ANALYTICAL FORMULAS FOR THE 3RD-ORDER DIAMAGNETIC ENERGY OF A HYDROGEN-ATOM

Analytical expressions are presented for the third-order diamagnetic c orrections to the energy of nondegenerate hydrogen levels with arbitra ry principal quantum number n and the magnetic quantum number \m\ = n- 1,n-2,n-3. The leading term for the third-order energy correction for levels with high n is determined to be Delta E-(3)approximate to 3/128 n(16)B(6). Together with the well-known first- and second-order correc tions Delta E-(1)approximate to 1/gn(4)B(2) and Delta E-(2)approximate to-1/32n(10)B(4) it determines the upper and lower bounds for the lev el energy in field and also the range of magnetic fields where the fir st-and second-order perturbation theory terms are valid for calculatin g the Zeeman energy in hydrogenlike states of atoms.