K--proton atomic transitions

The relation between the K--P scattering length and the X-ray spectrum for the 2p → 1s electromagnetic transition in K--P atoms is examined. A coupled-channel potential model is used to explicitly calculate the energy of the S-matrix pole in the 1s channel, which is then compared with the energy obtained from the scattering lengths via the standard equation. The X-ray spectrum is calculated and compared with the Lorentzian shape associated with the complex energy of the S-matrix pole. In addition, the K-p branching ratios are compared at threshold and at the complex S-matrix pole energy. (orig.)