mathrm{lab}}=135$ MeV and $^{48}\mathrm{Ca}$ at ${E}_{\mathrm{lab}}=134$ MeV and ${E}_{\mathrm{lab}}=160$ MeV, and $(^{3}\mathrm{He},t)\mathrm{IAS}$ on $^{58}\mathrm{Ni},$ $^{90}\mathrm{Zr},$ and $^{208}\mathrm{Pb}$ at ${E}_{\mathrm{lab}}=420$ MeV. Experimental results are well described without the necessity of any rescaling of the strength of the optical potential. A clear improvement in the description of the differential cross sections for the $(^{3}\mathrm{He},t)\mathrm{IAS}$ reactions on $^{58}\mathrm{Ni}$ and $^{90}\mathrm{Zr}$ targets is found when the neutron excess density is used to determine the transition densities. Our results show that the density and isospin dependences of the $G$ matrices play a non-negligible role in the description of the experimental data.

In this work, the Coulomb mixing and the isospin mixing in the ground states of even-even nuclei are evaluated in perturbation theory. The calculation of the isospin mixing is performed by using the connection to isovector monopole resonance properties. The uncertainty in the results that depends on different choices of the Skyrme interactions is shown. While Coulomb mixing turns out to be large in the ground states of heavy nuclei, isospin mixing is very small., Comment: 14 pages, 2 figures

The double Gamow-Teller strength distributions in even-$A$ calcium isotopes were calculated using the nuclear shell model by applying the single Gamow-Teller operator two times sequentially on the ground state of the parent nucleus. The number of intermediate states actually contributing to the results was determined. The sum rules for the double Gamow-Teller operator in the full calculation were approximately fulfilled. In the case that the symmetry is restored approximately by introducing degeneracies of the $f$ levels, and the $p$ levels in the $fp$-model space, the agreement with the sum rules was very close.

In this work we study the charge-exchange reaction to Isobaric Analog State using two types of transition densities. We show that for projectiles that do not probe the interior of the nucleus but mostly the surface of this nucleus, distinct differences in the cross-section arise when the two types of transition densities are employed. We demonstrate this by considering the (3He,t) reaction., 11 pages, 7 figures

It is widely accepted that nuclear Gamow-Teller transitions are quenched; shell-model calculations also showed a clear anticorrelation between the Gamow-Teller strength and the transition rate of the collective quadrupole excitation from the ground state. We discuss the physics beyond this observation. It is based on the existence of spin-orbit coupling that is responsible for the non-zero probabilities of Gamow-Teller transitions in self-conjugate nuclei (N = Z). The shell-model calculations in the f p-space demonstrate the effects of the gradual artificial removal of the spin-orbit coupling that influences Gamow-Teller and quadrupole modes in opposite way. The realistic spin-orbit splitting moves the cumulative Gamow-Teller strength up and leads to stronger fragmentation; both trends are discussed in terms of simple symmetry arguments. Along with this process, the Gamow-Teller operator excites, in addition to the main line of L = 0 states, states with L = 2 which should be added, with the interference terms, to account for the total strength., Comment: 16 pages, 8 figures

Realistic density dependent CDM3Yn versions of the M3Y interaction have been used in an extended Hartree-Fock (HF) calculation of nuclear matter (NM), with the nucleon single-particle potential determined from the total NM energy based on the Hugenholtz-van Hove theorem that gives rise naturally to a rearrangement term (RT). Using the RT of the single-nucleon potential obtained exactly at different NM densities, the density- and energy dependence of the CDM3Yn interactions was modified to account properly for both the RT and observed energy dependence of the nucleon optical potential. Based on a local density approximation, the double-folding model of the nucleus-nucleus optical potential has been extended to take into account consistently the rearrangement effect and energy dependence of the nuclear mean-field potential, using the modified CDM3Yn interactions. The extended double-folding model was applied to study the elastic $^{12}$C+$^{12}$C and $^{16}$O+$^{12}$C scattering at the refractive energies, where the Airy structure of the nuclear rainbow has been well established. The RT was found to affect significantly the real nucleus-nucleus optical potential at small internuclear distances, giving the potential strength close to that implied by the realistic optical model description of the Airy oscillation., Comment: Accepted for publication in Physical Review C. arXiv admin note: text overlap with arXiv:1508.05568

The nucleon mean-field potential has been thoroughly investigated in an extended Hartree-Fock (HF) calculation of nuclear matter (NM) using the CDM3Y3 and CDM3Y6 density dependent versions of the M3Y interaction. The single-particle (s/p) energies of nucleons in NM are determined according to the Hugenholtz-van Hove theorem, which gives rise naturally to a rearrangement term (RT) of the s/p potential at the Fermi momentum. Using the RT obtained exactly at the different NM densities and neutron-proton asymmetries, a consistent method is suggested to take into account effectively the momentum dependence of the RT of the s/p potential within the standard HF scheme. To obtain a realistic momentum dependence of the nucleon optical potential (OP), the high-momentum part of the s/p potential was accurately readjusted to reproduce the observed energy dependence of the nucleon OP over a wide range of energies. The impact of the RT and momentum dependence of the s/p potential on the density dependence of the nuclear symmetry energy and nucleon effective mass has been studied in details. The high-momentum tail of the s/p potential was found to have a sizable effect on the slope of the symmetry energy and the neutron-proton effective mass splitting at supranuclear densities of the NM. Based on a local density approximation, the folding model of the nucleon OP of finite nuclei has been extended to take into account consistently the RT and momentum dependence of the nucleon OP in the same mean-field manner, and successfully applied to study the elastic neutron scattering on the lead target at the energies around the Fermi energy., Accepted for publication in Physical Review C

The description of nucleons scattering off doubly closed-shell nuclei $^{16}\mathrm{O}$ and $^{208}\mathrm{Pb}$ at energies below 50 MeV is carried out in a fully self-consistent framework of the particle-vibration coupling approach. The applications are performed with commonly used Skyrme-type effective interactions. Nucleon-nucleus optical potentials are thus calculated without ad hoc adjusted parameters. These potentials are then solved with standard optical model codes (dwba98 in the present case). Empirical nucleon-nucleus elastic angular distributions are thus successfully reproduced.

The Fermi transition (\Delta L=\Delta S=0 and \Delta T=1) between the nuclear isobaric analog states (IAS), induced by the charge-exchange (p,n) or (3He,t) reaction, can be considered as "elastic" scattering of proton or 3He by the isovector term of the optical potential (OP) that flips the projectile isospin. The accurately measured (p,n) or (3He,t) scattering cross-section to the IAS can be used, therefore, to probe the isospin dependence of the proton or 3He optical potential. Within the folding model, the isovector part of the OP is determined exclusively by the neutron-proton difference in the nuclear densities and the isospin dependence of the effective nucleon-nucleon (NN) interaction. Because the isovector coupling explicitly links the isovector part of the proton or 3He optical potential to the cross section of the charge-exchange (p,n) or (3He,t) scattering to the IAS, the isospin dependence of the effective (in-medium) NN interaction can be well tested in the folding model analysis of these charge-exchange reactions. On the other hand, the same isospin- and density dependent NN interaction can also be used in a Hartree-Fock calculation of asymmetric nuclear matter, to estimate the nuclear matter energy and its asymmetry part (the nuclear symmetry energy). As a result, the fine-tuning of the isospin dependence of the effective NN interaction against the measured (p,n) or (3He,t) cross sections should allow us to make some realistic prediction of the nuclear symmetry energy and its density dependence., Comment: Accepted for publication in European Physical Journal A - "Hadrons and Nuclei"

The charge-exchange (3He,t) scattering to the isobaric analog state (IAS) of the target can be considered as "elastic" scattering of 3He by the isovector term of the optical potential (OP) that flips the projectile isospin. Therefore, the accurately measured charge-exchange scattering cross- section for the IAS can be a good probe of the isospin dependence of the OP, which is determined exclusively within the folding model by the difference between the neutron and proton densities and isospin dependence of the nucleon-nucleon interaction. Given the neutron skin of the target is related directly to the same density difference, it can be well probed in the analysis of the charge- exchange (3He,t) reactions at medium energies when the two-step processes can be neglected and the t-matrix interaction can be used in the folding calculation. For this purpose, the data of the (3He,t) scattering to the IAS of 90Zr and 208Pb targets at Elab = 420 MeV have been analyzed in the distorted wave Born approximation using the double-folded charge-exchange form factor. The neutron skin deduced for these two nuclei turned out to be in a good agreement with the existing database., Comment: Accepted for publication in Physical Review C

Analysis of data involving nuclei far from stability often requires optical potential (OP) for neutron scattering. Since neutron data is seldom available, while proton scattering data is more abundant, it is useful to have estimates of the difference of the neutron and proton optical potentials. This information is contained in the isospin dependence of the nucleon OP. Here we attempt to provide it for the nucleon-208Pb system. The goal of this paper is to obtain accurate n+208Pb scattering data, and use it, together with existing p+208Pb and 208Pb(p,n)208$Bi*_{IAS} data, to obtain an accurate estimate of the isospin dependence of the nucleon OP at energies in the 30-60 MeV range. Cross sections for n+208Pb scattering were measured at 30.4 and 40.0 MeV, with a typical relative (normalization) accuracy of 2-4% (3%). An angular range of 15 to 130 degrees was covered using the beam-swinger time of flight system at Michigan State University. These data were analyzed by a consistent optical model study of the neutron data and of elastic p+208Pb scattering at 45 MeV and 54 MeV. These results were combined with a coupled-channel analysis of the 208Pb(p,n) reaction at 45 MeV, exciting the 0^+ isobaric analog state in 208Bi. The new data and analysis give an accurate estimate the isospin impurity of the nucleon-208Pb OP at 30.4 MeV, caused by the Coulomb correction to the proton OP. The corrections to the real proton OP given by the CH89 global systematics was found to be only few percent, while for the imaginary potential it was over 20% at the nuclear surface. Based on the analysis of the measured elastic p+208Pb data at 40 MeV, a Coulomb correction of similar strength and shape was also predicted for the p+208Pb OP at energy around 54 MeV., Comment: Version accepted for publication in Physical Review C