Van der Waals interactions between two hydrogen atoms: The next orders

Van der Waals interactions between two hydrogen atoms: The next orders

Eric Cancès (1) , Rafaël Coyaud (2) , L. Ridgway Scott (3)

1 MATHERIALS - MATHematics for MatERIALS
2 MATHRISK - Mathematical Risk Handling
3 University of Chicago

We extend a method (E. Canc\`es and L.R. Scott, SIAM J. Math. Anal., 50, 2018, 381--410) to compute more terms in the asymptotic expansion of the van der Waals attraction between two hydrogen atoms. These terms are obtained by solving a set of modified Slater-Kirkwood partial differential equations. The accuracy of the method is demonstrated by numerical simulations and comparison with other methods from the literature. It is also shown that the scattering states of the hydrogen atom, that are the states associated with the continuous spectrum of the Hamiltonian, have a major contribution to the C$_6$ coefficient of the van der Waals expansion.

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Electrons fortement corrélés [cond-mat.str-el]; Physique Atomique [physics.atom-ph]

Eric Cancès, Rafaël Coyaud, L. Ridgway Scott. Van der Waals interactions between two hydrogen atoms: The next orders. 2020. ⟨hal-02894550⟩