Calculation of the ${}^3$He(in-flight $K^{-}$,$n$) reaction for searching the deeply-bound $K^{-}pp$ state

Abstract

The formation of a deeply-bound $K^{-}pp$ state by the ${}^3$He(in-flight $K^{-}$,$n$) reaction is investigated theoretically in the distorted-wave impulse approximation using the Green's function method. The expected inclusive and semi-exclusive spectra at $p_{K^{-}}$ = 1.0 GeV/c and $\hat{I}{¸}_n=0^{\circ }$ are calculated for the forthcoming J-PARC E15 experiment. We employ optical potentials between the $K^{-}$ and ``$pp$'' core-nucleus, and demonstrate systematically the dependence of the spectral shape on $V_0$ and $W_0$, which are the real and imaginary parts of the strength for the optical potential, respectively. The necessary condition to observe a distinct peak of the $K^{-}pp$ bound state with $I=1/2$, $J^{\ddot{I}}€=0^{-}$ in the spectrum turns out to be that the value of $V_0$ is deeper than $\sim -100$ MeV and $W_0$ shallower than $\sim -100$ MeV, of which the strength parameters come up to recent theoretical predictions.

18 pages, 6 figures, REVTeX 4, accepted for publication in Physics Letters B