Abstract
Using the hyperspherical adiabatic method with the realistic nuclear potentials Argonne V14, Argonne V18, and Argonne V18 with the Urbana IX three-body potential, we calculate the adiabatic potentials and the triton bound state energies. We find that a discrete variable representation with the slow variable discretization method along the hyperradial degree of freedom results in energies consistent with the literature. However, using a Laguerre basis results in missing energy, even when extrapolated to an infinite number of basis functions and channels. We do not include the isospin T = 3/2 contribution in our analysis.
Similar content being viewed by others
References
Macek J.: Properties of autoionizing states of He. J. Phys. B: At. Mol. Opt. 1(5), 831 (1968)
Lin C.D.: Correlations of excited electrons. The study of channels in hyperspherical coordinates. Phys. Rev. A 10(6), 1986 (1974)
Garrido E., Romero-Redondo C., Kievsky A., Viviani M.: Integral relations and the adiabatic expansion method for 1 + 2 reactions above the breakup threshold: helium trimers with soft-core potentials. Phys. Rev. A 86(5), 052709 (2012)
Wang, J.: Hyperspherical approach to quantal three-body theory. Ph.D. thesis, University of Colorado, Boulder (2012)
Garrido E., Kievsky A., Viviani M.: Breakup of three particles within the adiabatic expansion method. Phys. Rev. C 90, 014607 (2014)
Wiringa R.B., Smith R.A., Ainsworth T.L.: Nucleon-nucleon potentials with and without Δ(1232) degrees of freedom. Phys. Rev. C 29(4), 1207 (1984)
Wiringa R.B., Stoks V.G.J., Schiavilla R.: Accurate nucleon-nucleon potential with charge-independence breaking. Phys. Rev. C 51(1), 38 (1995)
Pieper, S., Pandharipande, V.R., Wiringa, R.B., Carlson, J.: Accurate nucleon-nucleon potential with charge-independence breaking. Phys. Review C, 64(1) 014001 (2001)
Kievsky A., Marcucci L.E., Rosati S., Viviani M.: High-precision calculation of the triton ground state within the hyperspherical-harmonics method. Few-Body Syst. 22(1), 1 (1997)
Navarro Pérez, R., Garrido, E., Amaro, J.E., Ruiz Arriola, E.: Triton binding energy with realistic statistical uncertainties. Phys. Rev. C 90(4), 047001 (2014)
Light J.C., Hamilton I.P., Lill J.V.: Generalized discrete variable approximation in quantum mechanics. J. Chem. Phys. 82(3), 1400 (1985)
Rescigno T.N., McCurdy C.W.: Numerical grid methods for quantum-mechanical scattering problems. Phys. Rev. A 62(3), 032706 (2000)
Tolstikhin O.I., Watanabe S., Matsuzawa M.: ‘Slow’ variable discretization: a novel approach for hamiltonians allowing adiabatic separation of variables. J. Phys. B: At., Mol. Opt. 29(11), L389 (1996)
Nogga, A., Kievsky, A., Kamada, H., Glöckle, W., Marcucci, L.E., Rosati, S., Viviani, M.: Three-nucleon bound states using realistic potential models. Phys. Rev. C 67(3), 034004 (2003)
Kievsky, A., Viviani, M., Marcucci, L.E.: Theoretical description of three- and four-nucleon scattering states using bound-state-like wave functions. Phys. Rev. C 85(1), 014001 (2012)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Daily, K.M., Kievsky, A. & Greene, C.H. Adiabatic Hyperspherical Analysis of Realistic Nuclear Potentials. Few-Body Syst 56, 753–759 (2015). https://doi.org/10.1007/s00601-015-1012-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00601-015-1012-x