Isoscalar giant resonances in the Sn nuclei and implications for the asymmetry term in the nuclear-matter incompressibility

Abstract

We have investigated the isoscalar giant resonances in the Sn isotopes using inelastic scattering of 386-MeV α-particles at extremely forward angles, including 0 • . We have obtained completely "background-free" inelastic-scattering spectra for the Sn isotopes over the angular range 0 • -9 • and up to an excitation energy of 31.5 MeV. The strength distributions for various multipoles were extracted by a multipole decomposition analysis based on the expected angular distributions of the respective multipoles. We find that the centroid energies of the isoscalar giant monopole resonance (ISGMR) in the Sn isotopes are significantly lower than the theoretical predictions. In addition, based on the ISGMR results, a value of K τ = −550 ± 100 MeV is obtained for the asymmetry term in the nuclear incompressibility. Constraints on interactions employed in nuclear structure calculations are discussed on the basis of the experimentally-obtained values for K ∞ and K τ .2

Deformation effects on isoscalar giant resonances inMg24

“…5 for comparison with the experimental data. This mismatch between theoretical and experimental strengths is not too worrisome considering that the experimental strengths can have ∼20% systematic uncertainty resulting from the choice of the OMPs used and the DWBA calculations, as has been noted in previous works as well [2,32,42]. In addition to the strengths obtained for the prolate-deformed ground state, the strength distributions are obtained for a spherical configuration for comparison.…”

“…The DWBA calculations were performed employing the "hybrid" optical-model potential (OMP) proposed by Satchler and Khoa [31]. In this procedure, the real part of the OMP is generated by single-folding with a density-dependent Gaussian α-nucleon interaction [32]. A Woods-Saxon potential is used for the imaginary term of the OMP.…”

Giant monopole energies from a constrained relativistic mean-field approach

“…Having computed various ground-state properties one is now in a position to compute the linear response of the mean-field ground state to a variety of probes. In the present case we are interested in computing the isoscalar monopole response as probed, for example, in α-scattering experiments [28,[45][46][47][48]. Although the MF+RPA calculations carried out here follow closely the formalism developed in much greater detail in Ref.…”

“…The first two terms (κ and λ) are responsible for a softening of the equation of state of symmetric nuclear matter at normal density that results in a significant reduction of the incompressibility coefficient relative to that of the original Walecka model [41,43,44]. Indeed, such a softening is demanded by the measured distribution of isoscalar monopole strength in medium to heavy nuclei [13,21,28,[45][46][47][48][49]. Further, ω-meson self-interactions, as described by the parameter ζ , serve to soften the equation of state of symmetric nuclear matter at high densities and at present can only be meaningfully constrained by the limiting masses of neutron stars [50].…”

Effect of ground-state deformation on isoscalar giant resonances inSi28

“…where m, A and r n are the nucleon mass, the mass number, and the n th moment of the ground state density respectively, E x is the excitation energy corresponding a given state, and is given by: , respectively [13]. While the DWBA cross sections up to L = 7 were utilized in the MDA, only the L ≤ 2 strength distributions are presented in this paper since it was not possible to reliably extract meaningful strength distributions for L > 2 due to the limited experimental angular range.…”