An analytical expression of the angular correlation function of a pair of Lyman-$\alpha$ photons in the photodissociation of a hydrogen molecule is derived theoretically in a manner based on both atomic and molecular physics and quantum optics. The angular correlation function turns out to be expressed in terms of cosine (sine) functions of four angular variables of detectors with five coefficients. The angular correlation function is expanded in terms of the spherical harmonics for investigating which terms are involved, and we discuss the reason why they are involved. Interesting features are revealed in the expansion. We then search for a special detector arrangement where the angular-dependent terms vanish in the angular correlation function expressed in terms of the spherical harmonics. It turns out that no such detector arrangement in fact exists, but there is a special pair of detector arrangements where the angular-dependent terms vanish in the summation of two values of the angular correlation function expressed in terms of the spherical harmonics. We refer to such a pair of detector arrangements as a magic pair.

中文翻译：

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氢分子光解中两个Lyman-α光子角相关函数的解析表达式

一对Lyman-角相关函数的解析表达式$\alpha$ 氢分子光解中的光子在理论上以基于原子和分子物理学以及量子光学的方式推导出来。结果证明，角相关函数可以用具有五个系数的探测器的四个角变量的余弦（正弦）函数来表示。角相关函数在球谐函数方面展开以研究涉及哪些项，并讨论涉及它们的原因。扩展中揭示了有趣的功能。然后我们寻找一种特殊的探测器布置，其中角相关项在以球谐函数表示的角相关函数中消失。事实证明，实际上不存在这样的探测器布置，但是有一对特殊的探测器布置，其中角相关项在以球谐函数表示的角相关函数的两个值的总和中消失。我们将这样一对探测器布置称为魔术对。