Isospin Properties of ($K^{-}$, $N$) Reactions for the Formation of Deeply-bound Antikaonic Nuclei

Abstract

The formation of deeply-bound antikaonic $K^{-}/{\bar{K}}^0$ nuclear states by nuclear ($K^{-}$, $N$) reactions is investigated theoretically within a distorted-wave impulse approximation (DWIA), considering the isospin properties of the Fermi-averaged $K^{-}+N\to N+\bar{K}$ elementary amplitudes. We calculate the formation cross sections of the deeply-bound $\bar{K}$ states by the ($K^{-}$, $N$) reactions on the nuclear targets, ${}^{12}$C and ${}^{28}$Si, at incident $K^{-}$ lab momentum $p_{K^{-}}$ = 1.0 GeV/c and $\hat{I}{¸}_{\mathrm{lab}}=0^{\circ }$, introducing a complex effective nucleon number $N_{\mathrm{eff}}$ for unstable bound states in the DWIA. The results show that the deeply-bound $\bar{K}$ states can be populated dominantly by the ($K^{-}$, $n$) reaction via the total isoscalar $\hat{I}”T=0$ transition owing to the isospin nature of the $K^{-}+N\to N+\bar{K}$ amplitudes, and that the cross sections described by $\mathrm{Re}{N}_{\mathrm{eff}}$ and $\mathrm{Arg}{N}_{\mathrm{eff}}$ enable to deduce the structure of the $\bar{K}$ nuclear states; the calculated inclusive nucleon spectra for a deep $\bar{K}$-nucleus potential do not show distinct peak structure in the bound region. The few-body $\bar{K}\otimes [NN]$ and $\bar{K}\otimes [NNN]$ states formed in ($K^{-}$, $N$) reactions on $s$-shell nuclear targets, ${}^3$He, ${}^3$H and ${}^4$He, are also discussed.

61 pages, 17 figures, proofread version to be published in Nucl. Phys. A