A study on yield and energy expenditure of negative pion and the determination of its optimal production conditions for muon catalyzed fusion

In previous calculations of yield and energy expenditure for negative pion production, the Coulomb scattering energy loss of projectile particles on target nucleus is not taken into account. Our calculations show that this is an important parameter. Also, in most calculations, the target thickness is assumed very thick near to infinity. This assumption will increase the Coulomb scattering energy loss, and also the chance of charge exchange reactions will increase for pions; all these combined will reduce outcoming pions from the target. In this paper, we provide a simple method for a theoretical calculation of energy expenditure for negative pion production in finite thickness target materials. By the given method, the energy loss of pions in target by Coulomb scattering and charge exchange of pions is calculated and the optimal conditions of projectile particles, their energy and target thickness are determined. Finally, it is shown that using finite target has the advantage of facilitating the use of heavier targets for pion production while it has low tritium inventory.