Comment on the spherical quantum dot with interaction effects

A series of studies of the lowest 3P state of a model of a two-electron quantum dot, that consists of a finite spherical well [see, for example, Sivakami et al., Int. J. Mod. Phys. B 24, 5561 (2010)], exhibited a range of interesting applications. However, the quantity of central interest, the expectation value of the interelectronic repulsion (that must be nonnegative) was calculated erroneously, yielding negative values. In the present note, this expectation value is evaluated with respect to the exact first-order perturbation theory wavefunction (the scheme considered in the papers cited above) as well as with respect to a minimal basis set Gaussian variational wavefunction. Reasonable agreement between the two schemes is confirmed, both yielding the expected positive values of the expectation value of the interelectronic repulsion, over the whole range of the relevant parameters.