The quasiparticle Tamm-Dancoff approximation has been applied to a calculation of the low-lying states in single-closed-shell nuclei with N = 82 neutrons. A central force of Gaussian shape with spin exchange is taken as the residual nucleon-nucleon interaction. An extensive study is made of the resemblance with the realistic Elliott interaction. The singleparticle energies are determined by the iterative inverse-gap-equation method. The Hamiltonian matrix is diagonalized in a one- and three-quasiparticle space after elimination of spurious states. Transition rates, half-lifes, magnetic dipole moments and electric quadrupole moments are calculated, discussed in detail and compared with results obtained with the realistic Elliott interaction and the experimental data. The evaluated spectroseopic factors are studied and compared with the experimental one-nucleon transfer data with good quantitative agreement.