Nucleon-antinucleon interaction in the new Tamm-Dancoff approximation

The nucleon-antinucleon ( N-N ) problem is formulated in the new Tamm-Dancoff (NTD) approximation in the lowest order, and the integral equation for N-N̅ scattering derived, taking account of both the exchange and annihilation interactions. It is found convenient to represent the N-N̅ wave-function as a 4 x 4 matrix, rather than the usual 16 x 1 matrix for the nucleon-nucleon wave-function, and a complete correspondence is established between these two representations. The divergences associated with the annihilation interaction and their renormalization are discussed in detail in the following paper (Mitra & Saxena 1960; referred to as II). The integral equation with the exchange interaction alone, is then separated into eigenstates of T, J, L and S in the usual manner and the various phase shifts obtained. The results of II for the contribution of the annihilation term are then used to calculate the complete phase shifts from which the various cross-sections (scattering and charge exchange) are derived. The results indicate that while the exchange term alone gives too small values for the total cross-sections versus energy, inclusion of the annihilation interaction without renormalization effects makes the cross-sections nearly three times larger than those observed. On the other hand, inclusion of the finite effects of renormalization (which manifest themselves essentially as a suppression of the virtual meson propagator) brings down these cross-sections to the order of magnitude of the observed ones.