This article studies the photodetachment of a single electron anion near an attractive center. Both the differential and total photodetachment cross section are analysed. We obtain the electron flux crossing through a spherical detector centered at t
he force center using the semiclassical approximation. The closed-orbit theory gives the total cross section which contains a smooth background and an oscillatory part. Concrete calculations and discussions are carried out for two types of wave source: the $s$- and $p_z$-wave source. Photodetachment processes for three conditions are compared: an anion near an attractive center, near a repulsive center and in a homogeneous electric field.
