Anti-Shrinkage of thep-$\bar{p}$ Diffraction Scattering

T\=osaku Kunimasa, Takesi Ogimoto
1964 Progress of theoretical physics  
The aim of this note is to show that the forward peak of high-energy p-p scattering has a tendency to corpulence. We assume that the p-p interaction range R is finite, but may be energy dependent, and has a very strong absorptive force. where k is the center-of-mass momentum, J(b, k) is the phase shift with the impact parameter b, and J 0(kb0) is the Bessel function of the zeroth order. Equation (1) is obtained from the usual partial wave expansion by replacing PtCcosO) by Jo(kbO) and summation
more » ... by integral. This approximation is most accurate for large l and small angles. In the case of _potential scattering, Eq. (1) corresponds to the socalled eikonal approximation, and J(b, k) can be expressed by potential only. From our assumption on the p-p interaction, the following simple approximation for S(b, k) may be permitted: Then we have f(O)=ik~:.lo(kbO)bdb =i(kR 2 Vt(kRO)/(kRO) (4) and dtotCk) =( 4n/k)Imf(O) =2nR 2 •
doi:10.1143/ptp.31.325 fatcat:aowo5ycfbzafveoeknus6ykj6y