Spreading widths of giant resonances in spherical nuclei: Damped transient response

Abstract

We propose the universal approach to describe spreading widths of monopole, dipole and quadrupole giant resonances in heavy and superheavy spherical nuclei. Our approach is based on the ideas of the random matrix distribution of the coupling between one-phonon and two-phonon states generated in the random phase approximation. We use the Skyrme interaction SLy4 as our model Hamiltonian to create a single-particle spectrum and to analyze excited states of the doubly magic nuclei 132 Sn, 208 Pb and 310 126. Our results demonstrate that the universal approach enables to describe gross structure of the spreading widths of the considered giant resonances. PACS numbers: 24.60.Lz, 21.60.Jz, 27.80.+w Damping of collective motion in finite many-body quantum systems is among topical subjects in mesoscopic physics. The question of how, for example, multipole giant resonances (GRs) in nuclei [1] and metal clusters [2] dissolve their energy is still not well understood. There is, however, a consensus of opinion that, in particular, in a nucleus, once excited by an external field, a GR progresses to a fully equilibrated system via direct particle emission and by coupling to more complicated states produced by the intrinsic motion of nucleons (see, for example, Ref.[3]). The former mechanism gives rise to escape width Γ p . It is expected that the decay evolution along the hierarchy of more complex configurations till compound states determines spreading width Γ. A full description of this decay represents a fundamental problem which is, however, difficult to solve (if even is possible at all ?) due to existence of many degrees of freedom.In general, the description of spreading width in mesoscopic systems is based on the study of the electromagnetic strength distribution (strength function) [4] in some energy interval. This interval should be large enough to catch hold of basic features of a GR under investigation. Note, that in deformed systems the experimental widths are systematically larger and may develop a two-or threepeak structure. In this paper we consider only spherical nuclei in order to highlight a generic nature of the width Γ in monopole, dipole and quadrupole resonances in heavy and super-heavy systems.Nuclear shell model may be used to analyse spreading widths of GRs. However, the complexity of the calculations increases rapidly with the size of the configuration space. This fact severely restricts the feasibility of shell model calculations for heavy and super-heavy nuclei. In addition, even for a medium 48 Ca isotope the state-of-art shell model calculations [5], which operate with the Hamiltonian matrices of a huge dimension, produce questionable results for the dipole GR. Although these calculations reproduce reasonably well its peak position and peak width, the enhancement of the classical Thomas-Reiche-Kuhn sum rules is too overestimated. As a result, the number of shell model studies, in particular, dipole GRs in heavy and super-heavy nuclei are limited and rather focused on details of low-energy regio...

Origin of Low- and High-Energy Monopole Collectivity in 132Sn

“…In 208 Pb, the octupole vibration is lowest in terms of energy and the LTP 0 + state was first observed as the lowest-spin member of the [3 − 1 ⊗3 − 1 ] multiplet [42]. As proposed in [34,43], the extension of the variational space from standard QRPA to two-phonon configurations results in the formation of the low-energy 0 + states. The self-consistent RPA calculation gives the first 0 + state above 11 MeV in the case of 132 Sn [21].…”

“…The tool we employed was the QRPA with Skyrme interaction in the finite rank separable approximation (FRSA) [46,47]. It is worth mentioning that the so-called FRSA has been successfully used to study the electromagnetic transitions between excited states [48,49] and the ISGMR strength distribution within and beyond the QRPA [34,43]. The eigenvalues of the QRPA equations are found numerically as the roots of a relatively simple secular equation, which allows one to perform the calculation in large configurational space [46].…”

“…They are also derived from relativistic Lagrangians, e.g., [17,22,[27][28][29]. The effects of the quasiparticle-phonon interaction are important for the damping properties of the ISGMR [25,[30][31][32][33][34]. Thanks to experimental advancements, especially at rare isotope beam facilities, the investigation of GMR energies of neutron-rich nuclei along long isotope chains has recently become possible, facilitating more accurate and extensive analyses of the isospin dependence of the incompressibility of infinite nuclear matter.…”

Recent applications of the subtracted SRPA approximation

“…However, it is not suited to describe other important properties as for example the GR's fine structure and the spreading width, generated by the coupling between 1p1h configurations with more complex degrees of freedom. Approaches aimed at the description of this coupling are for example the particle-phonon coupling models based on the so-called time-blocking approximation [1,2] and the relativistic quasiparticle timeblocking approxi-mation [3,4], the quasiparticle-phonon model [5,6], particle-phonon (or quasiparticle-phonon) coupling models [7,8].…”

Microscopic description of the pygmy dipole resonance in neutron-rich Ca isotopes

“…The FRSA was used while studing the electric lowenergy excitations and giant resonances within and beyond the Skyrme-QRPA approach [9][10][11]. In this paper, we discuss the PPC effect on the properties of PDR in the Ca isotopes.…”