Ab initio symplectic no-core shell model

The no-core shell model (NCSM) is a prominent ab initio method that yields a good description of the low-lying states in few-nucleon systems as well as in more complex p-shell nuclei. Nevertheless, its applicability is limited by the rapid growth of the many-body basis with larger model spaces and increasing number of nucleons. The symplectic no-core shell model (Sp-NCSM) aspires to extend the scope of the NCSM beyond the p-shell region by augmenting the conventional spherical harmonic oscillator basis with the physically relevant symplectic symmetry-adapted configurations of the symplectic shell model that describe naturally the monopole?quadrupole vibrational and rotational modes, and also partially incorporate ?-cluster correlations. In this review, the models underpinning the Sp-NCSM approach, namely, the NCSM, the Elliott SU(3) model and the symplectic shell model, are discussed. Following this, a prescription for constructing translationally invariant symplectic configurations in the spherical harmonic oscillator basis is given. This prescription is utilized to unveil the extent to which symplectic configurations enter into low-lying states in 12C and 16O nuclei calculated within the framework of the NCSM with the JISP16 realistic nucleon?nucleon interaction. The outcomes of this proof-of-principle study are presented in detail.

[1]  K. Hecht.  Relation between cluster and shell-model wave functions , 1977 .

[2]  E. Salpeter.  Nuclear Reactions in Stars Without Hydrogen. , 1952 .

[3]  S. Avancini,et al.  The physical content of the Sp(1,R) model , 1993 .

[4]  E. Burtin,et al.  Parity-violating electron scattering from 4He and the strange electric form factor of the nucleon. , 2005, Physical review letters.

[5]  B. J. Verhaar,et al.  A method for the elimination of spurious states in the nuclear harmonic oscillator shell model , 1960 .

[6]  W. Glöckle,et al.  Three-body interactions and on-shell equivalent two-body interactions , 1990 .

[7]  Glenn Starkman,et al.  Differentiating between modified gravity and dark energy , 2004 .

[8]  M. Harvey,et al.  Collective motion in the nuclear shell model III. The calculation of spectra , 1963, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[9]  Partial Dynamical Symmetry in the Symplectic Shell Model , 2001, nucl-th/0110030.

[10]  R. Wiringa,et al.  Accurate nucleon-nucleon potential with charge-independence breaking. , 1995, Physical review. C, Nuclear physics.

[11]  S. C. Pieper,et al.  Realistic models of pion-exchange three-nucleon interactions , 2001 .

[12]  K. Hecht,et al.  Vector coherent state theory and its application to the orthogonal groups , 1988 .

[13]  The High precision, charge dependent Bonn nucleon-nucleon potential (CD-Bonn) , 2000, nucl-th/0006014.

[14]  J. Draayer,et al.  Monopole-pairing and deformation in atomic nuclei , 1995 .

[15]  W. Gerace,et al.  The effect of deformed states in the Ca isotopes , 1967 .

[16]  D. R. Entem,et al.  Accurate charge dependent nucleon nucleon potential at fourth order of chiral perturbation theory , 2003 .

[17]  D. Rowe.  Analytical expressions for the matrix elements of the non-compact symplectic algebra , 1984 .

[18]  Modern nuclear force predictions for the alpha particle , 2000, Physical review letters.

[19]  R. Wiringa,et al.  Three-nucleon interaction in 3-, 4- and ∞-body systems☆ , 1983 .

[20]  W. Plessas,et al.  Nonlocality in the nucleon-nucleon interaction and three-nucleon bound states , 2003 .

[21]  K. Hecht,et al.  Sp(6, R) symmetry and α-breakup amplitudes of giant E2 excitations in light nuclei , 1978 .

[22]  P. Navrátil,et al.  Spectra and Binding Energy Predictions of Chiral Interactions for 7Li , 2005, nucl-th/0511082.

[23]  G. E. Brown,et al.  Even parity states of 16O and 17O , 1966 .

[24]  Johnson,et al.  Weak-interaction rates in 16O. , 1990, Physical review letters.

[25]  N. Barnea,et al.  Wave function for no-core effective interaction approaches , 2004 .

[26]  W. Gloeckle,et al.  Two-pion-exchange three-nucleon potential: Partial wave analysis in momentum space , 1981 .

[27]  E. Sheldon,et al.  Unified Theory of the Nucleus , 1977 .

[28]  A. Miyazaki,et al.  Acoustic Phonon Softening and Spontaneous Strains in KD3(SeO3)2 , 1978 .

[29]  Construction of high-quality NN potential models. , 1994, Physical review. C, Nuclear physics.

[30]  R. Young,et al.  Testing the standard model by precision measurement of the weak charges of quarks. , 2007, Physical review letters.

[31]  J. Broeckhove,et al.  The Sp(2,R) nuclear model of 12C , 1982 .

[32]  Song,et al.  Nonlocal nature of the nuclear force and its impact on nuclear structure. , 1996, Physical review. C, Nuclear physics.

[33]  Jerry P. Draayer,et al.  Dominant role of symplectic symmetry in ab initio no-core shell model results for light nuclei , 2007 .

[34]  T. Skyrme,et al.  Centre-of-mass effects in the nuclear shell-model , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[35]  J. Wilson,et al.  Superdeformation in the Doubly Magic Nucleus 40Ca , 2001 .

[36]  J. Draayer,et al.  Highly deformed modes in the ab initio symplectic no-core shell model , 2008 .

[37]  T. W. Donnelly,et al.  The interpretation of parity-violating electron-scattering experiments , 1992 .

[38]  G. Stephenson,et al.  SHAPE OF THE FOUR-PARTICLE, FOUR-HOLE STATE OF ¹⁶O. , 1967 .

[39]  Ab initio shell model with a genuine three-nucleon force for the p-shell nuclei , 2003, nucl-th/0305090.

[40]  J. Broeckhove,et al.  The Sp(2, R) model applied to 8Be , 1979 .

[41]  K. Ikeda,et al.  Chapter II. Comprehensive Study of Alpha-Nuclei , 1980 .

[42]  Y. Suzuki.  Cluster and symplectic excitations in nuclei , 1986 .

[43]  Y. Suzuki,et al.  Structure Study of T = 0 States in 16O by 12C + α Cluster-Coupling Model. II , 1976 .

[44]  Wilson,et al.  Renormalization of Hamiltonians. , 1993, Physical review. D, Particles and fields.

[45]  E. Verlinde,et al.  Elliptic de Sitter space: dS/Z(2) , 2002, hep-th/0209120.

[46]  Kenji Suzuki,et al.  Convergent Theory for Effective Interaction in Nuclei , 1980 .

[47]  Kenji Suzuki.  Unitary-Model-Operator Approach to Nuclear Effective Interaction. II : Effects of Three-Body Cluster Term , 1982 .

[48]  Steven Weinberg,et al.  Nuclear forces from chiral Lagrangians , 1990 .

[49]  J. Draayer,et al.  Pairing-plus-quadrupole model and nuclear deformation: A look at the spin-orbit interaction , 1998 .

[50]  David J Rowe,et al.  Nuclear Sp(3,R) model , 1977 .

[51]  D. R. Entem,et al.  Towards a consistent approach to nuclear structure: EFT of two- and many-body forces , 2005, nucl-th/0503025.

[52]  J. Wood,et al.  Implications of deformation and shape coexistence for the nuclear shell model. , 2006, Physical review letters.

[53]  J. Draayer,et al.  Fermion realization of the nuclear Sp(6,R) model , 1998 .

[54]  Effective Operators Within the Ab Initio No-Core Shell Model , 2004, nucl-th/0412004.

[55]  K. Hecht.  The use of SU(3) in the elimination of spurious center of mass states , 1971 .

[56]  L. Biedenharn,et al.  Nuclear rotational bands and SL(3, R) symmetry , 1970 .

[57]  D. Rowe,et al.  Coupled SU(3) models of rotational states in nuclei and quasi-dynamical symmetry , 2006 .

[58]  Poisson algebra of diffeomorphism generators in a space-time containing a bifurcation , 2004, hep-th/0403219.

[59]  Ab-initio coupled-cluster study of 16O. , 2005, Physical review letters.

[60]  H. T. Coelho,et al.  Taming the two-pion exchange three-nucleon potential , 1986 .

[61]  S. Coon,et al.  Reworking the Tucson-Melbourne Three-Nucleon Potential , 2000, nucl-th/0101003.

[62]  W. Greiner,et al.  The general collective model applied to the chains of Pt, Os and W isotopes , 1981 .

[63]  R. Blin-stoyle.  A Unified Theory of the Nucleus , 1978 .

[64]  P. Navrátil,et al.  Ab initio shell model calculations with three-body effective interactions for p-shell nuclei. , 2002, Physical review letters.

[65]  P. Navrátil,et al.  Shell Model in a First Principles Approach , 2004 .

[66]  Stoks,et al.  Partial-wave analysis of all nucleon-nucleon scattering data below 350 MeV. , 1993, Physical review. C, Nuclear physics.

[67]  A Nogga,et al.  Structure of A=10-13 nuclei with two- plus three-nucleon interactions from chiral effective field theory. , 2007, Physical review letters.

[68]  Kenji Suzuki.  Construction of Hermitian Effective Interaction in Nuclei--General Relation between Hermitian and Non-Hermitian Forms , 1982 .

[69]  P. Heenen,et al.  On the deformation energy surface of 16O , 1984 .

[70]  A unitary correlation operator method , 1997, nucl-th/9709038.

[71]  J. P. Elliott,et al.  Collective motion in the nuclear shell model. I. Classification schemes for states of mixed configurations , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[72]  From non-Hermitian effective operators to large-scale no-core shell model calculations for light nuclei , 2006, nucl-th/0603034.

[73]  Petr Navratil,et al.  Large-basis ab initio no-core shell model and its application to 12 C , 2000 .

[74]  A. Zuker,et al.  Structure of O 16 , 1968 .

[75]  Tensor correlations in the unitary correlation operator method , 2002, nucl-th/0207013.

[76]  G. Rosensteel.  Irreducible U(3) tensor interactions in the symplectic collective model , 1980 .

[77]  E. Boeker.  HARTREE--FOCK CALCULATIONS IN LIGHT NUCLEI. , 1967 .

[78]  U. van Kolck,et al.  Few-nucleon forces from chiral Lagrangians. , 1994 .

[79]  J. Vary.  How Effective are Strong Interactions , 2005 .

[80]  Franz Wegner.  Flow‐equations for Hamiltonians , 1994 .

[81]  R. Furnstahl,et al.  Similarity renormalization group for nucleon-nucleon interactions , 2006, nucl-th/0611045.

[82]  Tomás Dytrych,et al.  Evidence for symplectic symmetry in Ab initio no-core shell model results for light nuclei. , 2007, Physical review letters.

[83]  David J Rowe,et al.  Microscopic theory of the nuclear collective model , 1985 .

[84]  A. Richter,et al.  Structure of the Hoyle state in 12C. , 2007, Physical review letters.

[85]  A. I. Mazur,et al.  Novel NN interaction and the spectroscopy of light nuclei [rapid communication] , 2004, nucl-th/0407018.

[86]  J. Draayer,et al.  Shell-model operator for KJ-band splitting in odd-A nuclei , 1992 .

[87]  D. Rowe.  Coherent state theory of the noncompact symplectic group , 1984 .

[88]  B. G. Wybourne,et al.  Classical Groups for Physicists , 1974 .

[89]  L. Zamick,et al.  Four-particle-four-hole states in 4He , 1984 .

[90]  J P Vary,et al.  Properties of 12C in the Ab initio nuclear shell model. , 2000, Physical review letters.

[91]  Y. Leschber,et al.  Shape variables and the shell model , 1988 .

[92]  P. Navrátil,et al.  Few-nucleon systems in a translationally invariant harmonic oscillator basis , 1999, nucl-th/9907054.

[93]  Suzuki,et al.  Isoscalar monopole and quadrupole strength of 16O in an alpha +12C cluster and symplectic mixed basis. , 1989, Physical review. C, Nuclear physics.

[94]  J. Draayer,et al.  SU(3) symmetry breaking in lower fp-shell nuclei , 2000, nucl-th/0009014.

[95]  S. Gupta,et al.  PHENOMENOLOGICAL APPROACH TO FOUR-PARTICLE, FOUR-HOLE STATES IN $sup 16$O. , 1969 .

[96]  W. Greiner,et al.  Collective potential energy surfaces and nuclear structure , 1971 .

[97]  F. Hoyle,et al.  On Nuclear Reactions Occuring in Very Hot STARS.I. the Synthesis of Elements from Carbon to Nickel. , 1954 .

[98]  J. P. Elliott,et al.  Collective motion in the nuclear shell model II. The introduction of intrinsic wave-functions , 1958, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[99]  Wilson loops as precursors , 1999, hep-th/9909013.

[100]  J. Draayer,et al.  Shell-model operator for K-band splitting , 1990 .

[101]  H. Ui.  Quantum Mechanical Rigid Rotator with an Arbitrary Deformation. I Dynamical Group Approach to Quadratically Deformed Body , 1970 .

[102]  A. I. Mazur,et al.  Nucleon–Nucleon Interaction in the J-Matrix Inverse Scattering Approach and Few-Nucleon Systems , 2003, nucl-th/0312029.

[103]  Nd elastic scattering as a tool to probe properties of 3N forces , 2000, nucl-th/0010013.

[104]  J. Draayer.  Structure calculations for 25Mg-25Al , 1973 .

[105]  Barrett,et al.  No-core shell-model calculations with starting-energy-independent multivalued effective interactions. , 1996, Physical review. C, Nuclear physics.

[106]  K. Hecht,et al.  Symplectic and cluster excitations in nuclei:: Evaluation of interaction matrix elements , 1986 .

[107]  David J Rowe,et al.  On the algebraic formulation of collective models III. The symplectic shell model of collective motion , 1980 .

[108]  S. Pollock,et al.  Intermediate-energy semileptonic probes of the hadronic neutral current☆ , 1993, nucl-th/9307022.

[109]  G. E. Brown,et al.  Collective admixtures in the odd-parity states of O16 , 1965 .