FINITE-FIELD MANY-BODY-PERTURBATION-THEORY CALCULATION OF THE STATIC HYPERPOLARIZABILITIES AND POLARIZABILITIES OF MG, AL+, AND CA

The dipole-dipole-quadrupole (B) and second dipole (gamma) hyperpolarizabilities and the dipole (alpha-1) and quadrupole (alpha-2) polarizabilities are calculated for the ground states of the magnesium and calcium atoms and the aluminum cation. The results are based on finite-field fourth-order many-body perturbation theory using a finite-field self-consistent-field wave function as the zeroth-order wave function. Our fourth-order results are alpha-1 = 71.7e2a0(2)EH-1, alpha-2 = 809e2a0(4)EH-1, B = (-7.75 x 10(3))e3a0(4)EH-2, and gamma = (1.02 x 10(5))e4a0(4)EH-3 for Mg; alpha-1 = 24.2e2a0(2)EH-1, alpha-2 = 124e2a0(4)EH-1, B = -642e3a0(4)EH-2, and gamma = (2.37 x 10(3))e4a0(4)EH-3 for Al+; and alpha-1 = 157e2a0(2)EH-1, alpha-2 = (3.02 x 10(3))e2a0(4)EH-1, B = (-3.29 x 10(4))e3a0(4)EH-2, and gamma = (3.83 x 10(5))e4a0(4)EH-3 for Ca.