Three-body force effect on off-shell mass operator and spectral functions in nuclear matter

Within the framework of the Brueckner theory, the off-shell behaviors of the mass operator $M(k,\omega)=V(k,\omega)+iW(k,\omega)$, i.e., its dependence upon the momentum $k$ and upon the nucleon frequency $\omega$, are investigated by including nuclear three-body force (TBF). The first two terms of the hole-line expansion of the mass operator are taken into account. The TBF effects on their off-shell properties are discussed. A comparison is made between the on-shell and off-shell values of $M_{1}$. The nucleon spectral function and nucleon momentum distribution are also calculated, and the calculation shows that they are hardly affected by the TBF effect at the saturation density. At a high density two times greater than the saturation density, inclusion of the TBF may lead to a visible effect on the spectral function and may enhance the depletion of the hole states.