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

Fanto, P.; Alhassid, Yoram

doi:10.1103/physrevc.103.064310

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

Journal Article · Thu Jun 10 00:00:00 EDT 2021 · Physical Review. C

DOI:https://doi.org/10.1103/physrevc.103.064310· OSTI ID:1850433

Fanto, P. ^[1]; ^[2]

Yale Univ., New Haven, CT (United States); OSTI
Yale Univ., New Haven, CT (United States)

We report that 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 must 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 ^148–155Sm 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 with 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.

View Accepted Manuscript (DOE)

Research Organization:: Krell Institute, Ames, IA (United States); Univ. of California, Oakland, CA (United States); Yale Univ., New Haven, CT (United States)

Sponsoring Organization:: National Energy Research Scientific Computing Center (NERSC); USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC)

Grant/Contract Number:: AC02-05CH11231; NA0003960; SC0019521

OSTI ID:: 1850433

Journal Information:: Physical Review. C, Journal Name: Physical Review. C Journal Issue: 6 Vol. 103; ISSN 2469-9985

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (58)

Everything You Wanted to Know About Data Analysis and Fitting but Were Afraid to Ask Young, Peter SpringerBriefs in Physics https://doi.org/10.1007/978-3-319-19051-8	book	January 2015
Statistical properties of many-particle spectra Mon, K. K.; French, J. B. Annals of Physics, Vol. 95, Issue 1 https://doi.org/10.1016/0003-4916(75)90045-7	journal	November 1975
The RPA-SPA approximation to level densities Puddu, G.; Bortignon, P. F.; Broglia, R. A. Annals of Physics, Vol. 206, Issue 2 https://doi.org/10.1016/0003-4916(91)90006-T	journal	February 1991
Thermal and quantal fluctuations in deformed nuclei Lauritzen, B.; Puddu, G.; Bortignon, P. F. Physics Letters B, Vol. 246, Issue 3-4 https://doi.org/10.1016/0370-2693(90)90608-9	journal	August 1990
SPA+RPA approach to canonical and grandcanonical treatments of nuclear level densities Agrawal, B. K.; Sahu, P. K. Physics Letters B, Vol. 351, Issue 1-3 https://doi.org/10.1016/0370-2693(95)00406-B	journal	May 1995
Level density parameters for the back-shifted fermi gas model in the mass range 40 < A < 250 Dilg, W.; Schantl, W.; Vonach, H. Nuclear Physics A, Vol. 217, Issue 2 https://doi.org/10.1016/0375-9474(73)90196-6	journal	December 1973
Microscopic theory of the isovector dipole resonance at high angular momenta Ring, P.; Robledo, L. M.; Egido, J. L. Nuclear Physics A, Vol. 419, Issue 2 https://doi.org/10.1016/0375-9474(84)90393-2	journal	May 1984
Extraction of level density and γ strength function from primary γ spectra Schiller, A.; Bergholt, L.; Guttormsen, M. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 447, Issue 3 https://doi.org/10.1016/S0168-9002(99)01187-0	journal	June 2000
The perturbed static path approximation at finite temperature: observables and strength functions Attias, H.; Alhassid, Y. Nuclear Physics A, Vol. 625, Issue 3 https://doi.org/10.1016/S0375-9474(97)00486-7	journal	November 1997
EMPIRE: Nuclear Reaction Model Code System for Data Evaluation Herman, M.; Capote, R.; Carlson, B. V. Nuclear Data Sheets, Vol. 108, Issue 12 https://doi.org/10.1016/j.nds.2007.11.003	journal	December 2007
RIPL – Reference Input Parameter Library for Calculation of Nuclear Reactions and Nuclear Data Evaluations Capote, R.; Herman, M.; Obložinský, P. Nuclear Data Sheets, Vol. 110, Issue 12 https://doi.org/10.1016/j.nds.2009.10.004	journal	December 2009
Modern Nuclear Data Evaluation with the TALYS Code System Koning, A. J.; Rochman, D. Nuclear Data Sheets, Vol. 113, Issue 12 https://doi.org/10.1016/j.nds.2012.11.002	journal	December 2012
Global microscopic nuclear level densities within the HFB plus combinatorial method for practical applications Hilaire, S.; Goriely, S. Nuclear Physics A, Vol. 779 https://doi.org/10.1016/j.nuclphysa.2006.08.014	journal	November 2006
Stochastic estimation of nuclear level density in the nuclear shell model: An application to parity-dependent level density in 58 Ni Shimizu, Noritaka; Utsuno, Yutaka; Futamura, Yasunori Physics Letters B, Vol. 753 https://doi.org/10.1016/j.physletb.2015.12.005	journal	February 2016
The impact of individual nuclear properties on r -process nucleosynthesis Mumpower, M. R.; Surman, R.; McLaughlin, G. C. Progress in Particle and Nuclear Physics, Vol. 86 https://doi.org/10.1016/j.ppnp.2015.09.001	journal	January 2016
White paper on nuclear astrophysics and low-energy nuclear physics, Part 2: Low-energy nuclear physics Carlson, Joe; Carpenter, Michael P.; Casten, Richard Progress in Particle and Nuclear Physics, Vol. 94 https://doi.org/10.1016/j.ppnp.2016.11.002	journal	May 2017
Quantum Monte Carlo Methods Gubernatis, James; Kawashima, Naoki; Werner, Philipp Cambridge University Press https://doi.org/10.1017/CBO9780511902581	book	January 2016
Sensitivity studies for the weak r process: neutron capture rates Surman, R.; Mumpower, M.; Sinclair, R. AIP Advances, Vol. 4, Issue 4 https://doi.org/10.1063/1.4867191	journal	April 2014
The statistical model and nuclear level densities Ericson, Torleif Advances in Physics, Vol. 9, Issue 36 https://doi.org/10.1080/00018736000101239	journal	October 1960
The impact of (n, γ ) reaction rate uncertainties of unstable isotopes near N = 50 on the i-process nucleosynthesis in He-shell flash white dwarfs Denissenkov, Pavel; Perdikakis, Georgios; Herwig, Falk Journal of Physics G: Nuclear and Particle Physics, Vol. 45, Issue 5 https://doi.org/10.1088/1361-6471/aabb6e	journal	April 2018
The Inelastic Scattering of Neutrons Hauser, Walter; Feshbach, Herman Physical Review, Vol. 87, Issue 2 https://doi.org/10.1103/PhysRev.87.366	journal	July 1952
Thermodynamics of ultrasmall metallic grains in the presence of pairing and exchange correlations: Mesoscopic fluctuations Nesterov, Konstantin N.; Alhassid, Y. Physical Review B, Vol. 87, Issue 1 https://doi.org/10.1103/PhysRevB.87.014515	journal	January 2013
Microscopic calculations of nuclear level densities with the Lanczos method Ormand, W. E.; Brown, B. A. Physical Review C, Vol. 102, Issue 1 https://doi.org/10.1103/PhysRevC.102.014315	journal	July 2020
Mean-field study of the nuclear partition function: application to level density and compound nucleus fission Kerman, A. K.; Levit, S. Physical Review C, Vol. 24, Issue 3 https://doi.org/10.1103/PhysRevC.24.1029	journal	September 1981
Nuclear level densities including thermal and quantal fluctuations Puddu, G.; Bortignon, P. F.; Broglia, R. A. Physical Review C, Vol. 42, Issue 5 https://doi.org/10.1103/PhysRevC.42.R1830	journal	November 1990
Thermal and quantal fluctuations in the pairing plus quadrupole model Puddu, G. Physical Review C, Vol. 47, Issue 3 https://doi.org/10.1103/PhysRevC.47.1067	journal	March 1993
Monte Carlo evaluation of path integrals for the nuclear shell model Lang, G. H.; Johnson, C. W.; Koonin, S. E. Physical Review C, Vol. 48, Issue 4 https://doi.org/10.1103/PhysRevC.48.1518	journal	October 1993
Thermal and microcanonical treatments of a pairing Hamiltonian Rossignoli, R. Physical Review C, Vol. 54, Issue 3 https://doi.org/10.1103/PhysRevC.54.1230	journal	September 1996
Effects of repulsive forces on thermal fluctuations Canosa, N.; Rossignoli, R. Physical Review C, Vol. 56, Issue 2 https://doi.org/10.1103/PhysRevC.56.791	journal	August 1997
γ -ray strength function and pygmy resonance in rare earth nuclei Voinov, A.; Guttormsen, M.; Melby, E. Physical Review C, Vol. 63, Issue 4 https://doi.org/10.1103/PhysRevC.63.044313	journal	March 2001
Fixed spin and parity nuclear level density for restricted shell model configurations Horoi, Mihai; Ghita, Monica; Zelevinsky, Vladimir Physical Review C, Vol. 69, Issue 4 https://doi.org/10.1103/PhysRevC.69.041307	journal	April 2004
Contour integral method for thermal and quantal fluctuations Kaneko, K.; Hasegawa, M. Physical Review C, Vol. 72, Issue 6 https://doi.org/10.1103/PhysRevC.72.061306	journal	December 2005
Nuclear moment of inertia and spin distribution of nuclear levels Alhassid, Y.; Bertsch, G. F.; Fang, L. Physical Review C, Vol. 72, Issue 6 https://doi.org/10.1103/PhysRevC.72.064326	journal	December 2005
Breaking of nucleon Cooper pairs at finite temperature in Mo 93 − 98 Kaneko, K.; Hasegawa, M.; Agvaanluvsan, U. Physical Review C, Vol. 74, Issue 2 https://doi.org/10.1103/PhysRevC.74.024325	journal	August 2006
Spin distribution of nuclear levels using the static path approximation with the random-phase approximation Kaneko, K.; Schiller, A. Physical Review C, Vol. 75, Issue 4 https://doi.org/10.1103/PhysRevC.75.044304	journal	April 2007
Improved microscopic nuclear level densities within the Hartree-Fock-Bogoliubov plus combinatorial method Goriely, S.; Hilaire, S.; Koning, A. J. Physical Review C, Vol. 78, Issue 6 https://doi.org/10.1103/PhysRevC.78.064307	journal	December 2008
Temperature-dependent combinatorial level densities with the D1M Gogny force Hilaire, S.; Girod, M.; Goriely, S. Physical Review C, Vol. 86, Issue 6 https://doi.org/10.1103/PhysRevC.86.064317	journal	December 2012
Level densities of nickel isotopes: Microscopic theory versus experiment Bonett-Matiz, M.; Mukherjee, Abhishek; Alhassid, Y. Physical Review C, Vol. 88, Issue 1 https://doi.org/10.1103/PhysRevC.88.011302	journal	July 2013
Nuclear state densities of odd-mass heavy nuclei in the shell model Monte Carlo approach Özen, C.; Alhassid, Y.; Nakada, H. Physical Review C, Vol. 91, Issue 3 https://doi.org/10.1103/PhysRevC.91.034329	journal	March 2015
Benchmarking mean-field approximations to level densities Alhassid, Y.; Bertsch, G. F.; Gilbreth, C. N. Physical Review C, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevC.93.044320	journal	April 2016
Nuclear level density: Shell-model approach Sen'kov, Roman; Zelevinsky, Vladimir Physical Review C, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevC.93.064304	journal	June 2016
Particle-number projection in the finite-temperature mean-field approximation Fanto, P.; Alhassid, Y.; Bertsch, G. F. Physical Review C, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevC.96.014305	journal	July 2017
Nuclear deformation in the laboratory frame Gilbreth, C. N.; Alhassid, Y.; Bertsch, G. F. Physical Review C, Vol. 97, Issue 1 https://doi.org/10.1103/PhysRevC.97.014315	journal	January 2018
Statistical theory of deformation distributions in nuclear spectra Mustonen, M. T.; Gilbreth, C. N.; Alhassid, Y. Physical Review C, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevC.98.034317	journal	September 2018
Level densities of Ge 74 , 76 from compound nuclear reactions Voinov, A. V.; Renstrøm, T.; Bleuel, D. L. Physical Review C, Vol. 99, Issue 5 https://doi.org/10.1103/PhysRevC.99.054609	journal	May 2019
Heavy Deformed Nuclei in the Shell Model Monte Carlo Method Alhassid, Y.; Fang, L.; Nakada, H. Physical Review Letters, Vol. 101, Issue 8 https://doi.org/10.1103/PhysRevLett.101.082501	journal	August 2008
Odd-Particle Systems in the Shell Model Monte Carlo Method: Circumventing a Sign Problem Mukherjee, Abhishek; Alhassid, Y. Physical Review Letters, Vol. 109, Issue 3 https://doi.org/10.1103/PhysRevLett.109.032503	journal	July 2012
Crossover from Vibrational to Rotational Collectivity in Heavy Nuclei in the Shell-Model Monte Carlo Approach Özen, C.; Alhassid, Y.; Nakada, H. Physical Review Letters, Vol. 110, Issue 4 https://doi.org/10.1103/PhysRevLett.110.042502	journal	January 2013
Novel technique for Constraining r -Process ( n , γ ) Reaction Rates Spyrou, A.; Liddick, S. N.; Larsen, A. C. Physical Review Letters, Vol. 113, Issue 23 https://doi.org/10.1103/PhysRevLett.113.232502	journal	December 2014
Calculation of Partition Functions Hubbard, J. Physical Review Letters, Vol. 3, Issue 2 https://doi.org/10.1103/PhysRevLett.3.77	journal	July 1959
Nuclear Level Densities in the Static-Path Approximation Lauritzen, B.; Arve, P.; Bertsch, G. F. Physical Review Letters, Vol. 61, Issue 25 https://doi.org/10.1103/PhysRevLett.61.2835	journal	December 1988
Practical solution to the Monte Carlo sign problem: Realistic calculations of Fe 54 Alhassid, Y.; Dean, D. J.; Koonin, S. E. Physical Review Letters, Vol. 72, Issue 5 https://doi.org/10.1103/PhysRevLett.72.613	journal	January 1994
Shell Model Monte Carlo Studies of γ-Soft Nuclei Alhassid, Y.; Bertsch, G. F.; Dean, D. J. Physical Review Letters, Vol. 77, Issue 8 https://doi.org/10.1103/PhysRevLett.77.1444	journal	August 1996
Thermal and Quantal Fluctuations for Fixed Particle Number in Finite Superfluid Systems Rossignoli, R.; Canosa, N.; Ring, P. Physical Review Letters, Vol. 80, Issue 9 https://doi.org/10.1103/PhysRevLett.80.1853	journal	March 1998
Signature of a Pairing Transition in the Heat Capacity of Finite Nuclei Liu, S.; Alhassid, Y. Physical Review Letters, Vol. 87, Issue 2 https://doi.org/10.1103/PhysRevLett.87.022501	journal	June 2001
Nuclear Physics B. Nuclear Dynamics, Theoretical Bethe, H. A. Reviews of Modern Physics, Vol. 9, Issue 2 https://doi.org/10.1103/RevModPhys.9.69	journal	April 1937
A Composite Nuclear-Level Density Formula with Shell Corrections Gilbert, A.; Cameron, A. G. W. Canadian Journal of Physics, Vol. 43, Issue 8 https://doi.org/10.1139/p65-139	journal	August 1965
Finite-temperature mean-field approximations for shell model Hamiltonians: the code HF-SHELL Ryssens, W.; Alhassid, Y. The European Physical Journal A, Vol. 57, Issue 2 https://doi.org/10.1140/epja/s10050-021-00365-3	journal	February 2021

Similar Records

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

Journal Article · Wed Mar 06 19:00:00 EST 2024 · Physical Review. C · OSTI ID:2378620

Magnetic dipole γ-ray strength functions in the crossover from spherical to deformed neodymium isotopes

Journal Article · Tue Nov 12 19:00:00 EST 2024 · Physical Review. C · OSTI ID:2538533

Microscopic linear response calculations based on the Skyrme functional plus the pairing contribution

Journal Article · Sun Dec 14 23:00:00 EST 2008 · Physical Review. C, Nuclear Physics · OSTI ID:21199415

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
energy levels
level densities
many-body techniques
nuclear many-body theory
shell model
statistical models
thermal models

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

Citation Formats

References (58)

Similar Records

Related Subjects