import math


def pressure_delta ( density, r_cut ):
    """Calculates correction for Lennard-Jones pressure due to discontinuity in the potential at r_cut."""

    
    # density, r_cut, and the results, are in LJ units where sigma = 1, epsilon = 1
    sr3 = 1.0 / r_cut**3 
    return math.pi * (8.0/3.0) * ( sr3**3  - sr3 ) * density**2