Properties of the isoscalar giant dipole resonance

Abstract

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

Investigation of the energy-averaged double transition density of isoscalar monopole excitations in medium-heavy mass spherical nuclei

“…This transition density, employed in Refs. [3][4][5][6]11] as the energy-dependent transition density of the corresponding giant resonance, fulfils the condition that the strength function is obtained by…”

Overtones of isoscalar giant resonances in medium-heavy and heavy nuclei

“…In Refs. [18,23,26] the branching ratios calculated for a few overtones in 208 Pb are overestimated because of ignoring absorption of escaped nucleons inside the nucleus. This shortcoming is partially eliminated in Ref.…”

“…The relative energy-weighted strength function y L (ω) = ωS L (ω)/(EW SR) L is used to show exhaustion of the respective energy-weighted sum rule (EWSR) by a particular GR. The use of the reduced energy-dependent transition density R L (r, ω) = r 2ρ L (r, ω)S −1/2 L (ω) normalized by the condition R L (r, ω)V L (r)dr = 1 is convenient to compare the transition densities related to different energy re- gions [18]. The squared and properly normalized energyaveraged direct-nucleon-escape amplitude determines the respective differential partial branching ratio:…”

“…[22,27], while the values of parameter f ex = −(2.7 − 2.9) are found in Ref. [18] in the above- MeV are taken the same, as in Ref. [18], except for the α value (α = 0.085 MeV −1 is used in Ref.…”

“…[18] in the above- MeV are taken the same, as in Ref. [18], except for the α value (α = 0.085 MeV −1 is used in Ref. [18] together with R * = 1.8R).…”