Meson Production in Meson-Nucleon Interaction

Abstract

The meson production by mesons in the low-energy limit has been re-examined in the frame of static model of the extended source theory. Using Feynman's technique the calculation has been performed up to fifth order in the coupling constant. The renormalization procedure is the same as developed and applied by Chew in meson-nucleon scattering processes. To reduce the Feynman diagram an approximation similar to that of the T amm-Dancoff type has been used. The total cross section for charged and neutral pions from the pion-nucleon collision. in T=3/2, }=3/2 state are obtained for incident meson energy 260 to 570 Mev. The theoretical results have been compared with those of Franklin, Barshay and others. Franklin's result that production of charged pions is higher than that of neutral pions in the cut-off theory is confirmed. The present calculation predicts the charged pion production of about 7 mb at 500 Mev against the available experimental cross section of a maximum of 10 mb at the same energy. ~ 1. IntroductionIn VIew of the recent experimental evidences 1 ) of the production of one additional pion in pion-nucleon scattering at low energy, the problem of double scattering of 1f -mesons by nucleons has of late been approached by Barshay2) and Franklin 3 ). They have made use of the extended fixed source meson theory of Chew 4 ) et aI, and based their calculations on a new method for meson-nucleon scattering developed by Wick 5 ) which involves the study of the eigenstates of the meson-nucleon Hamiltonian. Franklin has calculated the transition matrix from one meson state to two meson state using two meson eigenstate of the total meson-nucleon Hamiltonian analogous to ordinary meson-nucleon scattering, which needs the one meson eigenstate to describe the transition matrix of the scattering process. Barshay also, using a similar procedure (as studied by Low(n), has obtained results which are quite different from those obtained by Franklin. The discrepancy between the results of Fra.nklin and Barshay can be seen by comparing Franklin's equation (27) with Barshay's equation (20) for the production T-matrix. It is noted that apart from a factor 1/V/2 (due to different procedure of normalization) Barshay has obtained only twice the first term of ( 2 7), the second term of ( 27), however, vanishes for the 3/2 isotopic spin state and the rest of the discrepancy as has been pointed out by Franklin is due to the fact that Barshay has used different approximation to identify the certain parts of the production T-matrix with the elastic scattering T-matrix.