Application of the Dashen-Frautschi method to the calculation of the difference between the nn and np singlet scattering lengths

Abstract

The difference between the1S0 np and nn scattering lengths is calculated by a method due to Dashen and Frautschi. In the calculation the driving term used is the change in the one-pion exchange contribution between the two channels due to differences in the charged and neutral pion masses which are exchanged, in the charged and neutralπN coupling constants, and in the external proton and neutron masses. The split in the coupling constants is also estimated with the same formalism, and constitutes an independent result. The over-all result obtained isann−anp=−(3.8±3.4) fermi, if the elementary-particle physics definition of scattering length is used. This is in qualitative agreement with recent experimental findings.