A consistent folding model analysis of the ( S = 0, T = 1) charge exchange (p, n) reaction measured with 48 Ca, 90 Zr, 120 Sn, and 208 Pb targets at the proton energies of 35 and 45 MeV is done within a two-channel coupling formalism. The nuclear ground state densities given by the Hartree-Fock-Bogoliubov formalism and the density-dependent CDM3Y6 interaction were used as inputs for the folding calculation of the nucleon optical potential and (p, n) form factor. To have an accurate isospin dependence of the interaction, a complex isovector density dependence of the CDM3Y6 interaction has been carefully calibrated against the microscopic Brueckner-Hartree-Fock calculation by Jeukenne, Lejeune, and Mahaux before being used as folding input. Since the isovector coupling was used to explicitly link the isovector part of the nucleon optical potential to the cross section of the (p, n) reaction exciting the 0 + isobaric analog states in 48 Sc, 90 Nb, 120 Sb, and 208 Bi, the newly parametrized isovector density dependence could be well tested in the folding model analysis of the (p, n) reaction. The isospin-and density-dependent CDM3Y6 interaction was further used in the Hartree-Fock calculation of asymmetric nuclear matter, and a realistic estimation of the nuclear symmetry energy was made.

Analyses of the inelastic α+ 12 C scattering at medium energies have indicated that the strength of the Hoyle state (the isoscalar 0 + 2 excitation at 7.65 MeV in 12 C) seems to exhaust only 7 to 9% of the monopole energy weighted sum rule (EWSR), compared to about 15% of the EWSR extracted from inelastic electron scattering data. The full monopole transition strength predicted by realistic microscopic αcluster models of the Hoyle state can be shown to exhaust up to 22% of the EWSR. To explore the missing monopole strength in the inelastic α+ 12 C scattering, we have performed a fully microscopic folding model analysis of the inelastic α+ 12 C scattering at E lab = 104 to 240 MeV using the 3-α resonating group wave function of the Hoyle state obtained by Kamimura, and a complex density-dependent M3Y interaction newly parametrized based on the Brueckner Hartree Fock results for nuclear matter. Our folding model analysis has shown consistently that the missing monopole strength of the Hoyle state is not associated with the uncertainties in the analysis of the α+ 12 C scattering, but is most likely due to the short lifetime and weakly bound structure of this state which significantly enhances absorption in the exit α+ 12 C * (0 + 2 ) channel.Given a vital role in the stellar synthesis of Carbon, the isoscalar 0 + 2 state at 7.65 MeV in 12 C (known as the Hoyle state) has been studied over the years in numerous experiments. Although this state was clearly identified long ago in the inelastic α+ 12 C scattering at medium energies [1,2,3,4] and inelastic electron scattering [5] as an isoscalar E0 excitation, our knowledge about its ⋆ Research supported, in part, by Natural Science Council of Vietnam, EU Asia-Link Program CN/ASIA-LINK/008 (94791) and Vietnam Atomic Energy Commission (VAEC).

Background: The (spin and isospin zero) α-particle is an efficient projectile for the excitation of the isoscalar, natural-parity states of 12 C. Among those states that have pronounced α-cluster structure, the Hoyle state (0 + 2 state at 7.65 MeV) has been observed in many (α, α ) experiments while the second 2 + state of 12 C, predicted at E x ≈ 10 MeV as an excitation of the Hoyle state, has not been observed until a recent high-precision experiment of the α+ 12 C scattering at E α = 386MeV. A plausible reason is a strong population of the narrow 3 state in the (α, α ) spectra measured at E α = 240 and 386 MeV has been consistently confirmed by the present folding model + coupled channel analysis.

The energetic beam of (spin and isospin zero) α-particles remains a very efficient probe for the nuclear isoscalar giant resonances. In the present work, a microscopic folding model study of the isoscalar giant resonances in 208 Pb induced by inelastic α+ 208 Pb scattering at E lab = 240 and 386 MeV has been performed using the (complex) CDM3Y6 interaction and nuclear transition densities given by both the collective model and Random Phase Approximation (RPA) approach. The fractions of energy weighted sum rule around the main peaks of the isoscalar monopole, dipole and quadrupole giant resonances were probed in the Distorted Wave Born Approximation analysis of inelastic α+ 208 Pb scattering using the double-folded form factors given by different choices of the nuclear transition densities. The energy distribution of the E0, E1 and E2 strengths given by the multipole decomposition analyses of the (α, α ′ ) data under study are compared with those predicted by the RPA calculation.

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