Abstract
Triplet low-energy parameters of neutron-proton scattering, including high-order shape parameters, are calculated on the basis of approximating the effective-range function k cot δ t by polynomials and rational functions with the aid of the latest experimental data on phase shifts from the SAID nucleon-nucleon database. With the resulting values of the low-energy parameters, a good description of phase shifts over a broad energy interval is obtained by using the effective-range expansion featuring a small number of terms. The properties of the deuteron that were calculated on the basis of the values found for the triplet low-energy parameters of scattering agree very well with experimental values. The triplet low-energy parameters and the properties of the deuteron that were obtained here by using present-day data from the SAID database differ markedly from the analogous results obtained for data of the Nijmegen group. Possible reasons behind this discrepancy are discussed. Highly precise new approximate formulas for determining the shape parameter v 2 are proposed and are shown to be efficient in calculations. The effective-range expansion for the D wave is considered, and preliminary results of calculations of low-energy scattering parameters for this case are obtained.
Similar content being viewed by others
References
L. D. Landau and Ya. A. Smorodinskiĭ, Zh. Éksp. Teor. Fiz. 14, 269 (1944).
J. S. Schwinger, Phys. Rev. 72, 742 (1947).
J. M. Blatt and J. D. Jackson, Phys. Rev. 76, 18 (1949).
H. A. Bethe, Phys. Rev. 76, 38 (1949).
L. Hulthén and M. Sugawara, in Handbuch der Physik, Ed. by S. Flügge (Springer-Verlag, New York, Berlin, 1957), p. 1.
H. P. Noyes, Phys. Rev. 130, 2025 (1963).
R. Wilson, The Nucleon-Nucleon Interaction (Interscience, New York, 1963; Mir, Moscow, 1965).
T. L. Houk and R. Wilson, Rev. Mod. Phys. 39, 546 (1967); 40, 672 (1968).
T. L. Houk, Phys. Rev. C 3, 1886 (1971).
H. P. Noyes, Annu. Rev. Nucl. Sci. 22, 465 (1972).
E. Lomon and R. Wilson, Phys. Rev. C 9, 1329 (1974).
F. Lambert, O. Corbella, and Z. D. Thome, Nucl. Phys. B 90, 267 (1975).
K. Hartt, Phys. Rev. C 22, 1377 (1980); 23, 2399 (1981).
M. W. Kermode, L. J. Allen, J. P. McTavish, and A. McKerrell, J. Phys. G 10, 773 (1984).
L. Mathelitsch and B. J. VerWest, Phys. Rev. C 29, 739 (1984).
J. J. de Swart, C. P. F. Terheggen, and V. G. J. Stoks, Invited talk at The 3rd International Symposium “Dubna Deuteron 95”, Dubna, Russia, 1995, nucl-th/9509032.
T. D. Cohen and J. M. Hansen, Phys. Rev. C 59, 13 (1999).
T. D. Cohen and J. M. Hansen, Phys. Rev. C 59, 3047 (1999).
V. A. Babenko and N. M. Petrov, Yad. Fiz. 66, 1359 (2003) [Phys. At. Nucl. 66, 1319 (2003)].
V. A. Babenko and N. M. Petrov, Yad. Fiz. 68, 244 (2005) [Phys. At. Nucl. 68, 219 (2005)]; nucl-th/0502041.
L. D. Blokhintsev, I. Borbely, and E. I. Dolinsky, Fiz. Élem. Chastits At. Yadra 8, 1189 (1977) [Sov. J. Part. Phys. 8, 485 (1977)].
D. W. L. Sprung, in Proceedings of the IX European Conference on Few-Body Problems in Physics, Tbilisi, USSR, 1984 (World Sci., Singapore, 1984), p. 234.
T. E. O. Ericson, Nucl. Phys. A 416, 281 (1984).
S. Klarsfeld, J. Martorell, J. A. Oteo, et al., Nucl. Phys. A 456, 373 (1986).
D. W. L. Sprung, H. Wu, and J. Martorell, Phys. Rev. C 42, 863 (1990).
R. K. Bhaduri, W. Leidemann, G. Orlandini, and E. L. Tomusiak, Phys. Rev. C 42, 1867 (1990).
M. W. Kermode, S. A. Moszkowski, M. M. Mustafa, and W. van Dijk, Phys. Rev. C 43, 416 (1991).
P. F. Bedaque and U. van Kolck, Annu. Rev. Nucl. Part. Sci. 52, 339 (2002).
U. van Kolck, Nucl. Phys. A 645, 273 (1999).
M. P. Valderrama and E. R. Arriola, nucl-th/0407113.
M. P. Valderrama and E. R. Arriola, Phys. Lett. B 580, 149 (2004); nucl-th/0405057.
E. Epelbaum, W. Glöckle, and U.-G. Meissner, Eur. Phys. J. A 19, 401 (2004).
E. Epelbaum, W. Glöckle, and U.-G. Meissner, Nucl. Phys. A 747, 362 (2005).
R. A. Arndt, I. I. Strakovsky, and R. L. Workman, Partial-Wave Analysis Facility SAID, The George Washington University, http://gwdac.phys.gwu.edu; Phys. Rev. C 62, 034005 (2000).
H. P. Noyes and D. Y. Wong, Phys. Rev. Lett. 3, 191 (1959).
V. de Alfaro and T. Regge, Potential Scattering (North-Holland, Amsterdam, 1965; Mir, Moscow, 1966).
J. Dobaczewski, nucl-th/0301069.
V. I. Kukulin, I. T. Obukhovsky, V. N. Pomerantsev, and A. Faessler, Yad. Fiz. 64, 1748 (2001) [Phys. At. Nucl. 64, 1667 (2001)].
G. A. Baker, Jr., and P. Graves-Morris, Pade Approximants (Addison-Wesley, London, 1981; Mir, Moscow, 1986).
V. A. Babenko and N. M. Petrov, Yad. Fiz. 63, 1798 (2000) [Phys. At. Nucl. 63, 1709 (2000)].
W. T. H. van Oers and J. D. Seagrave, Phys. Lett. B 24, 562 (1967).
M. Cini, S. Fubini, and A. Stanghellini, Phys. Rev. 114, 1633 (1959).
K. Hartt and P. V. A. Yidana, Phys. Rev. C 31, 1105 (1985).
W. van Dijk, M. W. Kermode, and D. C. Zheng, Phys. Rev. C 47, 1898 (1993).
W. van Dijk and M. W. Kermode, Phys. Rev. C 45, 1528 (1992).
C. W. Wong, Nucl. Phys. A 536, 269 (1992).
M. W. Kermode and M. M. Mustafa, J. Phys. G 17, L101 (1991).
M. W. Kermode, A. McKerrell, J. P. McTavish, and L. J. Allen, Z. Phys. A 303, 167 (1981).
R. V. Reid, Jr., Ann. Phys. (N.Y.) 50, 411 (1968).
V. I. Kukulin, V. M. Krasnopol’skiĭ, V. N. Pomerantsev, and P. B. Sazonov, Yad. Fiz. 43, 559 (1986) [Sov. J. Nucl. Phys. 43, 355 (1986)].
M. M. Mustafa, E. M. Hassan, M. W. Kermode, and E. M. Zahran, Phys. Rev. C 45, 2603 (1992).
Nijmegen NN-Online program, http://nn-online.org
O. Dumbrajs, R. Koch, H. Pilkuhn, et al., Nucl. Phys. B 216, 277 (1983).
J. M. Blatt and L. C. Biedenharn, Phys. Rev. 86, 399 (1952).
H. P. Stapp, T. J. Ypsilantis, and N. Metropolis, Phys. Rev. 105, 302 (1957).
V. G. J. Stoks, R. A. M. Klomp, M. C. M. Rentmeester, and J. J. de Swart, Phys. Rev. C 48, 792 (1993).
R. Machleidt and I. Slaus, J. Phys. G 27, R69 (2001).
V. G. J. Stoks, R. A. M. Klomp, C. P. F. Terheggen, and J. J. de Swart, Phys. Rev. C 49, 2950 (1994).
R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Phys. Rev. C 51, 38 (1995).
R. Machleidt, F. Sammarruca, and Y. Song, Phys. Rev. C 53, 1483 (1996).
R. Machleidt, Phys. Rev. C 63, 024001 (2001).
M. P. Locher and T. Mizutani, Phys. Rep. 46, 43 (1978).
C. van der Leun and C. Anderliesten, Nucl. Phys. A 380, 261 (1982).
I. Borbély, W. Grübler, V. König, et al., Phys. Lett. B 160, 17 (1985).
R. W. Berard, F. R. Buskirk, E. B. Dally, et al., Phys. Lett. B 47, 355 (1973).
G. G. Simon, Ch. Schmitt, and V. H. Walther, Nucl. Phys. A 364, 285 (1981).
D. W. L. Sprung and H. Wu, Acta Phys. Pol. B 24, 503 (1993).
J. Martorell, D. W. L. Sprung, and D. C. Zheng, Phys. Rev. C 51, 1127 (1995).
I. Sick and D. Trautmann, Phys. Lett. B 375, 16 (1996).
G. L. Squires and A. T. Stewart, Proc. R. Soc. London, Ser. A 230, 19 (1955).
H. Kaiser, H. Rauch, G. Badurek, et al., Z. Phys. A 291, 231 (1979).
D. Plümper, J. Flender, and M. F. Gari, Phys. Rev. C 49, 2370 (1994).
Author information
Authors and Affiliations
Additional information
Original Russian Text © V.A. Babenko, N.M. Petrov, 2006, published in Yadernaya Fizika, 2006, Vol. 69, No. 9, pp. 1586–1605.
Rights and permissions
About this article
Cite this article
Babenko, V.A., Petrov, N.M. On triplet low-energy parameters of nucleon-nucleon scattering. Phys. Atom. Nuclei 69, 1552–1572 (2006). https://doi.org/10.1134/S1063778806090134
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1134/S1063778806090134