Analytical expression for the angular correlation function of two Lyman- α photons in the photodissociation of hydrogen molecules

Abstract

An analytical expression of the angular correlation function of a pair of Lyman-$\ensuremath{\alpha}$ 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.