Gasparameter

Gasparameter is a dimensionless quantity used in the study of gases to quantify the degree of dilution and the relevance of interparticle interactions. In many contexts it is defined as n a^3, where n is the number density (particles per unit volume) and a is an effective short-range length scale characterizing interactions (often the s-wave scattering length in quantum gases or the hard-sphere diameter in classical models). In some classical treatments of hard-sphere gases, a similar form is written as n d^3 with d the particle diameter. A small value (much less than 1) indicates a dilute gas in which two-body collisions are the primary source of non-ideality, and higher-order corrections are small.

In quantum gases, the parameter na^3 plays a central role: remaining well below unity justifies mean-field approaches and the use of dilute-gas theories, including the Gross-Pitaevskii equation for Bose gases and perturbative treatments of interactions. The same idea appears in virial expansions of the equation of state, where deviations from ideal gas behavior scale with powers of na^3.

An alternative but related quantity in quantum statistical mechanics is the phase-space density nλ^3, where λ is the thermal de Broglie wavelength. When nλ^3 ≈ 1, quantum statistics become important and degenerate behavior emerges.

Calculation example: for a gas with density n = 10^20 m^-3 and an effective interaction length a = 1×10^-9 m, the gas parameter na^3 equals 10^20 × (1×10^-9)^3 = 10^-7, indicating a highly dilute regime.