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Binding of muonated hydrogen molecules and Born-Oppenheimer approximation revisited

Authors: Varandas, AJC; da Providencia, J; da Providencia, JP

Ref.: Can. J. Phys. 98(4), 379-384 (2020)

Abstract: The stability of four fermionic particles with unit charge, of which two are positively and two negatively charged, is discussed. Except for using the simplest approximation of a single Gaussian orbital per particle, the problem is exactly solved variationally by varying the masses to simulate molecular di-hydrogen, mono-muonated di-hydrogen, and di-muonated di-hydrogen. We illustrate the celebrated Born–Oppenheimer approximation 2 years after the occasion of its 90th anniversary. It is suggested that this method is valid only for di-hydrogen.

DOI: 10.1139/cjp-2019-0061