Probing the isovector transition strength of the low-lying nuclear excitations induced by inverse kinematics proton scattering

A compact approach based on the folding model is suggested for the determination of the isoscalar and isovector transition strengths of the low-lying ($\Delta S=\Delta T=0$) excitations induced by inelastic proton scattering measured with exotic beams. Our analysis of the recently measured inelastic $^{18,20}$O+p scattering data at $E_{\rm lab}=30$ and 43 MeV/nucleon has given for the first time an accurate estimate of the isoscalar $\beta_0$ and isovector $\beta_1$ deformation parameters (which cannot be determined from the (p,p') data alone by standard methods) for 2$^+_1$ and $3^-_1$ excited states in $^{18,20}$O. Quite strong isovector mixing was found in the 2$^+_1$ inelastic $^{20}$O+p scattering channel, where the strength of the isovector form factor $F_1$ (prototype of the Lane potential) corresponds to a $\beta_1$ value almost 3 times larger than $\beta_0$ and a ratio of nuclear transition matrix elements $M_n/M_p\simeq 4.2$.Comment: 5 pages, 3 figure

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

Folding model study of the charge-exchange scattering to the isobaric analog state and implication for the nuclear symmetry energy

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

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.

Equation of state of the neutron star matter, and the nuclear symmetry energy

The nuclear mean-field potentials obtained in the Hartree-Fock method with different choices of the in-medium nucleon-nucleon (NN) interaction have been used to study the equation of state (EOS) of the neutron star (NS) matter. The EOS of the uniform NS core has been calculated for the np$e\mu$ composition in the $\beta$-equilibrium at zero temperature, using version Sly4 of the Skyrme interaction as well as two density-dependent versions of the finite-range M3Y interaction (CDM3Y$n$ and M3Y-P$n$), and versions D1S and D1N of the Gogny interaction. Although the considered effective NN interactions were proven to be quite realistic in numerous nuclear structure and/or reaction studies, they give quite different behaviors of the symmetry energy of nuclear matter at supranuclear densities that lead to the \emph{soft} and \emph{stiff} scenarios discussed recently in the literature. Different EOS's of the NS core and the EOS of the NS crust given by the compressible liquid drop model have been used as input of the Tolman-Oppenheimer-Volkov equations to study how the nuclear symmetry energy affects the model prediction of different NS properties, like the cooling process as well as the gravitational mass, radius, and moment of inertia.Comment: To be published in Physical Review