Formation spectra of light kaonic nuclei by in-flight ({bar K},N) reactions with chiral unitary amplitude

We study theoretically the in-flight ($K^-,N$) reactions for the formation of light kaonic nuclear systems to get deeper physical insights on the expected spectra, and to investigate the experimental feasibility of the reaction at new facilities like J-PARC. We show the expected spectra for the formation of the $K^-pp, K^-pn$, $K^-nn$ and $K^-$-$^{11}$B systems which are accessible by the ($K^-,N$) experiments. By considering the conversion part of the Green's function, we can show the missing mass spectra of the ($K^-,N$) reactions coincidence with the particle emissions due to ${\bar K}$ absorption in ${\bar K}N\to \pi Y$ processes. To calculate the cross sections, we use the so-called $T\rho$ approximation to evaluate the optical potential. As for the amplitude $T$, we adopt the chiral unitary amplitude of ${\bar K}N$ channel in vacuum for simplicity, and we also check the medium effects by applying the chiral amplitude at finite density. The effects of the p-wave optical potential of $\Sigma$(1385) channel and the contribution from ${\bar K^0}$ mixing in $^3$He($K^-,n$) reaction are also evaluated numerically. To understand the meanings of the spectrum shape, we also study the behavior of the poles of kaon Green's function in nuclear matter. We conclude that $^3$He($K^-,n$) and $^3$He($K^-,p$) reactions coincident with the $\pi\Sigma$ emission due to ${\bar K}$ absorption may show the certain structure in the bound region spectra indicating the existence of the unstable kaonic nuclear bound states. As for the $^{12}$C($K^-,p$) spectra with the $\pi\Sigma$ emission, we may also observe the structure in the bound region, however, we need to evaluate the medium effects carefully for larger nuclei.