State densities of heavy nuclei in the static-path plus random-phase approximation

Abstract

Nuclear state densities are important inputs to statistical models of compound-nucleus reactions. State densities are often calculated with self-consistent mean-field approximations that do not include important correlations and have to be augmented with empirical collective enhancement factors. Here, we benchmark the static-path plus random-phase approximation (SPA+RPA) to the state density in a chain of samarium isotopes ${}^{148-155}$Sm against exact results (up to statistical errors) obtained with the shell model Monte Carlo (SMMC) method. The SPA+RPA method incorporates all static fluctuations beyond the mean field together with small-amplitude quantal fluctuations around each static fluctuation. Using a pairing plus quadrupole interaction, we show that the SPA+RPA state densities agree well with the exact SMMC densities for both the even- and odd-mass isotopes. For the even-mass isotopes, we also compare our results with mean-field state densities calculated with the finite-temperature Hartree-Fock-Bogoliubov (HFB) approximation. We find that the SPA+RPA repairs the deficiencies of the mean-field approximation associated with broken rotational symmetry in deformed nuclei and the violation of particle-number conservation in the pairing condensate. In particular, in deformed nuclei the SPA+RPA reproduces the rotational enhancement of the state density relative to the mean-field state density.

arXiv comment13 pages, 5 figures, 3 tables

References in corpus (27)

• The impact of individual nuclear properties on $r$-process nucleosynthesis
• Extraction of level density and gamma strength function from primary gamma spectra
• Monte Carlo evaluation of path integrals for the nuclear shell model
• Practical solution to the Monte Carlo sign problem: Realistic calculations of 54Fe
• Novel technique for constraining r-process (n,$\gamma$) reaction rates
• Gamma-ray strength function and pygmy resonance in rare earth nuclei
• Signature of a Pairing Transition in the Heat Capacity of Finite Nuclei
• Heavy deformed nuclei in the shell model Monte Carlo method
• Crossover from vibrational to rotational collectivity in heavy nuclei in the shell-model Monte Carlo approach
• Shell Model Monte Carlo Studies of $\gamma$-Soft Nuclei
• Nuclear Level Density: Shell Model vs Mean Field
• The Perturbed Static Path Approximation at Finite Temperature: Observables and Strength Functions
• Breaking of nucleon Cooper pairs at finite temperature in 93-98Mo
• The nuclear moment of inertia and spin distribution of nuclear levels
• Stochastic Estimation of Nuclear Level Density in the Nuclear Shell Model: An Application to Parity-Dependent Level Density in ${}^{58}$Ni
• Benchmarking mean-field approximations to level densities
• Statistical theory of deformation distributions in nuclear spectra
• Microscopic calculations of nuclear level densities with the Lanczos method
• Level densities of nickel isotopes: microscopic theory versus experiment
• Particle-number projection in the finite-temperature mean-field approximation
• Thermodynamics of ultrasmall metallic grains in the presence of pairing and exchange correlations: Mesoscopic fluctuations
• Spin distribution of nuclear levels using static path approximation with random-phase approximation
• Odd-particle systems in the shell model Monte Carlo: circumventing a sign problem
• Nuclear deformation in the laboratory frame
• Contour integral method for thermal and quantal fluctuations
• Finite-temperature mean-field approximations for shell model Hamiltonians: the code HF-SHELL
• SPA+RPA approach to canonical and grandcanonical treatments of nuclear level densities

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