Isoscalar monopole and quadrupole modes in Mo isotopes: microscopic analysis

The recent RCNP $(\alpha, \alpha')$ data on the Isoscalar Giant Monopole Resonance (ISGMR) and Isoscalar Giant Quadrupole Resonance (ISGQR) in $^{92,94,96,98,100}$Mo are analyzed within a fully self-consistent Quasiparticle Random Phase Approximation (QRPA) approach with Skyrme interactions, in which pairing correlations and possible axial deformations are taken into account. The Skyrme sets SkM*, SLy6, SVbas and SkP$^{\delta}$, that explore a diversity of nuclear matter properties, are used. We discuss the connection between the line shape of the monopole strength ISGMR and the deformation-induced coupling between the ISGMR and the $K=0$ branch of the ISGQR. The ISGMR centroid energy is best described by the force SkP$^{\delta}$, having a low incompressibility $K_{\infty}$ = 202 MeV. The ISGQR data are better reproduced by SVbas, that has large isoscalar effective mass $m^*/m$ = 0.9. The need of describing simultaneously the ISGMR and ISGQR data is stressed, with the requirement of suitable values of $K_\infty$ and $m^*/m$. Possible extensions of the QRPA to deal with soft systems are also envisaged.