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A general expression for the imaginary part of the one-electron interband dielectric function of a solid in the presence of an electric field is derived. The result is valid for all regions of k-space and explicitly takes into account the variation of the dipole matrix element and effective mass throughout the Brillouin zone. Under certain approximations the finite electric field dielectric function reduces to the convolution of the zero field dielectric function with an Airy function. This result can be used in conjunction with band structure calculations which have already been done in order to predict the line shape of the electroreflectance spectra as a function of electric field. The convolution expression reduces further at non-degenerate critical points, and the forms for the four types of critical points are presented. In certain instances it is possible to unfold the convolution integral and obtain the zero field dielectric function from either the finite field dielectric constant or the electroreflectance data at isolated critical points. (Author)

Electric perturbations of the nuclear magnetic resonances of the ${\mathrm{Al}}^{27}$ nuclei in single-crystal aluminum oxide are discussed. Splittings of the quadrupole satellite resonance lines have been obtained using fields as high as 300 kV/cm. The splittings are caused by equal and opposite changes in the electric-field gradient tensor at crystallographic aluminum sites related to each other by inversion symmetry. Magnitudes and relative signs of the five independent $R$-tensor elements which completely describe the electrically induced shifts for the ${C}_{3}$ site symmetry of the aluminum nucleus have been determined by applying electric and magnetic fields in various crystallographic directions. These data are compared with similar data obtained earlier from electric shifts in the electron spin resonances of the ${\mathrm{Cr}}^{3+}$ ion in the same crystal.

Morphic effects are effects induced in a crystal by the lowering of its symmetry through the application of a generalized external force. In this paper we study the effects of static electric fields and of strains on the frequencies of localized vibration modes associated with substitutional impurity atoms in homo-polar crystals. It is shown that the splitting of the triple degeneracy of such modes when the impurity is at a site of cubic symmetry by the application of these generalized forces can yield information about the anharmonic forces, electric dipole moment, and electronic polarizability associated with the impurity atom.

Calculations of the imaginary part of the dielectric constant of an anisotropic solid in the region of a critical point are used to obtain the real part of the dielectric constant through Kramers-Kronig relations. Changes in the real and imaginary parts of the dielectric constant are expressed in closed form for all four types of critical points. Description of these changes can be made with only two functions. The effect of the finite extent of a band is investigated, and it is shown that previous calculations of the change in the imaginary part of the dielectric constant, based on bands of infinite extent, are valid as long as transitions are restricted to regions near the critical point. Closed-form expressions for the Lorentzian broadening of the changes in the dielectric constants are given in terms of Airy functions of complex argument.

Techniques are described which utilize the "print out effect" to obtain both the direction and velocity of photoelectrons in silver chloride crystals in an electric field. Hall mobility of the electrons is calculated from their change in direction produced by crossed electric and magnetic fields. Drift mobility of the electrons is obtained by measurement of their velocity in known electric fields. The value obtained for the Hall mobility ($R\ensuremath{\sigma}$) multiplied by $\frac{8}{3\ensuremath{\pi}}$ is 51 ${\mathrm{cm}}^{2}$/volt sec at 25\ifmmode^\circ\else\textdegree\fi{}C. The values obtained for the drift mobility are shown to be a function of temperature. A value of 49.5 ${\mathrm{cm}}^{2}$/volt sec was obtained at 25\ifmmode^\circ\else\textdegree\fi{}C, which is within experimental error of $(\frac{8}{3\ensuremath{\pi}})R\ensuremath{\sigma}$, indicating that acoustical scattering is the principal mechanism and that temporary trapping is unimportant. A summary of the behavior of conduction electrons in silver chloride, calculated from the results of these experiments, is included.

A situation can arise in semiconductors similar to the space-charge limited emission of electrons in vacuum. The theory of Shockley and Prim for this phenomenon has been extended to the high field case using the approximation that the drift velocity of the carriers is $v=\ensuremath{\mu}{(E{E}_{0})}^{\frac{1}{2}}$, where $\ensuremath{\mu}$ is the low field mobility, $E$ the electric field, and ${E}_{0}$ the "critical field." For this approximation the current density analogous to Child's law for a plane parallel diode is $J=\frac{(\frac{2}{3}){(\frac{5}{3})}^{\frac{3}{2}}K\ensuremath{\mu}{{E}_{0}}^{\frac{1}{2}}{{V}_{a}}^{\frac{3}{2}}}{{w}^{\frac{5}{2}}},$ where ${V}_{a}$ is the potential across a diode of thickness $w$ and $K$ is the dielectric constant in mks units. Good agreement between theory and experiment for hole flow in germanium at liquid air temperature has been obtained, using values of $\ensuremath{\mu}$ and ${E}_{0}$ obtained independently by Ryder.

It is shown that the loss of energy of a fast charged particle due to the ionization of the material through which it is passing is considerably affected by the density of the material. The effect is due to the alteration of the electric field of the passing particle by the electric polarization of the medium. A theory based on classical electrodynamics shows that by equal mass of material traversed, the loss is larger in a rarefied substance than in a condensed one. The application of these results to cosmic radiation problems is discussed especially in view of the possible explanation on this basis of part of the difference in the absorption of mesotrons in air and in condensed materials that is usually interpreted as evidence for a spontaneous decay of the mesotron.

The inverse piezoelectric effect of Rochelle salt has been studied by means of mechanical dilatometers. The dilatation of a crystal along a direction 45\ifmmode^\circ\else\textdegree\fi{} to the $b$ and $c$ axes and 90\ifmmode^\circ\else\textdegree\fi{} to the $a$ axis, caused by an electric field impressed in a given direction along the $a$ axis, has been found, in general, not to be the same as the dilatation caused by an equal field impressed in the opposite direction. This indicates a permanent electric polarization within the crystal. A prolonged application of voltage along the $a$ axis slowly changes this "permanent" polarization, which gives rise to an inverse piezoelectric fatigue effect, and is associated with the fatigue effect as observed by Valasek. Oscillograms showing the rate of deformation of a Rochelle salt crystal were taken. The forms of these curves, for small distortions of the crystal or small applied fields along the $a$ axis, are in approximate agreement with the exponential type as required by the theory of Schulwas-Sorokin and Posnov. The relaxation times varied from zero at the Curie points to a maximum approximately midway between the critical temperatures. The thermal expansion of Rochelle salt along the three crystallographic axes was determined through the upper critical temperature. No discontinuities were observed, but a change in the rate of expansion occurred at the Curie point for the $b$ and $c$ axes.

In a qualitative way the anomalous properties of Rochelle salt can be explained on the basis of four different theories: ($a$) on the dipole theory, ($b$) by assuming polymorphic transitions at the Curie points, ($c$) by postulating an anomalous piezoelectric effect, and ($d$) with an inter-action theory which assumes that the structure and the fundamental properties of the crystal have no unusual characteristics and which ascribes the observed anomalies to an accidental degeneration of the piezoelectric interaction between the elastic deformation and the electric polarization. The existence of a polymorphic transition at the upper Curie point is demonstrated in a new experiment and it is shown that this transition is a spontaneous elastic deformation. It can be explained on the basis of either one of the four theories. A quantitative analysis of the experimental data, which leads to a new interpretation of the elastic and piezoelectric measurements, shows that the theories ($b$) and ($c$) are not valid for Rochelle salt. The experimental data verify the conclusions of the dipole theory insofar as they lead to the result that Rochelle salt would show an abnormal temperature dependence of the dielectric constant even if the crystal were not piezo-electric or if the piezoelectric deformations could be suppressed. However, it is doubtful whether the clamped crystal has a Curie point. The observed Curie points of the free crystal result from the lattice-dipole coupling as described by the interaction theory.

A search was made for an electric dipole moment in the muon with a sensitivity of 0.1% of a muon Compton wavelength times the electronic charge. The motivation for this investigation is provided by the interest in finding some property of the muon which would indicate a structure different from that of the electron, even though such a structure would violate both parity conservation and time reversal invariance. The muons pass through the fringe field of the cyclotron amd an additional system of magnets producing an electric field in their rest frame. Any electric dipole moment would precess about this field producing a vertical plane component of spin transverse to the momentum. This is detected by measuring the electron asymmetry in the plane perpendicular to the momentum. The absence of such a component within the stated sensitivity gives an upper limit to the electric dipole moment of the muons as 2 x 10/sup -16/ cm x the charge of the electron. (auth)

The dielectric susceptibility of a noncentrosymmetric anharmonic crystal is computed by finding and solving the equations of motion for the appropriate Green's functions. The effect of a static field is also investigated. The main absorption line has an additional shift and broadening when the crystal is in a static electric field. In the absence of a static electric field, the higher order electric dipole moments contribute only to the sideband structure of the absorption spectrum, while in a static electric field both the higher order electric dipole moments and the anharmonic terms contribute to the main absorption peak as well as to the sidebands.

Impact ionization of electron-hole pairs by hot electrons, which exist when a strong Hall electric field is present, is proposed. Theoretical arguments indicate that the saturated value of the Hall electric field should coincide with the breakdown electric field in a sample whose Hall electric field is shorted. Experiments substantiate this. The existence of electrons and holes in the region of applied field where the Hall electric field saturated was demonstrated by the decrease of resistance between the Hall contacts, as well as by the observation of a strong Suhl effect in a wide sample. The observed decrease in the Hall electric field just above the onset of ionization is related to the contribution of the holes to the Hall field. Thus, the drift-velocity saturation in strong crossed electric and magnetic fields is explained in consistent fashion as due to impact ionization occurring primarily in the E\ifmmode\times\else\texttimes\fi{}B direction.

The limitations of the conventional microwave cavity method of measuring the electron density are derived. The conventional method permits the electron density to be measured over a range of approximately two decades. The upper limit of the measurement of the electron density, roughly 5\ifmmode\times\else\texttimes\fi{}${10}^{9}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, is caused by plasma resonance due to the macroscopic polarization of the plasma and by the overlapping from higher order modes. The lower limit of the measurement of the electron density, roughly 5\ifmmode\times\else\texttimes\fi{}${10}^{7}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, is determined by how accurately the resonant frequency can be measured. The macroscopic electric polarization can be eliminated and the overlapping modes suppressed by designing the cavity so that the probing microwave field and the plasma have rotational symmetry around the same axis. The electric polarization limit is then replaced by a magnetic polarization limit and the available range is increased approximately one additional decade at 3000 Mc/sec. By decreasing the frequency from 3000 Mc/sec to 1 Mc/sec and by measuring the $Q$ or the losses of the plasma in a properly designed solenoid instead of a cavity the magnetic polarization limit can be raised even more. At 1 Mc/sec and at a pressure of 1 mm Hg the electron density corresponding to the magnetic polarization limit is ${10}^{15}$ to ${10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. The lower limit for the measurable electron density or the conductivity is determined by the sensitivity of the detecting arrangement, and the noise originating in the electron-ion plasma and is probably ${10}^{4}$ to ${10}^{5}$ times less than the maximum measurable electron density.

A theoretical model for the behavior of an optical maser is presented in which the electromagnetic field is treated classically, and the active medium is made up of thermally moving atoms which acquire nonlinear electric dipole moments under the action of the field according to the laws of quantum mechanics. The corresponding macroscopic electric polarization of the medium acts as a source for an electromagnetic field. The self-consistency requirement that a quasistationary field should be sustained by the induced polarization leads to equations which determine the amplitudes and frequencies of multimode oscillation as functions of the various parameters characterizing the maser. Among the results obtained are: threshold conditions, single-mode output as a function of cavity tuning, frequency pulling and pushing, mode competition phenomena including frequency locking, production of combination tones, and population pulsations. A more approximate discussion of maser action using rate equations is also given in which the concept of "hole burning" plays a role.

The low-density or Wigner limiting case of the electron gas is studied for its response to a longitudinal electric field. The long-wavelength static dielectric constant is seen to be negative. Some curious features of the dielectric function are explained by comparison of the electron 'solid' with the classical Lorentz lattice of which the Wigner lattice is seen to be a limiting case. (Author)

High electric fields produce a shift of the optical band edge to longer wavelengths in single crystals of Pb${\mathrm{I}}_{2}$ and Hg${\mathrm{I}}_{2}$. Fields in the range of ${10}^{5}$ to ${10}^{6}$ v/cm cause shifts of the band edge up to 30 A. The magnitude of the shift is proportional to the square of the applied field in agreement with the theoretical prediction of Franz. Using ac fields, the frequency response of the effect has been followed up to 5 kc/sec with no observable inertia.

The possibility of measuring a very small nuclear electric dipole moment is explored by calculating the interaction of this moment with an external electric field. It is shown that for a quantum system of point, charged, electric dipoles in an external electrostatic potential of arbitrary form, there is complete shielding; i.e., there is no term in the interaction energy that is of first order in the electric dipole moments, regardless of the magnitude of the external potential. This is true even if the particles are of finite size, provided that the charge and dipole moment of each have the same spatial distribution. Relativistic and second-order effects are uninterestingly small. There is, however, a first-order interaction if the charge and moment distributions are different, and also for a point electric dipole if it also carries a magnetic dipole moment. Explicit calculations of both effects are given for hydrogen and helium atoms. It is found that the effective electric field at a ${\mathrm{He}}^{3}$ nucleus arising from the magnetic dipole effect is about a hundred times that arising from the finite size effect, and is roughly ${10}^{\ensuremath{-}7}$ times the external electric field.

Proposals that nuclear spin relaxation in an appropriate system could serve as a test for the existence of a nuclear electric dipole moment are examined with attention to the consequences of the fact that the electric field at the nucleus is proportional to the nuclear acceleration. It is found that low-frequency fluctuations of the local electric field are suppressed. In particular, the necessarily negative correlation of the momentum transferred in consecutive collisions of an atom in a gas alters the spectral density of the perturbation, from that of uncorrelated pulses, by the factor $\frac{{\ensuremath{\omega}}^{2}{{\ensuremath{\tau}}_{c}}^{2}}{(1+{\ensuremath{\omega}}^{2}{{\ensuremath{\tau}}_{c}}^{2})}$, where ${\ensuremath{\tau}}_{c}$ is the mean time between collisions. It follows that fairly low gas density is preferable to high. At optimum density a light gas at room temperature carrying electric dipole moments of magnitude $e\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ cm should have a spin relaxation time, in the absence of competing processes, of around 10 minutes. A formula is given for the electrically induced spin relaxation rate in a crystal. The process is hopelessly slow. In the electric coupling of the lattice vibrations to the spin the ordinarily dominant "two-phonon" or "Raman" process is absent, because of the linearity of the connection between local electric field and nuclear motion.

The effects of an externally applied electric field on the absorption of light by silicon have been measured under a wide variety of experimental conditions. The measurements on 52 samples of both $n$ and $p$ type and a variety of doping species show conclusively that the electro-absorption spectrum is associated with the pure silicon lattice and not with any impurity or imperfection. The spectral characteristics of the electro-absorption peaks associated with phonon-assisted processes are strongly affected by the magnitude of the applied electric field over the measured range of ${10}^{4}$ to ${10}^{6}$ V/cm. The electro-absorption spectrum is unchanged, however, in relative magnitude and peak position by a change in temperature, and the absolute spectral positions follow the band-gap dependence on temperature. Concurrent measurements of the maximum-electro-absorption-peak position and high-resolution, field-free optical absorption establish the final state in the transition process as an exciton state. An interpretation of these measurements is given, based on an optically assisted tunneling process to a final exciton state.

The classical problem of the dielectric ellipsoid involves the determination of the field within a homogeneous, isotropic, dielectric ellipsoid when it is placed in a uniform electric field. In the present generalization, both the ellipsoid and the medium in which it is placed, although still homogeneous, are anisotropic and also possess conductivities which are anisotropic. The principal axes of the ellipsoid, of the two dielectric tensors, and of the two conductivity tensors, may all be differently oriented. The external field, although uniform in space, varies sinusoidally with time. The condition specified in the last sentence is consistent with the electromagnetic field equations only in a region whose maximum dimension is small compared with $\frac{\ensuremath{\lambda}}{2\ensuremath{\pi}}$ where $\ensuremath{\lambda}$ is the wave-length which corresponds to the frequency in question. Thus the solution given here is restricted by the condition that the maximum dimension of the ellipsoid must be small compared with $\frac{\ensuremath{\lambda}}{2\ensuremath{\pi}}$.

The electromechanical response of BaTi${\mathrm{O}}_{3}$ single-domain crystals was investigated as a function of temperature from room temperature to above the Curie point. It was found that when we eliminate domain effects, either by using a perfect single-domain crystal or by aligning the domains by an external electric field, we are dealing with a true linear piezoeffect. The linear piezoeffect was measured by both a static and a dynamic method. The values of the ${d}_{31}$ piezoelectric coefficient were compared with those calculated from the dielectric constant and the spontaneous polarization. The behavior of the piezoelectric resonance frequency was observed also through the same temperature range. Although the crystal is cubic above the Curie point and has a center of symmetry, the piezoelectric response persisted under the application of an external d.c. field because the external field will induce a tetragonal crystal structure through the electrostrictive effect, so that the crystal becomes piezoelectric again above the Curie point. Optical and dielectric measurements were found to verify these results.