  This paper investigates two conjectures for calculating the density
dependence of the density-scaling exponent of a single-component,
pair-potential liquid with strong virial potential-energy correlations. The
first conjecture gives an analytical expression for the density-scaling
exponent directly in terms of the pair potential. The second conjecture is a
refined version of this, which involves the most likely nearest-neighbor
distance determined from the pair-correlation function. The two conjectures for
the density-scaling exponent are tested by simulations of three systems, one of
which is the standard Lennard-Jones liquid. While both expressions give
qualitatively correct results, the second expression is more accurate.
