A shortcut to quantum-mechanical absolute scattering phase-shift computations in van der Waals systems

ABSTRACT

We discuss the advantages of a single-valued function (and related formula) for the absolute definition and computation of scattering phase shifts in spherically symmetric van der Waals potentials. Although the expression, as such, is known since the 2000s [K. Chadan, R. Kobayashi, and T. Kobayashi, J. Math. Phys. 42, 4031 (2001)], only little numerical evidence of its effectiveness has been available so far. Our effort, here, is to give this device the recognition it deserves and to make it more widely known as an alternative to standard methods. This is all the more interesting as in the standard approaches the access to absolute is not straightforward but needs additional operations to be performed. We show how the formula can be derived, as a consequence of variable-phase approaches from the two broadly accepted methods for , and compare its performance with these methods. He–He and two of its keynote thermophysical properties, namely, the ⁴He and ³He second virial and acoustic virial coefficients are being studied for the purpose. The use of absolute is mandatory for those coefficients. Other important points related to the concept of phase function and its connection with Volterra equation are given in Supplementary material.

GRAPHICAL ABSTRACT

KEYWORDS:

• Thermophysical and transport properties
• elastic scattering
• atomic collisions
• helium
• van der Waals interactions

Acknowledgements

We wish to acknowledge thesis fellowship support from the French Ministry of Education to one of us (HP).

Disclosure statement

No potential conflict of interest was reported by the authors.