def eta(z, x, beta):
    """
    Eq. (6) from Ref[1] (coeffient of alpha)
    Note that 'x' here corresponds to 'chi = x/rho', 
    and 'z' here corresponds to 'xi = z/2/rho' in the paper. 
    """
    return -6 * z / beta**2 / (1+x)