def UJ_to_UdJH(U, J):
    """
    Given Kanamori :math:`U` and :math:`J`, return :math:`U_d` and :math:`J_H`,
    for :math:`t2g`-orbitals.

    Parameters
    ----------
    U: float
        Coulomb interaction :math:`U`.
    J: float
        Hund's coupling :math:`J`.

    Returns
    -------
    Ud: float
        Coulomb interaction :math:`U_d`.
    JH: float
        Hund's coupling :math:`J_{H}`.
    """
    F2 = J / (3.0 / 49.0 + 20 * 0.625 / 441.0)
    F4 = 0.625 * F2
    JH = (F2 + F4) / 14.0
    Ud = U - 4.0 / 49.0 * (F2 + F4)
    return Ud, JH
