发表机构
University of Alberta（阿尔伯塔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过减法方法处理部分波展开慢收敛问题，数值和解析地计算了类氢离子中带电标量粒子束缚态衰变率，并给出与全阶数值一致的微扰展开结果。
AI 中文摘要
我们通过数值和解析方法确定了束缚在轻原子核上的标量粒子的衰变率 $\Gamma$。作为模型系统，我们考虑一个类氢离子基态中的带负电 kaon 衰变为带电和中性标量 pion，即 $K^-\to \pi^-\pi^0$。所有粒子均假设为点状；原子核无限重。部分波展开收敛缓慢，正如最近对束缚 muon 衰变的分析一样。为克服这一困难，我们引入一种减法方法：自由 $\pi^-$ 贡献被单独评估，而部分波求和仅用于库仑畸变。我们得到了轻核（$1\leq Z\leq 10$）的束缚态与自由态衰变率之比 $\Gamma/\Gamma_0$。数值计算辅以图解的小 $\alpha Z$ 展开。我们发现 $\Gamma/\Gamma_0 = 1-(\alpha Z)^2/2 + 17(\alpha Z)^4/24 +\mathcal{O}((\alpha Z)^5)$，与低 $Z$ 下的全阶数值计算一致。
英文摘要
We determine the decay rate $Γ$ of a scalar particle bound to a light nucleus, numerically and analytically. As a model system, we consider a negatively charged kaon in the ground state of a hydrogen-like ion decaying into charged and neutral scalar pions, $K^-\to π^-π^0$. All particles are assumed point-like; the nucleus is infinitely heavy. The partial wave expansion converges slowly, as in a recent analysis of the bound-muon decay. To overcome this difficulty, we introduce a subtraction method: the free $π^-$ contribution is evaluated separately, while the partial-wave sum is used only for the Coulomb distortion. The ratio of bound-to-free decay rates, $Γ/Γ_0$, is found for light nuclei, $1\leq Z\leq 10$. The numerical calculation is complemented by a diagrammatic small-$αZ$ expansion. We find $ Γ/Γ_0 = 1-(αZ)^2/2 + 17(αZ)^4/24 +\mathcal{O}((αZ)^5)$, in agreement with the all-orders numerical calculation at low $Z$.
