Study of intermediate valence by the time-dependent collision approach

An approximation method has been worked out for studying intermediate-valence systems by the time-dependent collision approach of Lal [Phys. Rev. B 27, 2535 (1983)]. A practical expression for the density operator of the intermediate-valence state has been obtained which includes distortion effects which are calculated in terms of the radial wave packets of the ($4f$ or $5d$-band) electrons. Matrix elements of the density operator for the transitions $f\to f$ and $f\to d$ are calculated and normalized properly to yield the value of the $f$-state occupation and the collision-generated hybridization. It is found that this hybridization assumes a maximum value when the $f$-state energy is equal to the Fermi energy. It is also found that the collision-generated hybridization is significantly weaker than the Coulomb interaction between the $4f$ electron and the band electron.