Neutron- <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>H</mi></mrow><mprescripts></mprescripts><mrow></mrow><mrow><mn>3</mn></mrow><mrow></mrow><mrow></mrow></mmultiscripts></mrow></math></span> and Proton- <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>H</mi></mrow><mprescripts></mprescripts><mrow></mrow><mrow><mn>3</mn></mrow><mrow></mrow><mrow></mrow></mmultiscripts></mrow><mi>e</mi></math></span> Zero Energy Scattering

M. Viviani; S. Rosati; A. Kievsky

doi:10.1103/PhysRevLett.81.1580

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Neutron- ${}^{3}H$ and Proton- ${}^{3}H e$ Zero Energy Scattering

M. Viviani¹, S. Rosati^1,2, and A. Kievsky¹

¹Istituto Nazionale di Fisica Nucleare, Piazza Torricelli 2, 56100 Pisa, Italy
²Dipartimento di Fisica, Universita' di Pisa, Piazza Torricelli 2, 56100 Pisa, Italy

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Phys. Rev. Lett. 81, 1580 – Published 24 August, 1998

DOI: https://doi.org/10.1103/PhysRevLett.81.1580

Abstract

The Kohn variational principle and the (correlated) hyperspherical harmonics technique are applied to study the $n -^{3} H$ and $p -^{3} He$ scattering at zero energy. Predictions for the singlet and triplet scattering lengths are obtained for nonrelativistic nuclear Hamiltonians including two- and three-body potentials. The calculated $n -^{3} H$ total cross section agrees well with the measured value, while some small discrepancy is found for the coherent scattering length. For the $p -^{3} He$ channel, the calculated scattering lengths are in reasonable agreement with the values extrapolated from the measurements made above 1 MeV.

References (32)

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[c1] W. Glöckle et al., Phys. Rep. 274, 107 (1996).

[c2] A. Kievsky, S. Rosati, W. Tornow, and M. Viviani, Nucl. Phys. A607, 402 (1996).

[c3] B. S. Pudliner et al., Phys. Rev. C 56, 1720 (1997).

[c4] K. Varga, Y. Ohbayashi, and Y. Suzuki, Phys. Lett. B 396, 1 (1997).

[c5] M. Viviani, A. Kievsky, and S. Rosati, Few-Body Syst. 18, 25 (1995).

[c6] T. A. Tombrello, Phys. Rev. 138, B40 (1965).

[c7] T. W. Phillips, B. L. Berman, and J. D. Seagrave, Phys. Rev. C 22, 384 (1980).

[c8] S. Hammerschmied, H. Rauch, H. Clerc, and U. Kischko, Z. Phys. A 302, 323 (1981).

[c9] H. Rauch, D. Tuppinger, H. Woelwitsch, and T. Wroblewski, Phys. Lett. 165B, 39 (1985).

[c10] G. M. Hale et al., Phys. Rev. C 42, 438 (1990).

[c11] P. E. Tegnér and C. Bargholtz, Astrophys. J. 272, 311 (1983).

[c12] M. T. Alley and L. D. Knutson, Phys. Rev. C 48, 1901 (1993).

[c13] D. R. Tilley, H. R. Weller, and G. M. Hale, Nucl. Phys. A541, 1 (1992).

[c14] J. A. Tjon, Phys. Lett. 63B, 391 (1976).

[c15] A. C. Fonseca, Phys. Rev. C 19, 1711 (1979).

[c16] V. F. Kharchenko and V. P. Levashev, Phys. Lett. 60B, 317 (1976); Nucl. Phys. A343, 249 (1980).

[c17] L. M. Delves, Advances in Nuclear Physics, M. Baranger and E. Vogt (Plenum Press, New York, London, 1972), Vol. 5, p. 126.

[c18] H. H. Hackenbroich and P. Heiss, Z. Phys. 231, 225 (1970); I. Reichstein, D. R. Thompson, and Y. C. Tang, Phys. Rev. C 3, 2139 (1971).

[c19] H. M. Hofmann, W. Zahn, and H. Stöwe, Nucl. Phys. A357, 139 (1981).

[c20] V. P. Permyakov, V. V. Pustolatov, Yu. I. Fenin, and V. D. Efros, Sov. J. Nucl. Phys. 14, 317 (1972).

[c21] F. Ciesielsky, J. Carbonell, and C. Cignoux, in Proceedings of the XV International Conference of Few-Body Problems in Physics, Groningen, Holland, 1997 (to be published); J. Carbonell (private communication).

[c22] A. Kievsky, S. Rosati, and M. Viviani, Nucl. Phys. A551, 241 (1993).

[c23] A. Kievsky, M. Viviani, and S. Rosati, Nucl. Phys. A577, 511 (1994).

[c24] C. R. Chen, G. L. Payne, J. L. Friar, and B. F. Gibson, Phys. Rev. C 39, 1261 (1989).

[c25] C. R. Chen, G. L. Payne, J. L. Friar, and B. F. Gibson, Phys. Rev. C 31, 2266 (1985).

[c26] W. Glöckle et al., Few-Body Syst. Suppl. 8, 9 (1995); S. Ishikawa, T. Sasakawa, T. Sawada, and T. Ueda, Phys. Rev. Lett. 53, 1877 (1984); T. Sasakawa and S. Ishikawa, Few-Body Syst. 1, 3 (1986).

[c27] R. B. Wiringa, R. A. Smith, and T. L. Ainsworth, Phys. Rev. C 29, 1207 (1984).

[c28] R. B. Wiringa (unpublished).

[c29] R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Phys. Rev. C 51, 38 (1995).

[c30] R. B. Wiringa, Phys. Rev. C 43, 1585 (1991).

[c31] H. T. Coelho, T. K. Das, and M. R. Robilotta, Phys. Rev. C 28, 1812 (1983).

[c32] L. D. Knutson (private communication).

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Neutron- ${}^{3}H$ and Proton- ${}^{3}H e$ Zero Energy Scattering

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Neutron- ${}^{3}H$ and Proton- ${}^{3}H e$ Zero Energy Scattering