Folding model study of the elastic α+α\alpha + \alpha scattering at low energies

The folding model analysis of the elastic $\alpha + \alpha$ scattering at the incident energies below the reaction threshold of 34.7 MeV (in the lab system) has been done using the well-tested density dependent versions of the M3Y interaction and realistic choices for the $^4$He density. Because the absorption is negligible at the energies below the reaction threshold, we were able to probe the $\alpha + \alpha$ optical potential at low energies quite unambiguously and found that the $\alpha + \alpha$ overlap density used to construct the density dependence of the M3Y interaction is strongly distorted by the Pauli blocking. This result gives possible explanation of a long-standing inconsistency of the double-folding model in its study of the elastic $\alpha + \alpha$ and $\alpha$-nucleus scattering at low energies using the same realistic density dependent M3Y interaction

Neutron star cooling - a challenge to the nuclear mean field

The two recent density-dependent versions of the finite-range M3Y interaction (CDM3Y$n$ and M3Y-P$n$) have been probed against the bulk properties of asymmetric nuclear matter (NM) in the nonrelativistic Hartree Fock (HF) formalism. The same HF study has also been done with the famous Skyrme (SLy4) and Gogny (D1S and D1N) interactions which were well tested in the nuclear structure calculations. Our HF results are compared with those given by other many-body calculations like the Dirac-Brueckner Hartree-Fock approach or ab-initio variational calculation using free nucleon-nucleon interaction, and by both the nonrelativistic and relativistic mean-field studies using different model parameters. Although the two considered density-dependent versions of the M3Y interaction were proven to be quite realistic in the nuclear structure or reaction studies, they give two distinct behaviors of the NM symmetry energy at high densities, like the Asy-soft and Asy-stiff scenarios found earlier with other mean-field interactions. As a consequence, we obtain two different behaviors of the proton fraction in the $\beta$-equilibrium which in turn can imply two drastically different mechanisms for the neutron star cooling. While some preference of the Asy-stiff scenario was found based on predictions of the latest microscopic many-body calculations or empirical NM pressure and isospin diffusion data deduced from heavy-ion collisions, a consistent mean-field description of nuclear structure database is more often given by some Asy-soft type interaction like the Gogny or M3Y-P$n$ ones. Such a dilemma poses an interesting challenge to the modern mean-field approaches.Comment: Version accepted for publication in Phys. Rev.

Neutron transition strengths of 21+2^+_1 states in the neutron rich Oxygen isotopes determined from inelastic proton scattering

A coupled-channel analysis of the $^{18,20,22}$O$(p,p')$ data has been performed to determine the neutron transition strengths of 2$^+_1$ states in Oxygen targets, using the microscopic optical potential and inelastic form factor calculated in the folding model. A complex density- and \emph{isospin} dependent version of the CDM3Y6 interaction was constructed, based on the Brueckner-Hatree-Fock calculation of nuclear matter, for the folding model input. Given an accurate isovector density dependence of the CDM3Y6 interaction, the isoscalar ($\delta_0$) and isovector ($\delta_1$) deformation lengths of 2$^+_1$ states in $^{18,20,22}$O have been extracted from the folding model analysis of the $(p,p')$ data. A specific $N$-dependence of $\delta_0$ and $\delta_1$ has been established which can be linked to the neutron shell closure occurring at $N$ approaching 16. The strongest isovector deformation was found for 2$^+_1$ state in $^{20}$O, with $\delta_1$ about 2.5 times larger than $\delta_0$, which indicates a strong core polarization by the valence neutrons in $^{20}$O. The ratios of the neutron/proton transition matrix elements ($M_n/M_p$) determined for 2$^+_1$ states in $^{18,20}$O have been compared to those deduced from the mirror symmetry, using the measured $B(E2)$ values of 2$^+_1$ states in the proton rich $^{18}$Ne and $^{20}$Mg nuclei, to discuss the isospin impurity in the $2^+_1$ excitation of the $A=18,T=1$ and $A=20,T=2$ isobars.Comment: Version accepted for publication in Physical Review

Elastic transfer and parity dependence of the nucleus-nucleus optical potential

Background: A recent coupled-reaction-channel (CRC) study shows that the enhanced oscillation of the elastic 16O + 12C section at backward angles is due mainly to the elastic α transfer or the core exchange. Such a process gives rise to a parity-dependent term in the total elastic S matrix, an indication of the parity dependence of the 16O + 12C optical potential (OP). Purpose: To explicitly determine the core exchange potential (CEP) induced by the symmetric exchange of the two 12C cores in the elastic sup>16O + 12C scattering at Elab = 132 and 300 MeV and explore its parity dependence. Method: S matrix generated by CRC description of the elastic 16O + 12C scattering is used as the input for the inversion calculation to obtain the effective local OP that contains both the Wigner and Majorana terms. Results: The high-precision inversion results show a strong contribution by the complex Majorana term in the total OP of the 16O + 12C system and thus provide for the first time a direct estimation of the parity-dependent CEP. Conclusions: The elastic α transfer or exchange of the two 12C cores in the 16O + 12C system gives rise to a complex parity dependence of the total OP. This should be a general feature of the OP for the light heavy-ion systems that contain two identical cores

Suppression of the nuclear rainbow in the inelastic nucleus-nucleus scattering

The nuclear rainbow observed in the elastic $\alpha$-nucleus and light heavy-ion scattering is proven to be due to the refraction of the scattering wave by a deep, attractive real optical potential. The nuclear rainbow pattern, established as a broad oscillation of the Airy minima in the elastic cross section, originates from an interference of the refracted far-side scattering amplitudes. It is natural to expect a similar rainbow pattern also in the inelastic scattering of a nucleus-nucleus system that exhibits a pronounced rainbow pattern in the elastic channel. Although some feature of the nuclear rainbow in the inelastic nucleus-nucleus scattering was observed in experiment, the measured inelastic cross sections exhibit much weaker rainbow pattern, where the Airy oscillation is suppressed and smeared out. To investigate this effect, a novel method of the near-far decomposition of the inelastic scattering amplitude is proposed to explicitly reveal the coupled partial-wave contributions to the inelastic cross section. Using the new decomposition method, our coupled channel analysis of the elastic and inelastic $^{12}$C+$^{12}$C and $^{16}$O+$^{12}$C scattering at the refractive energies shows unambiguously that the suppression of the nuclear rainbow pattern in the inelastic scattering cross section is caused by a destructive interference of the partial waves of different multipoles. However, the inelastic scattering remains strongly refractive in these cases, where the far-side scattering is dominant at medium and large angles like that observed in the elastic scattering.Comment: Dedicated to the memory of Jacques Raynal; to be published in EPJ