Clustering in structure and reactions using configuration interaction techniques

Kravvaris, Konstantinos; Volya, Alexander

doi:10.1103/PhysRevC.100.034321

Title: Clustering in structure and reactions using configuration interaction techniques

Abstract

Atomic nuclei are remarkable quantum many-body systems where clustering properties develop naturally from underlying interactions between the constituent nucleons. Clustering degrees of freedom manifest themselves in multiple structure and reaction observables. Our goal is to study nuclear clustering and its emergence in many-nucleon dynamics from nucleon-nucleon interactions. Clustering is a phenomenon that is known to emerge on the boundary between structure and reactions, therefore developing appropriate techniques that bridge the structure-reaction divide and establishing connections to observables is among our principal objectives. Showing consistency and how the new techniques can be reduced to well established other methods is an important part of this work. Here, the configuration-interaction technique based on second quantization is used to treat the quantum many-body problem assuring that fermionic antisymmetry is fully satisfied. The use of the harmonic oscillator single-particle basis allows for the center-of-mass coordinate to be separated and prepared in a desired oscillator state for each cluster. The relative motion reaction basis channels are constructed by coupling clusters in different harmonic oscillator states with respect to their relative motion. Finally, using a resonating group method strategy we solve the generalized eigenvalue problem to obtain scattering channels. Structural clustering characteristics are discussed and the modifiedmore »« less

Authors:

Kravvaris, Konstantinos ^[1];

^[2]

Florida State Univ., Tallahassee, FL (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Florida State Univ., Tallahassee, FL (United States)

Publication Date:: Mon Sep 23 00:00:00 EDT 2019

Research Org.:: Florida State Univ., Tallahassee, FL (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1594020

Alternate Identifier(s):: OSTI ID: 1592990

Report Number(s):: LLNL-JRNL-758083
Journal ID: ISSN 2469-9985; PRVCAN; TRN: US2101105

Grant/Contract Number:: SC0009883; AC52-07NA27344

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review C

Additional Journal Information:: Journal Volume: 100; Journal Issue: 3; Journal ID: ISSN 2469-9985

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Alpha decay; Cluster models; H & He induced nuclear reactions; Nuclear forces; Nuclear many-body theory; Shell model

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                    Kravvaris, Konstantinos, and Volya, Alexander. Clustering in structure and reactions using configuration interaction techniques.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevC.100.034321.

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                    Kravvaris, Konstantinos, & Volya, Alexander. Clustering in structure and reactions using configuration interaction techniques.  United States.  https://doi.org/10.1103/PhysRevC.100.034321

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                    Kravvaris, Konstantinos, and Volya, Alexander. Mon .  
"Clustering in structure and reactions using configuration interaction techniques".  United States.  https://doi.org/10.1103/PhysRevC.100.034321.  https://www.osti.gov/servlets/purl/1594020.

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@article{osti_1594020,

  title        = {Clustering in structure and reactions using configuration interaction techniques},

  author       = {Kravvaris, Konstantinos and Volya, Alexander},

  abstractNote = {Atomic nuclei are remarkable quantum many-body systems where clustering properties develop naturally from underlying interactions between the constituent nucleons. Clustering degrees of freedom manifest themselves in multiple structure and reaction observables. Our goal is to study nuclear clustering and its emergence in many-nucleon dynamics from nucleon-nucleon interactions. Clustering is a phenomenon that is known to emerge on the boundary between structure and reactions, therefore developing appropriate techniques that bridge the structure-reaction divide and establishing connections to observables is among our principal objectives. Showing consistency and how the new techniques can be reduced to well established other methods is an important part of this work. Here, the configuration-interaction technique based on second quantization is used to treat the quantum many-body problem assuring that fermionic antisymmetry is fully satisfied. The use of the harmonic oscillator single-particle basis allows for the center-of-mass coordinate to be separated and prepared in a desired oscillator state for each cluster. The relative motion reaction basis channels are constructed by coupling clusters in different harmonic oscillator states with respect to their relative motion. Finally, using a resonating group method strategy we solve the generalized eigenvalue problem to obtain scattering channels. Structural clustering characteristics are discussed and the modified harmonic oscillator representation for scattering equations method is used to extract scattering observables. New methods for treating clustering problems have been put forward. We demonstrate broad applicability of the developed techniques. Examples highlight connections with algebraic techniques, and the role of approximations leading to algebraic limits is assessed using realistic examples. Various types of clustering characteristics are used to study alpha clustering in light nuclei that are relevant to currently ongoing experimental efforts. We demonstrate the emergence of strongly clustered bands of states in beryllium, triple alpha channels in 12C, and molecular type clustering in 21Ne. Starting from nucleon-nucleon interactions without any additional assumptions scattering phase shifts for alpha-alpha scattering are determined and shown to be consistent with those observed. In this work we put forward a new configuration-interaction-based method that targets the physics of clustering, and further unifies nuclear structure and reactions. We provide detailed discussions and many examples highlighting features and advantages of the approach.},

  doi          = {10.1103/PhysRevC.100.034321},

  journal      = {Physical Review C},

  number       = 3,

  volume       = 100,

  place        = {United States},

  year         = {Mon Sep 23 00:00:00 EDT 2019},

  month        = {Mon Sep 23 00:00:00 EDT 2019}

}

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Algebraic model for scattering in three- s -cluster systems. II. Resonances in the three-cluster continuum of 6 He and 6 Be
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Vasilevsky, V.; Nesterov, A. V.; Arickx, F.
Physical Review C, Vol. 63, Issue 3
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On absolute values of α-decay rates
journal, May 1976

Fliessbach, T.; Mang, H. J.
Nuclear Physics A, Vol. 263, Issue 1
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Alpha-Structure Amplitudes for the 1 p Shell
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Kurath, D.
Physical Review C, Vol. 7, Issue 4
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$α$ decay in the complex-energy shell model
journal, September 2012

Betan, R. Id; Nazarewicz, W.
Physical Review C, Vol. 86, Issue 3
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Structure of the Hoyle State in ${}^{12}C$
journal, January 2007

Chernykh, M.; Feldmeier, H.; Neff, T.
Physical Review Letters, Vol. 98, Issue 3
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Neutron-Helium Interaction. II. Angular Distributions and Phase Shifts from 0.2 to 7.0 MeV
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Morgan, G. L.; Walter, R. L.
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The clustered nucleus—cluster structures in stable and unstable nuclei
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Freer, Martin
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Clustering aspects in nuclei and their microscopic description
journal, October 1979

Wildermuth, K.; Kanellopoulos, E. J.
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Alpha-transfer reactions in light nuclei. III. ( ${}^{7}{Li}, t$ ) stripping reaction
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Cobern, M. E.; Pisano, D. J.; Parker, P. D.
Physical Review C, Vol. 14, Issue 2
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Alpha-Cluster plus 16 O-Core Model for 20 Ne and Neighboring Nuclei
journal, September 1969

Hiura, Jun; Abe, Yasuhisa; Sait\=o, Sakae
Progress of Theoretical Physics, Vol. 42, Issue 3
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Neutron-Helium Interaction. II. Angular Distributions and Phase Shifts from 0.2 to 7.0 MeV
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Morgan, G. L.; Walter, R. L.
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Continuum Shell Model and Nuclear Physics at the Edge of Stability
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Volya, A.; Zelevinsky, V.
Ядерная физика, Vol. 77, Issue 08
DOI: 10.7868/s0044002714070186

How atomic nuclei cluster?
conference, January 2012

Ebran, J. -P.; Khan, E.; Nikšić, T.
NUCLEAR STRUCTURE AND DYNAMICS 2012, AIP Conference Proceedings
DOI: 10.1063/1.4764191

Ab initio many-body calculations of nucleon-nucleus scattering
text, January 2009

Quaglioni, Sofia; Navratil, Petr
arXiv
DOI: 10.48550/arxiv.0901.0950

Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems
text, January 2011

Auerbach, Naftali; Zelevinsky, Vladimir
arXiv
DOI: 10.48550/arxiv.1104.5462

Antisymmetrized molecular dynamics and its applications to cluster phenomena
preprint, January 2012

Kanada-En'yo, Yoshiko; Kimura, Masaaki; Ono, Akira
arXiv
DOI: 10.48550/arxiv.1202.1864

Shell Model States in the Continuum
text, January 2016

Shirokov, A. M.; Mazur, A. I.; Mazur, I. A.
arXiv
DOI: 10.48550/arxiv.1608.05885

Symmetry-guided large-scale shell-model theory
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Launey, Kristina D.; Dytrych, Tomas; Draayer, Jerry P.
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DOI: 10.48550/arxiv.1612.04298

P-matrix and J-matrix approaches. Coulomb asymptotics in the harmonic oscillator representation of scattering theory
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Bang, J. M.; Mazur, A. I.; Shirokov, A. M.
arXiv
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Gamow Shell Model Description of Neutron-Rich Nuclei
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Michel, N.; Nazarewicz, W.; Ploszajczak, M.
arXiv
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The algebraic cluster model. Three-body clusters
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arXiv
DOI: 10.48550/arxiv.nucl-th/0203072

Continuum Shell Model
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Volya, Alexander; Zelevinsky, Vladimir
arXiv
DOI: 10.48550/arxiv.nucl-th/0509051

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Title: Clustering in structure and reactions using configuration interaction techniques

Abstract

Citation Formats

Colloquium : Status of α -particle condensate structure of the Hoyle state journal, January 2017

Spherical proton emitters journal, October 1997

Ab initio no core shell model journal, March 2013

Symmetry-guided large-scale shell-model theory journal, July 2016

α -unbound levels in Ar 34 from Ar 36 ( p , t ) Ar 34 reaction measurements and implications for the astrophysical S 30 ( α , p ) Cl 33 reaction rate journal, May 2018

Cluster states in nuclei as representations of a U ( ν + 1 ) group journal, May 2000

Simple potential model for cluster states in light nuclei journal, May 1975

Alpha Cluster Condensation in C 12 and O 16 journal, October 2001

Genealogische Koeffizienten für α-Teilchen journal, January 1965

Interaction between Clusters and Pauli Principle journal, March 1969

Alpha Transfer Reactions in Light Nuclei journal, December 1979

The nuclear shell model towards the drip lines journal, January 2001

Limits for the 3α branching ratio of the decay of the 7.65 MeV, 0 2 + state in C 12 journal, April 1994

Super-radiant dynamics, doorways and resonances in nuclei and other open mesoscopic systems journal, September 2011

The cluster spectroscopic factors of the clusterized nuclei and nuclei of the 2s-2d shell and the quasi-elastic knock-out processes journal, November 1983

Ab initio many-body calculations of nucleon-nucleus scattering journal, April 2009

J−matrix method: Extensions to arbitrary angular momentum and to Coulomb scattering journal, January 1975

Constructing realistic alpha cluster channels journal, June 2017

The 7.68-Mev State in C 12 journal, November 1953

Alpha spectroscopic factors for light nuclei journal, May 1977

Microscopic Theory of α-Particle Resonance Spectra conference, June 2015

On the Origin of Nuclear Clustering journal, January 2012

Continuum shell model and nuclear physics at the edge of stability journal, August 2014

Alpha-transfer reactions in light nuclei. II. ( He 3 , Be 7 ) pickup reactions journal, August 1976

Microscopic theory of cluster radioactivity journal, February 1998

A Study of α-Widths of 20 Ne Based on 16 O and α-Cluster Model journal, May 1973

Ab Initio Calculation of the Hoyle State journal, May 2011

How atomic nuclei cluster journal, July 2012

Continuum shell model journal, December 2006

R-matrix formulation and phase shifts for n-4He and p-4He scattering for energies up to 20 MeV journal, January 1972

On Nuclear Reactions Occuring in Very Hot STARS.I. the Synthesis of Elements from Carbon to Nickel. journal, September 1954

Evidence for Tetrahedral Symmetry in O 16 journal, April 2014

Indirect study of the stellar Ar 34 ( α , p ) K 37 reaction rate through Ca 40 ( p , t ) Ca 38 reaction measurements journal, May 2017

Cluster spectroscopic factors for the p -shell nuclei journal, January 1977

Coulomb displacement energy and the low-energy astrophysical S17 factor for the 7Be(p,γ)8B reaction journal, January 1996

The Systematic Structure-Change into the Molecule-like Structures in the Self-Conjugate $4n$ Nuclei journal, January 1968

Quantitative properties of clustering within modern microscopic nuclear models journal, September 2016

Mass Defect Curve and Nuclear Constitution journal, March 1930

P-Matrix and J-Matrix Approaches: Coulomb Asymptotics in the Harmonic Oscillator Representation of Scattering Theory journal, March 2000

α-cluster and α-binucleon states of 1p-shell nuclei journal, August 2010

Molecular structures in T = 1 states of 10 B journal, November 2011

Association of the C 12 + 12 C breakup states in Mg 24 with the quasimolecular resonances journal, March 1995

Realistic nuclear Hamiltonian: Ab exitu approach journal, January 2007

Further Improvement of the Upper Limit on the Direct 3 α Decay from the Hoyle State in C 12 journal, September 2014

Spurious center-of-mass motion journal, December 1974

Evidence for a direct eight-nucleon transfer reaction and multiparticle excitation of 20Ne journal, April 1971

The Alpha-Particle Model of the Nucleus journal, November 1938

A PSDPF interaction to describe the 1 ℏω intruder states in sd shell nuclei journal, August 2011

Simple Formula for the General Oscillator Brackets journal, May 1972

New “USD” Hamiltonians for the sd shell journal, September 2006

Nuclear Spectroscopy, Nuclear Clustering and Exotic Shapes journal, January 2000

A Unified Theory of the Nucleus book, January 1977

Quantum Monte Carlo calculations of A = 8 nuclei journal, June 2000

Dynamics of quantum systems embedded in a continuum journal, February 2003

Shell-model predictions of alpha-spectroscopic factors between ground states of 16 ⩽ A ⩽ 40 nuclei journal, December 1978

Recoil corrected continuum shell model calculations for four-nucleon systems journal, June 1979

Nuclear clustering using a modern shell model approach journal, April 2015

Evidence for α-particle condensation in nuclei from the Hoyle state deexcitation journal, November 2011

Symplectic and cluster excitations in nuclei: journal, July 1986

Alpha-clustering systematics from the quasifree ( p , p α ) knockout reaction journal, January 1981

Reduced widths for nucleon clusters in shell model journal, August 1961

Antisymmetrized molecular dynamics and its applications to cluster phenomena journal, January 2012

Alpha-particle stripping to Ne 21 journal, August 1978

Shell model states in the continuum journal, December 2016

A Formulation of the Theory of Alpha-particle Decay from Time-independent Equations journal, September 1954

Effects of translational invariance violation in particle-hole calculations. Application to 208Pb journal, July 1968

Understanding emergent collectivity and clustering in nuclei from a symmetry-based no-core shell-model perspective journal, April 2017

Systematic Survey of the α − α Interaction journal, January 1969

Alpha-particle spectroscopic amplitudes and the su(3) model journal, April 1973

Study of the Alpha-Clustering Structure of 20Ne Based on the Resonating Group Method for 16O+ : Analysis of Alpha-Decay Widths and the Exchange Kernel journal, February 1975

Evidence for a highly deformed band in O 16 + 16 O breakup of S 32 journal, April 1996

Study of Nuclear Clustering from an Ab Initio Perspective journal, August 2017

Gamow Shell Model Description of Neutron-Rich Nuclei journal, July 2002

Nuclear clusters and nuclear molecules journal, September 2006

High-Precision Probe of the Fully Sequential Decay Width of the Hoyle State in C 12 journal, September 2017

Ab initio alpha–alpha scattering journal, December 2015

Alpha-particle strengths from the 16O(6Li, d)20Ne reaction journal, January 1979

Colloquium : Status of $α$ -particle condensate structure of the Hoyle state
journal, January 2017

Spherical proton emitters
journal, October 1997

Ab initio no core shell model
journal, March 2013

Symmetry-guided large-scale shell-model theory
journal, July 2016

$α$ -unbound levels in ${}^{34}{Ar}$ from ${}^{36}{Ar} (p, t) {}^{34}{Ar}$ reaction measurements and implications for the astrophysical ${}^{30}S (α, p) {}^{33}{Cl}$ reaction rate
journal, May 2018

Cluster states in nuclei as representations of a $U (ν + 1)$ group
journal, May 2000

Simple potential model for cluster states in light nuclei
journal, May 1975

Alpha Cluster Condensation in ${}^{12}C$ and ${}^{16}O$
journal, October 2001

Genealogische Koeffizienten für α-Teilchen
journal, January 1965

Interaction between Clusters and Pauli Principle
journal, March 1969

Alpha Transfer Reactions in Light Nuclei
journal, December 1979

The nuclear shell model towards the drip lines
journal, January 2001

Limits for the 3α branching ratio of the decay of the 7.65 MeV, $0_{2}^{+}$ state in ${}^{12}C$
journal, April 1994

Super-radiant dynamics, doorways and resonances in nuclei and other open mesoscopic systems
journal, September 2011

The cluster spectroscopic factors of the clusterized nuclei and nuclei of the 2s-2d shell and the quasi-elastic knock-out processes
journal, November 1983

Ab initio many-body calculations of nucleon-nucleus scattering
journal, April 2009

J−matrix method: Extensions to arbitrary angular momentum and to Coulomb scattering
journal, January 1975

Constructing realistic alpha cluster channels
journal, June 2017

The 7.68-Mev State in C 12
journal, November 1953

Alpha spectroscopic factors for light nuclei
journal, May 1977

Microscopic Theory of α-Particle Resonance Spectra
conference, June 2015

On the Origin of Nuclear Clustering
journal, January 2012

Continuum shell model and nuclear physics at the edge of stability
journal, August 2014

Alpha-transfer reactions in light nuclei. II. ( He 3 , Be 7 ) pickup reactions
journal, August 1976

Microscopic theory of cluster radioactivity
journal, February 1998

A Study of α-Widths of 20 Ne Based on 16 O and α-Cluster Model
journal, May 1973

Ab Initio Calculation of the Hoyle State
journal, May 2011

How atomic nuclei cluster
journal, July 2012

Continuum shell model
journal, December 2006

R-matrix formulation and phase shifts for n-4He and p-4He scattering for energies up to 20 MeV
journal, January 1972

On Nuclear Reactions Occuring in Very Hot STARS.I. the Synthesis of Elements from Carbon to Nickel.
journal, September 1954

Evidence for Tetrahedral Symmetry in ${}^{16}O$
journal, April 2014

Indirect study of the stellar ${}^{34}{Ar} (α, p) {}^{37}K$ reaction rate through ${}^{40}{Ca} (p, t) {}^{38}{Ca}$ reaction measurements
journal, May 2017

Cluster spectroscopic factors for the $p$ -shell nuclei
journal, January 1977

Coulomb displacement energy and the low-energy astrophysical S17 factor for the 7Be(p,γ)8B reaction
journal, January 1996

The Systematic Structure-Change into the Molecule-like Structures in the Self-Conjugate $4n$ Nuclei
journal, January 1968

Quantitative properties of clustering within modern microscopic nuclear models
journal, September 2016

Mass Defect Curve and Nuclear Constitution
journal, March 1930

P-Matrix and J-Matrix Approaches: Coulomb Asymptotics in the Harmonic Oscillator Representation of Scattering Theory
journal, March 2000

α-cluster and α-binucleon states of 1p-shell nuclei
journal, August 2010

Molecular structures in $T = 1$ states of $^{10}$ B
journal, November 2011

Association of the C 12 + 12 C breakup states in Mg 24 with the quasimolecular resonances
journal, March 1995

Realistic nuclear Hamiltonian: Ab exitu approach
journal, January 2007

Further Improvement of the Upper Limit on the Direct $3 α$ Decay from the Hoyle State in ${}^{12}C$
journal, September 2014

Spurious center-of-mass motion
journal, December 1974

Evidence for a direct eight-nucleon transfer reaction and multiparticle excitation of 20Ne
journal, April 1971

The Alpha-Particle Model of the Nucleus
journal, November 1938

A PSDPF interaction to describe the 1 ℏω intruder states in sd shell nuclei
journal, August 2011

Simple Formula for the General Oscillator Brackets
journal, May 1972

New “USD” Hamiltonians for the $sd$ shell
journal, September 2006

Nuclear Spectroscopy, Nuclear Clustering and Exotic Shapes
journal, January 2000

A Unified Theory of the Nucleus
book, January 1977

Quantum Monte Carlo calculations of $A = 8$ nuclei
journal, June 2000

Dynamics of quantum systems embedded in a continuum
journal, February 2003

Shell-model predictions of alpha-spectroscopic factors between ground states of 16 ⩽ A ⩽ 40 nuclei
journal, December 1978

Recoil corrected continuum shell model calculations for four-nucleon systems
journal, June 1979

Nuclear clustering using a modern shell model approach
journal, April 2015

Evidence for α-particle condensation in nuclei from the Hoyle state deexcitation
journal, November 2011

Symplectic and cluster excitations in nuclei:
journal, July 1986

Alpha-clustering systematics from the quasifree ( $p, p α$ ) knockout reaction
journal, January 1981

Reduced widths for nucleon clusters in shell model
journal, August 1961

Antisymmetrized molecular dynamics and its applications to cluster phenomena
journal, January 2012

Alpha-particle stripping to Ne 21
journal, August 1978

Shell model states in the continuum
journal, December 2016

A Formulation of the Theory of Alpha-particle Decay from Time-independent Equations
journal, September 1954

Effects of translational invariance violation in particle-hole calculations. Application to 208Pb
journal, July 1968

Understanding emergent collectivity and clustering in nuclei from a symmetry-based no-core shell-model perspective
journal, April 2017

Systematic Survey of the $α - α$ Interaction
journal, January 1969

Alpha-particle spectroscopic amplitudes and the su(3) model
journal, April 1973

Study of the Alpha-Clustering Structure of 20Ne Based on the Resonating Group Method for 16O+ : Analysis of Alpha-Decay Widths and the Exchange Kernel
journal, February 1975

Evidence for a highly deformed band in O 16 + 16 O breakup of S 32
journal, April 1996

Study of Nuclear Clustering from an Ab Initio Perspective
journal, August 2017

Gamow Shell Model Description of Neutron-Rich Nuclei
journal, July 2002

Nuclear clusters and nuclear molecules
journal, September 2006

High-Precision Probe of the Fully Sequential Decay Width of the Hoyle State in ${}^{12}C$
journal, September 2017

Ab initio alpha–alpha scattering
journal, December 2015

Alpha-particle strengths from the 16O(6Li, d)20Ne reaction
journal, January 1979

New Measurement of the Direct $3 α$ Decay from the ${}^{12}C$ Hoyle State
journal, September 2017

The Algebraic Cluster Model: Three-Body Clusters
journal, June 2002

Stripping Reactions and the Structure of Light and Intermediate Nuclei
journal, July 1960