μ子从μ子氢到μ子氧原子转移的超球椭圆坐标处理
Hyperspherical elliptic coordinates treatment of muon transfer from muonic hydrogen to atomic oxygen
摘要：
本文用量子力学方法计算了碰撞能量在$10^{-3} - 10^3$ eV范围内的$s$波在μ介子氢核和μ介子氧核之间的转移。紧耦合的时间无关的薛定谔方程，写在超球椭圆坐标沿超半径积分，以获得部分和总的μ子转移概率。结果表明，预期的Wigner-Bethe阈值行为的顺序$10^{-2}$ eV的碰撞能量和$10^2$ eV的显着的最大值，这可以解释在对应于入口通道状态$(μp)_{1s} + \mO$和两个产品通道的渐近相关的$p + (\mOμ)_{n=5,6}$的势能曲线之间的交叉。具有不同的轨道角动量的末态的人口被发现是基本上独立的能量范围内考虑在这项工作中。这可以归因于与其中一个椭圆超角相关的量子数守恒的强选择规则。
英文摘要：
Quantum-mechanical calculations of muon transfer between muonic hydrogen and an oxygen nuclei for $s$ waves and collision energies in the range $10^{-3} - 10^3$ eV, are presented. Close-coupling time-independent Schrödinger equations, written in terms of hyperspherical elliptic coordinates were integrated along the hyper-radius to obtain the partial and total muon-transfer probabilities. The results show the expected Wigner-Bethe threshold behavior up to collision energies of the order of $10^{-2}$ eV and pronounced maxima at $10^2$ eV which can be interpreted in terms of crossings between potential energy curves corresponding to the entrance channel state $(μp)_{1s} + \mO$ and two product channels which asymptotically correlate to $p + (\mOμ)_{n=5,6}$. The population of the final states with different orbital angular momenta is found to be essentially independent of energy in the range considered in this work. This can be attributed to a strong selection rule for the conservation of the quantum number associated to one of the elliptic hyperangles.
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