Theoretical binding energies have been obtained for the metastable np(3) S-
4(o) states in the alkaline-earth sequence using a B-spline configuration-i
nteraction approach. The results agree with available experimental and theo
retical data within 5 meV for Be- and within 10 meV for Mg-. The binding en
ergies of the p(3) S-4(o) state in Mg-, Ca-, and Sr- are larger than the on
e in Be- by roughly 250 meV due to the stronger interactions with the d(2)p
configurations. For Ca-, the S-4(o) binding energy is determined to be 555
.5 meV, including a contribution of - 70 meV due to dielectronic cole polar
ization. For Sr- the S-4(o) binding energy is 557.9 meV, including a decrea
se of only 6 meV due to dielectronic core polarization. This behavior for t
he S-4(o) states in Ca- and Sr- is ascribed to the different neutral-atom s
tates to which the S-4(o) states are bound. [S1050-2947(99)02402-6].