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Register a new userMicroscopic Study of the Isoscalar Giant Monopole Resonance in Cd, Sn and Pb Isotopes
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Li-Gang Cao
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The isoscalar giant monopole resonance (ISGMR) in Cd, Sn and Pb isotopes has been studied within the self-consistent Skyrme Hartree-Fock+BCS and quasi-particle random phase approximation (QRPA). Three Skyrme parameter sets are used in the calculations, i.e., SLy5, SkM* and SkP, since they are characterized by different values of the compression modulus in symmetric nuclear matter, namely K=230, 217, and 202 MeV, respectively. We also investigate the effect of different types of pairing forces on the ISGMR in Cd, Sn and Pb isotopes. The calculated peak energies and the strength distributions of ISGMR are compared with available experimental data. We find that SkP fails completely to describe the ISGMR strength distribution for all isotopes due to its low value of the nuclear matter incompressibility, namely K=202 MeV. On the other hand, the SLy5 parameter set, supplemented by an appropriate pairing interaction, gives a reasonable description of the ISGMR in Cd and Pb isotopes. A better description of ISGMR in Sn isotopes is achieved by the SkM* interaction, that has a somewhat softer value of the nuclear incompressibility.
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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.
The isoscalar giant monopole resonance (ISGMR) in even-A Cd isotopes has been studied by inelastic ${alpha}$-scattering at 100 MeV/u and at extremely forward angles, including 0deg. The asymmetry term in the nuclear incompressibility extracted from the ISGMR in Cd isotopes is found to be $K_{tau} = -555 pm 75$ MeV, confirming the value previously obtained from the Sn isotopes. ISGMR strength has been computed in relativistic RPA using NL3 and FSUGold effective interactions. Both models significantly overestimate the centroids of the ISGMR strength in the Cd isotopes. Combined with other recent theoretical effort, the question of the softness of the open-shell nuclei in the tin region remains open still.
Experiments investigating the fine structure of the IsoScalar Giant Monopole Resonance (ISGMR) of 48Ca were carried out with a 200 MeV alpha inelastic-scattering reaction, using the high energy-resolution capability and the zero-degree setup at the K600 magnetic spectrometer of iThemba LABS, Cape Town, South Africa. Considerable fine structure is observed in the energy region of the ISGMR. Characteristic energy scales are extracted from the experimental data by means of a wavelet analysis and compared with the state-of-the-art theoretical calculations within a Skyrme-RPA (random phase approximation) approach using the finite-rank separable approximation with the inclusion of phonon-phonon coupling (PPC). Good agreement was observed between the experimental data and the theoretical predictions.
The excitation of the isoscalar giant monopole resonance (ISGMR) in $^{116}$Sn and $^{208}$Pb has been investigated using small-angle (including $0^circ$) inelastic scattering of 100 MeV/u deuteron and multipole-decomposition analysis (MDA). The extracted strength distributions agree well with those from inelastic scattering of 100 MeV/u $alpha$ particles. These measurements establish deuteron inelastic scattering at E$_d sim$ 100 MeV/u as a suitable probe for extraction of the ISGMR strength with MDA, making feasible the investigation of this resonance in radioactive isotopes in inverse kinematics.
We have investigated the isoscalar giant monopole resonance (GMR) in the Sn isotopes, using inelastic scattering of 400-MeV $alpha$-particles at extremely forward angles, including 0 deg. A value of -550 pm 100 MeV has been obtained for the asymmetry term, $K_tau$, in the nuclear incompressibility.
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