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Quantum theory of free carrier absorption in polar semiconductors
ANNALS
OF PHYSICS:
80, 228-229 (1973)
Abstracts
of Papers
to Appear
in Future
Issues
Dominance in Reggeized Higher Symmetry Model. A. M. HARUN-AR Imperial College of Science and Technology, Prince Consort Road, London, SW 7 2BZ, England. The requirements of the vector-meson dominance model on the smoothness of the invariant amplitudes for the process rr + N -+ V + N are investigated with the SU(6)w-invariant vertex functions thus generalizing the electric Born model of Cho and Sakurai. However, it is shown that their conclusions remain unaltered. A Reggeized version of the model can explain the forward peak in the photo-production experiment provided the pion-conspirator trajectory is assumed to contribute. A Test of Vector-Meson RASHID.
Low-Energy
Theorems
and Dispersion
Relations
to All
Orders
in the Electromagnetic
Interaction.
L. D. SOLOVIEV. Institute for High Energy Physics, Serpukhov. Report, submitted to the XVI International Conference on High Energy Physics, Chicago, 6-13 September, 1972). An S-matrix theory of the electromagnetic interaction without infrared divergences is proposed. With the help of it the effects of the soft (both real and virtual) photons are considered without perturbation theory approximations. The following results are obtained. 1) The terms of order K-I, In K, ~0 and K ln% are found in the bremsstrahlung matrix element where K is the radiated energy (they are expressed through the matrix element of the process without radiation). 2) It is shown, that if dispersion relations exist at nonzero photon mass, then they exist at zero mass too. 3) The first three terms of the series expansion in energy near the threshold are found for the Compton scattering matrix element at fixed momentum transfers. Relation of the obtained results to high-energy scattering and relativistic eikonal models is considered. Matrices for Helicity and Invariant Amplitudes for y + N+ l+ + N. L. MANNY AND ROBERT BECK CLARK. Center for Particle Theory. The University of Texas at Austin, Austin, Texas 78712. The Algebraic transformation matrices, valid for all s and t, connecting the s- and t-channel helicity amplitudes to a corresponding set of gauge invariant covariant amplitudes are presented for the photoproduction processes y + N -+ l* + N. s- and t-Channel RONALD
Transformation
G. PARSONS,
BEN
Theory of Free Carrier Absorption in Polar Semiconductors. B. JENSEN. Physics Department, Columbia University, New York, New York AND THOMAS J. WATSON. Research Center, Yorktown Heights, New York. A quantum mechanical treatment of the free carrier absorption by electrons in polar semiconductors has been constructed in terms of the Kane model. It takes into account Matz overlap wavefunction factors, intermediate states in other bands, the finite optical phonon energy, and the effects of arbitrary spin orbit splitting on the electron energy and wavefunction. The scattering mechanisms considered include polar optical mode scattering, ionic scattering, piezoelectric and deformation coupled acoustic mode scattering, and electron4ectron scattering. The theory, in the appropriate limits, applies to a wide range of photon energies, electron concentrations, and lattice temperatures. It relates the dominant scattering mechanism involved in the various limits to the characteristic behavior of the absorption coefficient as a function of the Quantum
Copyright All rights
0 1973 by Academic Press, Inc. of reproduction in any form reserved.
228
229
ABSTRACTS OF PAPERS TO APPEAR IN FUTURE ISSUES
photon energy. In particular, the dominant scattering mechanism for small carrier concentrations is found to be polar optical mode scattering, which exhibits a X3 dependence of the absorption coefficient times the index of refraction, (except at the lowest frequencies, where the expected X2 dependence is obtained). Ionic, or impurity, scattering becomes important as the carrier concentration is increased, and the characteristic wavelength dependence of the electron cross section times the index of refraction varies from h* to X3, and the absorption coefficient times the index of refraction from X4 to /\*, depending on the ratio of the photon energy to the initial electron energies. Comparisons are made with the available data over a wide range of photon energies, temperatures, and electron concentrations, for the III-V compounds InSb, InAs, InP, and GaAs. S- and P-Wave Neutron Spectroscopy. Part Xd: Intermediate Structure, Particle-Vibration States. M. DIVADEENAM. North Carolina Central University and Triangle Universities Nuclear Laboratory, Durham, N. C. 27706, WILLIAM P. BERES. Wayne State University, Detroit, Michigan 48202 AND HENRY W. NEWSON.Duke University and Triangle Universities Laboratory, Durham, N. C. 27706. The weak coupling particle-vibration model is extended to low-lying neutron resonances in certain even-even or odd-odd nuclei by coupling the extra particle to core excited states of the odd mass target. The odd hole or particle in the target is treated as a passive spectator. zoePb and zlOBi are studied as test cases and the calculated resonance quantities are in good general agreement with the average features of high resolution experiments. The resonances in zosPb and *loBi are related to the same intrinsic doorway in 20DPb.The zlOBi data is presented here for the first time.
Printed
in Belgium
OF PHYSICS:
80, 228-229 (1973)
Abstracts
of Papers
to Appear
in Future
Issues
Dominance in Reggeized Higher Symmetry Model. A. M. HARUN-AR Imperial College of Science and Technology, Prince Consort Road, London, SW 7 2BZ, England. The requirements of the vector-meson dominance model on the smoothness of the invariant amplitudes for the process rr + N -+ V + N are investigated with the SU(6)w-invariant vertex functions thus generalizing the electric Born model of Cho and Sakurai. However, it is shown that their conclusions remain unaltered. A Reggeized version of the model can explain the forward peak in the photo-production experiment provided the pion-conspirator trajectory is assumed to contribute. A Test of Vector-Meson RASHID.
Low-Energy
Theorems
and Dispersion
Relations
to All
Orders
in the Electromagnetic
Interaction.
L. D. SOLOVIEV. Institute for High Energy Physics, Serpukhov. Report, submitted to the XVI International Conference on High Energy Physics, Chicago, 6-13 September, 1972). An S-matrix theory of the electromagnetic interaction without infrared divergences is proposed. With the help of it the effects of the soft (both real and virtual) photons are considered without perturbation theory approximations. The following results are obtained. 1) The terms of order K-I, In K, ~0 and K ln% are found in the bremsstrahlung matrix element where K is the radiated energy (they are expressed through the matrix element of the process without radiation). 2) It is shown, that if dispersion relations exist at nonzero photon mass, then they exist at zero mass too. 3) The first three terms of the series expansion in energy near the threshold are found for the Compton scattering matrix element at fixed momentum transfers. Relation of the obtained results to high-energy scattering and relativistic eikonal models is considered. Matrices for Helicity and Invariant Amplitudes for y + N+ l+ + N. L. MANNY AND ROBERT BECK CLARK. Center for Particle Theory. The University of Texas at Austin, Austin, Texas 78712. The Algebraic transformation matrices, valid for all s and t, connecting the s- and t-channel helicity amplitudes to a corresponding set of gauge invariant covariant amplitudes are presented for the photoproduction processes y + N -+ l* + N. s- and t-Channel RONALD
Transformation
G. PARSONS,
BEN
Theory of Free Carrier Absorption in Polar Semiconductors. B. JENSEN. Physics Department, Columbia University, New York, New York AND THOMAS J. WATSON. Research Center, Yorktown Heights, New York. A quantum mechanical treatment of the free carrier absorption by electrons in polar semiconductors has been constructed in terms of the Kane model. It takes into account Matz overlap wavefunction factors, intermediate states in other bands, the finite optical phonon energy, and the effects of arbitrary spin orbit splitting on the electron energy and wavefunction. The scattering mechanisms considered include polar optical mode scattering, ionic scattering, piezoelectric and deformation coupled acoustic mode scattering, and electron4ectron scattering. The theory, in the appropriate limits, applies to a wide range of photon energies, electron concentrations, and lattice temperatures. It relates the dominant scattering mechanism involved in the various limits to the characteristic behavior of the absorption coefficient as a function of the Quantum
Copyright All rights
0 1973 by Academic Press, Inc. of reproduction in any form reserved.
228
229
ABSTRACTS OF PAPERS TO APPEAR IN FUTURE ISSUES
photon energy. In particular, the dominant scattering mechanism for small carrier concentrations is found to be polar optical mode scattering, which exhibits a X3 dependence of the absorption coefficient times the index of refraction, (except at the lowest frequencies, where the expected X2 dependence is obtained). Ionic, or impurity, scattering becomes important as the carrier concentration is increased, and the characteristic wavelength dependence of the electron cross section times the index of refraction varies from h* to X3, and the absorption coefficient times the index of refraction from X4 to /\*, depending on the ratio of the photon energy to the initial electron energies. Comparisons are made with the available data over a wide range of photon energies, temperatures, and electron concentrations, for the III-V compounds InSb, InAs, InP, and GaAs. S- and P-Wave Neutron Spectroscopy. Part Xd: Intermediate Structure, Particle-Vibration States. M. DIVADEENAM. North Carolina Central University and Triangle Universities Nuclear Laboratory, Durham, N. C. 27706, WILLIAM P. BERES. Wayne State University, Detroit, Michigan 48202 AND HENRY W. NEWSON.Duke University and Triangle Universities Laboratory, Durham, N. C. 27706. The weak coupling particle-vibration model is extended to low-lying neutron resonances in certain even-even or odd-odd nuclei by coupling the extra particle to core excited states of the odd mass target. The odd hole or particle in the target is treated as a passive spectator. zoePb and zlOBi are studied as test cases and the calculated resonance quantities are in good general agreement with the average features of high resolution experiments. The resonances in zosPb and *loBi are related to the same intrinsic doorway in 20DPb.The zlOBi data is presented here for the first time.
Printed
in Belgium