Close-coupling calculations are performed on the photodetachments of the me
tastable nsnp(2) P-4 states of the negative beryllium (n = 2), magnesium (n
= 3), and calcium (n = 4) ions by using the R-matrix method. The calculati
ons are carried out with the consideration of excitations of one electron f
rom core. The results show that this effect is much more important for Ca-
than for Be- and Mg-. For Be-, the total and partial cross sections an obta
ined from the threshold to 3 photon energy of 0.5 Ry. The calculated total
cross section exhibits two P-4(o) Feshbach resonances and one D-4(o) shape
resonance. Close agreement is found with the available theoretical calculat
ions and the only experimental datum of Pegg and co-workers [Phys. Rev. A 5
0, 3861 (1993)]. For the Ca- and Mg- ions, the total and partial cross sect
ions are calculated from the threshold to a photon energy of 0.25 Ry. For t
he Ca- ion, the resonances are found for both P-4(o) and D-4(o) symmetries
just below the D-3 threshold. For the Mg- ion, only a P-4(o) resonance is p
redicted. No rapid increase associated with the opening of the 4s5s (3) cha
nnel is found in the total cross section of Ca-. The rapid increase of the
photodetachment cross section of Ca- in the experiment by Hanstorp et al. [
D. Hanstorp et al., Phys. Rev. Leu. 63, 368 (1989)] should not be attribute
d to the Ca-(4s4p(2) P-4) + hv --> Ca(4s5s S-3) + kp ionization process. Th
is result is consistent with the conclusion of Petrunin and co-workers [Phy
s. Rev. Lett. 76, 744 (1996)] that there was no Ca- (4s4p(2) P-4) ions obse
rved by Hanstorp et al.