No abstract

The isoscalar giant monopole resonances (ISGMRs) in 90,92,94 Zr and 92,96,98,100 Mo have been studied with inelastic scattering of 240-MeV α particles at small angles including 0 o . Strength corresponding to approximately 100% of the ISGMR (E0) energy-weighted sum rule was identified in each nucleus. In all cases the strength consisted of two components separated by 7-9 MeV. Except for the mass 92 nuclei, the upper component contained 14-22% of the E0 energy-weighted sum rule (EWSR); however 38% and 65% of the E0 EWSR were located in the upper components in 92 Zr and 92 Mo, respectively. The energies of the ISGMRs for 92 Zr and 92 Mo are 1.22 and 2.80 MeV, respectively, higher than for 90 Zr, suggesting a significant nuclear structure contribution to the energy of the ISGMR in these nuclei. This has a large effect on the compression modulus of the nucleus with the values extracted for 92 Zr and 92 Mo being 27 and 56 MeV, respectively, higher than that for 90 Zr.

The main properties ͑strength function, energy-dependent transition density, branching ratios for direct nucleon decay͒ of the isoscalar giant dipole resonance in several medium-heavy mass spherical nuclei are described within a continuum random-phase approximation approach, taking into account the smearing effect. All model parameters used in the calculations are taken from independent data. The calculation results are compared with available experimental data.Recently, several experimental ͓1,2͔ and theoretical ͓3-6͔ works have been published describing results of studies of properties of the isoscalar giant dipole resonance ͑ISGDR͒ in several medium-heavy mass spherical nuclei. It was found in Ref. ͓2͔, from an analysis of the (␣,␣Ј) reaction at small angles, that the isoscalar dipole strength distribution exhibits two main regions of strength concentration, corresponding to the lower ͑pygmy͒ and upper ͑main͒ ISGDR components. Microscopic approaches used in recent theoretical studies of the ISGDR are based on ͑i͒ continuum random-phase approximation ͑RPA͒ calculations with the use of the Landau-Migdal particle-hole interaction ͓3͔, ͑ii͒ Hartree-Fock ϩ RPA calculations with the use of the Skyrme interactions ͓4,6͔, and ͑iii͒ relativistic RPA calculations ͓5͔. In each of these approaches, the strength distribution of the ISGDR shows two main regions of strength concentration with corresponding centroid energies that are in qualitative agreement with those of Ref. ͓2͔. References to previous experimental and theoretical studies of the ISGDR are given, respectively, in Refs. ͓1,2͔ and ͓3-6͔. Here, we mention Ref. ͓7͔, where the low-energy isoscalar 1 Ϫ strength was identified from an analysis of the (␣,␣Ј␥) reaction.In connection with the above-mentioned investigations it seems reasonable to realize the next step in theoretical studies, which consists in a rather full description of ISGDR properties. Such a description includes calculations of ͑i͒ the ISGDR strength distribution in a wide excitation-energy interval, taking into account the smearing effect, ͑ii͒ the energy-dependent ISGDR transition density also in a wide energy interval, and ͑iii͒ the partial branching ratios for direct nucleon decay of the ISGDR. In each of the abovementioned theoretical approaches, used in earlier works, this program was only partially realized. In the present work we attempt to describe ISGDR characteristics listed above in an extended version of the continuum RPA ͑CRPA͒ approach of Ref. ͓3͔. Calculation results obtained for 90 Zr, 116 Sn, 144 Sm, and 208 Pb are compared with available experimental data.Apart from the description of some ISGDR properties, the partially self-consistent continuum RPA approach was mainly used in Ref. ͓3͔ to describe in a quantitative way the direct neutron decay of the isoscalar giant monopole resonance ͑ISGMR͒. To realize a rather full description of PHYSICAL REVIEW C, VOLUME 64, 047301

A semi-microscopic approach based on both the continum-random-phase-approximation (CRPA) method and a phenomenological treatment of the spreading effect is extended and applied to describe the main properties (particle-hole strength distribution, energy-dependent transition density, partial direct-nucleon-decay branching ratios) of the isoscalar giant dipole, second monopole, and second quadrupole resonances. Abilities of the approach are checked by description of gross properties of the main-tone resonances. Calculation results obtained for the resonances in a few singly-and doubly-closed-shell nuclei are compared with available experimental data.