s-WaveK−NScattering by theNDMethod

Abstract

The $K-N$ $s$-wave scattering lengths and effective-range parameters have been calculated for both isotopic spin states, using the $\frac{N}{D}$ method. The nearby part of the interaction cut has been approximated by two poles, whereas following Balázs' procedure the entire distant cut has been replaced by two effective-range poles at predetermined positions, but with unknown residues. The residues of the effective-range poles are determined by matching the $\frac{N}{D}$ amplitude with that calculated with a fixed energy dispersion relation, at two properly chosen points. In calculating the latter amplitudes only the contributions of $\Lambda$, $\Sigma$, ${Y_1}^{*}$, $\rho$, and $\omega$ exchange terms are retained and the values of ${Y_1}^{*}$, $\rho$, and $\omega$ coupling constants are taken from a unitary symmetry scheme. The calculated values of scattering length, effective range, and low-energy phase shifts for the I=1 state are in good agreement with the experimental results of Goldhaber et al. For the I=0 state, the calculated phase shifts are consistent with the large $s$-wave solution of Goldhaber et al.