Deviations from charge independence in n-p and n-n scattering lengths by S-matrix methods

Abstract

The difference between the zero-energy ¹S₀n-p and n-n scattering lengths is calculated, using the dispersion-theoretic method of Dashen and Frautschi, originally employed for calculating electromagnetic mass splittings. We assume that the deviation is due to the perturbative effect of (i) magnetic interaction between nucleons, (ii) electromagnetic mass shifts between exchange bosons, and (iii) electromagnetic mass difference between neutron and proton. Our calculation predicts a(np)-a(nn)=3.58 F, if the definition lim_q→0(qcotδ)^-1=1/a is used. The result is in qualitative agreement with the experimental value a(np)-a(nn)=7.28±1.9 F. The effects of the ρ⁺-ρ⁰ mass difference and the vertex corrections, which have been ignored in the calculation, may, hopefully, account for the remaining deviation.