K −-Proton atomic transitions

The relation between theK ^}-P scattering length and the X-ray spectrum for the 2p → 1s electromagnetic transition inK ^?-P atoms is examined. A coupled-channel potential model is used to explicitly calculate the energy of theS-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 theS-matrix pole. In addition, theK ^?p branching ratios are compared at threshold and at the complexS-matrix pole energy.