Infrared length scale and extrapolations for the no-core shell model

We precisely determine the infrared (IR) length scale of the no-core shell model (NCSM). In the NCSM, the A-body Hilbert space is truncated by the total energy, and the IR length can be determined by equating the intrinsic kinetic energy of A nucleons in the NCSM space to that of A nucleons in a 3(A - 1)-dimensional hyper-radial well with a Dirichlet boundary condition for the hyper radius. We demonstrate that this procedure indeed yields a very precise IR length by performing large-scale NCSM calculations for Li-6. We apply our result and perform accurate IR extrapolations for bound states of He-4, He-6, Li-6, and Li-7. We also attempt to extrapolate NCSM results for B-10 and O-16 with bare interactions from chiral effective field theory over tens of MeV.

[1]  Jerry P. Draayer,et al.  Ab initio symplectic no-core shell model , 2008 .

[2]  P. Navrátil,et al.  Large basis ab initio shell model investigation of 9Be and 11Be , 2004, nucl-th/0412049.

[3]  S. Konig,et al.  Ultraviolet extrapolations in finite oscillator bases , 2014, 1409.5997.

[4]  R. J. Furnstahl,et al.  Evolution of nuclear many-body forces with the similarity renormalization group. , 2009, Physical review letters.

[5]  R. J. Furnstahl,et al.  Corrections to Nuclear Energies and Radii in Finite Oscillator Spaces , 2012, 1207.6100.

[6]  M. Hjorth-Jensen,et al.  Coupled-cluster computations of atomic nuclei , 2013, Reports on progress in physics. Physical Society.

[7]  P. Navrátil,et al.  Ab initio study of 40Ca with an importance-truncated no-core shell model. , 2007, Physical review letters.

[8]  R. Furnstahl,et al.  Universal properties of infrared oscillator basis extrapolations , 2013, 1302.3815.

[9]  T. Luu,et al.  Two-nucleon systems in a finite volume: Quantization conditions , 2013, 1305.4903.

[10]  Self-consistent Green's function method for nuclei and nuclear matter , 2004, nucl-th/0402034.

[11]  Robert Roth,et al.  Evolved Chiral NN+3N Hamiltonians for Ab Initio Nuclear Structure Calculations , 2013, 1311.3563.

[12]  R. Briceño.  Two-Nucleon Systems in a Finite Volume , 2013, 1309.7923.

[13]  Dean Lee,et al.  Effective field theory for bound state reflection , 2012, 1206.6280.

[14]  S. Quaglioni,et al.  Recent developments in no-core shell-model calculations , 2009, 0904.0463.

[15]  Dean Lee,et al.  Non-relativistic bound states in a finite volume , 2011, 1109.4577.

[16]  D. J. Dean,et al.  Coupled-cluster approach to nuclear physics , 2004 .

[17]  C. Forss'en,et al.  Microscopic description of translationally invariant core+N+N overlap functions , 2013, 1309.5810.

[18]  R. Furnstahl,et al.  Systematic expansion for infrared oscillator basis extrapolations , 2013, 1312.6876.

[19]  K. Wendt,et al.  Infrared extrapolations for atomic nuclei , 2014, 1408.0252.

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

[21]  R. Roth,et al.  Ab initio path to heavy nuclei , 2013, 1312.5685.

[22]  N. Barnea,et al.  Construction of hyperspherical functions symmetrized with respect to the orthogonal and the symmetric groups , 1997 .

[23]  G. Hagen,et al.  Ab initio coupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions , 2010, 1005.2627.

[24]  W. E. Ormand,et al.  Structure of p-shell nuclei using three-nucleon interactions evolved with the similarity renormalization group , 2013 .

[25]  S. Bogner,et al.  In-medium similarity renormalization group for nuclei. , 2010, Physical review letters.

[26]  Pieter Maris,et al.  Convergence properties of ab initio calculations of light nuclei in a harmonic oscillator basis , 2012, 1205.3230.

[27]  S. Bogner,et al.  In-medium similarity renormalization group with chiral two- plus three-nucleon interactions , 2012, 1212.1190.

[28]  T. Luu,et al.  Two-nucleon systems in a finite volume . II . 3 S 1-3 D 1 coupled channels and the deuteron , 2013 .

[29]  J. Vary,et al.  Ab initio no-core full configuration calculations of light nuclei , 2008, 0808.3420.

[30]  M. Hjorth-Jensen,et al.  Medium-mass nuclei from chiral nucleon-nucleon interactions. , 2008, Physical review letters.

[31]  Calvin W. Johnson,et al.  Factorization in large-scale many-body calculations , 2013, Comput. Phys. Commun..

[32]  M. Lüscher,et al.  Volume dependence of the energy spectrum in massive quantum field theories , 1986 .

[33]  Petr Navrátil,et al.  Ab initio many-body calculations of n-3H, n-4He, p-3,4He, and n-10Be scattering. , 2008, Physical review letters.

[34]  Giuseppina Orlandini,et al.  Microscopic calculation of six-body inelastic reactions with complete final state interaction: photoabsorption of (6)He and (6)Li. , 2002, Physical review letters.

[35]  T. Duguet,et al.  Ab initio Gorkov-Green's function calculations of open-shell nuclei , 2012, 1208.2472.

[36]  Stefan M. Wild,et al.  Optimized chiral nucleon-nucleon interaction at next-to-next-to-leading order. , 2013, Physical review letters.