Applications of the modified Hulthén-Kohn method for bound and scattering states

Sharaf, Mamoon A.; Shirokov, Andrey M.; Du, Weijie; Vary, James P.

doi:10.1103/bhgh-d9s7

Title: Applications of the modified Hulthén-Kohn method for bound and scattering states

Journal Article · Wed Aug 27 00:00:00 UTC 2025 · Physical Review. C

DOI: https://doi.org/10.1103/bhgh-d9s7 · OSTI ID:2910634

^[1];

^[2];

^[1];

^[3]

Chinese Academy of Sciences, Lanzhou (China); Iowa State University, Ames, IA (United States)
Lomonosov Moscow State University (Russia)
Iowa State University, Ames, IA (United States)

We adapt the Hulthén–Kohn method suggested by Efros [Phys. Rev. C 99, 034620 (2019)] for calculating various observables in the continuum and discrete spectrum using two-body interactions in single- and coupled channel systems. We explore the convergence of phase shifts and wave functions as well as the location of S-matrix poles which enables obtaining both resonance and bound state parameters. We find that employing a harmonic oscillator basis, together with an interaction smoothing scheme introduced by Gyarmati et al. [Nucl. Phys. A 326, 119 (1979)], and adopting approximate bound-state solutions for the short-range components of basis wave functions lead to good convergence even with restricted oscillator quanta accessible for modern no-core shell model codes. The adapted Efros method will facilitate ab initio many-body nuclear structure applications.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Iowa State University, Ames, IA (United States)

Sponsoring Organization:: Gansu Province; USDOE

Grant/Contract Number:: SC0023692; SC0023707

OSTI ID:: 2910634

Journal Information:: Physical Review. C, Journal Name: Physical Review. C Journal Issue: 2 Vol. 112; ISSN 2469-9985; ISSN 2469-9993

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (73)

Improving the scalability of a symmetric iterative eigensolver for multi-core platforms: IMPROVING THE SCALABILITY OF A SYMMETRIC ITERATIVE EIGENSOLVER Aktulga, Hasan Metin; Yang, Chao; Ng, Esmond G. Concurrency and Computation: Practice and Experience, Vol. 26, Issue 16 https://doi.org/10.1002/cpe.3129	journal	September 2013
Analyzing the contribution of individual resonance poles of the S‐matrix to two‐channel scattering Rakityansky, S. A.; Elander, N. International Journal of Quantum Chemistry, Vol. 106, Issue 5 https://doi.org/10.1002/qua.20859	journal	November 2005
P-Matrix and J-Matrix Approaches: Coulomb Asymptotics in the Harmonic Oscillator Representation of Scattering Theory Bang, J. M.; Mazur, A. I.; Shirokov, A. M. Annals of Physics, Vol. 280, Issue 2 https://doi.org/10.1006/aphy.1999.5992	journal	March 2000
True many-particle scattering in the oscillator representation Zaitsev, S. A.; Smirnov, Yu. F.; Shirokov, A. M. Theoretical and Mathematical Physics, Vol. 117, Issue 2 https://doi.org/10.1007/BF02557169	journal	November 1998
6He + 6He Clustering of 12Be in a Microscopic Algebraic Approach Filippov, G. F.; Lashko, Yu. A.; Korennov, S. V. Few-Body-Systems, Vol. 34, Issue 4 https://doi.org/10.1007/s00601-003-0020-4	journal	May 2004
Bound states of a many-particle system Coester, F. Nuclear Physics, Vol. 7 https://doi.org/10.1016/0029-5582(58)90280-3	journal	June 1958
Short-range correlations in nuclear wave functions Coester, F.; Kümmel, H. Nuclear Physics, Vol. 17 https://doi.org/10.1016/0029-5582(60)90140-1	journal	June 1960
Many-fermion theory in expS- (or coupled cluster) form Kümmel, H.; Lührmann, K. H.; Zabolitzky, J. G. Physics Reports, Vol. 36, Issue 1 https://doi.org/10.1016/0370-1573(78)90081-9	journal	February 1978
A rigorous foundation of an easy-to-apply approximation method for bound state problems Gyarmati, B.; Kruppa, A. T.; Revai, J. Nuclear Physics A, Vol. 326, Issue 1 https://doi.org/10.1016/0375-9474(79)90371-3	journal	September 1979
A realistic three-body model of 6Li with local interactions Bang, J.; Gignoux, C. Nuclear Physics A, Vol. 313, Issue 1-2 https://doi.org/10.1016/0375-9474(79)90571-2	journal	January 1979
Allowance for the Coulomb interaction in the framework of an algebraic version of the resonating group method Okhrimenko, I. P. Nuclear Physics A, Vol. 424, Issue 1 https://doi.org/10.1016/0375-9474(84)90131-3	journal	July 1984
Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling Moiseyev, N. Physics Reports, Vol. 302, Issue 5-6 https://doi.org/10.1016/S0370-1573(98)00002-7	journal	September 1998
Loosely bound three-body nuclear systems in the J-matrix approach Lurie, Yu. A.; Shirokov, A. M. Annals of Physics, Vol. 312, Issue 2 https://doi.org/10.1016/j.aop.2004.02.002	journal	August 2004
Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver Shao, Meiyue; Aktulga, H. Metin; Yang, Chao Computer Physics Communications, Vol. 222 https://doi.org/10.1016/j.cpc.2017.09.004	journal	January 2018
Harmonic oscillator representation of scattering theory in the presence of Coulomb potential Yanikov, U. M.; Kulikov, V. A.; Shirokov, A. M. Journal of Subatomic Particles and Cosmology, Vol. 4 https://doi.org/10.1016/j.jspc.2025.100075	journal	December 2025
Quantum Monte Carlo Calculations of Light Nuclei Pieper, Steven C. Nuclear Physics A, Vol. 751 https://doi.org/10.1016/j.nuclphysa.2005.02.018	journal	April 2005
Microscopic three-cluster model of 10Be Lashko, Yu. A.; Filippov, G. F.; Vasilevsky, V. S. Nuclear Physics A, Vol. 958 https://doi.org/10.1016/j.nuclphysa.2016.11.004	journal	February 2017
N3LO NN interaction adjusted to light nuclei in ab exitu approach Shirokov, A. M.; Shin, I. J.; Kim, Y. Physics Letters B, Vol. 761 https://doi.org/10.1016/j.physletb.2016.08.006	journal	October 2016
Direct ab initio calculation of the 4He nuclear electric dipole polarizability Yin, Peng; Shirokov, Andrey M.; Maris, Pieter Physics Letters B, Vol. 855 https://doi.org/10.1016/j.physletb.2024.138857	journal	August 2024
Ab initio no core shell model Barrett, Bruce R.; Navrátil, Petr; Vary, James P. Progress in Particle and Nuclear Physics, Vol. 69 https://doi.org/10.1016/j.ppnp.2012.10.003	journal	March 2013
Scaling of ab-initio nuclear physics calculations on multicore computer architectures Maris, Pieter; Sosonkina, Masha; Vary, James P. Procedia Computer Science, Vol. 1, Issue 1 https://doi.org/10.1016/j.procs.2010.04.012	journal	May 2010
Tetraneutron resonance: Theory Shirokov, A. M.; Kim, Y.; Mazur, A. I. 6TH INTERNATIONAL CONFERENCE ON PRODUCTION, ENERGY AND RELIABILITY 2018: World Engineering Science & Technology Congress (ESTCON), AIP Conference Proceedings https://doi.org/10.1063/1.5078857	conference	January 2018
J−matrix method: Extensions to arbitrary angular momentum and to Coulomb scattering Yamani, Hashim A. Journal of Mathematical Physics, Vol. 16, Issue 2 https://doi.org/10.1063/1.522516	journal	January 1975
Resonance partial widths and partial photodetachment rate using the rotated-coordinate method Noro, T.; Taylor, H. S. Journal of Physics B: Atomic and Molecular Physics, Vol. 13, Issue 12 https://doi.org/10.1088/0022-3700/13/12/005	journal	June 1980
Unified ab initio approaches to nuclear structure and reactions Navrátil, Petr; Quaglioni, Sofia; Hupin, Guillaume Physica Scripta, Vol. 91, Issue 5 https://doi.org/10.1088/0031-8949/91/5/053002	journal	April 2016
Note on the use of harmonic-oscillator wavefunctions in scattering calculations Revai, J.; Sotona, M.; Zofka, J. Journal of Physics G: Nuclear Physics, Vol. 11, Issue 6 https://doi.org/10.1088/0305-4616/11/6/011	journal	June 1985
Monopole excitations of the¹²C nucleus in the cluster model Mikhelashvili, T. Ya; Shirokov, A. M.; Smirnov, Yu F. Journal of Physics G: Nuclear and Particle Physics, Vol. 16, Issue 8 https://doi.org/10.1088/0954-3899/16/8/020	journal	August 1990
White paper: from bound states to the continuum Johnson, Calvin W.; Launey, Kristina D.; Auerbach, Naftali Journal of Physics G: Nuclear and Particle Physics, Vol. 47, Issue 12 https://doi.org/10.1088/1361-6471/abb129	journal	November 2020
Phase-Shift Analysis of 310-Mev Proton-Proton Scattering Experiments Stapp, H. P.; Ypsilantis, T. J.; Metropolis, N. Physical Review, Vol. 105, Issue 1 https://doi.org/10.1103/PhysRev.105.302	journal	January 1957
Variational Methods in Nuclear Collision Problems Kohn, W. Physical Review, Vol. 74, Issue 12 https://doi.org/10.1103/PhysRev.74.1763	journal	December 1948
The Formulation of the Kohn-Hulthén Variational Principle in Terms of the Scattering Operator Formalism Moses, Harry E. Physical Review, Vol. 92, Issue 3 https://doi.org/10.1103/PhysRev.92.817	journal	November 1953
Partial widths obtained by the complex resonance-scattering theory Moiseyev, Nimrod; Peskin, Uri Physical Review A, Vol. 42, Issue 1 https://doi.org/10.1103/PhysRevA.42.255	journal	July 1990
Ab initio no-core Gamow shell-model calculations of multineutron systems Li, J. G.; Michel, N.; Hu, B. S. Physical Review C, Vol. 100, Issue 5 https://doi.org/10.1103/PhysRevC.100.054313	journal	November 2019
n + H 3 , p + He 3 , p + H 3 , and n + He 3 scattering with the hyperspherical harmonic method Viviani, M.; Girlanda, L.; Kievsky, A. Physical Review C, Vol. 102, Issue 3 https://doi.org/10.1103/PhysRevC.102.034007	journal	September 2020
Angular-momentum projection in coupled-cluster theory: Structure of Mg34 Hagen, G.; Novario, S. J.; Sun, Z. H. Physical Review C, Vol. 105, Issue 6 https://doi.org/10.1103/PhysRevC.105.064311	journal	June 2022
Calculations of the np→dγ reaction in chiral effective field theory Du, Weijie; Pal, Soham; Sharaf, Mamoon Physical Review C, Vol. 106, Issue 5 https://doi.org/10.1103/PhysRevC.106.054608	journal	November 2022
SS-HORSE extension of the no-core shell model: Application to resonances in He7 Mazur, I. A.; Shin, I. J.; Kim, Y. Physical Review C, Vol. 106, Issue 6 https://doi.org/10.1103/PhysRevC.106.064320	journal	December 2022
Coupled-cluster theory for strong entanglement in nuclei Sun, Z. H.; Hagen, G.; Papenbrock, T. Physical Review C, Vol. 108, Issue 1 https://doi.org/10.1103/PhysRevC.108.014307	journal	July 2023
Variational Monte Carlo calculations of n+H3 scattering Flores, Abraham R.; Nollett, Kenneth M. Physical Review C, Vol. 108, Issue 3 https://doi.org/10.1103/PhysRevC.108.034001	journal	September 2023
Trineutron resonances in the SS-HORSE extension of the no-core shell model Mazur, I. A.; Efimenko, M. K.; Mazur, A. I. Physical Review C, Vol. 110, Issue 1 https://doi.org/10.1103/PhysRevC.110.014004	journal	July 2024
Ab initio investigation of the Li7(p,e+e−)Be8 process and the X17 boson Gysbers, P.; Navrátil, P.; Kravvaris, K. Physical Review C, Vol. 110, Issue 1 https://doi.org/10.1103/PhysRevC.110.015503	journal	July 2024
Role of momentum in the generator-coordinate method applied to barrier penetration Hagino, K.; Bertsch, G. F. Physical Review C, Vol. 110, Issue 5 https://doi.org/10.1103/PhysRevC.110.054610	journal	November 2024
Green’s function Monte Carlo study of light nuclei Carlson, J. Physical Review C, Vol. 36, Issue 5 https://doi.org/10.1103/PhysRevC.36.2026	journal	November 1987
Quantum Monte Carlo calculations of A = 9 , 10 nuclei Pieper, Steven C.; Varga, K.; Wiringa, R. B. Physical Review C, Vol. 66, Issue 4 https://doi.org/10.1103/PhysRevC.66.044310	journal	October 2002
Ab initio many-body calculations of nucleon-nucleus scattering Quaglioni, Sofia; Navrátil, Petr Physical Review C, Vol. 79, Issue 4 https://doi.org/10.1103/PhysRevC.79.044606	journal	April 2009
Ab initio many-body calculations of nucleon scattering on He 4 , Li 7 , Be 7 , C 12 , and O 16 Navrátil, Petr; Roth, Robert; Quaglioni, Sofia Physical Review C, Vol. 82, Issue 3 https://doi.org/10.1103/PhysRevC.82.034609	journal	September 2010
Unified ab initio approach to bound and unbound states: No-core shell model with continuum and its application to 7 He Baroni, Simone; Navrátil, Petr; Quaglioni, Sofia Physical Review C, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevC.87.034326	journal	March 2013
Ab initio no-core Gamow shell model calculations with realistic interactions Papadimitriou, G.; Rotureau, J.; Michel, N. Physical Review C, Vol. 88, Issue 4 https://doi.org/10.1103/PhysRevC.88.044318	journal	October 2013
Shell model states in the continuum Shirokov, A. M.; Mazur, A. I.; Mazur, I. A. Physical Review C, Vol. 94, Issue 6 https://doi.org/10.1103/PhysRevC.94.064320	journal	December 2016
Neutron width statistics in a realistic resonance-reaction model Fanto, P.; Bertsch, G. F.; Alhassid, Y. Physical Review C, Vol. 98, Issue 1 https://doi.org/10.1103/PhysRevC.98.014604	journal	July 2018
Nucleon- α scattering and resonances in He 5 and Li 5 with JISP16 and Daejeon16 NN interactions Shirokov, A. M.; Mazur, A. I.; Mazur, I. A. Physical Review C, Vol. 98, Issue 4 https://doi.org/10.1103/PhysRevC.98.044624	journal	October 2018
Calculating reactions with use of no-core shell-model states Efros, Victor D. Physical Review C, Vol. 99, Issue 3 https://doi.org/10.1103/PhysRevC.99.034620	journal	March 2019
Ab Initio Many-Body Calculations of n − H 3 , n − He 4 , p − He 3 , 4 , and n − Be 10 Scattering Quaglioni, Sofia; Navrátil, Petr Physical Review Letters, Vol. 101, Issue 9 https://doi.org/10.1103/PhysRevLett.101.092501	journal	August 2008
Evolution of Shell Structure in Neutron-Rich Calcium Isotopes Hagen, G.; Hjorth-Jensen, M.; Jansen, G. R. Physical Review Letters, Vol. 109, Issue 3 https://doi.org/10.1103/PhysRevLett.109.032502	journal	July 2012
Ab Initio Description of the Exotic Unbound He 7 Nucleus Baroni, Simone; Navrátil, Petr; Quaglioni, Sofia Physical Review Letters, Vol. 110, Issue 2 https://doi.org/10.1103/PhysRevLett.110.022505	journal	January 2013
Prediction for a Four-Neutron Resonance Shirokov, A. M.; Papadimitriou, G.; Mazur, A. I. Physical Review Letters, Vol. 117, Issue 18 https://doi.org/10.1103/PhysRevLett.117.182502	journal	October 2016
Study of Nuclear Clustering from an Ab Initio Perspective Kravvaris, Konstantinos; Volya, Alexander Physical Review Letters, Vol. 119, Issue 6 https://doi.org/10.1103/PhysRevLett.119.062501	journal	August 2017
Ab Initio Prediction of the He4(d,γ)Li6 Big Bang Radiative Capture Hebborn, C.; Hupin, G.; Kravvaris, K. Physical Review Letters, Vol. 129, Issue 4 https://doi.org/10.1103/PhysRevLett.129.042503	journal	July 2022
Quantum Monte Carlo Calculations of A ≤ 6 Nuclei Pudliner, B. S.; Pandharipande, V. R.; Carlson, J. Physical Review Letters, Vol. 74, Issue 22 https://doi.org/10.1103/PhysRevLett.74.4396	journal	May 1995
Properties of 12 C in the Ab Initio Nuclear Shell Model Navrátil, P.; Vary, J. P.; Barrett, B. R. Physical Review Letters, Vol. 84, Issue 25 https://doi.org/10.1103/PhysRevLett.84.5728	journal	June 2000
Ab-Initio Coupled-Cluster Study of O 16 Włoch, M.; Dean, D. J.; Gour, J. R. Physical Review Letters, Vol. 94, Issue 21 https://doi.org/10.1103/PhysRevLett.94.212501	journal	June 2005
Quantum Monte Carlo Calculations of Neutron- α Scattering Nollett, Kenneth M.; Pieper, Steven C.; Wiringa, R. B. Physical Review Letters, Vol. 99, Issue 2 https://doi.org/10.1103/PhysRevLett.99.022502	journal	July 2007
Quantum Monte Carlo calculations of neutron- α scattering via an integral relation Flores, Abraham R.; Nollett, Kenneth M.; Piarulli, Maria Physical Review C, Vol. 112, Issue 1 https://doi.org/10.1103/q4dy-vhv1	journal	July 2025
SS-HORSE method for studying resonances Blokhintsev, L. D.; Mazur, A. I.; Mazur, I. A. Physics of Atomic Nuclei, Vol. 80, Issue 2 https://doi.org/10.1134/S1063778817020077	journal	March 2017
SS-HORSE Method for Analysis of Resonances: Charged-Particle Scattering Blokhintsev, L. D.; Mazur, A. I.; Mazur, I. A. Physics of Atomic Nuclei, Vol. 80, Issue 6 https://doi.org/10.1134/S1063778817060072	journal	November 2017
On the Convergence of Oscillator Basis Calculations Shirokov, A. M.; Mazur, A. I.; Kulikov, V. A. Physics of Atomic Nuclei, Vol. 84, Issue 2 https://doi.org/10.1134/S1063778821020149	journal	March 2021
Bound and Resonant States of the $${}^{{9}}$$Li Nucleus with Daejeon16 Nucleon–Nucleon Interaction Mazur, I. A.; Mazur, A. I.; Kulikov, V. A. Physics of Atomic Nuclei, Vol. 85, Issue 6 https://doi.org/10.1134/S1063778823010349	journal	December 2022
Description of Continuum Spectrum States of Light Nuclei in the Shell Model Mazur, I. A.; Shirokov, A. M.; Mazur, A. I. Physics of Particles and Nuclei, Vol. 50, Issue 5 https://doi.org/10.1134/S1063779619050186	journal	September 2019
Effect of the end sill angle on the hydrodynamic parameters of a stilling basin Tajabadi, Faezeh; Jabbari, Ehsan; Sarkardeh, Hamed The European Physical Journal Plus, Vol. 133, Issue 1 https://doi.org/10.1140/epjp/i2018-11837-y	journal	January 2018
Quantum Theory of Angular Momentum Varshalovich, D. A.; Moskalev, A. N.; Khersonskii, V. K. https://doi.org/10.1142/0270	book	October 1988
Q UANTUM M ONTE C ARLO C ALCULATIONS OF L IGHT N UCLEI Pieper, Steven C.; Wiringa, R. B. Annual Review of Nuclear and Particle Science, Vol. 51, Issue 1 https://doi.org/10.1146/annurev.nucl.51.101701.132506	journal	December 2001
О сходимости расчетов в осцилляторном базисе Широков, А. М.; Мазур, А. И.; Куликов, В. А. Ядерная физика, Vol. 84, Issue 02 https://doi.org/10.31857/S0044002721020148	journal	January 2021
Истинно многочастичное рассеяние в осцилляторном представлении Зайцев, С А; Zaytsev, S. A.; Смирнов, Ю Ф Теоретическая и математическая физика, Vol. 117, Issue 2 https://doi.org/10.4213/tmf929	journal	January 1998

Similar Records

The Cornell Andes Project: An interdisciplinary study of mountain building

Journal Article · · Engineering, Cornell Quarterly; (United States) · OSTI ID:5145814

Intraatomic correlation correction in the FORS model

Journal Article · Thu May 23 04:00:00 UTC 1985 · J. Phys. Chem.; (United States) · OSTI ID:5133773

Lam, B; Schmidt, M W; Ruedenberg, K

A Perturbative Solution for Nonlinear Stratified Upwelling over a Frictional Slope

Journal Article · Sun Oct 01 04:00:00 UTC 2023 · Journal of Physical Oceanography · OSTI ID:2580152

Choi, Jang-Geun; Pringle, James; Lippmann, Thomas

Related Subjects

Nuclear reactions
Nuclear structure & decays

Title: Applications of the modified Hulthén-Kohn method for bound and scattering states

Citation Formats

References (73)

Similar Records

Related Subjects