Nuclear dipole response in the finite-temperature relativistic time-blocking approximation

Abstract

Background:The radiative neutron capture reaction rates of the r-process nucleosynthesis are immensely affected by the microscopic structure of the low-energy spectra of compound nuclei. The relativistic (quasiparticle) time blocking approximation (R(Q)TBA) has successfully provided a good description of the lowenergy strength, in particular, the strength associated with pygmy dipole resonance, describing transitions from and to the nuclear ground state. The finite-temperature generalization of this method is designed for thermally excited compound nuclei and has the potential to enrich the fine structure of the dipole strength, especially in the low-energy region. Purpose: To formulate the thermal extension of RTBA, i.e., finite-temperature relativistic time blocking approximation (FT-RTBA) for the nuclear response, and to implement it numerically for calculations of the dipole strength in medium-light and medium-heavy nuclei. Methods: The FT-RTBA equations are derived using the Matsubara Green's function formalism. We show that with the help of a temperature-dependent projection operator on the subspace of the imaginary time it is possible to reduce the Bethe-Salpeter equation for the nuclear response function to a single frequency variable equation also at finite temperatures. The approach is implemented self-consistently in the framework of quantum hadrodynamics and keeps the ability of connecting the high-energy scale of heavy mesons and the low-energy domain of nuclear medium polarization effects in a parameter-free way. Results: The method was applied to the medium-light 48 Ca, 68 Ni and to the medium-heavy 100,120,132 Sn nuclei. The excitation energies E * of the considered compound nuclei were calculated and found to increase quickly starting from temperatures 0.5 ≤ T ≤ 1.0 MeV. The nucleonic single-particle energies and occupancies change accordingly because of the increasing diffuseness of the Fermi-Dirac distribution with the temperature increase. The dipole response of these nuclei was computed in the FT-RTBA and compared to the finite-temperature relativistic RPA (FT-RRPA). It was found that the giant dipole resonance (GDR) undergoes additional fragmentation (i) due to the thermal unblocking of the transitions between single-particle states located on the same side of the Fermi surface and (ii) because of the general reinforcement of the particle-vibration coupling (PVC) with the temperature growth. The low-energy part of the dipole strength distribution is moderately enhanced at temperatures T ≤ 4.0 MeV and increases dramatically above this temperature range. The width of the strength distribution grows rapidly with temperature at T ≥ 1.0 MeV. The energy-weighted sum rule (EWSR) in a wide finite energy interval remains nearly flat as the temperature increases. The traditional view of the PDR as an oscillation of the weakly bound neutron excess against the isospin-saturated core is nearly maintained up to the temperature T = 5.0 MeV and changes to the GDR-like pattern above this temperature. The col...

Pygmy resonances: what’s in a name?

“…as testified by the transition density displayed in Fig. 10, and of the corresponding wavefunction made out mainly of ph components with ε ph > ε F , namely (3s 1/2 → 3p 3/2 )n, (2d 5/2 → 3p 3/2 )n and (3s 1/2 → 3p 1/2 )n (see Table I of [110]). Increasing the temperature to T = 4 MeV, the strongest dipole state lying below 10 MeV, and carrying 72.4% of the 0-10 MeV strength, moves down in energy to E x = 2.55 MeV.…”

“…Let us conclude this section by noting that, if one would like to transform essentially any stable nucleus into systems displaying low-energy dipole modes, one has just to warm the system up, and study the γ-decay of the corresponding compound nucleus. Recent theoretical results [110,111] indicate the presence of PDR in hot nuclei at T ≈ 3 MeV, e.g.…”

Nuclear Shell Structure in a Finite-Temperature Relativistic Framework

“…In practice, employing effective interactions and the random phase approximation based on these interactions for the computation of the phonon characteristics provide quite a realistic description of the dynamical self-energy. In this work, we use the effective interaction of the covariant energy density functional (CEDF) [59,60] with the NL3 parametrization [68] and the relativistic random phase approximation [69] adopted to finite temperature in our previous developments for calculations of the phonon modes [4,5,67].…”

“…Understanding the behavior of atomic nuclei and nuclear matter at finite temperature is extremely important for advancements at the frontiers of the nuclear science. The modification of in-medium nucleonic correlations with temperature changes considerably the nuclear structure, leading to the transition to the non-superfluid phase, weakening of collective effects, the appearance of shape fluctuations, and the formation of new structures in the excitation spectra due to the thermal unblocking [1][2][3][4][5][6]. The microscopic interpretation of these phenomena is crucial for accurate predictions of nuclear processes in astrophysical environments, such as the neutron star mergers and supernovae [7][8][9][10][11][12].…”

Low-energy enhancement in the magnetic dipole $γ$-ray strength functions of heavy nuclei

“…While most theoretical studies have focused on the strength function built on the ground state, finitetemperature methods enable the study of γSFs built on excited states. The finite-temperature quasiparticle random-phase approximation (QRPA) has been applied to calculate finite-temperature γSFs [20][21][22][23], and the zero-temperature QRPA with empirical corrections has also been applied to γSF calculations [24,25]. How-ever, the QRPA has limitations in that it only includes small-amplitude quantal fluctuations around the meanfield configuration, and its finite-temperature version has been mostly limited to spherical nuclei.…”