One-pion exchange and the optical model

Abstract

Starting with the two-body scattering amplitude, an optical model potential for nucleon-nucleus scattering has been calculated (1) using the one-pion exchange interaction alone, (2) modifying the s-wave part of this by using effective range theory, and (3) using the modified phase shift analysis for p-p scattering supplemented by charge independence and the Gammel-Thaler potential for the n-p scattering information. Part (1) works sufficiently well to suggest that the one-pion exchange force contributes more importantly to the nucleon-nucleus interaction than to the basic two-nucleon scattering process. Part (2) produces an indifferent improvement on part (1). Part (3) represents the optical potential inferred from the most accurate two-nucleon data presently available. This last evaluation of the optical potential is considered the most reliable to date since it includes, in a good approximation, an infinite number of the high angular momentum states of the two-nucleon amplitude, which play a very essential part in the optical potential. A systematic derivation of the optical model equations is included with special emphasis on the needs of the present calculation; in addition, criteria for the validity of the model are discussed. Allowance has been made for the nuclear volume not being strictly proportional to the mass number (nuclear size effect) and for the inequality of the numbers of neutrons and protons in the nucleus (effect of neutron excess). For heavy nuclei, these effects influence the results up to 25%.