Prog. Theor. Phys. Vol. 87 No. 6 (1992) pp. 1399-1410

[ Full Text PDF : FREE ACCESS (447K) ]

Nucleon-Trinucleon Scattering in Terms of the Schmidt Expansion. II

— Optical Theorem —

Yoshiko Matsui

Department of Applied Physics, Faculty of Technology, Tokyo University of Agriculture and Technology, Koganei 184

(Received October 2, 1991)

Abstract:

From the general operator from are derived the unitarity relations for the nucleon-trinucleon scattering amplitudes. The obtained unitarity relations give the optical theorem. The two-nucleon interaction is assumed to be a general rank n separable potential. The Schmidt expansion theorem is used to express the amplitudes for 3 + 1 and 2 + 2 subsystems at energies in the continuous spectrum region. In order to get the four-nucleon amplitudes describing each scattering process, the connection between the Fredholm and the spectral representation is defined by the pole term decomposition. The result of this study has proved that the cross sections of the partial or full breakup reaction for the nucleon-trinucleon scattering must include the contributions which originate from the discontinuity of the transition operator for the (2 + 1 + 1) subsystem.

URL : http://ptp.ipap.jp/link?PTP/87/1399/
DOI : 10.1143/PTP.87.1399

References:

L. D. Faddeev, Mathematical Aspects of the Three-Body Problem in the Quantum Scattering Theory (Davey, New York, 1965).
T. A. Osborn and D. Bolle, Phys. Rev. C8 (1973), 1198[APS].
B. R. Karlson and E. M. Zeiger, Phys. Rev. D9 (1974), 1761[APS]; ibid. D11 (1975), 939[APS]; ibid. D16 (1977), 2553[APS].
Y. Matsui, J. Math. Phys. 29 (1988), 2450[CrossRef].
Y. Matsui, Phys. Rev. C26 (1982), 2620[APS]; ibid. C29 (1984), 253[APS].
I. M. Narodetskii, Yadern. Fiz. 20 (1974), 1063 [Sov. J. Nucl. Phys. 20 (1975), 560].
S. Oryu and H. Kamada, Nucl. Phys. A534 (1991), 221.
Y. Matsui, J. Math. Phys. 28 (1987), 2677[CrossRef].

Citing Article(s) :

Progress of Theoretical Physics Vol. 87 No. 6 (1992) pp. 1411-1420 :
Nucleon-Trinucleon Scattering in Terms of the Schmidt Expansion. III

Yoshiko Matsui
Progress of Theoretical Physics Vol. 91 No. 3 (1994) pp. 495-506 :
Four-Boson Resonance

Yoshiko Matsui