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Finite-energy sum rules (FESR) are used to study the $u$-channel baryon Regge exchanges in $\ensuremath{\pi}N$ and $\mathrm{KN}$ elastic scattering. The low-energy integrals over the $\overline{N}N\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ and $\overline{N}N\ensuremath{\rightarrow}\overline{K}K$ cuts are evaluated by resonance saturation, including $\ensuremath{\sigma}({0}^{+})$, $\ensuremath{\rho}({1}^{\ensuremath{-}})$, $\ensuremath{\omega}({1}^{\ensuremath{-}})$, ${A}_{2}({2}^{+})$, ${f}^{0}({2}^{+})$, $\ensuremath{\rho}({3}^{\ensuremath{-}})$, and $\ensuremath{\omega}({3}^{\ensuremath{-}})$ meson poles. The integral over the $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\pi}N$ cut is evaluated in both the phase-shift and the resonance-dominance approximation, whereas resonance saturation only is used for the $\overline{K}N\ensuremath{\rightarrow}\overline{K}N$ and $\mathrm{KN}\ensuremath{\rightarrow}\mathrm{KN}$ discontinuities. The FESR integrals thus obtained are in reasonable agreement with existing Regge-exchange fits to high-energy scattering data. In particular, the following interesting results are obtained from the FESR: (i) The ${N}_{\ensuremath{\alpha}}$ and ${\ensuremath{\Lambda}}_{\ensuremath{\alpha}}$ exchange amplitudes change sign at $u$ values appropriate to $\ensuremath{\alpha}=\ensuremath{-}\frac{1}{2}$, as required by conventional Regge theory. (ii) The spin dependence of the ${N}_{\ensuremath{\alpha}}$ and ${\ensuremath{\Lambda}}_{\ensuremath{\alpha}}$ exchange amplitudes is predicted in the scattering region. (iii) The $\ensuremath{\Lambda}$ exchange contributions dominate over $\ensuremath{\Sigma}$ exchange contributions in $\mathrm{KN}$ backward elastic scattering.

Microscopic calculation of barrier free energy of Josephson junctions, discussing validity of tunneling Hamiltonian method

A model for high-energy $\ensuremath{\pi}p$, $\mathrm{pp}$, and $\overline{p}p$ elastic scattering at small momentum transfer is presented, based on the assumed dominance of a few Regge poles in the crossed channel. For $\ensuremath{\pi}p$ scattering these are the $P$, ${P}^{\ensuremath{'}}$, and $\ensuremath{\rho}$ poles; for $\mathrm{pp}$ and $\overline{p}p$, ignoring isospin dependence, they are $P$, ${P}^{\ensuremath{'}}$, and $\ensuremath{\omega}$. This model fits a wide variety of data, including the differential cross sections that shrink for $\mathrm{pp}$ but not for $\ensuremath{\pi}p$ or $\overline{p}p$, recent results from Brookhaven on total cross sections and ratios of the real to imaginary parts of the forward scattering amplitude, and also recent $\ensuremath{\pi}p$ and $\mathrm{pp}$ polarization results, but it gives zero polarization for $\ensuremath{\pi}p$ charge-exchange scattering. (Although the latter disagrees with experiment, additions to the model to correct this insufficiency would affect the other results but little.) The factorization property of Regge poles is tested by these fits to data for the $P$ and ${P}^{\ensuremath{'}}$ couplings.

Koopmans' theorem states that if the wave function of a many-electron system is approximated by a Slater determinant of Hartree-Fock one-electron wave functions, with one-electron energies defined as the difference in energy of (N + 1)- and N-particle systems, then these one-electron energies are given by the expectation value of the HartreeFock Hamiltonian with respect to the one-electron wave functions. Koopmans' theorem is generalized to include correlation effects by using Hubbard's expression for the total energy of a free-electron gas. The resulting oneelectron Hamiltonian contains in first-order screened exchange. Hubbard's lowest polarization diagram gives, in addition, part of the screened second-order Coulomb interactions, which is small for metallic densities. Collective terms are also obtained. Comparison with the Bohm-Pines Hamiltonian shows a one-to-one correspondence, but with different cutoff functions in each term. Following Hubbard, -the method to include the effects of a periodic potential to first order is extended. The resulting one-electron Hamiltonian provides a convenient and accurate basis for self consistent energy band calculations including exchange and correlation in metals and semiconductors. (auth)

A general method is described for calculating lattice deformation energies in covalent structures. The formulas are presented explicitly for harmonic energies in diamond-type crystals. The theory differs intrinsically from linear screening theories because of the inclusion of bond-stretching terms. These are calculated using a dynamical covalent sum rule. The results show that bond stretching leads to large bond-bond interaction energies that are similar to those in a nearest-neighbor classical shell model. The theory can be used to infer the covalent screening function from lattice vibration spectra measured by inelastic neutron scattering.

An a posteriori theory is developed for the structural energy of covalent crystals. The microscopic theory is based on ionic pseudopotentials and valence dielectric screening. The theory explains the difference between empirical pseudopotential form factors derived from the optical spectra of semiconductors and the metallic form factors calculated from free-ion term values by Animalu and Heine. A byproduct of the theory, which utilizes Penn's model isotropic semiconductor dielectric function, is a relation between the covalent bonding charge and the macroscopic dielectric constant. In self-consistent form the theory is an example of the "bootstrap" approach, applied here to treat the effect of covalent bonding on the ground-state energy of the valence electron gas. It is argued that the axiomatic character of the covalent theory is to be expected on symmetry grounds, and it is shown that the theory is superior to a nonlinear multiple-scattering theory based on the free-electron dielectric function. The extension of the theory to III---V and II---VI semiconductors is described briefly. The theory may be used to calculate elastic and macroscopic dielectric properties of covalent crystals starting only from ionic pseudopotential form factors.

Energy levels and interband oscillator strengths of antimony calculated in Brillouin zone by pseudopotential method, predicting polarization effects and spin-orbit splittings

A wide range of experimental data now indicates that uv structure depends primarily on crystal structure and only secondarily on atomic composition. We assign characteristic structure of ultraviolet absorption to interband transitions at symmetry points of the Brillouin zone. The crystal structures that are discussed are zincblende and wurtzite. The experimental information required for comparison with theoretical calculations is discussed, with special emphasis laid on the importance of polarization studies of the reflectance of hexagonal crystals.

The general theory of covalent bonding developed previously is extended to heteropolar crystals. In diatomic crystals the theory depends on two parameters; an energy gap for each atom, or an energy gap for the medium and a polarizability parameter $\ensuremath{\eta}$. The latter can be determined by comparison with empirical pseudopotential form factors; the value obtained for GaAs and ZnSe which brings the form factors of the latter into agreement with the ion-core form factors of Animalu and Heine is $\ensuremath{\eta}=\ensuremath{-}0.05\ifmmode\pm\else\textpm\fi{}0.05$. This polarizability parameter can be used to estimate the effective charge ${{e}_{c}}^{*}$ defined by Callen, which describes the splitting of longitudinal and transverse optic modes of vibration at $q=0$. The result in GaAs is $\frac{{{e}_{c}}^{*}}{e}=0.14\ifmmode\pm\else\textpm\fi{}0.04$, in rough agreement with the experimental value of 0.20\ifmmode\pm\else\textpm\fi{}0.03. The experimental values for ${{e}_{c}}^{*}$ may be used to estimate the gap parameters for each atom when complete data are available.

Recently G\"ottlicher and W\"olfel have measured x-ray scattering factors from diamond powder that differ appreciably from the older values of Brill. Because scattering from the $1s$ core is small, information about the crystal covalent band can be obtained. In the Brillouin zone theory of crystal wave functions the valence charge density varies throughout the valence band. Free-atom approximations to the diamond charge density replace the $s{p}^{3}$ crystal wave functions at k=0 by atomic $s{p}^{3}$ charge densities. This approximation is insufficient to explain covalent bonding effects, such as the "forbidden" reflection ${F}_{222}$. We have examined crystal charge densities throughout the valence band. We find that there are two important mechanisms which affect the valence charge density. The first is a linear response to the ionic potentials. This may be called dielectric screening; it is dominant in metals, and it gives no contribution to ${F}_{222}$. The second is nonlinear in the ionic potentials, and may be called crystal hybridization; it is responsible for covalent effects in the charge density, and it makes no contribution to ${F}_{220}$. The contributions of both mechanisms to ${F}_{111}$, ${F}_{220}$, ${F}_{222}$, ${F}_{311}$, and ${F}_{400}$ have been computed. Surprisingly, the results are in good agreement with the older data of Brill and simple models of the covalent bond, while significant disagreement with G\"ottlicher and W\"olfel's measurements is found.

Exciton and impurity states in optical absorption spectra of nonmetallic crystals in pseudopotential theory

A proof is given that the vector interaction of neutral vector mesons and fermions can be renormalized, to replace a fallacious proof by Matthews. A new interaction representation, formally different from the usual one, is used. The basic idea, not a new one, is that the objectionable part of the interaction can be identified with a certain scalar meson interaction, known to be illusory.

Infrared absorption in InSb near the absorption edge has been interpreted as the superposition of two indirect transitions requiring phonons of 100\ifmmode^\circ\else\textdegree\fi{} and 30\ifmmode^\circ\else\textdegree\fi{}, the former transition involving the smaller electronic energy gap. The first transition is consistent with a band scheme having electrons at the center of the zone and holes either at the corner of the zone or about halfway along the [1,1,1] line. The other transition may indicate a second hole with an energy gap about 0.025 ev larger than that of the first.

It has been suggested that $u$-channel exchanges may explain the structure versus energy of total cross sections and forward amplitudes at fixed $t$, and an application to $\ensuremath{\pi}N$ scattering has been made. We remark that this idea cannot be generally valid, since it does not work in many reactions, such as ${K}^{\ifmmode\pm\else\textpm\fi{}}p$ scattering. Hence, the $\ensuremath{\pi}N$ application seems implausible.