Computing the QRPA level density with the finite amplitude method

Bjelčić, A.; Schunck, N.

doi:10.1016/j.cpc.2024.109387

Title: Computing the QRPA level density with the finite amplitude method

Journal Article · 21 September 2024 · Computer Physics Communications

DOI: https://doi.org/10.1016/j.cpc.2024.109387 · OSTI ID:2459408

^[1]; Schunck, N. ^[1]

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Here, we describe a new algorithm to calculate the vibrational nuclear level density of an atomic nucleus. Fictitious perturbation operators that probe the response of the system are generated by drawing their matrix elements from some probability distribution function. We use the Finite Amplitude Method to explicitly compute the response for each such sample. With the help of the Kernel Polynomial Method, we build an estimator of the vibrational level density and provide the upper bound of the relative error in the limit of infinitely many random samples. The new algorithm can give accurate estimates of the vibrational level density. Since it is based on drawing multiple samples of perturbation operators, its computational implementation is naturally parallel and scales like the number of available processing units.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2459408

Report Number(s):: LLNL--JRNL-866460; 1101196

Journal Information:: Computer Physics Communications, Journal Name: Computer Physics Communications Vol. 306; ISSN 0010-4655

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (31)

Efficient estimation of eigenvalue counts in an interval: Efficient estimation of eigenvalue counts in an interval Di Napoli, Edoardo; Polizzi, Eric; Saad, Yousef Numerical Linear Algebra with Applications, Vol. 23, Issue 4 https://doi.org/10.1002/nla.2048	journal	March 2016
Combinatorial nuclear level densities based on the Gogny nucleon-nucleon effective interaction Hilaire, S.; Delaroche, J. P.; Girod, M. The European Physical Journal A, Vol. 12, Issue 2 https://doi.org/10.1007/s100500170025	journal	October 2001
Shell effects on state densities with given numbers of excited protons and neutrons Berger, J. F.; Martinot, M. Nuclear Physics A, Vol. 226, Issue 3 https://doi.org/10.1016/0375-9474(74)90491-6	journal	July 1974
Self-consistent RPA calculations with Skyrme-type interactions: The skyrme_rpa program Colò, Gianluca; Cao, Ligang; Van Giai, Nguyen Computer Physics Communications, Vol. 184, Issue 1 https://doi.org/10.1016/j.cpc.2012.07.016	journal	January 2013
Implementation of the quasiparticle finite amplitude method within the relativistic self-consistent mean-field framework: The program DIRQFAM Bjelčić, A.; Nikšić, T. Computer Physics Communications, Vol. 253 https://doi.org/10.1016/j.cpc.2020.107184	journal	August 2020
Chebyshev kernel polynomial method for efficient calculation of the quasiparticle random phase approximation response function Bjelčić, A.; Nikšić, T.; Drmač, Z. Computer Physics Communications, Vol. 280 https://doi.org/10.1016/j.cpc.2022.108477	journal	November 2022
Implementation of the quasiparticle finite amplitude method within the relativistic self-consistent mean-field framework (II): The program DIRQFAM v2.0.0 Bjelčić, A.; Nikšić, T. Computer Physics Communications, Vol. 287 https://doi.org/10.1016/j.cpc.2023.108689	journal	June 2023
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
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
High-performance algorithm for calculating non-spurious spin- and parity-dependent nuclear level densities Senʼkov, R. A.; Horoi, M.; Zelevinsky, V. G. Physics Letters B, Vol. 702, Issue 5 https://doi.org/10.1016/j.physletb.2011.07.004	journal	August 2011
A new approach to nuclear level densities: The QRPA plus boson expansion Hilaire, S.; Goriely, S.; Péru, S. Physics Letters B, Vol. 843 https://doi.org/10.1016/j.physletb.2023.137989	journal	August 2023
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
Energy Density Functional Methods for Atomic Nuclei Schunck, Nicolas https://doi.org/10.1088/2053-2563/aae0ed	book	January 2019
An Attempt to Calculate the Number of Energy Levels of a Heavy Nucleus Bethe, H. A. Physical Review, Vol. 50, Issue 4 https://doi.org/10.1103/PhysRev.50.332	journal	August 1936
Theory of Nuclear Level Density Bloch, Claude Physical Review, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRev.93.1094	journal	March 1954
Low-energy cluster modes in N=Z nuclei Mercier, F.; Bjelčić, A.; Nikšić, T. Physical Review C, Vol. 103, Issue 2 https://doi.org/10.1103/PhysRevC.103.024303	journal	February 2021
Spin- and parity-dependent nuclear level densities and the exponential convergence method Horoi, Mihai; Kaiser, Joshua; Zelevinsky, Vladimir Physical Review C, Vol. 67, Issue 5 https://doi.org/10.1103/PhysRevC.67.054309	journal	May 2003
Nuclear level statistics: Extending shell model theory to higher temperatures Alhassid, Y.; Bertsch, G. F.; Fang, L. Physical Review C, Vol. 68, Issue 4 https://doi.org/10.1103/PhysRevC.68.044322	journal	October 2003
Finite amplitude method for the solution of the random-phase approximation Nakatsukasa, Takashi; Inakura, Tsunenori; Yabana, Kazuhiro Physical Review C, Vol. 76, Issue 2 https://doi.org/10.1103/PhysRevC.76.024318	journal	August 2007
Isospin-projected nuclear level densities by the shell model Monte Carlo method Nakada, H.; Alhassid, Y. Physical Review C, Vol. 78, Issue 5 https://doi.org/10.1103/PhysRevC.78.051304	journal	November 2008
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
Linear response strength functions with iterative Arnoldi diagonalization Toivanen, J.; Carlsson, B. G.; Dobaczewski, J. Physical Review C, Vol. 81, Issue 3 https://doi.org/10.1103/PhysRevC.81.034312	journal	March 2010
Self-consistent Skyrme quasiparticle random-phase approximation for use in axially symmetric nuclei of arbitrary mass Terasaki, J.; Engel, J. Physical Review C, Vol. 82, Issue 3 https://doi.org/10.1103/PhysRevC.82.034326	journal	September 2010
Finite amplitude method for the quasiparticle random-phase approximation Avogadro, Paolo; Nakatsukasa, Takashi Physical Review C, Vol. 84, Issue 1 https://doi.org/10.1103/PhysRevC.84.014314	journal	July 2011
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
Low-energy collective modes of deformed superfluid nuclei within the finite-amplitude method Hinohara, Nobuo; Kortelainen, Markus; Nazarewicz, Witold Physical Review C, Vol. 87, Issue 6 https://doi.org/10.1103/PhysRevC.87.064309	journal	June 2013
Direct microscopic calculation of nuclear level densities in the shell model Monte Carlo approach Alhassid, Y.; Bonett-Matiz, M.; Liu, S. Physical Review C, Vol. 92, Issue 2 https://doi.org/10.1103/PhysRevC.92.024307	journal	August 2015
Collective inertia of the Nambu-Goldstone mode from linear response theory Hinohara, Nobuo Physical Review C, Vol. 92, Issue 3 https://doi.org/10.1103/PhysRevC.92.034321	journal	September 2015
Large-scale deformed quasiparticle random-phase approximation calculations of the γ -ray strength function using the Gogny force Martini, M.; Péru, S.; Hilaire, S. Physical Review C, Vol. 94, Issue 1 https://doi.org/10.1103/PhysRevC.94.014304	journal	July 2016
Total and Parity-Projected Level Densities of Iron-Region Nuclei in the Auxiliary Fields Monte Carlo Shell Model Nakada, H.; Alhassid, Y. Physical Review Letters, Vol. 79, Issue 16 https://doi.org/10.1103/PhysRevLett.79.2939	journal	October 1997
Approximating Spectral Densities of Large Matrices Lin, Lin; Saad, Yousef; Yang, Chao SIAM Review, Vol. 58, Issue 1 https://doi.org/10.1137/130934283	journal	January 2016

Similar Records

Comparison of density estimators. [Estimation of probability density functions]

Conference · 1977 · OSTI ID:5259503

Kao, S; Monahan, J F

A sparse matrix–vector multiplication based algorithm for accurate density matrix computations on systems of millions of atoms

Journal Article · 2018 · Computer Physics Communications · OSTI ID:1538209

Ghale, Purnima; Johnson, Harley T.

Simulating lattice QCD at finite density

Journal Article · 1988 · Phys. Rev. Lett.; (United States) · OSTI ID:6722029

Gocksch, A

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
Finite amplitude method
Kernel polynomial method
Nuclear level density
Random phase approximation

Title: Computing the QRPA level density with the finite amplitude method

Citation Formats

References (31)

Similar Records

Related Subjects