Low energy Σ−-nucleus interaction

Abstract

We have fitted consistently the Σ*u− atomic and the ΣN scattering data within a finite range potential model.The analysis of the ΣN scattering data by G. Alexander et al.1, produced two sets of complex scattering lengths. Together with the data on atomic level widths and shifts of Σ− atoms of C. J. Batty et.al.2 it is possible to analyse the combined data to see if they are consistent and also to see if the atomic data can distinguish between the two sets of scattering lengths.The calculations were done by first fitting Yukawa shape complex potentials VΣN(r) =VJI e−μrμr to reproduce the complex scattering lengths as a function of the potential range by varying μ from 1.5 fm−1 to 3.0 fm−1. These poentials were then folded3 into the nuclear distribution to produce the Σ− nucleus effective potential, and the Schrodinger equation solved for the level widths and shifts. The inverse range μ was fixed at the value which minimized the deviation of the calculated level widths and shifts from the measured data. As a further step, the depths of the potentials were then varied within the uncertainty in the fit to the scattering lengths, to minimize the overall χ2 further. The resultant fits are shown in the tables.