  A simple approximation to shell model is proposed in which the low energy
excitation spectra corresponds to the identical nucleons occupying the same
single particle states where they preferred to form pairs for the ground
states. We call this approximation as nonzero angular momentum pairing shell
model. It not only reduces the dimensionality of the shell model but also
matches the number of low energy levels in experimental spectra for few cases
where exact shell model predicts many more states. The special focus has been
done to consider the realistic interaction derived from free nucleon-nucleon
scattering data to cope with the experimental spectra. The proposed
approximation to shell model has been applied to calculate the energy spectra
of O18 and Ni58 nuclei where only two neutrons occupy the valence states
outside the core. When compared with the experimental data, the results are
found to be encouraging. It is expected that results will be more pronounced if
the even-even nuclei with higher number of valence nucleons are considered.
