@staticmethod
def d_alpha_dr(r, sigma0, r_core):
    """
        radial derivatives of the radial deflection angle

        :param r: radius (angular scale)
        :param sigma0: convergence in the core
        :param r_core: core radius
        :return: dalpha/dr
        """
    return 2 * sigma0 * ((1 + (r / r_core) ** 2) ** (-3.0 / 2) - (r_core /
        r) ** 2 * (1 - (1 + (r / r_core) ** 2) ** (-1.0 / 2)))
