All-Angle Structure of Nucleon-Nucleon Scattering Amplitudes

Abstract

All-angle behavior of nucleon-nucleon elastic scattering is examined in terms of fac­ torizable urbaryon rearrangement · amplitudes. The regions relevant to Regge-like form, scaling form s-N f (cosO) and transitional form of the all-angle amplitudes are found from detailed study of angular distribution, effective Regge trajectory, effective exponent Nand exp(-s·sinO/const) behavior of da/dt. The Regge-like form has only the restricted range O:$Jtl:$1 (GeY)' of application: It is also found that the existing data (P£:$25 GeV/c) comes nearer to the scaling form but . do not reach it. In the all-angle amplitudes, the scaling could be attained in the energy region PL:?:50 GeV/c at large momentum transfer. The correspondence of the respective forms of the urbaryon rearrangement amplitudes to the experimental data gives evidence in support of the factorizable structure of the amplitudes. § I. Introduction Recently an all-angle formula for hadronic two-body scattering at high energies has been proposed1l in terms of urbaryon rearrangement amplitudes2> (hereafter abbreviated to UR amplitudes). The UR amplitudes over all angles are based ·on a picture in which constituent urbaryons are . rearranged as if ingependent in the large momentum transfer region, whereas in the small mo­ mentum transfer region the rearranged urbaryons strongly correlate .with each other and Regge-like behavior dominates. Each UR amplitude is composed of a product of factors (overlapping integrals with some exponents) corresponding to urbaryon lines in the UR diagram.8> The exponent represents the degree of the correlation among the rearranged urbaryons and specifies the type of transition from correlated urbaryon states to uncorrelated ones around the criti­ cal momentum transfer tc. The behavior of the exponent around tc may be understood as a kind of phase transition. The factorizable structure of the UR amplitudes and one-to-one correspondence of the factors of the amplitude and urbaryon lines of UR diagram are ramarkable features of high energy hadronic reactions and seem to be very suggestive of a peculiar property of the under­ lying dynamics of hadron. One of the purposes of this paper is to examine the above factorizable structure of scattering amplitude by the use of nucleon­ nucleon scattering data which are most accumulated in comparison with the other processes. The proposed amplitude ~xhibits Regge-like behavior for forward and back