Abstract
We determine energy independent local nucleon-nucleon (NN) potentials for radial Schrödinger equations with Gelfand-Levitan and Marchenko inversion from today’s optimum phase shifts. Based on four phase shift sets, quantitative and complete results for all partial waves, with J ≤ 3, and all charge states are presented. The potential results are confronted with known features and other NN potentials. A first application to triton binding energy and bremsstrahlung calculations falls well within our expectations.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
K. Holinde, Nucl. Phys. A 543, 143 (1992)
J. Wambach, see this Proceedings and cited references
A. de Shalit and H. Feshbach, Theoretical nuclear physics: Nuclear structure, Wiley (1974)
H. Feshbach, Theoretical nuclear physics: Nuclear reactions, Wiley (1992)
B. Gibson, Nucl. Phys. A 543, l (1992)
A.J. Sarty ibid 49c, I. Slaus and A. Marusic, ibid 213c
V. Stoks and J. de Swart, Phys. Rev. C 47, 761 (1993)
I.M. Gelfand and B.M. Levitan, On the determination of a differential equation by its spectral function, Amer. Math. Soc. Trans. Ser. 21, 253 (1955)
Z.S. Agranovich and V.A. Marchenko, The Inverse Problem of Scattering Theory, Gordon and Breach (1963)
K. Chadan and P.C. Sabatier, Inverse problems in quantum scattering theory, Springer (1977), 2nd Ed. (1989)
B.N. Zakhariev and A.A. Suzko, Direct and Inverse Problems, Springer (1990).
M. Coz, J. Kuberczyk and H.V. von Geramb, Z. Phys A 326, 345 (1987), ibid A328, 259 and 265 (1987)
Th. Kirst, Nukleon-Nukleon Potentiale aus der Inversion, Thesis, Hamburg (1989)
Th. Kirst, J. Math. Phys. 32, 1318 (1991)
Th. Kirst et al., Phys. Rev. C 40, 912 (1989)
Th. Kirst, H. Kohlhoff and H.V. von Geramb, in Inverse Methods in Action, P.C. Sabatier (Ed.), Springer (1990)
M. Küker, Proton-Proton Inversions-Potentiale, Diplomarbeit, Hamburg (1992)
M. Küker, H. Kohlhoff and H.V. von Geramb, Nucleon Nucleon Potentials from Inversion: pp and np Single Channel Potentials, XIII. Int. Conf. Few Body Problems in Physics, Adelaide ( Australia ), January (1992)
H. Kohlhoff, M. Küker, H. Freitag and H.V. von Geramb, PhysicaScripta 48, 238 (1993)
H. Kohlhoff, Nukleon-Nukleon Potentiale und Quanteninversion der Streumatrix, Thesis, Hamburg (1993) and Rationale Darstellungen der NN S-Matrizen, Diplomarbeit (1989)
M. Sander, Nukleonen Potentiale für die Praxis, Diplomarbeit, Hamburg (1993)
The central server of the Nuclear Theory Group, an IBM RISC-6000 workstation, can be reached by INTERNET and anonymous ftp. Use: ftp I04KTHA.DESY.DE or 131.169.81.53; user: anonymous; password: give your home-address. Change directory: pub, this subdirectory contains several subdirectories, change directory: INVERSION_POTENTIALS, contains 5 directories referring to 4 phase shift inversion potential sets ARNDT_PHASESHIFTS_1992, NIJMEGEN_PHASESHIFTS_NIJ3_REIDLIKE, BONN_BONNB_POTENTIAL_PHASESHIFTS PARIS_POTENTIAL_PHASESHIFTS and OPEP. Select and change directory for potential files. The first letter signals P/N (proton-proton/neutron-proton systems) and thereafter follows the configuration. Coupled channels use C as identifier and the rest is a source identifier. Each of these files contain a header line and thereafter 800 lines with: R [fm] and V(R) [MeV]. The directory OPEP contains a Fortran routine OPEP potential which is optional for J 4. In case of questions, please forward an E-mail to I04GERODHHDESY3.BITNET or I04GERODSYIBM.DESY.DE (131.169.93.32).
R.A. Arndt and L.D. Roper, Nucleon-nucleon partial-wave analysis to 1 GeV, Phys. Rev. D 28, 97 (1983)
R.A. Arndt, J.S. Hyslop III and D.L. Roper, Nucleon-nucleon partial-wave analysis to 1100 MeV, Phys. Rev. D 35, 128 (1986)
R.A. Arndt, Nucleon-nucleon partial-wave analysis to 1.6 GeV, Phys. Rev. D 45, 3995 (1992)
R.A. Arndt, Scattering Analysis Interactive Dial-in (SAID) with interpolation files -93, Virginia Polytechnic Institute, Blacksbury, access via Telnet: 128.173.7.3 (VTINTE.PHYS.VT.EDU), Logon: PHYSICS, Password: QUANTUM). private communication (1992)
J. Bystricky et al., Nucleon-Nucleon phase shift analysis, J. Physique 48, 199 (1987)
D.V. Bugg, np phase shifts, 142 to 800 Me V, Phys. Rev. C 41, 2708 (1990)
V. Stoks and J.J. de Swart, Nijmegen NN potential subroutine code, we use option #3/nonrelativistic and follow their suggestion to call this local potential Nijmegen-3 alias Nijm-3 which is equivalent to NijmRdl, private communication (1992)
J.J. de Swart, R.A.M. Klomp, T.A. Rijken and V.G.J. Stoks, A New partial wave analysis and the nucleon-nucleon interaction, Few-Body Systems Suppl. 6, 105 (1992)
J.R. Bergervoet, P.C. van Campen, R.A.M. Klomp, J.L. de Kok, T.A. Rijken, V.G.J. Stoks and J.J. de Swart, Phase shift analysis of all proton-proton scattering data below T(lab) = 350-MeV, Phys. Rev. C 41, 1435 (1990)
T.A. Rijken, V.G.J. Stoks, R.A.M. Klomp, J.L. De Kok, J.J. De Swart, The Nijmegen NN phase shift analyses, Nucl. Phys. A 508, 173 (1990)
J.R. Bergervoet, P.C. van Campen, W.A. van der Sanden and J.J. de Swart, Phase shift analysis of O-30 MeV pp scattering data, Phys. Rev. C 38, 15 (1989)
J.R. Bergervoet, P.C. Van Campen, T.A. Rijken and J.J. De Swart, Optimal polynomial theory applied to O-MEV - 350 MeV pp scattering, Phys. Rev. C 38, 770 (1988)
J. Raynal, DWBA-92, a nonlocal microscopic optical model and inelastic scattering code, CEA-Saclay (1992)
W.R. Theis, Z. f. Naturforschung 11, 889 (1956).
G.A. Baker and P. Graves-Morris, Padé-Approximants, Part I: Basic Theory, and Padé-Approximants, Part II: Extensions and Applications, Encyclopedia of Mathematics and its Applications, Vols. 13 and 14, Addison-Wesley (1981)
W.B. Gragg, SIAM Review 14, 1 (1972)
Y.L. Luke, Algorithms for the Computation of Mathematical Functions, Academic Press (1977) and Mathematical Functions and their Approximations, Academic Press (1975)
R. Newton, Scattering Theory of Waves and Particles, Springer, 2nd Ed. (1982)
C.E. Froeberg, Introduction to Numerical Analysis, Addison-Wesley (1979)
E.B. Saff and R.S. Varga, On the zeros and Poles of Padé-Approximants to ez, Num. Math. 25, 1 (1975), ibid 30, 241 (1978)
E.B. Saff and Varga, R. S. (Eds.), Padé and Rational Approximation, Academic Press (1977)
M.Z. Nashed, Generalized Inverses and Applications, Academic Press (1976)
A. Tikhonov and V. Arsenin, Solutions of ill-posed problems, Winston Wiley (1977)
A. Tikhonov and A. Goncharskij, Improperly posed problems in natural sciences, Mir, Moscow (1987)
K. Clancey and I. Gohberg, Factorization of matrix functions and singular integral operators, OT3, Birkhäuser (1981)
M. Lacombe et al., Phys. Rev. C 21, 861 (1980)
R. Machleidt,R. Holinde and Ch. Elster, Phys. Rep. 149, 1 (1987)
R. Machleidt, The Meson Theory of Nuclear Forces and Nuclear Structure, Adv. Nuclear Physics, E. Voigt and J. Negele (Eds.), 19, 189 (1989)
L. Mathelitsch and B.L. VerWest, Phys. Rev. C 29, 739 (1984)
H.V. von Geramb and K.A. Amos, Phys. Rev.C 41, 1384 (1990), ibid C 44 (1), 73 (1991)
I. Slaus, Phys. At. Nucl. 56, 948 (1993)
V.G.J. Stoks, P.C. Van Campen, T.A. Rijken and J.J. de Swart, Phys. Rev. Lett. 61, 1702 (1988)
M. Jetter, see this Proceedings and cited references
I. Slaus, R. Machleidt, W. Tornow, W. Glöckle, W. Witala, Comments Nucl. Part. Phys. 20, 85 (1991)
H. Kamada, H. Witala and W. Glöckle, Phys. At. Nucl. 56, 873 (1993)
W. Glöckle and H. Kamada, Universität Bochum, private communication (1992)
W. Glöckle, T. Cornelius and H. Witala, Nucl. A 508, 115 (1990)
H. Witala, W. Tornow and W. Glöckle, Few Body Systems 13
B.H.J. Mckellar and W. Glöckle, Nucl. Phys. A 416, 435 (1984) 11 and 189 (1992)
J. Strate et al., Nucl. Phys. A 501, 51 (1989)
B. Gibson, Theory Division, LAMPF. private communication (1993)
B. Gibson and H.V. von Geramb, in preparation is an extensive study with 5, 9, 18 and 32 channels using genuine and inversion potentials — a correlation between PD, deuteron D-state probability, and lack of triton binding energy is manifest
V.R. Pandharipande, Nucl. Phys. A 553, 191c (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
von Geramb, H.V., Kohlhoff, H. (1994). Nucleon—Nucleon Potentials from Phase Shifts and Inversion. In: von Geramb, H.V. (eds) Quantum Inversion Theory and Applications. Lecture Notes in Physics, vol 427. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13969-1_18
Download citation
DOI: https://doi.org/10.1007/978-3-662-13969-1_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-13971-4
Online ISBN: 978-3-662-13969-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)