Elastic anomaly of heavy fermion systems in a crystalline field

An elastic anomaly, observed in the heavy fermi liquid state of Ce alloys (for example, CeCu$_6$ and CeTe), is analyzed by using the infinite-$U$ Anderson lattice model. The four atomic energy levels are assumed for f-electrons. Two of them are mutually degenerate. A small crystalline splitting $2\Delta$ is assumed between two energy levels. The fourfold degenerate conduction bands are also considered in the model. We solve the model using the mean field approximation to slave bosons, changing the Fermi energy in order to keep the total electron number constant. The nonzero value of the mean field of the slave bosons persists over the temperatures much higher than the Kondo temperature. This is the effect of the constant electron number. Next, the linear susceptibility with respect to $\Delta$ is calculated in order to obtain the renomalized elastic constant. The resulting temperature dependence of the constant shows the downward dip. We point out the relation of our finding with the experimental data.