Dynamical Statistical Model of High Energy Elastic Scattering

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High energy elastic scattering is discussed through a proposal of the "dynamical statistical model", in which large angle elastic scattering at high energies is considered to be caused by some sort of irreversible process taking place in the inner system of colliding nucleons. The "dynamical statistical model" enables us to get both the rapid decrease of the differential cross section for increasing energy and the small fluctuation of the scattering amplitude, for the large angle elastic scattering at high energies. After a few manipulations, it is shown that the present model can derive the differential cross section proportional to exp(-ap⊥) similar to Orear's empirical formula for large p⊥, α and p⊥ being, respectively, the Orear constant and the transverse momentum. The present model also gives the relationship between the exponential p⊥-dependence for large p⊥ and the Gaussian p⊥-dependence for small p⊥ within a unified theoretical framework, from which follows α^<-1>≳0.158 M, M being the nucleon mass. This is in good agreement with experiment. Furthermore it is remarked that the present model has the possibility of deriving, even for large p⊥, the Gaussian p⊥-dependence like Krisch's empirical formula in some extreme cases, which may not be obtained by the simple statistical model given by Hagedorn and others and by the unitarity-analyticity argument. The irreversibility of the large angle scattering-to be realized even by the time-reversal invariant Hamiltonian-does not permit us to impose the time-reversal inveriance requirement and the simple unitarity-analyticity argument on the large angle scattering amplitude except on the forward amplitude. Its consequence may be used for a crucial test of the model. The "dynamical statistical model" has been built on the basis of critical discussion against the simple statistical model. For this reason a detailed discussion of the latter is given.
理論物理学刊行会の論文
1967-08-25

Dynamical Statistical Model of High Energy Elastic Scattering

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