Magnetic and electric dipole transitions between levels of the 4fx configuration perturbed by a static crystalline field are treated. The expression obtained for the pure‐electronic electric‐dipole transition probability involves matrix elements of an even‐order unit tensor between the two 4fx states involved in the transition. The contributions to the transition probability from interactions, via the crystalline field, with the nd 94fx−1, 4fx−1 nd, 4fx−1 ng configurations are shown to add linearly, in such a manner as to multiply each odd k crystal‐field parameter Ak q by a constant. If ``J mixing'' in the 4fx configuration is neglected ΔJ between the upper and lower 4fx levels is restricted to six units or less. If ``L mixing'' is neglected then ΔL is also restricted to six units or less. Application is made to the fluorescence spectra of PrCl3 and EuCl3. Many of the missing and weak transitions are explained.

Intensities of Crystal Spectra of Rare‐Earth Ions

We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

The transition metal dichalcogenides are about 60 in number. Two-thirds of these assume layer structures. Crystals of such materials can be cleaved down to less than 1000 A and are then transparent in the region of direct band-to-band transitions. The transmission spectra of the family have been correlated group by group with the wide range of electrical and structural data available to yield useful working band models that are in accord with a molecular orbital approach. Several special topics have arisen; these include exciton screening, d-band formation, and the metal/insulator transition; also magnetism and superconductivity in such compounds. High pressure work seems to offer the possibility for testing the recent theory of excitonic insulators.

The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties

The demand for compact ultraviolet laser devices is increasing, as they are essential in applications such as optical storage, photocatalysis, sterilization, ophthalmic surgery and nanosurgery. Many researchers are devoting considerable effort to finding materials with larger bandgaps than that of GaN. Here we show that hexagonal boron nitride (hBN) is a promising material for such laser devices because it has a direct bandgap in the ultraviolet region. We obtained a pure hBN single crystal under high-pressure and high-temperature conditions, which shows a dominant luminescence peak and a series of s-like exciton absorption bands around 215 nm, proving it to be a direct-bandgap material. Evidence for room-temperature ultraviolet lasing at 215 nm by accelerated electron excitation is provided by the enhancement and narrowing of the longitudinal mode, threshold behaviour of the excitation current dependence of the emission intensity, and a far-field pattern of the transverse mode.

Direct-bandgap properties and evidence for ultraviolet lasing of hexagonal boron nitride single crystal.

We report experiments and theory on the effects of electric fields on the optical absorption near the band edge in GaAs/AlGaAs quantum-well structures. We find distinct physical effects for fields parallel and perpendicular to the quantum-well layers. In both cases, we observe large changes in the absorption near the exciton peaks. In the parallel-field case, the excitons broaden with field, disappearing at fields \ensuremath{\sim}${10}^{4}$ V/cm; this behavior is in qualitative agreement with previous theory and in order-of-magnitude agreement with direct theoretical calculations of field ionization rates reported in this paper. This behavior is also qualitatively similar to that seen with three-dimensional semiconductors. For the perpendicular-field case, we see shifts of the exciton peaks to lower energies by up to 2.5 times the zero-field binding energy with the excitons remaining resolved at up to \ensuremath{\sim}${10}^{5}$ V/cm: This behavior is qualitatively different from that of bulk semiconductors and is explained through a mechanism previously briefly described by us [D. A. B. Miller et al., Phys. Rev. Lett. 53, 2173 (1984)] called the quantum-confined Stark effect. In this mechanism the quantum confinement of carriers inhibits the exciton field ionization. To support this mechanism we present detailed calculations of the shift of exciton peaks including (i) exact solutions for single particles in infinite wells, (ii) tunneling resonance calculations for finite wells, and (iii) variational calculations of exciton binding energy in a field. We also calculate the tunneling lifetimes of particles in the wells to check the inhibition of field ionization. The calculations are performed using both the 85:15 split of band-gap discontinuity between conduction and valence bands and the recently proposed 57:43 split. Although the detailed calculations differ in the two cases, the overall shift of the exciton peaks is not very sensitive to split ratio. We find excellent agreement with experiment with no fitted parameters.

Electric field dependence of optical absorption near the band gap of quantum-well structures.

The secular determinants obtained in the previous paper are solved for the energy levels which are important in the absorption spectra of the normal complex ions, leaving the crystalline field strength as a parameter The values of B and C (Racah's parameters) there needed are determined from the observed spectra of free ions or in some cases by extrapolation The f -values of the transitions which connect the energy levels calculated are estimated and compared with the observed intensities The difference of the spectral width among absorption bands and lines is also considered using the energy diagram obtained Following the assignments determined by the above considerations, the calculated positions of lines and bands are rather in good agreement with the experimental data in divalent ions [MX 6 ] 2+ (M=Cr, Mn, Fe, Co, Ni), when we adjust the crystalline field parameter D q suitably In trivalent ions [MX 6 ] 3+ (M=Ti, V, Cr, Mn, Fe), it is necessary besides the adjustment of D q to use smaller values 

On the Absorption Spectra of Complex Ions II

By using the effective-mass theory for exciton, the allowed and forbidden direct interband transitions in extremely anisotropic semiconductors are discussed. In this case, the problem is reduced to solving the Schrodinger equation for a hypothetical two-dimensional hydrogen atom. The bound and unbound solutions of the equation are obtained, and the absorption intensities in the discrete, quasi-continuous, and continuous spectral regions are calculated. It is shown that, in the allowed transitions, a small peak may appear just above the absorption edge because of the Coulomb interaction between an excited electron and a hole. This result is compared with the experimental curves of the absorption in layer-type semiconductors, CaS, GaSe, and GaTe.

Interband Optical Transitions in Extremely Anisotropic Semiconductors. I. Bound and Unbound Exciton Absorption

The secular determinants obtained in the previous paper are solved for the energy levels which are important in the absorption spectra of the normal complex ions, leaving the crystalline field strength as a parameter. The values of B and C (Racah's parameters) there needed are determined from the observed spectra of free ions or in some cases by extrapolation. The f -values of the transitions which connect the energy levels calculated are estimated and compared with the observed intensities. The difference of the spectral width among absorption bands and lines is also considered using the energy diagram obtained. Following the assignments determined by the above considerations, the calculated positions of lines and bands are rather in good agreement with the experimental data in divalent ions [MX 6 ] 2+ (M=Cr, Mn, Fe, Co, Ni), when we adjust the crystalline field parameter D q suitably. In trivalent ions [MX 6 ] 3+ (M=Ti, V, Cr, Mn, Fe), it is necessary besides the adjustment of D q to use smaller values ...

On the absorption spectra of complex ions. II

In the frame-work of the crystalline field theory, the excited states of Cr 3+ in Al 2 O 3 and the optical transitions to these states are studied taking into account the effect of trigonal field and spin-orbit interaction. Initial splittings and optical anisotropies of the broad band (transitions to quartet states) and the sharp lines (transitions to doublet states) are examined. For the sharp lines, the Zeeman effect is also examined and the Zeeman patterns are predicted. Comparing these theoretical results with those of the experimental ones given in Part B, the assignments of U , Y bands and R 1 , R 2 , B 1 , B 2 lines have been established. It is shown that the g -shifts of the excited doublets observed in the Zeeman patterns can also be explained under such assignments. It is also shown that the experimental data of the optical absorption can be reasonably connected to those of the paramagnetic resonance absorption.

Satoru Sugano

Papers

On the Absorption Spectra of Complex Ions II

Interband Optical Transitions in Extremely Anisotropic Semiconductors. I. Bound and Unbound Exciton Absorption

On the absorption spectra of complex ions. II

Absorption Spectra of Cr3+ in Al2O3 Part A. Theoretical Studies of the Absorption Bands and Lines

Magnon-Induced Electric Dipole Transition Moment