Extended Fayans energy density functional: optimization and analysis

Reinhard, Paul-Gerhard; O’Neal, Jared; Wild, Stefan M.; Nazarewicz, Witold

doi:10.1088/1361-6471/ad633a

Title: Extended Fayans energy density functional: optimization and analysis

Journal Article · 21 August 2024 · Journal of Physics. G, Nuclear and Particle Physics

DOI: https://doi.org/10.1088/1361-6471/ad633a · OSTI ID:2434068

^[1];

^[2];

^[3];

^[4]

Universität Erlangen-Nürnberg (Germany)
Argonne National Laboratory (ANL), Argonne, IL (United States)
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Northwestern University, Evanston, IL (United States)
Michigan State University, East Lansing, MI (United States)

The Fayans energy density functional (EDF) has been very successful in describing global nuclear properties (binding energies, charge radii, and especially differences of radii) within nuclear density functional theory. In a recent study, supervised machine learning methods were used to calibrate the Fayans EDF. Building on this experience, in this work we explore the effect of adding isovector pairing terms, which are responsible for different proton and neutron pairing fields, by comparing a 13D model without the isovector pairing term against the extended 14D model. At the heart of the calibration is a carefully selected heterogeneous dataset of experimental observables representing ground-state properties of spherical even–even nuclei. To quantify the impact of the calibration dataset on model parameters and the importance of the new terms, we carry out advanced sensitivity and correlation analysis on both models. The extension to 14D improves the overall quality of the model by about 30%. The enhanced degrees of freedom of the 14D model reduce correlations between model parameters and enhance sensitivity.

View Journal Article

Cite

Export

Save

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Michigan State University, East Lansing, MI (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC02-05CH11231; AC02-06CH11357; SC0013365; SC0023175; SC0023688

OSTI ID:: 2434068

Journal Information:: Journal of Physics. G, Nuclear and Particle Physics, Journal Name: Journal of Physics. G, Nuclear and Particle Physics Journal Issue: 10 Vol. 51; ISSN 1361-6471; ISSN 0954-3899

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

References (57)

Transition Probability from the Ground to the First-Excited 2+ State of Even–Even Nuclides Raman, S.; Nestor, C. W.; Tikkanen, P. Atomic Data and Nuclear Data Tables, Vol. 78, Issue 1 https://doi.org/10.1006/adnd.2001.0858	journal	May 2001
The Nuclear Energy Density Functional Formalism Duguet, T. The Euroschool on Exotic Beams, Vol. IV https://doi.org/10.1007/978-3-642-45141-6_7	book	January 2014
The Skyrme—Hartree—Fock Model of the Nuclear Ground State Reinhard, P. -G.; Langanke, K.; Maruhn, Joachim A. Computational Nuclear Physics 1 https://doi.org/10.1007/978-3-642-76356-4_2	book	January 1991
The zero-point energy for rotation Reinhard, P. -G. Zeitschrift f�r Physik A, Vol. 285, Issue 1 https://doi.org/10.1007/BF01410231	journal	March 1978
Pairing gaps from nuclear mean-fieldmo dels Bender, M.; Rutz, K.; Reinhard, P. -G. The European Physical Journal A, Vol. 8, Issue 1 https://doi.org/10.1007/s10050-000-4504-z	journal	July 2000
Isotope shifts within the energy-density functional approach with density dependent pairing Fayans, S. A.; Tolokonnikov, S. V.; Trykov, E. L. Physics Letters B, Vol. 338, Issue 1 https://doi.org/10.1016/0370-2693(94)91334-X	journal	October 1994
The salient features of charge density distributions of medium and heavy even-even nuclei determined from a systematic analysis of elastic electron scattering form factors Friedrich, J.; Voegler, N. Nuclear Physics A, Vol. 373, Issue 2 https://doi.org/10.1016/0375-9474(82)90147-6	journal	January 1982
An improved pairing interaction for mean field calculations using skyrme potentials* Krieger, S. J.; Bonche, P.; Flocard, H. Nuclear Physics A, Vol. 517, Issue 2 https://doi.org/10.1016/0375-9474(90)90035-K	journal	October 1990
Nuclear effective forces and isotope shifts Reinhard, P. -G.; Flocard, H. Nuclear Physics A, Vol. 584, Issue 3 https://doi.org/10.1016/0375-9474(94)00770-N	journal	February 1995
Nuclear isotope shifts within the local energy-density functional approach Fayans, S. A.; Tolokonnikov, S. V.; Trykov, E. L. Nuclear Physics A, Vol. 676, Issue 1-4 https://doi.org/10.1016/S0375-9474(00)00192-5	journal	August 2000
Table of experimental nuclear ground state charge radii: An update Angeli, I.; Marinova, K. P. Atomic Data and Nuclear Data Tables, Vol. 99, Issue 1 https://doi.org/10.1016/j.adt.2011.12.006	journal	January 2013
The Axial Hartree–Fock + BCS Code SkyAx Reinhard, P. -G.; Schuetrumpf, B.; Maruhn, J. A. Computer Physics Communications, Vol. 258 https://doi.org/10.1016/j.cpc.2020.107603	journal	January 2021
Do you trust derivatives or differences? Moré, Jorge J.; Wild, Stefan M. Journal of Computational Physics, Vol. 273 https://doi.org/10.1016/j.jcp.2014.04.056	journal	September 2014
The Ame2003 atomic mass evaluation Audi, G.; Wapstra, A. H.; Thibault, C. Nuclear Physics A, Vol. 729, Issue 1 https://doi.org/10.1016/j.nuclphysa.2003.11.003	journal	December 2003
Unexpectedly large charge radii of neutron-rich calcium isotopes Garcia Ruiz, R. F.; Bissell, M. L.; Blaum, K. Nature Physics, Vol. 12, Issue 6 https://doi.org/10.1038/nphys3645	journal	February 2016
Evidence of a sudden increase in the nuclear size of proton-rich silver-96 Reponen, M.; de Groote, R. P.; Al Ayoubi, L. Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-24888-x	journal	July 2021
Proton superfluidity and charge radii in proton-rich calcium isotopes Miller, A. J.; Minamisono, K.; Klose, A. Nature Physics, Vol. 15, Issue 5 https://doi.org/10.1038/s41567-019-0416-9	journal	February 2019
Charge radii of exotic potassium isotopes challenge nuclear theory and the magic character of N = 32 Koszorús, Á.; Yang, X. F.; Jiang, W. G. Nature Physics, Vol. 17, Issue 4 https://doi.org/10.1038/s41567-020-01136-5	journal	January 2021
Measurement and microscopic description of odd–even staggering of charge radii of exotic copper isotopes de Groote, R. P.; Billowes, J.; Binnersley, C. L. Nature Physics, Vol. 16, Issue 6 https://doi.org/10.1038/s41567-020-0868-y	journal	April 2020
Structural trends in atomic nuclei from laser spectroscopy of tin Yordanov, Deyan T.; Rodríguez, Liss V.; Balabanski, Dimiter L. Communications Physics, Vol. 3, Issue 1 https://doi.org/10.1038/s42005-020-0348-9	journal	June 2020
Self-consistent nuclear mean-field models: example Skyrme–Hartree–Fock Erler, J.; Klüpfel, P.; Reinhard, P-G Journal of Physics G: Nuclear and Particle Physics, Vol. 38, Issue 3 https://doi.org/10.1088/0954-3899/38/3/033101	journal	January 2011
Error estimates of theoretical models: a guide Dobaczewski, J.; Nazarewicz, W.; Reinhard, P-G Journal of Physics G: Nuclear and Particle Physics, Vol. 41, Issue 7 https://doi.org/10.1088/0954-3899/41/7/074001	journal	May 2014
Error estimates for the Skyrme–Hartree–Fock model Erler, J.; Reinhard, P-G Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 3 https://doi.org/10.1088/0954-3899/42/3/034026	journal	February 2015
First applications of the Fayans functional to deformed nuclei Tolokonnikov, S. V.; Borzov, I. N.; Kortelainen, M. Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 7 https://doi.org/10.1088/0954-3899/42/7/075102	journal	May 2015
Statistical aspects of nuclear mass models Kejzlar, V.; Neufcourt, L.; Nazarewicz, W. Journal of Physics G: Nuclear and Particle Physics, Vol. 47, Issue 9 https://doi.org/10.1088/1361-6471/ab907c	journal	July 2020
Optimization and supervised machine learning methods for fitting numerical physics models without derivatives Bollapragada, Raghu; Menickelly, Matt; Nazarewicz, Witold Journal of Physics G: Nuclear and Particle Physics, Vol. 48, Issue 2 https://doi.org/10.1088/1361-6471/abd009	journal	January 2021
Energy Density Functional Methods for Atomic Nuclei Schunck, Nicolas https://doi.org/10.1088/2053-2563/aae0ed	book	January 2019
The Calculation of Errors by the Method of Least Squares Birge, Raymond T. Physical Review, Vol. 40, Issue 2 https://doi.org/10.1103/PhysRev.40.207	journal	April 1932
Beyond the charge radius: The information content of the fourth radial moment Reinhard, P. -G.; Nazarewicz, W.; Garcia Ruiz, R. F. Physical Review C, Vol. 101, Issue 2 https://doi.org/10.1103/PhysRevC.101.021301	journal	February 2020
Quantified limits of the nuclear landscape Neufcourt, Léo; Cao, Yuchen; Giuliani, Samuel A. Physical Review C, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRevC.101.044307	journal	April 2020
Information content of the differences in the charge radii of mirror nuclei Reinhard, Paul-Gerhard; Nazarewicz, Witold Physical Review C, Vol. 105, Issue 2 https://doi.org/10.1103/PhysRevC.105.L021301	journal	February 2022
Universal trend of charge radii of even-even Ca–Zn nuclei Kortelainen, Markus; Sun, Zhonghao; Hagen, Gaute Physical Review C, Vol. 105, Issue 2 https://doi.org/10.1103/PhysRevC.105.L021303	journal	February 2022
Statistical correlations of nuclear quadrupole deformations and charge radii Reinhard, Paul-Gerhard; Nazarewicz, Witold Physical Review C, Vol. 106, Issue 1 https://doi.org/10.1103/PhysRevC.106.014303	journal	July 2022
Odd-even mass differences from self-consistent mean field theory Bertsch, G. F.; Bertulani, C. A.; Nazarewicz, W. Physical Review C, Vol. 79, Issue 3 https://doi.org/10.1103/PhysRevC.79.034306	journal	March 2009
Information content of a new observable: The case of the nuclear neutron skin Reinhard, P. -G.; Nazarewicz, W. Physical Review C, Vol. 81, Issue 5 https://doi.org/10.1103/PhysRevC.81.051303	journal	May 2010
Nuclear energy density optimization Kortelainen, M.; Lesinski, T.; Moré, J. Physical Review C, Vol. 82, Issue 2 https://doi.org/10.1103/PhysRevC.82.024313	journal	August 2010
Surface symmetry energy of nuclear energy density functionals Nikolov, N.; Schunck, N.; Nazarewicz, W. Physical Review C, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevC.83.034305	journal	March 2011
Nuclear energy density optimization: Large deformations Kortelainen, M.; McDonnell, J.; Nazarewicz, W. Physical Review C, Vol. 85, Issue 2 https://doi.org/10.1103/PhysRevC.85.024304	journal	February 2012
Nuclear energy density optimization: Shell structure Kortelainen, M.; McDonnell, J.; Nazarewicz, W. Physical Review C, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevC.89.054314	journal	May 2014
Toward a global description of nuclear charge radii: Exploring the Fayans energy density functional Reinhard, P. -G.; Nazarewicz, W. Physical Review C, Vol. 95, Issue 6 https://doi.org/10.1103/PhysRevC.95.064328	journal	June 2017
Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements McDonnell, J. D.; Schunck, N.; Higdon, D. Physical Review Letters, Vol. 114, Issue 12 https://doi.org/10.1103/PhysRevLett.114.122501	journal	March 2015
From Calcium to Cadmium: Testing the Pairing Functional through Charge Radii Measurements of Cd 100 − 130 Hammen, M.; Nörtershäuser, W.; Balabanski, D. L. Physical Review Letters, Vol. 121, Issue 10 https://doi.org/10.1103/PhysRevLett.121.102501	journal	September 2018
Laser Spectroscopy of Neutron-Rich Tin Isotopes: A Discontinuity in Charge Radii across the N = 82 Shell Closure Gorges, C.; Rodríguez, L. V.; Balabanski, D. L. Physical Review Letters, Vol. 122, Issue 19 https://doi.org/10.1103/PhysRevLett.122.192502	journal	May 2019
Nuclear Charge Radii of the Nickel Isotopes Ni 58 − 68 , 70 Malbrunot-Ettenauer, S.; Kaufmann, S.; Bacca, S. Physical Review Letters, Vol. 128, Issue 2 https://doi.org/10.1103/PhysRevLett.128.022502	journal	January 2022
Impact of Nuclear Deformation and Pairing on the Charge Radii of Palladium Isotopes Geldhof, S.; Kortelainen, M.; Beliuskina, O. Physical Review Letters, Vol. 128, Issue 15 https://doi.org/10.1103/PhysRevLett.128.152501	journal	April 2022
Evidence of Two-Source King Plot Nonlinearity in Spectroscopic Search for New Boson Hur, Joonseok; Aude Craik, Diana P. L.; Counts, Ian Physical Review Letters, Vol. 128, Issue 16 https://doi.org/10.1103/PhysRevLett.128.163201	journal	April 2022
Charge Radii of Ni55,56 Reveal a Surprisingly Similar Behavior at N=28 in Ca and Ni Isotopes Sommer, Felix; König, Kristian; Rossi, Dominic M. Physical Review Letters, Vol. 129, Issue 13 https://doi.org/10.1103/PhysRevLett.129.132501	journal	September 2022
Combined Theoretical Analysis of the Parity-Violating Asymmetry for Ca48 and Pb208 Reinhard, Paul-Gerhard; Roca-Maza, Xavier; Nazarewicz, Witold Physical Review Letters, Vol. 129, Issue 23 https://doi.org/10.1103/PhysRevLett.129.232501	journal	December 2022
Surprising Charge-Radius Kink in the Sc Isotopes at N = 20 König, Kristian; Fritzsche, Stephan; Hagen, Gaute Physical Review Letters, Vol. 131, Issue 10 https://doi.org/10.1103/PhysRevLett.131.102501	journal	September 2023
Self-consistent mean-field models for nuclear structure Bender, Michael; Heenen, Paul-Henri; Reinhard, Paul-Gerhard Reviews of Modern Physics, Vol. 75, Issue 1 https://doi.org/10.1103/RevModPhys.75.121	journal	January 2003
Towards a universal nuclear density functional Fayans, S. A. Journal of Experimental and Theoretical Physics Letters, Vol. 68, Issue 3 https://doi.org/10.1134/1.567841	journal	August 1998
Self-Consistent Calculation of the Charge Radii in a Long $${}^{\mathbf{58{-}82}}$$Cu Isotopic Chain Borzov, I. N.; Tolokonnikov, S. V. Physics of Atomic Nuclei, Vol. 83, Issue 6 https://doi.org/10.1134/S1063778820060101	journal	November 2020
Numerical Methods for Least Squares Problems Björck, Åke Society for Industrial and Applied Mathematics https://doi.org/10.1137/1.9781611971484	book	January 1996
Chapter 40: POUNDERS in TAO: Solving Derivative-Free Nonlinear Least-Squares Problems with POUNDERS Wild, Stefan M.; Terlaky, Tamás; Anjos, Miguel F. Advances and Trends in Optimization with Engineering Applications https://doi.org/10.1137/1.9781611974683.ch40	book	April 2017
Estimating Computational Noise Moré, Jorge J.; Wild, Stefan M. SIAM Journal on Scientific Computing, Vol. 33, Issue 3 https://doi.org/10.1137/100786125	journal	January 2011
Systematics of collective correlation energies from self-consistent mean-field calculations Klüpfel, P.; Erler, J.; Reinhard, P. -G. The European Physical Journal A, Vol. 37, Issue 3 https://doi.org/10.1140/epja/i2008-10633-3	journal	September 2008
Estimating Derivatives of Noisy Simulations Moré, Jorge J.; Wild, Stefan M. ACM Transactions on Mathematical Software, Vol. 38, Issue 3 https://doi.org/10.1145/2168773.2168777	journal	April 2012

Similar Records

Modern energy density functional for nuclei and the nuclear matter equation of state

Journal Article · 2010 · Physics of Atomic Nuclei · OSTI ID:21426685

Shlomo, S

Isovector nuclear matter properties and neutron skin thickness

Journal Article · 2006 · Physical Review. C, Nuclear Physics · OSTI ID:20771446

Yoshida, Satoshi; Sagawa, Hiroyuki

Microscopic Nuclear Mass Table with High-Performance Computing

Conference · 2012 · OSTI ID:1185323

Erler, J.; Birge, N.; Kortelainen, M.; +4 more

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
density functional theory
model calibration
nuclear pairing
numerical optimization
sensitivity analysis
statistical analysis

Title: Extended Fayans energy density functional: optimization and analysis

Citation Formats

References (57)

Similar Records

Related Subjects