Prog. Theor. Phys. Vol. 35 No. 3 (1966) pp. 485-507

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An Impact Parameter Formalism. III

— Strong Absorption Model —

The Tokyo Metropolitan Technical College, Shinagawa, Tokyo
^*Department of Physics, Tokyo Metropolitan University, Setagaya, Tokyo

(Received November 19, 1965)

Abstract:

In order to understand the physical meaning of an impact parameter amplitude, the formalism proposed by us is applied to various strong absorption models. A simple black disc model with a sharp boundary is not self-consistent; that is, the total elastic cross section derived from the angular distribution is not equal to what is calculated from the impact parameter amplitude. This inconsistency is expressed as the violation of the unitarity relation. It disappears in the high energy limit, where the semi-classical particle picture is applicable. A general rule is given for getting consistent results even in the finite energy region. It is observed that the model proposed by Fernbach, Serber and Taylor contains the same inconsistency. On the other hand, a sharp cutoff model with a sharp cutoff angular momentum involves no such difficulty. The strong interaction region expressed by this model has a diffuse edge with respect to the impact parameter. Thus, the concept of a radius of this region is introduced. It is pointed out that the so-called high energy approximation to the familiar partial-wave expansion of the scattering amplitude for large angular momenta does not include any limitation on the scattering angle.

URL : http://ptp.ipap.jp/link?PTP/35/485/
DOI : 10.1143/PTP.35.485

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