Module potential 

Screened-Coulomb interatomic potentials.

The interaction of two atoms with atomic numbers Z1, Z2 at separation r is written

V(r) = Z1 Z2 e^2 / (4 pi eps0 r) * phi(r / a)

where phi is a universal screening function (phi(0) = 1, decreasing to 0) and a a screening length that depends on Z1 and Z2. Everything in the scattering code is expressed in the reduced variables x = r / a and eps = a E_cm / (Z1 Z2 e^2 / (4 pi eps0)), in which phi is the only input; the screening length only converts to and from SI.

Coefficients follow the cited papers. The status of each set is recorded in its docs/data-provenance.md row. The Firsov and Lindhard screening lengths have been checked against the primary papers (page references below). The ZBL, Kr-C and Moliere screening sets have been cross-checked against an independent MIT-licensed implementation. The Lenz-Jensen set agrees with a textbook tabulation, but not with a primary source. The universal-length prefactor has been seen only in secondary sources.

Structs

Potential

A screened-Coulomb pair potential for a specific (Z1, Z2).

Enums

Screening

Screening function phi(x), x = r / a.

ScreeningLength

Screening length a(Z1, Z2).

Functions

thomas_fermi_constant

The Thomas-Fermi constant (9 pi^2 / 128)^(1/3) = 0.8853, which multiplies the Bohr radius in the Firsov and Lindhard lengths. The closed form is Firsov’s (Sov. Phys. JETP 6, 534 (1958), p. 535), and the rounded value 0.8853 is the one printed by Lindhard, Scharff and Schiott (1963), p. 8.