We investigate theoretically productions of ${}_{\mathrm{\Lambda }}^{3,4}$H bound states in the exothermic ($K^{-}$, ${\pi }^0$) reactions on ^3,4He targets at $p_{K^{-}}=$ 1.0 GeV/c in a distorted-wave impulse approximation with the optimal Fermi-averaging $K^{-}p\to {\pi }^0\mathrm{\Lambda }$ t matrix. We calculate angular distributions of the laboratory differential cross sections $d\sigma /d{\mathrm{\Omega }}_{\mathrm{lab}}$ and the integrated cross sections ${\sigma }_{\mathrm{lab}}$ for a $J^P=0^{+}$ ground state and a $J^P=1^{+}$ excited state of ${}_{\mathrm{\Lambda }}{}^4\mathrm{H}$ at ${\pi }^0$ forward-direction angles of ${\theta }_{\mathrm{lab}}=$ 0^∘–20^∘, and those for a $J^P=1/2^{+}$ ground state of ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}$. The production of a $J^P=3/2^{+}$ excited state of ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}$ as a virtual state is also evaluated. The comparison in $d\sigma /d{\mathrm{\Omega }}_{\mathrm{lab}}$ and ${\sigma }_{\mathrm{lab}}$ between ${}_{\mathrm{\Lambda }}{}^4\mathrm{H}$ and ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}$ provides examining the mechanism of the production and structure of ${}_{\mathrm{\Lambda }}^{3,4}$H, as well as in the endothermic (${\pi }^{-}$, $K^0$) reactions at $p_{{\pi }^{-}}=$ 1.05 GeV/c. This investigation confirms the feasibility of lifetime measurements of ${}_{\mathrm{\Lambda }}^3$H at the J-PARC experiments.

我们从理论上研究了 ${}_{\mathrm{\Lambda }}^{3,4}$放热中的 H 束缚态 (${钾}^{-}$, ${\pi }^0$) 对^3,4 He 的反应目标为${磷}_{{钾}^{-}}=$ 1.0 GeV/c 在具有最佳费米平均的失真波脉冲近似中 ${钾}^{-}磷\to {\pi }^0\mathrm{\Lambda }$ t矩阵。我们计算实验室差分横截面的角度分布$d\sigma /d{\mathrm{\Omega }}_{\mathrm{实验室}}$ 和综合横截面 ${\sigma }_{\mathrm{实验室}}$ 为一个 $J^{磷}=0^{+}$ 基态和 $J^{磷}=1^{+}$ 兴奋状态 ${}_{\mathrm{\Lambda }}{}^4\mathrm{H}$ 在 ${\pi }^0$ 前向角 ${\theta }_{\mathrm{实验室}}=$0 ^∘ –20 ^∘，以及$J^{磷}=1/2^{+}$ 的基态 ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}$. 生产一个$J^{磷}=3/2^{+}$ 兴奋状态 ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}$作为虚拟状态也被评估。中的比较$d\sigma /d{\mathrm{\Omega }}_{\mathrm{实验室}}$ 和 ${\sigma }_{\mathrm{实验室}}$ 之间 ${}_{\mathrm{\Lambda }}{}^4\mathrm{H}$ 和 ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}$ 提供检查产生和结构的机制 ${}_{\mathrm{\Lambda }}^{3,4}$H，以及在吸热（${\pi }^{-}$, ${钾}^0$) 反应在 ${磷}_{{\pi }^{-}}=$1.05 GeV/c。这项调查证实了寿命测量的可行性${}_{\mathrm{\Lambda }}^3$J-PARC 实验中的 H。