Teoria non locale dell’ interazione tra particelle di fermi

Riassunto

Si elabora una teoria relativistica non locale dell’interazione diretta tra particelle di Fermi e si danno i due primi elementi della matriceS seguendo il metodo di Yang e Feldman. Sono discussi i risultati della teoria applicata al problema della cattura nucleare del mesone μ^~

Summary

A non local, relativistically invariant, treatment of the renornializable interaction between Fermi particles is given. Following the Kristensen and Möller’s schema a theory is outlined starting from the Lagrangian interaction (3), whereF is an arbitrary, invariant form factor depend’ng on four space-time points. The S-matrix in the Heisenberg representation is defined through the relation (11), where ψ^pa and, respectively, ψ^ar mean the out and in-going fields, which are defined by Eqs. (9). The outfields and the right hand side of Eq. (11) are expanded in power series, then, by the aid of the usual procedure, the S-matrix is derived to the first (Eq. (15)) and to the second (Eq. (16)) approximation. The formalism is applied to the study of the first order process μ^- + P → N +v (§ 4). In this case it is sufficient to take a two-points form factor (formula (19) and Fig. 16). With the choice (24) of the Fourier transform of the form factor (which although not of the ≪ normal class ≫ in our case gives the same results as the normal one) the formalism becomes the same as if one would have supposed the considered process io be μ^- + P→ μ^- + π + N → N + e. The effect of the non localizability of the interaction (with λ = 1.4-l0^-13 cm) on the life time of the capture of the μ^- is described by the formula (34) were T_{non loc}and t_loc mean the non local and the local life time. The reduction function versusZ is plotted in fig. 2. The possibility of verifying the calculated effect is discussed.