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A theoretical study of optical absorption and emission measurements of Fe2+ as a substitutional impurity in InP and GaP is presented. A new interpretation of the low-temperature absorption spectrum is proposed based on a weak Jahn-Teller interaction between the electronic excited states and a local gap mode of 5 symmetry. The model also includes the crystal potential, hybridization with the orbitals of the ligands of the host crystal, spin-orbit interaction and a weak dynamic Jahn-Teller coupling of the orbital ground state of Fe2+ with transverse acoustic phonons of 3 symmetry. The theoretical model describes with good accuracy the measured positions and relative intensities of the spectral lines. In addition, the mass dependence of the local gap mode of 5 symmetry reproduces the general features of the fine structures associated with the isotopic shifts of the zero-phonon line and the contribution to the isotopic shifts arising from the difference in zero-point energy between the initial and final states of the transition is evaluated.

A theoretical calculation for the ground state energy of a bound magneto-polaron as a function of the magnetic field is presented. The theory is based on a variational approach using the trial function |Ψ> = c(1 + Σ k (g k * /c) V k * (e -ik.r - Q k ) α k + ) |φ>. |0>, representing the envelope wave function of the ground state already proposed by Devreese et al. in absence of a magnetic field. This function is adequate for all electron-phonon coupling α and γ 0 values, where γ 0 is the ratio between the LO phonon energy and the Coulomb one. For the electronic part of the trial wave function we have adopted a new linear combination function which covers all magnetic field domains. Analytical results are obtained in the weak coupling limit.

A theory of theg-factor for electrons bound to donors in zincblende semiconductors is presented for all magnetic fields. Simple analytical expressions are obtained for weak, intermediate and high magnetic-field intensities. A comparison between theory and the experimental result in the case of InSb is made.

The 5 D terms of Fe 2+ and Cr 2+ in the tetrahedral potential at cation sites in II-VI compounds split into orbital doublet and triplet states. While in Cr 2+ the orbital triplet has lower energy than the doublet, the opposite is the case in Fe 2+ . Both ions have singlet ground states after the spin-orbit interaction is taken into account and, hence, both are Van Vleck paramagnets. The optical absorption spectra of Fe and Cr based materials differ and are explained on the basis of a dynamic Jahn-Teller effect in the former and a static one in the latter. These considerations permit us to explain the optical as well as the magnetic properties observed in these materials.

A detailed characterization of the impurity centers involved in the photoluminescence (PL) of doped and undoped CdTe has been performed. Special attention has been devoted to the temperature dependence of the band between 1.54 and 1.55 eV observed in As and Sb doped samples. The longitudinal optical (LO) phonon replicas are characterized by a Huang-Rhys factor S. The various electron-hole recombination processes are explained by means of a simple analytic model correlating the position of the zero-phonon lines to the relative intensities of the phonon side-bands. The model accounts for the chemical shift of the defect centers and describes the effect of the charge carrier LO-phonon interaction in the framework of the adiabatic approximation within the envelope function approach.

We present a theoretical study of the effect of longitudinal-optical phonons and surface-optical phonons on the electronic states of conduction electrons and donorlike excitons in a spherical semiconductor quantum dot. The effect of the quantum confinement is described by an infinitely deep potential well in the framework of the envelope-function approximation associated with two nondegenerate bands. The charge-carrier\char21{}phonon coupling is treated within the adiabatic approximation. A variational calculation of the ground-state energy of the donorlike exciton is performed using a one-parameter trial envelope function, which includes electron-hole correlation effects. The results show that in the case of a donorlike exciton located at the center of the microsphere, the effect of the lattice polarization gives rise to a lowering of the absolute value of the energy for all values of the microsphere radius R. The Huang-Rhys factor S, which is a measure of the charge-carrier\char21{}phonon interaction and the extent of the charge-carrier density, has been determined as a function of R. For the donorlike exciton, S reaches a minimum value, respectively, equal to ${\mathit{S}}_{0}$=0.2 for ${\mathit{R}}_{0}$=12.7 nm and ${\mathit{S}}_{0}$=3.1 for ${\mathit{R}}_{0}$=2.3 nm in the case of CdSe and CuCl.

We present a study of the Van Vleck paramagnets ${\mathit{A}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Cr}}_{\mathit{x}}$B and ${\mathit{A}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$B, where AB is a II-VI semiconductor having the zinc-blende or the wurtzite structure. In cubic zinc-blende hosts the nonlinear magnetization M depends on the orientation of the external magnetic field B with respect to the cubic axes of the crystal. We show that, while for iron M is largest when B is along a cubic axis and a minimum for B\ensuremath{\parallel}[111], for chromium the anisotropy is reversed and the largest value of M occurs for B\ensuremath{\parallel}[111]. Expansions of the angular variation of the magnetization in terms of combinations of spherical harmonics invariant under the operations of the symmetry group (${\mathit{T}}_{\mathit{d}}$ or ${\mathit{C}}_{3\mathit{v}}$) of the site of the impurity are used to analyze the anisotropy. The magnetic-field dependence of the coefficients in the expansion is investigated. The magnetic susceptibility of ${\mathrm{Cr}}^{2+}$ in wurtzite-structure hosts is expected to be particularly large.

We present a study of the magnetic-field dependence of the energy levels of ${\mathrm{Fe}}^{2+}$ in a wurtzite diluted magnetic semiconductor. We limit our considerations to transitions in the infrared region of the electromagnetic spectrum. The Hamiltonian of the ion has been diagonalized to fourth power in the parameter \ensuremath{\Vert}\ensuremath{\lambda}\ensuremath{\Vert}/\ensuremath{\Delta}, the ratio of the strength of the spin-orbit interaction \ensuremath{\lambda} to the splitting \ensuremath{\Delta} arising from the tetrahedral component of the crystal potential. We make no a priori assumption concerning the relative strengths of \ensuremath{\lambda} and the parameters describing the effect on the crystal field of the trigonal distortion. The parameters describing the ${\mathrm{Fe}}^{2+}$ ion in CdSe are obtained from near-infrared absorption data at zero magnetic field by Udo et al. [Phys. Rev. B 46, 7459 (1992)]. With these values we make a comparison with the electronic Raman-effect data obtained by Mauger et al. [Phys. Rev. B 43, 7102 (1991)] as functions of the intensity and direction of an applied magnetic field.

Extension de travaux precedents sur l'anisotropie de l'aimantation de Fe 2+ dans un champ tetrahedrique. On considere ici un champ magnetique B applique suivant la direction . La deviation par rapport a la linearite de l'aimantation de Van Vleck, quand B est applique dans cette direction, est intermediaire entre celles observees pour les directions et

Etude du spectre d'energie du terme 2 D des ions Cu 2+ dans ces cristaux. Analyse des facteurs g, des lois de selection optiques, et des intensites relatives des composantes de Zeeman des transitions du groupe 2 D de l'ion libre. Les intensites relatives predites sont deduites des donnees en l'absence de champ magnetique externe

Iron-based diluted magnetic semiconductors having the cubic zinc-blende structure display an unusual response to external magnetic fields. For low fields, B, the magnetic susceptibility is isotropic, as expected for cubic crystals. However, when the magnetic field is sufficiently high so that the Zeeman energy cannot be neglected in comparison to the spacing of the low-lying levels of ${\mathrm{Fe}}^{2+}$ (owing to the spin-orbit interaction), the nonlinear magnetization exhibits a striking anisotropy. This phenomenon is related to the Van Vleck paramagnetism primarily due to the nature of the ground state of the (3d${)}^{6}$ configuration of ${\mathrm{Fe}}^{2+}$, namely, a singlet. This paper is concerned with ${\mathrm{Fe}}^{2+}$ in a tetrahedral environment and the concomitant Van Vleck type of paramagnetism. We present an analytic investigation of the magnetic moment of an ${\mathrm{Fe}}^{2+}$ ion in a ${\mathit{T}}_{\mathit{d}}$ field. In this approach the spin-orbit interaction and the Zeeman energy are treated as small compared to the crystal-field splitting but are themselves regarded as comparable. We obtain expressions for the effective number of Bohr magnetons per ion for B along the 〈001〉 and 〈111〉 directions. The anisotropy of this quantity is of the order of 15% at liquid-helium temperatures in a magnetic field of 150 kG. Corrections proportional to the ratio of the spin-orbit interaction and the crystal-field splitting are evaluated in first order.

We present a theoretical investigation of the paramagnetism of individual Fe2+ ions in diluted magnetic semiconductors having the zinc- blende structure. This theory leads to analytic expressions for the magnetic moments. We show that the magnetization exhibits an anisotropy at high magnetic fields when it ceases to be linear in the magnetic field B. At liquid helium temperatures, this anisotropy is about 15% for B=150 kG in Cd1−xFexTe. This effect arises primarily from the anisotropy of the Van Vleck magnetic moment of the ground state of the ion. An interesting feature is that at very large fields the effective number of Bohr magnetons per ion is 4.0 independently of the orientation of B with respect to the crystal axes, as expected when the spin-orbit splitting of the 5Γ3 multiplet can be neglected compared to the Zeeman interaction. The anisotropy decreases with increasing temperature.

We present a theory of the integrated absorption coefficient by donors in a large-gap semiconductor having an arbitrary crystal structure. Comparison between theory and experiment in the case of Cd0.9Mn0.1Se leads to a value of the strength, λ, of the spin-orbit interaction equal to (2.7 ± 0.5) 10−10 eV cm and a value of a e = 44 A for the effective Bohr radius of a donor ground state.

Etude systematique des bas niveaux et des decompositions de Zeeman des ions de metaux de transition dans des semiconducteurs magnetiques dilues ayant une structure de type blende ou wurtzite. Determination generale des niveaux d'energie des termes les plus bas des configurations (3d) n pour tous les ions du groupe du fer, incluant ce couplage spin-orbite et l'effet Zeeman jusqu'au second-ordre-caracterisation des facteurs g de tous les niveaux

In this paper we study the low‐lying energy levels of Co2+ and Fe2+ in diluted magnetic semiconductors, such as Cd1−xCoxTe and Cd1−xCoxSe, and their iron‐based counterparts. In the first of these compounds, the magnetic ion sits on a site of symmetry Td, while in the second the symmetry is trigonal (C3v). We develop a formulation that permits a continuous variation from Td to C3v symmetry. Comparison with experimental data in Cd1−xCoxSe shows that the C3v distortion amounts to about 10% of the crystal potential at the Co2+ site. Our study of the energy spectra of Fe2+ in Td and C3v crystal potentials reveals that, even in the cubic field, the levels exhibit an anisotropy which manifests itself in an anisotropy of the magnetization M in the regime in which M is not a linear function of the magnetic field B. The study includes all the levels in the lowest terms of the (3d)7 and (3d)6 configurations of Co2+ and Fe2+, thus considerably extending work by previous authors. The calculations are carried out to se...

We present a study of all the levels in the lowest terms of the (3d)7 and (3d)6 configurations of Co2+ and Fe2+ in diluted magnetic semiconductors of the zinc-blende or wurtzite structure. The site symmetry of the magnetic ions is Td in the former and C3v in the latter. We develop a formulation that permits a continuous variation from Td to C3v symmetry. Comparison with experimental data in Cd1-xCoxSe shows that the C3v distortion amounts to about 10% of the crystal potential at the Co2+ site. Our study of the spectrum of Fe2+ reveals that, even in a cubic environment, the magnetization M is anisotropic in the region where it is non-linear in the magnetic field. The calculations are carried out to second order in the spin-orbit and Zeeman interactions. The g-factors of all the levels are obtained including their anisotropy for the Co2+ Г8 states.

We study the influence of the electron-optical phonon coupling on a donor like exciton for which the hole is localized at the centre of a spherical microcrystal. This work is performed within the envelope function approximation considering a non degenerated conduction band. The quantum confinement is described by an infinitively deep potential well. The electron-optical phonon coupling is treated within the adiabatic approximation. We determine the Huang-Rhys factor using a one parameter trial wave-function which allows to include the electron-hole correlation. The theoretical model is compared to experiment.

In wurtzite-structure semiconductors, the low-field magnetization of isolated Fe2+ ions for magnetic induction B along the trigonal axis, ĉ, of the crystal exceeds that when B is at right angles to ĉ. This anisotropy is reversed as the magnetic field intensity is increased. In this paper, we show that the reversal of the anisotropy occurs at different magnetic field intensities depending on the orientation of B in a plane perpendicular to ĉ. From a numerical study in conjunction with an expansion of the angular variation of the magnetization in terms of combinations of spherical harmonics invariant under the operations of the symmetry group, C3ν, of the ion site, we conclude that the magnetic field at which the reversal occurs is lowest if B lies on a σν plane and larges if B is normal to one of these planes.

A theoretical study of the resonant magneto-optical spin-flip transitions due to electrons bound to shallow donors is made. We present a general formalism of the integrated absorption coefficient for semiconductors having an arbitrary crystal structure. The model is based on the parity-violating spin-orbit interaction responsible for the active electric-dipole transition. Simple analytic expressions of the integrated absorption coefficient are obtained for the Faraday and Voigt field configurations and for any crystals having zinc-blende and wurtzite structure, respectively. A comparison between theory and far-infrared magneto-optical transmission measurements in InSb and ${\mathrm{Cd}}_{0.9}$${\mathrm{Mn}}_{0.1}$Se yields to the strength of the spin-orbit interaction and effective Bohr radius of the donors involved.

The influence of the ionic polarization on donor-like exciton states is studied theoretically in a spherical semiconductor quantum dot whithin the envelope function approximation associated with two non degenerated bands. The effect of the quantum confinement is described by an infinitely deep potential well. The electron-phonon coupling is treated within the adiabatic approximation. The ground state energy of the exciton is computed using a variational wave function taking into account the electron-hole correlation. The most stable state corresponds to a hole located at the center of the microsphere. The results show that the electron-phonon interaction leads to a decrease of the exciton energy. This effect depends on the size of the quantum dot, contrary to previous results.

A study is given of the effect of ultrasonic generation on the residual surface impedance of superconductors at microwave frequencies. We present an exact solution of the problem for London superconductors and give also general expressions for the residual surface resistance at zero temperature. Universal curves of the residual resistance as a function of the frequency and of the ratio of the correlation length to the electron mean free path are given using the Pippard and BCS kernels. Our investigation yields a lower limit to the surface impedance within the limits of the use of the free‐electon model. A comparison is given with experimental data available in the literature for niobium, lead, and indium as well as a critical analysis of previous theoretical work. For indium and lead our results are one or two orders of magnitude below selected experimental results. For niobium, the lowest experimental results agree fairly well with those estimated in the present work.

A new variational wave function to describe the ground state and the excited states of a bound polaron is proposed. It is of the form |Ψ〉 = c|O〉|o n 〉 + ∑ g k ∗ V k ∗ (e i k·r − ρ k ∗ )a k + |O〉|o n . It is argued that this form is reasonable for all electron—phonon coupling α and all strengths β of the Coulomb potential. Numerical and analytical results are derived for the energy of the ground state and compared to existing results. Results for the energy of the lowest p-type excited state of the bound polaron are obtained.

We present a discussion of the relation of the electron deformation potentials in metals to the matrix elements for electron scattering by long wavelength acoustic phonons. A recent result of Khan and Allen is shown to be valid in the deformable ion model of the electron-phonon interaction as well as in the rigid ion model.

We present a discussion of the relation of the electron deformation potentials in metals to the matrix elements for electron scattering by long-wavelength acoustic phonons. A recent result of Khan and Allen is shown to be valid in the deformable-ion model of the electron-phonon interaction as well as in the rigid-ion model. A microscopic theory is given of the reaction forces on the crystal lattice when the conduction electrons in a metal are accelerated by an external force.

The theory of the anomalous skin effect in metals is used in order to study the direct generation of ultrasound by electromagnetic radiation incident on a metal surface, in the absence and in the presence of a magnetic field. The non-monotonic behaviour of the acoustic flux observed experimentally, as a function of the magnetic field can be explained within the framework of the free-electron model assuming that the electrons are scattered diffusely from the metal surface. The reason for this behaviour is traced to the variation of the relative phases of the collision drag force on the bulk ions and that on the surface with increasing magnetic field. The relations between existing theories of direct generation of ultrasound have been investigated within both the free-electron approximation and the effective-mass theory. We conclude that, besides the collision drag force, the Lorentz force and the Bragg reaction force, an additional ‘deformation’ force acts upon the positive ions. We find that the ...

The effect of the electron–hole correlations on the effective mass electronic states of donor–acceptor (DA) pairs in polar semiconductors is investigated. Variational calculations are carried out and compared with previous theoretical work in the case of GaP and ZnSe. Analytic expressions for the energy, charge density, and pair distribution function of DA pairs are obtained as a function of the pair separation R. It is shown that whereas the energy and the charge distribution of a DA pair are only slightly affected by the electron–hole correlations, the pair distribution function shows a strong enhancement at short electron–hole distance. Die Wirkung der Elektron–Loch-Korrelationen auf die elektronischen Zustande von Donator-Akzeptor (DA)-Paaren in polaren Halbleitern wird im Rahmen der Effektivmassennaherung untersucht. Ein Variationsverfahren wird angewandt, und die Ergebnisse werden mit fruheren Berechnungen im Falle von GaP und ZnSe verglichen. Analytische Formeln fur die Elektron-Loch-Rekombinationsenergie, die Ladungsdichte und die radiale Verteilungsfunktion des DA-Paares werden als Funktion des Paarabstandes R gefunden. Die Rechnungen zeigen, das Rekombinationsenergie und Ladungsdichte nur wenig durch die Elektron–Loch-Korrelation beeinflust werden, die radiale Verteilungsfunktion dagegen bei kleinem Elektron–Loch-Paarabstand wesentlich verandert wird.

A theoretical study of the effect of direct ultrasonic generation on the surface impedance of superconductors at temperatures below the critical temperature Tc is presented. The temperature and frequency dependences of the additional surface resistance due to the ionic motion are analyzed using the Pippard and BCS kernels and parabolic electron energy bands.

La theorie de l'electron libre, modifiee par l'anisotropie elastique, montre que, le long de la direction d'anisotropie des ondes acoustiques transversales, l'amplitude acoustique varie de facon non monotone avec l'intensite du champ magnetique applique et independamment du mecanisme de diffusion des electrons a la surface du metal. On a donc un phenomene tout a fait different de ce qui se passe le long des directions de haute symetrie

The optical absorption by free and bound polarons in polar crystals with several LO phonon branches is described in the adiabatic approximation. In both cases, we calculate both zero and one phonon absorption. For free polarons, we find a behaviour similar to that obtained for the one LO phonon branch case. Additional structure can, however, appear in the Franck–Condon relaxation part of the spectrum. For bound polarons, we find that the oscillator strength of the one phonon replica associated to the ith phonon branch is proportional to its coupling constant and inversely proportional to the square root of the phonon frequency. A discussion of these results is made in relation to recent infrared spectra obtained in perovskites.

The intraband magnetoabsorption by optical polarons has been calculated to linear order in the carrier-phonon coupling constant for the case of a simple parabolic band. A finite lifetime has been introduced for the Landau levels to take into account scattering mechanisms other than that due to optical phonons. The pinning effect, line broadening, and phonon-assisted transitions are studied under these assumptions.

The effective hamiltonian for the electronic states of a donor-acceptor pair in a polar semiconductor is formulated as a Frohlich hamiltonian generalized to an electron and a positive hole interacting in the field of the positive donor and negative acceptor cores. The polarization of the lattice by the ion cores is simplified by a Platzman transformation; that by the electron and positive hole, by a further unitary transformation in the adiabatic approximation. The total effective hamiltonian including the lattice polarization energy is then considered for application of the variational principle to determine the parameters of the electron and positive hole effective mass functions. The Inglis-Williams analysis of the zero-phonon luminescent spactra of pairs is reconciled with the present theory by determining what single effective hamiltonian for the excited electronic state is consistent with their theoretical spactra. Within the approximations of their analysis, which are clarified, it is found to be the total effective hamiltonian. Finally, a more general and rigorously-derived effective hamiltonian is presented for the direct theoretical determination of the zero-phonon radiative transition energies of donor-acceptor pairs in compound semiconductors.

The electrical polarizability tensor of shallow donors in polar semiconductors is calculated in the presence of a weak magnetic field. A variational treatment of the donor is developed in the framework of the effective-mass theory, including the effects of interaction between the charge carriers and the longitudinal-optical (LO) phonons within the static approximation. The effective-mass Hamiltonian of the donor allows for central-cell corrections by means of a phenomenological impurity potential. The results are compared with previous theoretical work and experiment in the case of donor impurities in Si. It is shown that the donor polarizability depends strongly on the form chosen for the model impurity potential and undergoes a 30 to 50% decrease due to the electron—(LO)phonon interaction in the case of impurities in III–V and II–VI compounds, respectively. Der elektrische Polarisationstensor flacher Donatoren in polaren Hableitern wird fur den Fall schwacher Magnetfelder berechnet. Ein Variationsverfahren fur den Donator wird unter Benutzung der Effektivmassentheorie entwickelt, wobei die Wechselwirkung zwischen den geladenen Teilchen und den longitudinalen-optischen (LO)-Phononen einbegriffen ist und die statische Naherung benutzt wird. Der Effektivmassen-Hamiltonoperator enthalt ein phanomenologisches Potential, welches den „central cell”-Effekt berucksichtigt. Die Ergebnisse werden mit vorhergehenden theoretischen Berechnungen und Experimenten im Falle von Donatoren in Si verglichen. Es wird bewiesen, das die Polarisierbarkeit wesentlich von der Form des Storstellenpotentials abhangt und eine Verminderung von 30 bis 50% durch die Elektron—(LO)Phononen-Wechselwirkung im Falle der III–V-beziehungsweise II–VI-Halbleitern erfahrt.

An analytical model for the oscillatory behavior of the photoconductivity excitation spectrum in the photoconductivity of polar semiconductors is presented. The model is a simple version of the theory by Stocker and Kaplan [Phys. Rev. 150, 619 (1966)], modified to include the effects of thermal longitudinal optical phonons. The theory is applied to the case of n‐type CdTe. Comparison with the experimental results of Nicholas et al. [J. Phys. C 13, 5215 (1980)] suggests the existence of three trapping mechanisms: phonon‐assisted trapping by donor levels lying, respectively, at Ee=3 meV and E0=12 meV below the conduction band edge, and a direct capture by very shallow states acting on the slow electrons at the bottom of the band. A value of τ=2.2×10−12 s is obtained for the average lifetime of the electrons in the conduction band.

The absorption spectra of bound continuum polarons are calculated taking into account phonon dispersion and the finite lifetime of phonons. Our theory predicts a frequency shift of the emitted L.O. phonons (as observed in AgBr).

Cyclotron resonance of polarons in ionic crystals is studied by means of a Born-Oppenheimer type method. The Lee, Low, Pines approximation is made for the electron—phonon interaction and so the translational invariance along the magnetic field direction is exploited. Our approach is therefore valid at weak and intermediate couplings and cyclotron frequencies ωc larger than the L.O. phonon frequency ω, which requires rather intense magnetic fields. For relatively large electron—phonon coupling (α ≧ 4) the results also apply qualitatively for weak magnetic fields. The ground state energy and the energy of two excited levels are obtained. The excited states which are treated here are internal excited states of the polaron system and they are different from the normal Landau levels. The stability of some of these states is enhanced under the action of the magnetic field. This leads us to predict absorption at new cyclotron frequencies in ionic crystals especially relevant for intermediate coupling strengths α ≈ 4. [Russian Text Ignored].

The conservation of total angular momentum is considered in detail for polarons, using an expansion of the polarization field into spherical waves. This formalism is used to improve the Landau-Pekar approximation, taking the electron-phonon correlations partially into account. A value 10 to 20% lower is obtained for the polaron ground state energy for values of the coupling constant α ranging from 8 to 5. On etudie la conservation du moment angulaire dans la theorie du polaron, en introduisant un developpement du champ de polarisation en ondes spheriques. On utilise ce formalisme aux fins d'amelioration de l'approximation de Landau-Pekar, en tenant compte des correlations electron-phonons. On obtient une energie fondamentale du polaron 10 a 20% plus basse, pour des valeurs de la constante de couplage α comprises entre 8 et 5.

The velocity dependence of the free polaron optical absorption constant has been determined on solving the Heisenberg's equations of motion for the polaron. It has been shown that an enhancement of the carrier velocity exhibits two main modifications of the optical absorption line shape: first, a small shift of the absorption threshold towards lower frequencies, second an important increase of the peak intensity.

The energy spectrum of Frohlich polarons in a magnetic field is investigated theoretically. The constants of the motion of the system are studied and a “Feynman model” serves as B guide in this study. A crucial difference between the energy spectra of polarons and rigid particles is predicted at rather strong coupling strengthsor large magnetic fields. It is due to the internal structure of the polaron system. When the electron-LO-phonon coupling constant becomes large enough to allow internal excitations, a resonance may appear in the one-phonon continuum. This resonance is split by Zeeman effect at small field values and the components of the multiplet tend asymptotically to the Landau levels with increasing field strengths. The stability of one component at least is enhanced by the magnetic field, so that magnetic fields could be used to reveal internal excitations of polarons, in cyclotron resonance or magneto-optical absorption experiments. Recent experimental results on magneto-absorption by excitons are discussed in the light of the present work. Es wird das Energiespektrum Frohlichscher Polaronen im Magnetfeld theoretisch untersucht. Die Bewegungskonstanten des Systems werden untersucht, wobei ein „Feynman-Modell” als Fuhrer bei dieser Untersuchung dient. Fur starke Kopplungsstarken oder grose magnetische Felder wird eine entscheidende Differenz zwischen den Energiespektren der Polaronen und starren Partikel vorhergesagt. Diese wird durch die innere Struktur des Polaronensystems hervorgerufen. Wenn die Elektronen-LO-Phononen-Kopplungskon-stante gros genug wird, um innere Anregung zu erlauben, kann eine Resonanz im Einphononenkontinuum auftreten. Diese Resonanz wird durch den Zeemaneffekt bei kleinen Feldwerten aufgespalten und die Komponenten des Multiplett gehen mit steigenden Feldstarken asymptotisch in die Landau-Niveaus uber. Die Stabilitat wenigstens einer der Komponenten wird durch das magnetische Feld verstarkt, so das Magnetfelder benutzt werden konnen, um innere Anregung von Polaronen in Zyklotronresonanz- oder magneto-optischen Absorptionsexperimenten zu beobachten. Kurzlich erhaltene experimentelle Ergebnisse der Magneto-Absorption durch Exzitonen werden im Hinblick auf diese Arbeit diskutiert.

The classical analysis, due to Kliewer and Fuchs, of the optical polarization modes of an ionic crystal film in the long-wavelength limit is used to develop a quantum-mechanical treatment of the interaction between an electron and the optical-phonon field of the film. Retardation effects are neglected. The analog of Fr\"ohlich's polaron Hamiltonian is obtained, but with explicit inclusion of surface effects. As a first application of this theory, the case of a fast electron is treated, and the electron-crystal energy-exchange spectra are derived. The classical energy-loss spectrum is recovered and involves processes resulting in one-phonon excitation. Quantum-mechanical two-phonon processes are evaluated. The gain spectrum is obtained for the first time and shows a strong temperature dependence. The results are in good agreement with experimental spectra in LiF crystal films.

A quantum-mechanical treatment is developed for the interaction of an electron with optical phonons of an ionic crystal film. When applied to the case of a fast electron, the electron energy loss and gain spectra are obtained and agree well with the experimental data on LiF. The gain spectrum is obtained for the first time and shows the observed strong temperature-dependence. Losses through multi-phonon processes occur in the LO phonon energy range.

The decrease of the electron mobility at high electric field (E >40 V/cm) InSb is interpreted as due to the emission of real L.O. - phonons. This mobility at high field is evaluated by solving the Heisenberg equations of motion by iteration, which is valid at weak coupling. At first step of iteration, the L.O.-phonon emission is found to take place when the mean kinetic energy of the charge carrier is larger than a quantum h  ω of L.O.-lattice vibration. The slope of the curve μ vs. E is found in good agreement with the experiment.