Elasticity of nuclear medium as a principal macrodynamical promoter of electric pygmy dipole resonance

Abstract

Motivated by arguments of the nuclear core-layer model formulated in [S.I. Bastrukov, J.A. Maruhn, Z.Phys. A 335 (1990) 139], the macroscopic excitation mechanism of the electric pygmy dipole resonance (PDR) is considered as owing its origin to perturbationinduced effective decomposition of a nucleus into two spherical domains -undisturbed inner region treated as a static core and dynamical layer undergoing elastic shear vibrations. The elastic restoring force is central to the excitation mechanism under consideration and has the same physical meaning as in macroscopic model of nuclear giant resonances involving distortions of the Fermi-sphere providing unified description of isoscalar giant electric and magnetic resonances of multipole degree ℓ ≥ 2 in terms of two fundamental vibrational modes in an elastic sphere, to wit, as spheroidal (electric) and torsional (magnetic) modes of shear elastic oscillations of the nodeless field of material displacements excited in the entire nucleus volume. In the present paper focus is placed on the emergence of dipole overtone in the frequency spectrum of spheroidal elastic vibrations as Goldstone soft mode. To emphasis this feature of dipole resonant excitation imprinted in the core-layer model we regain spectral equation for the frequency of spheroidal elastic vibrations trapped in the finite-depth layer, derived in the above paper, but using canonical equation of an elastic continuous medium. The obtained analytic equations for the frequency of dipole vibrational state in question and its excitation strength lead to the following estimates for the PDR energy centroid E P DR (E1) = [31 ± 1] A −1/3 MeV and the total excitation probability B P DR (E1) = [1.85 ± 0.05] 10 −3 Z 2 A −2/3 e 2 fm 2 throughout the nuclear chart exhibiting fundamental character of this soft dipole mode of nuclear resonant response. PACS: 21.60.Ev; 24.30.Cz.

Properties and Significance of the Surface Dipole Mode

“…Beyond the RPA results [7][8][9] summarized next, the IS-LED modes have received limited theoretical attention as such, with likely exceptions in Refs. [10,11]. Some studies focused on pygmy strength attribute the IS-LED strength to neutron-skin oscillations.…”

Torsional Nodeless Vibrations of a Quaking Neutron Star Restored by the Combined Forces of Shear Elastic and Magnetic Field Stresses

“…Accordingly, the shear modulus of the crustal matter is ranged from the surface to the crust-core interface as 10 24 < μ < 10 29 dyn cm −2 . The much denser core matter compressed by self-gravity to nearly normal nuclear density ρ = 2.8 × 10 14 g cm −3 is much more resistant to elastic shear distortions and its shear modulus is estimated as μ ∼ 10 33 dyn cm −2 (e.g., Owen 2005;Bastrukov et al 2008b and references therein); in view of this the Fermi-degenerate neutron matter of atomic nuclei and neutron-star cores is designated as an elastic Fermi solid capable of transmitting shear elastic wave with the speed c t = √ μ/ρ ∼ 0.2 c, where c is the speed of light. conducting matter is capable of sustaining persistent currentcarrying flows, and by degeneracy pressure of nonrelativistic neutrons in the cores of neutron stars whose material can be in the state of paramagnetic magnetization caused by Pauli's mechanism of field-induced alignment of spin magnetic moment of neutrons along the frozen-in star fossil magnetic field (e.g., Bastrukov et al 2002aBastrukov et al , 2002b.…”

Pygmy dipole resonance: Collective features and symmetry energy effects

“…In spite of the theoretical progress in the interpretation of this mode within phenomenological studies based on hydrodynamical equations [9,10], non-relativistic microscopic approaches using Random Phase Approximation (RPA) with various effective interactions [11][12][13] or relativistic quasi-particle RPA [14,15], and new experimental information [16][17][18][19], a number of critical questions concerning the nature of the PDR still remains. This includes the macroscopic picture of neutron and proton vibrations, the exact location of the PDR excitation energy and the degree of collectivity of the low-energy dipole states, the role of the symmetry energy [20].…”