Magnetic structure of light nuclei from lattice QCD
Abstract
Lattice QCD with background magnetic fields is used to calculate the magnetic moments and magnetic polarizabilities of the nucleons and of light nuclei with $$A\le4$$, along with the cross-section for the $M1$ transition $$np\rightarrow d\gamma$$, at the flavor SU(3)-symmetric point where the pion mass is $$m_\pi\sim 806$$ MeV. These magnetic properties are extracted from nucleon and nuclear energies in six uniform magnetic fields of varying strengths. The magnetic moments are presented in a recent Letter. For the charged states, the extraction of the polarizability requires careful treatment of Landau levels, which enter non-trivially in the method that is employed. The nucleon polarizabilities are found to be of similar magnitude to their physical values, with $$\beta_p=5.22(+0.66/-0.45)(0.23) \times 10^{-4}$$ fm$^3$ and $$\beta_n=1.253(+0.056/-0.067)(0.055) \times 10^{-4}$$ fm$^3$, exhibiting a significant isovector component. The dineutron is bound at these heavy quark masses and its magnetic polarizability, $$\beta_{nn}=1.872(+0.121/-0.113)(0.082) \times 10^{-4}$$ fm$^3$ differs significantly from twice that of the neutron. A linear combination of deuteron scalar and tensor polarizabilities is determined by the energies of the $$j_z=\pm 1$$ deuteron states, and is found to be $$\beta_{d,\pm 1}=4.4(+1.6/-1.5)(0.2) \times 10^{-4}$$ fm$^3$. The magnetic polarizabilities of the three-nucleon and four-nucleon systems are found to be positive and similar in size to those of the proton, $$\beta_{^{3}\rm He}=5.4(+2.2/-2.1)(0.2) \times 10^{-4}$$ fm$^3$, $$\beta_{^{3}\rm H}=2.6(1.7)(0.1) \times 10^{-4}$$ fm$^3$, $$\beta_{^{4}\rm He}=3.4(+2.0/-1.9)(0.2) \times 10^{-4}$$ fm$^3$. Mixing between the $$j_z=0$$ deuteron state and the spin-singlet $np$ state induced by the background magnetic field is used to extract the short-distance two-nucleon counterterm, $${\bar L}_1$$, of the pionless effective theory for $NN$ systems (equivalent to the meson-exchange current contribution in nuclear potential models), that dictates the cross-section for the $$np\to d\gamma$$ process near threshold. Thus, combined with previous determinations of NN scattering parameters, this enables an ab initio determination of the threshold cross-section at these unphysical masses.
- Authors:
-
- Univ. of Washington, Seattle, WA (United States)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- College of William and Mary, Williamsburg, VA (United States); Jefferson Lab., Newport News, VA (United States)
- Univ. of Barcelona, Marti Franques (Spain)
- The City College of New York, New York, NY (United States); The CIty Univ. of New York, New York, NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- Contributing Org.:
- NPLQCD Collaboration
- OSTI Identifier:
- 1228040
- Alternate Identifier(s):
- OSTI ID: 1228722
- Report Number(s):
- JLAB-THY-15-2109; DOE/OR/23177-3492; arXiv:1506.05518
Journal ID: ISSN 1550-7998; PRVDAQ
- Grant/Contract Number:
- OCI1053575; PHY1206498; PHY1205778; AC02-05CH11231; AC05-00OR22725; FG02-04ER41302; AC05-06OR23177; FG02-00ER41132; SC0010495; FIS2011-24154
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. D, Particles, Fields, Gravitation and Cosmology
- Additional Journal Information:
- Journal Volume: 92; Journal Issue: 11; Journal ID: ISSN 1550-7998
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Chang, Emmanuel, Detmold, William, Orginos, Kostas, Parreño, Assumpta, Savage, Martin J., Tiburzi, Brian C., and Beane, Silas R. Magnetic structure of light nuclei from lattice QCD. United States: N. p., 2015.
Web. doi:10.1103/PhysRevD.92.114502.
Chang, Emmanuel, Detmold, William, Orginos, Kostas, Parreño, Assumpta, Savage, Martin J., Tiburzi, Brian C., & Beane, Silas R. Magnetic structure of light nuclei from lattice QCD. United States. https://doi.org/10.1103/PhysRevD.92.114502
Chang, Emmanuel, Detmold, William, Orginos, Kostas, Parreño, Assumpta, Savage, Martin J., Tiburzi, Brian C., and Beane, Silas R. Wed .
"Magnetic structure of light nuclei from lattice QCD". United States. https://doi.org/10.1103/PhysRevD.92.114502. https://www.osti.gov/servlets/purl/1228040.
@article{osti_1228040,
title = {Magnetic structure of light nuclei from lattice QCD},
author = {Chang, Emmanuel and Detmold, William and Orginos, Kostas and Parreño, Assumpta and Savage, Martin J. and Tiburzi, Brian C. and Beane, Silas R.},
abstractNote = {Lattice QCD with background magnetic fields is used to calculate the magnetic moments and magnetic polarizabilities of the nucleons and of light nuclei with $A\le4$, along with the cross-section for the $M1$ transition $np\rightarrow d\gamma$, at the flavor SU(3)-symmetric point where the pion mass is $m_\pi\sim 806$ MeV. These magnetic properties are extracted from nucleon and nuclear energies in six uniform magnetic fields of varying strengths. The magnetic moments are presented in a recent Letter. For the charged states, the extraction of the polarizability requires careful treatment of Landau levels, which enter non-trivially in the method that is employed. The nucleon polarizabilities are found to be of similar magnitude to their physical values, with $\beta_p=5.22(+0.66/-0.45)(0.23) \times 10^{-4}$ fm$^3$ and $\beta_n=1.253(+0.056/-0.067)(0.055) \times 10^{-4}$ fm$^3$, exhibiting a significant isovector component. The dineutron is bound at these heavy quark masses and its magnetic polarizability, $\beta_{nn}=1.872(+0.121/-0.113)(0.082) \times 10^{-4}$ fm$^3$ differs significantly from twice that of the neutron. A linear combination of deuteron scalar and tensor polarizabilities is determined by the energies of the $j_z=\pm 1$ deuteron states, and is found to be $\beta_{d,\pm 1}=4.4(+1.6/-1.5)(0.2) \times 10^{-4}$ fm$^3$. The magnetic polarizabilities of the three-nucleon and four-nucleon systems are found to be positive and similar in size to those of the proton, $\beta_{^{3}\rm He}=5.4(+2.2/-2.1)(0.2) \times 10^{-4}$ fm$^3$, $\beta_{^{3}\rm H}=2.6(1.7)(0.1) \times 10^{-4}$ fm$^3$, $\beta_{^{4}\rm He}=3.4(+2.0/-1.9)(0.2) \times 10^{-4}$ fm$^3$. Mixing between the $j_z=0$ deuteron state and the spin-singlet $np$ state induced by the background magnetic field is used to extract the short-distance two-nucleon counterterm, ${\bar L}_1$, of the pionless effective theory for $NN$ systems (equivalent to the meson-exchange current contribution in nuclear potential models), that dictates the cross-section for the $np\to d\gamma$ process near threshold. Thus, combined with previous determinations of NN scattering parameters, this enables an ab initio determination of the threshold cross-section at these unphysical masses.},
doi = {10.1103/PhysRevD.92.114502},
journal = {Physical Review. D, Particles, Fields, Gravitation and Cosmology},
number = 11,
volume = 92,
place = {United States},
year = {Wed Dec 09 00:00:00 EST 2015},
month = {Wed Dec 09 00:00:00 EST 2015}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 60 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Reconciling the lattice background field method with nonrelativistic QED: Spinor case
journal, October 2014
- Lee, Jong-Wan; Tiburzi, Brian C.
- Physical Review D, Vol. 90, Issue 7
Proton Compton effect: A measurement of the electric and magnetic polarizabilities of the proton
journal, September 1991
- Federspiel, F. J.; Eisenstein, R. A.; Lucas, M. A.
- Physical Review Letters, Vol. 67, Issue 12
180° Compton scattering by the proton below the pion threshold
journal, March 1992
- Zieger, A.; Van de Vyver, R.; Christmann, D.
- Physics Letters B, Vol. 278, Issue 1-2
Measurement of the electric and magnetic polarizabilities of the proton
journal, October 1995
- MacGibbon, B. E.; Garino, G.; Lucas, M. A.
- Physical Review C, Vol. 52, Issue 4
Review of Particle Physics
journal, July 2012
- Beringer, J.; Arguin, J. -F.; Barnett, R. M.
- Physical Review D, Vol. 86, Issue 1
Measurement of Compton Scattering from the Deuteron and an Improved Extraction of the Neutron Electromagnetic Polarizabilities
journal, December 2014
- Myers, L. S.; Annand, J. R. M.; Brudvik, J.
- Physical Review Letters, Vol. 113, Issue 26
Proton polarizabilities from Compton data using covariant chiral effective field theory
journal, March 2014
- Lensky, Vadim; McGovern, Judith
- Physical Review C, Vol. 89, Issue 3
Quasi-free Compton scattering and the polarizabilities of the neutron
journal, February 2003
- Kossert, K.; Camen, M.; Wissmann, F.
- The European Physical Journal A, Vol. 16, Issue 2
Compton Scattering from the Deuteron and Extracted Neutron Polarizabilities
journal, May 2003
- Lundin, M.; Adler, J. -O.; Boland, M.
- Physical Review Letters, Vol. 90, Issue 19
The chiral structure of the neutron as revealed in electron and photon scattering
journal, September 2009
- Phillips, D. R.
- Journal of Physics G: Nuclear and Particle Physics, Vol. 36, Issue 10
Hadron Polarizabilities
journal, October 2014
- Holstein, Barry R.; Scherer, Stefan
- Annual Review of Nuclear and Particle Science, Vol. 64, Issue 1
Electromagnetic polarisability of the nucleon in chiral perturbation theory
journal, November 1992
- Butler, Malcolm N.; Savage, Martin J.
- Physics Letters B, Vol. 294, Issue 3-4
Strong and electromagnetic decays of the baryon decuplet
journal, June 1993
- Butler, Malcolm N.; Savage, Martin J.; Springer, Roxanne P.
- Nuclear Physics B, Vol. 399, Issue 1
Response of nucleons to external probes in hedgehog models. I. Electromagnetic polarizabilities
journal, January 1993
- Broniowski, Wojciech; Cohen, Thomas D.
- Physical Review D, Vol. 47, Issue 1
The role of the Δ isobar in chiral perturbation theory and hedgehog soliton models
journal, October 1992
- Cohen, Thomas D.; Broniowski, Wojciech
- Physics Letters B, Vol. 292, Issue 1-2
Effective theory of the resonance in Compton scattering off the nucleon
journal, May 2003
- Pascalutsa, Vladimir; Phillips, Daniel R.
- Physical Review C, Vol. 67, Issue 5
Electromagnetic and spin polarizabilities in lattice QCD
journal, June 2006
- Detmold, W.; Tiburzi, B. C.; Walker-Loud, A.
- Physical Review D, Vol. 73, Issue 11
The polarizability of the deuteron
journal, December 1998
- Chen, Jiunn-Wei; Grießhammer, Harald W.; Savage, Martin J.
- Nuclear Physics A, Vol. 644, Issue 3
Using Effective Field Theory to analyse low-energy Compton scattering data from protons and light nuclei
journal, October 2012
- Grießhammer, H. W.; McGovern, J. A.; Phillips, D. R.
- Progress in Particle and Nuclear Physics, Vol. 67, Issue 4
Research opportunities at the upgraded HIγS facility
journal, January 2009
- Weller, Henry R.; Ahmed, Mohammad W.; Gao, Haiyan
- Progress in Particle and Nuclear Physics, Vol. 62, Issue 1
Real and virtual Compton scattering: The nucleon polarisabilities
journal, September 2011
- Downie, E. J.; Fonvieille, H.
- The European Physical Journal Special Topics, Vol. 198, Issue 1
Compton scattering from Li at 60 MeV
journal, October 2012
- Myers, L. S.; Ahmed, M. W.; Feldman, G.
- Physical Review C, Vol. 86, Issue 4
Compton scattering from using tagged photons in the energy range 65–115 MeV
journal, March 2014
- Myers, L. S.; Shoniyozov, K.; Preston, M. F.
- Physical Review C, Vol. 89, Issue 3
Compton scattering from at 86 MeV
journal, August 2014
- Myers, L. S.; Ahmed, M. W.; Feldman, G.
- Physical Review C, Vol. 90, Issue 2
Meson exchange effects in n + p → d + γ
journal, February 1972
- Riska, D. O.; Brown, G. E.
- Physics Letters B, Vol. 38, Issue 4
Meson exchange currents in deuteron electro-disintegration
journal, December 1973
- Hockert, J.; Riska, D. O.; Gari, M.
- Nuclear Physics A, Vol. 217, Issue 1
Magnetic Moments of Light Nuclei from Lattice Quantum Chromodynamics
journal, December 2014
- Beane, S. R.; Chang, E.; Cohen, S.
- Physical Review Letters, Vol. 113, Issue 25
Ab initio Calculation of the Radiative Capture Process
journal, September 2015
- Beane, Silas R.; Chang, Emmanuel; Detmold, William
- Physical Review Letters, Vol. 115, Issue 13
On-shell improved lattice gauge theories
journal, March 1985
- Lüscher, M.; Weisz, P.
- Communications in Mathematical Physics, Vol. 97, Issue 1-2
Improved continuum limit lattice action for QCD with wilson fermions
journal, September 1985
- Sheikholeslami, B.; Wohlert, R.
- Nuclear Physics B, Vol. 259, Issue 4
Light nuclei and hypernuclei from quantum chromodynamics in the limit of SU(3) flavor symmetry
journal, February 2013
- Beane, S. R.; Chang, E.; Cohen, S. D.
- Physical Review D, Vol. 87, Issue 3
Nucleon-nucleon scattering parameters in the limit of SU(3) flavor symmetry
journal, August 2013
- Beane, S. R.; Chang, E.; Cohen, S. D.
- Physical Review C, Vol. 88, Issue 2
Lattice Quantum-Chromodynamics Calculation of Some Baryon Magnetic Moments
journal, October 1982
- Bernard, Claude; Draper, Terrence; Olynyk, Kirk
- Physical Review Letters, Vol. 49, Issue 15
The proton and neutron magnetic moments in lattice QCD
journal, October 1982
- Martinelli, G.; Parisi, G.; Petronzio, R.
- Physics Letters B, Vol. 116, Issue 6
Baryon magnetic moments in the background field method
journal, October 2005
- Lee, F. X.; Kelly, R.; Zhou, L.
- Physics Letters B, Vol. 627, Issue 1-4
Magnetic polarizability of hadrons from lattice QCD in the background field method
journal, February 2006
- Lee, Frank X.; Zhou, Leming; Wilcox, Walter
- Physical Review D, Vol. 73, Issue 3
Lattice calculation of the magnetic moments of and baryons with dynamical clover fermions
journal, March 2009
- Aubin, C.; Orginos, K.; Pascalutsa, V.
- Physical Review D, Vol. 79, Issue 5
Extracting electric polarizabilities from lattice QCD
journal, May 2009
- Detmold, W.; Tiburzi, B. C.; Walker-Loud, A.
- Physical Review D, Vol. 79, Issue 9
Extracting nucleon magnetic moments and electric polarizabilities from lattice QCD in background electric fields
journal, March 2010
- Detmold, W.; Tiburzi, B. C.; Walker-Loud, A.
- Physical Review D, Vol. 81, Issue 5
Magnetic properties of the nucleon in a uniform background field
journal, February 2014
- Primer, Thomas; Kamleh, Waseem; Leinweber, Derek
- Physical Review D, Vol. 89, Issue 3
A study of hadron electric polarizability in quenched lattice QCD
journal, September 1989
- Fiebig, H. R.; Wilcox, W.; Woloshyn, R. M.
- Nuclear Physics B, Vol. 324, Issue 1
Electric polarizability of neutral hadrons from lattice QCD
journal, August 2005
- Christensen, Joe; Wilcox, Walter; Lee, Frank X.
- Physical Review D, Vol. 72, Issue 3
Electric polarizability of neutral hadrons from dynamical lattice QCD ensembles
journal, April 2014
- Lujan, M.; Alexandru, A.; Freeman, W.
- Physical Review D, Vol. 89, Issue 7
Sea quark contributions to the electric polarizability of hadrons
journal, September 2014
- Freeman, Walter; Alexandru, Andrei; Lujan, Mike
- Physical Review D, Vol. 90, Issue 5
A property of electric and magnetic flux in non-Abelian gauge theories
journal, January 1979
- 't Hooft, G.
- Nuclear Physics B, Vol. 153
The magnetic moments of the octet baryons in quenched chiral perturbation theory
journal, March 2002
- Savage, M. J.
- Nuclear Physics A, Vol. 700, Issue 1-2
Baryons in partially quenched chiral perturbation theory
journal, April 2002
- Chen, Jiunn-Wei; Savage, Martin J.
- Physical Review D, Vol. 65, Issue 9
Nucleons in two-flavor partially-quenched chiral perturbation theory
journal, October 2002
- Beane, Silas R.; Savage, Martin J.
- Nuclear Physics A, Vol. 709, Issue 1-4
Lattice study of quark and glue momenta and angular momenta in the nucleon
journal, January 2015
- Deka, M.; Doi, T.; Yang, Y. B.
- Physical Review D, Vol. 91, Issue 1
High-precision calculation of the strange nucleon electromagnetic form factors
journal, August 2015
- Green, Jeremy; Meinel, Stefan; Engelhardt, Michael
- Physical Review D, Vol. 92, Issue 3
Glueball masses and string tension in lattice QCD
journal, June 1987
- Albanese, M.; Costantini, F.; Fiorentini, G.
- Physics Letters B, Vol. 192, Issue 1-2
Nuclear correlation functions in lattice QCD
journal, June 2013
- Detmold, William; Orginos, Kostas
- Physical Review D, Vol. 87, Issue 11
Method to extract charged hadron properties from lattice QCD in magnetic fields
journal, March 2013
- Tiburzi, B. C.; Vayl, S. O.
- Physical Review D, Vol. 87, Issue 5
Comment on “Complete One-Loop Analysis of the Nucleon's Spin Polarizabilities”
journal, April 2001
- Birse, Michael C.; Ji, Xiangdong; McGovern, Judith A.
- Physical Review Letters, Vol. 86, Issue 14
Nuclear physics from lattice QCD
journal, January 2011
- Beane, S. R.; Detmold, W.; Orginos, K.
- Progress in Particle and Nuclear Physics, Vol. 66, Issue 1
Two-nucleon systems in a finite volume. II. coupled channels and the deuteron
journal, December 2013
- Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C.
- Physical Review D, Vol. 88, Issue 11
Perturbative calculation of the electromagnetic form factors of the deuteron
journal, February 1999
- Kaplan, David B.; Savage, Martin J.; Wise, Mark B.
- Physical Review C, Vol. 59, Issue 2
Nucleon-nucleon effective field theory without pions
journal, July 1999
- Chen, Jiunn-Wei; Rupak, Gautam; Savage, Martin J.
- Nuclear Physics A, Vol. 653, Issue 4
Rearranging pionless effective field theory
journal, November 2001
- Beane, Silas R.; Savage, Martin J.
- Nuclear Physics A, Vol. 694, Issue 3-4
Electroweak matrix elements in the two-nucleon sector from lattice QCD
journal, October 2004
- Detmold, William; Savage, Martin J.
- Nuclear Physics A, Vol. 743, Issue 1-3
Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states
journal, June 1986
- Lüscher, M.
- Communications in Mathematical Physics, Vol. 105, Issue 2
Two-particle states on a torus and their relation to the scattering matrix
journal, May 1991
- Lüscher, Martin
- Nuclear Physics B, Vol. 354, Issue 2-3
Two nucleons on a lattice
journal, April 2004
- Beane, S. R.; Bedaque, P. F.; Parreño, A.
- Physics Letters B, Vol. 585, Issue 1-2
How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation
journal, July 1990
- Lüscher, Martin; Wolff, Ulli
- Nuclear Physics B, Vol. 339, Issue 1
New class of quantum bound states: Diprotons in extreme magnetic fields
journal, March 2007
- Allor, Danielle; Bedaque, Paulo; Cohen, Thomas D.
- Physical Review C, Vol. 75, Issue 3
Helium nuclei in quenched lattice QCD
journal, June 2010
- Yamazaki, T.; Kuramashi, Y.; Ukawa, A.
- Physical Review D, Vol. 81, Issue 11
Helium nuclei, deuteron, and dineutron in flavor lattice QCD
journal, October 2012
- Yamazaki, Takeshi; Ishikawa, Ken-ichi; Kuramashi, Yoshinobu
- Physical Review D, Vol. 86, Issue 7
for big-bang nucleosynthesis
journal, November 1999
- Chen, Jiunn-Wei; Savage, Martin J.
- Physical Review C, Vol. 60, Issue 6
Precision calculation of cross section for big-bang nucleosynthesis
journal, October 2000
- Rupak, Gautam
- Nuclear Physics A, Vol. 678, Issue 4
The proton-thermal neutron capture cross section
journal, December 1965
- Cox, A. E.; Wynchank, S. A. R.; Collie, C. H.
- Nuclear Physics, Vol. 74, Issue 3
The Chroma Software System for Lattice QCD
journal, March 2005
- Edwards, Robert G.; Joó, Bálint
- Nuclear Physics B - Proceedings Supplements, Vol. 140
Discrete accidental symmetry for a particle in a constant magnetic field on a torus
journal, February 2009
- Al-Hashimi, M. H.; Wiese, U. -J.
- Annals of Physics, Vol. 324, Issue 2
Two-baryon systems with twisted boundary conditions
journal, April 2014
- Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C.
- Physical Review D, Vol. 89, Issue 7
Neutron electric polarizability from unquenched lattice QCD using the background field approach
journal, December 2007
- Engelhardt, M.
- Physical Review D, Vol. 76, Issue 11
Neutron in a strong magnetic field: Finite volume effects
journal, April 2014
- Tiburzi, Brian C.
- Physical Review D, Vol. 89, Issue 7
On Gauge Invariance and Vacuum Polarization
journal, June 1951
- Schwinger, Julian
- Physical Review, Vol. 82, Issue 5
Works referencing / citing this record:
Ab initio alpha–alpha scattering
journal, December 2015
- Elhatisari, Serdar; Lee, Dean; Rupak, Gautam
- Nature, Vol. 528, Issue 7580
Challenges in nuclear structure theory
journal, March 2016
- Nazarewicz, W.
- Journal of Physics G: Nuclear and Particle Physics, Vol. 43, Issue 4
Exposing novel quark and gluon effects in nuclei
journal, July 2019
- Cloët, I. C.; Dupré, R.; Riordan, S.
- Journal of Physics G: Nuclear and Particle Physics, Vol. 46, Issue 9
Nucleon polarisabilities at and beyond physical pion masses
journal, May 2016
- Grießhammer, Harald W.; McGovern, Judith A.; Phillips, Daniel R.
- The European Physical Journal A, Vol. 52, Issue 5
Hadrons and nuclei
journal, November 2019
- Detmold, William; Edwards, Robert G.; Dudek, Jozef J.
- The European Physical Journal A, Vol. 55, Issue 11
Nucleon Polarisabilities at and Beyond Physical Pion Masses
text, January 2015
- Griesshammer, Harald W.; McGovern, Judith A.; Phillips, Daniel R.
- arXiv
Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
text, January 2017
- Hammer, H. -W.; Pang, J. -Y.; Rusetsky, A.
- arXiv
Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
text, January 2017
- Hammer, H. -W.; Pang, J. -Y.; Rusetsky, A.
- arXiv
Exposing Novel Quark and Gluon Effects in Nuclei
text, January 2019
- Cloët, I. C.; Dupré, R.; Riordan, S.
- arXiv