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The band calculation scheme for $f$ electron compounds is developed on the basis of the dynamical mean field theory (DMFT) and the LMTO method. The auxiliary impurity problem is solved by a method named as NCA$f^{2}$v', which includes the correct exchange process of the $f^{1} \to f^{2}$ virtual excitation as the vertex correction to the non-crossing approximation (NCA) for the $f^{1} \to f^{0}$ fluctuation. This method leads to the correct magnitude of the Kondo temperature, $T_{\rm K}$, and makes it possible to carry out quantitative DMFT calculation including the crystalline field (CF) and the spin-orbit (SO) splitting of the self-energy. The magnetic excitation spectra are also calculated to estimate $T_{\rm K}$. It is applied to Ce metal and CeSb at T=300 K as the first step. In Ce metal, the hybridization intensity (HI) just below the Fermi energy is reduced in the DMFT band. The photo-emission spectra (PES) have a conspicuous SO side peak, similar to that of experiments. $T_{\rm K}$ is estimated to be about 70 K in $\gamma$-Ce, while to be about 1700 K in $\alpha$-Ce. In CeSb, the double-peak-like structure of PES is reproduced. In addition, $T_{\rm K}$ which is not so low is obtained because HI is enhanced just at the Fermi energy in the DMFT band., Comment: 30pages, 18 figures

We propose the pf+pd mixing model for CeSb to explain the stability of the ferromagnetic double layer structure in the magnetic ordering. The pd mixing causes the saddle type singular points, neighboring the $\Delta$ axis, for the bands which gain energy through the pf hybridization with the occupied f state. The peak of the density of states due to this combined effect of the pf mixing and the pd mixing enhances the stability of the double layer structure. The same combined effect also causes the saddle type singular points in the joint density of states of the optical transition. The peak structure of the magneto-optical spectra which has been observed in experiments is explained by the present model., Comment: 9 pages, 14 figures

We investigate the non-Fermi-liquid (NFL) behavior of the impurity Anderson model (IAM) with non-Kramers doublet ground state of the f$^2$ configuration under the tetragonal crystalline electric field (CEF). The low energy spectrum is explained by a combination of the NFL and the local-Fermi-liquid parts which are independent with each other. The NFL part of the spectrum has the same form to that of two-channel-Kondo model (TCKM). We have a parameter range that the IAM shows the $- \ln T$ divergence of the magnetic susceptibility together with the positive magneto resistance. We point out a possibility that the anomalous properties of U$_x$Th$_{1-x}$Ru$_2$Si$_2$ including the decreasing resistivity with decreasing temperature can be explained by the NFL scenario of the TCKM type. We also investigate an effect of the lowering of the crystal symmetry. It breaks the NFL behavior at around the temperature, $\delta /10$, where $\delta$ is the orthorhombic CEF splitting. The NFL behavior is still expected above the temperature, $\delta/10$., Comment: 25 pages, 12 figures

The resistivity for an extended two channel Anderson model is calculated. When the temperature decreases, it decreases logarithmically, and has T^1/2 anomaly at very low temperatures, as seen in some dilute U alloys. The single-particle and the spin excitation spectra are also calculated., Comment: 4 pages, LaTeX, epsf.sty 6 PostScript figures

Particle-hole symmetry breaking perturbation in two-channel pseudospin Kondo problem is studied by the numerical renormalization-group method. It is shown that the repulsion between conduction electrons at the impurity site and the single particle potential are the relevant perturbations against the conventional non-Fermi liquid fixed point. Although the repulsion (potential) with realistic strength prevents the overscreening of pseudospin, it induces in turn a {\it real spin}, which is also overscreened again. Thus the {\it real spin} susceptibility becomes anomalous contrary to the conventional two-channel Kondo problem., Comment: 4 pages (ReVTeX Ver. 3.0), 6 figures (available on request)