Finite-temperature Random Phase Approximation Research Articles

Temperature dependence of nuclear spin-isospin response and beta decay in hot astrophysical environments

A microscopic approach to the proton-neutron nuclear response is formulated in the finite-temperature relativistic nuclear field theory framework. The approach is based on the meson-nucleon Lagrangian of quantum hadrodynamics and advances the relativistic field theory for spin-isospin response beyond the finite-temperature random phase approximation. The dynamical contribution to the in-medium proton-neutron interaction amplitude is described in a parameter-free way by the coupling between the single nucleons and strongly-correlated particle-hole excitations (phonons) within the newly developed finite-temperature formalism. In this framework we investigate temperature dependence of the Gamow-Teller and spin dipole resonances in the closed-shell nuclei 48Ca, 78Ni, and 132Sn. Broader impacts of their temperature dependence are illustrated for the associated beta decay rates and lifetimes of 78Ni and 132Sn in hot astrophysical environments. We found a remarkable sensitivity of the beta decay rates to the enhanced low-energy spin-isospin strength at finite temperature, in particular, to the contribution of the first-forbidden transitions.

Transport properties of bilayer graphene due to charged impurity scattering: Temperature-dependent screening and substrate effects

We calculate the zero-temperature conductivity of bilayer graphene (BLG) impacted by Coulomb impurity scattering using four different screening models: unscreened, Thomas–Fermi (TF), overscreened and random phase approximation (RPA). We also calculate the conductivity and thermal conductance of BLG using TF, zero- and finite-temperature RPA screening functions. We find large differences between the results of the models and show that TF and finite-temperature RPA give similar results for diffusion thermopower S[Formula: see text]. Using the finite-temperature RPA, we calculate temperature and density dependence of S[Formula: see text] in BLG on SiO2, HfO2 substrates and suspended BLG for different values of interlayer distance c and distance between the first layer and the substrate d.

Stellar electron-capture rates on nuclei based on a microscopic Skyrme functional

We compute electron-capture rates for ${}^{54,56}$Fe and Ge isotopes using a self-consistent microscopic approach. The single-nucleon basis and the occupation factors in the target nucleus are calculated in the finite-temperature Skyrme Hartree-Fock model, and the ${J}^{\ensuremath{\pi}}={0}^{\ifmmode\pm\else\textpm\fi{}}$, ${1}^{\ifmmode\pm\else\textpm\fi{}}$, ${2}^{\ifmmode\pm\else\textpm\fi{}}$ charge-exchange transitions are determined in the finite-temperature random-phase approximation (RPA). The scheme is self-consistent; i.e., both the Hartree-Fock and the RPA equations are based on the same Skyrme functional. Several interactions are used in order to provide a theoretical uncertainty on the electron-capture rates for different astrophysical conditions. Comparing electron-capture rates obtained either with different Skyrme sets or with different available models indicates that differences up to one to two orders of magnitude can arise.

NUCLEAR EXCITATIONS AND WEAK INTERACTION RATES AT FINITE TEMPERATURE

Self-consistent theory frameworks have been introduced for description of excitations in nuclei at finite temperature, based on energy density functionals formulated using i) relativistic mean field Lagrangian with density dependent meson-nucleon vertex functions, and ii) Skyrme-type functionals. Finite temperature random phase approximation (FTRPA) has been employed in description of multipole excitations and charge-exchange modes. It is shown that in the temperature range T = 1–2 MeV additional transition strength appears at low energies due to thermal unblocking of single-particle orbitals close to the Fermi level. Within the finite temperature Hartree-Fock+RPA based on Skyrme functionals, the electron capture cross sections have been studied for target nuclei at temperatures relevant in modeling the supernova evolution.

Calculation of stellar electron-capture cross sections on nuclei based on microscopic Skyrme functionals

A fully self-consistent microscopic framework for the evaluation of nuclear weak-interaction rates at finite temperature is introduced, based on Skyrme functionals. The single-nucleon basis and the corresponding thermal occupation factors of the initial nuclear state are determined in the finite-temperature Skyrme Hartree-Fock model and charge-exchange transitions to excited states are computed using the finite-temperature random-phase approximation (RPA). Effective interactions are implemented self-consistently: Both the finite-temperature single-nucleon Hartree-Fock equations and the matrix equations of RPA are based on the same Skyrme energy density functional. Using a representative set of Skyrme functionals, the model is applied in the calculation of stellar electron-capture cross sections for selected nuclei in the iron mass group and for neutron-rich Ge isotopes.

Low-energy monopole and dipole response in nuclei at finite temperature

The multipole response of nuclei at temperatures T=0–2 MeV is studied using a self-consistent finite-temperature RPA (random phase approximation) based on relativistic energy density functionals. Illustrative calculations are performed for the isoscalar monopole and isovector dipole modes and, in particular, the evolution of low-energy excitations with temperature is analyzed, including the modification of pygmy structures. Both for the monopole and dipole modes, in the temperature range T=1–2 MeV additional transition strength appears at low energies due to thermal unblocking of single-particle orbitals close to the Fermi level. A concentration of dipole strength around 10 MeV excitation energy is predicted in 60,62Ni. The principal effect of finite temperature on low-energy strength that is already present at zero temperature, e.g. in 68Ni and 132Sn, is the spreading of this structure to even lower energy and the appearance of states that correspond to thermally unblocked transitions.

Test of finite temperature random-phase approximation on a Lipkin model

We investigate the applicability of the finite temperature random phase approximation (RPA) using a solvable Lipkin model. We show that the finite temperature RPA reproduces reasonably well the temperature dependence of total strength, both for the positive energy (i.e., the excitation) and the negative energy (i.e., the de-excitation) parts. This is the case even at very low temperatures, which may be relevant to astrophysical purposes.

The finite-temperature random-phase approximation for the spectroscopic properties of dense plasmas

The finite-temperature random-phase-approximation (FTRPA) is used to calculate selected spectral properties for 1 P excitations of dense neon plasmas. We present FTRPA calculations that include coupled-channel effects. The linear algebraic method is used to solve the resulting set of coupled-channel equations and, as a test of our method, oscillator strengths are calculated at zero-temperature and density and compared with previous calculations. Coupled-channel calculations of the oscillator strength for neon at various temperatures and densities are given; the inclusion of these effects is shown to cause significant differences in the oscillator strength when compared with single-channel and with average-atom calculations. Some trends as a function of temperature and density are also discussed.

Finite-temperature random-phase approximation for spectroscopic properties of neon plasmas

A finite-temperature random-phase approximation (FTRPA) is applied to calculate oscillator strengths for excitations in hot and dense plasmas. Application of the FTRPA provides a convenient, self-consistent method with which to explore coupled-channel effects of excited electrons in a dense plasma. We present FTRPA calculations that include coupled-channel effects. The inclusion of these effects is shown to cause significant differences in the oscillator strength for a prototypical case of $^{1}P$ excitation in neon when compared with single-channel and with average-atom calculations. Trends as a function of temperature and density are also discussed.

Photoabsorption in hot, dense plasmas—the average atom, the spherical cell model and the random phase approximation II

This work is a continuation of our earlier work on the finite temperature random phase approximation (FTRPA) for inhomogeneous, finite electron systems. In the earlier work we obtained the fundamental FTRPA eigenvalue equation for the spectral amplitudes of the linear response function via the use of the Matsubara Green's function technique arrived at earlier by des Cloizeaux via the density matrix technique. In this work we show that the normalization requirement for the FTRPA spectral amplitudes obtainable via the Matsubara Green's function technique is the same as the one obtained by des Cloizeaux. Thus, the two techniques in every respect give identical equations and formulas for the FTRPA. We also derive the fundamental equations for the actual linear responses of finite temperature inhomogeneous finite electron systems to specific external perturbations in the FTRPA. This side steps the problem of normalization by the use of an inhomogeneous integro–differential equation.

The finite temperature random phase approximation as a coupled-channel problem and the implementation of the single-channel random phase approximation (SCRPA) for the He atom in a finite temperature dense plasma

A theoretical approach for the description of “excited states” of an atom/ion in hot and dense plasmas is presented. It is based on the random phase approximation (RPA) for finite temperature fermion systems discussed earlier. It is shown here that after angular momentum and spin analysis are performed, the fundamental equations of the finite temperature RPA equations obtain the form of a coupled channel, coupled component integro-differential equation system, just as in the T=0 temperature case. Subsequently, the single-channel, uncoupled component approximation is introduced. A computer code written for this approximation was tested and results for He plasma at kT=10 eV and densities ranging from 10 18 to 10 23 atoms/cc are presented and discussed.

Thermal damping width of the giant dipole resonance in hot nuclei

An approach describing the thermal damping width of the giant dipole resonance (GDR) in hot nuclei is presented. The GDR is generated by the ph excitations within the finite-temperature random-phase approximation (FTRPA), while its damping at finite temperature arises from irreversible coupling of ph configurations to the thermal pp and hh ones beyond the FTRPA. A semimicroscopic unification of the quantal spreading and thermal damping widths is undertaken within the framework of motional damping. The numerical calculations are performed, using a schematic model with equally degenerate equidistant shells for a hot nucleus of mass A=112 carrying no angular momentum. The results show that the total width of the GDR increases strongly as a function of the excitation energy up to E{sup {asterisk}}{approximately}120{endash}130 MeV, where it reaches a saturation value. The limiting temperature for the GDR in very hot nuclei is discussed. {copyright} {ital 1997} {ital The American Physical Society}

Modified random phase approximation for multipole excitations at finite temperature.

The modified finite-temperature random phase approximation (FT-RPA) has been constructed by taking the influence of thermostat on the structure of quasiparticles into account. The modified FT-RPA linear response for electric quadrupole ({lambda}{sup {pi}}=2{sup +}) and octupole ({lambda}{sup {pi}}=3{sup {minus}}) excitations in {sup 58}Ni has been calculated as a function of the nuclear temperature. As compared to the conventional FT-RPA, the modified FT-RPA has given a stronger spreading for the strength distribution of quadrupole excitations at finite temperature {ital T}{le}3 MeV.

Finite temperature random phase approximation with the inclusion of scattering terms.

Effects associated with the inclusion of scattering terms, in the random phase approximation treatment of a two-body interaction at finite temperature, are investigated. Numerical results, for the case of quadrupole excitations in $^{116}\mathrm{Sn}$, are discussed. It is found that these terms could influence the low-energy region of the intensity distribution, for multipole excitations at finite temperature.

Thermo field boson realizations for operators of the finite temperature random phase approximation

A Dyson boson realization for two-quasiparticle operators at finite temperature is derived by using the thermo field dynamic formalism. The operators of the finite temperature random phase approximation (FT-RPA) are constructed from the zero temperature two-quasiparticle operators. The conditions are found under which these thermal RPA quadrupole operators close the SU (6) algebra. The fulfillment of the SU (6) enforcing conditions at finite temperature is discussed.

Effects of thermal and particle-number fluctuations on the giant isovector dipole modes for the58Ni nucleus in the finite-temperature random-phase approximation

Using the realistic single-particle energy spectrum obtained in the Woods-Saxon nucleon mean-field potential, the authors calculate the BCS pairing gap for 58Ni as a function of temperature taking into account the thermal and particle-number fluctuations. The strength distributions of the electric dipole transitions and the centroids of the isovector giant dipole resonance (IV-GDR) are computed in the framework of the finite-temperature random-phase approximation (RPA) based on the Hamiltonian of the quasiparticle-phonon nuclear model with separable dipole forces. It is shown that the change of the pairing gap at finite temperature can noticeably influence the IV-GDR localisation in realistic nuclei. By taking both thermal and quasiparticle fluctuations in the pairing gap into account the effect of the phase transition from superfluid to normal in the temperature dependence of the IV-GDR centroid is completely smeared out.

Vibrational modes at finite temperature: Restoring force and mass parameters for multipole excitations.

Temperature-dependent effects upon vibrational states are calculated within a finite temperature random phase approximation. Restoring force and mass parameters, calculated for a multipole-multipole interaction, are compared with liquid drop model values at nonzero temperature. Collective contributions to the level density parameter are discussed.

Local-density description of nuclear systems at finite temperature

A density functional approach for describing properties of nuclear systems at finite temperatures is developed by using local-scale point transformations. Within a mean-field approximation it leads to a fully practical procedure for solving the temperature-dependent Hartree-Fock problem in terms of the nuclear local-density distribution. The numerical results obtained in a large scale of temperatures for the nucleus,208Pb with Skyrme-type forces SkM are seen to reproduce quite accurately the average as well as the microscopic temperature-dependent Hartree-Fock results. Finite-temperature random-phase approximation sum rule expressions are applied for investigating nuclear scaling incompressibility and giant-monopole isoscalar and isovector energies as functions of temperature.

Influence of the superfluid pairing interaction on collective states in the finite-temperature random phase approximation

A set of finite-temperature RPA equations is obtained within the framework of the quasiparticle-phonon nuclear model using a separable multipole interaction. The calculations have been performed for the isovector dipole and isoscalar quadrupole modes in 58Ni. The author finds that the centroids of the giant resonances undergo a bending in the critical temperature region where the collapse of the pairing gap takes place.