Showing papers on "Absorption (logic) published in 1967"

X-Ray Wavelengths

Abstract: Inconsistencies in accepted values (in x units) of x-ray reference lines have recently been demonstrated, although all are supposedly based on "good" calcite crystals. Factors supporting the selection of the W $K{\ensuremath{\alpha}}_{1}$ line as the X-Ray Wavelength Standard are critically discussed. A review is given of the experimental measurements which are used to establish the wavelength of this line on an absolute angstrom basis. Its value is $\ensuremath{\lambda}$ W $K{\ensuremath{\alpha}}_{1}=(0.2090100\ifmmode\pm\else\textpm\fi{}5 \mathrm{ppm})$ \AA{}. This may be used to define a new unit, denoted by \AA{}*, such that the W $K{\ensuremath{\alpha}}_{1}$ wavelength is exactly 0.2090100 \AA{}*; hence 1\AA{}*=1\AA{}\ifmmode\pm\else\textpm\fi{}5 ppm. The wavelengths of the Ag $K{\ensuremath{\alpha}}_{1}$, Mo $K{\ensuremath{\alpha}}_{1}$, Cu $K{\ensuremath{\alpha}}_{1}$, and the Cr $K{\ensuremath{\alpha}}_{2}$ have been established as secondary standards with probable error of approximately one part per million. Sixty-one additional x-ray lines have been used as reference values in a comprehensive review and reevaluation of more than 2700 emission and absorption wavelengths. The recommended wavelength values are listed in \AA{}* units together with probable errors; corresponding energies are given in keV. A second table lists the wavelengths in numerical order, and likewise includes their energies in keV.

Probabilities for Radiative and Nonradiative Decay of Er 3 + in La F 3

Abstract: The rates of radiative and nonradiative decay were determined for several excited states of ${\mathrm{Er}}^{3+}$ in La${\mathrm{F}}_{3}$ from calculated spontaneous emission probabilities and measured lifetimes. Electric-dipole, magnetic-dipole, and electric-quadrupole transition probabilities were evaluated using intermediate coupled states derived from computer diagonalization of the combined spin-orbit and electrostatic energy matrix. The required spin-orbit and Racah parameters for La${\mathrm{F}}_{3}$: ${\mathrm{Er}}^{3+}$ were obtained from a least-squares fit of experimental and theoretical energy levels. The probabilities for electric-dipole transitions were calculated using the theory of Judd and Ofelt; the phenomenological parameters needed in this approach were derived from measurements of integrated absorption coefficients. By comparing the total calculated radiative lifetimes and the observed lifetimes, the probabilities for nonradiative decay from nine different excited states were determined. The probability of nonradiative decay was found to be very dependent upon the proximity of lower energy levels, which for the levels investigated ranged from approximately 1600 to 6000 ${\mathrm{cm}}^{\ensuremath{-}1}$, and hence upon the number of phonons required to conserve energy. The rates of nonradiative transitions corresponding to the simultaneous emission of as many as five phonons were found to make significant contributions to the lifetimes of fluorescent states of rare earths in La${\mathrm{F}}_{3}$.

Pair production in photon-photon collisions.

Abstract: General formulas for the absorption probability from the process $\ensuremath{\gamma}+{\ensuremath{\gamma}}^{\ensuremath{'}}\ensuremath{\rightarrow}{e}^{+}+{e}^{\ensuremath{-}}$ are given for high-energy photons traversing isotropic photon gases having various spectra. Asymptotic formulas are derived and general results are given in graphical form for photon spectra having blackbody and power-law form. The results are applied in a following paper to calculate the absorption probability for high-energy photons traversing cosmic distances.

Opacity of the Universe to High-Energy Photons

Abstract: Based on observational data, the spectra of cosmic radio, microwave, infrared, optical, and x-ray photons are estimated. The absorption probability per unit path length by the process of pair production in photon-photon collisions is then computed as a function of energy for high-energy photons traversing this photon gas, using the results of the previous paper. These calculations show that there should be a dip in the intensity of the high-energy cosmic photon spectrum by about a factor of 10 between ${10}^{12}$ and ${10}^{13}$ eV due to absorption by optical (\ensuremath{\sim} a few eV) photons. Above ${10}^{14}$ eV, the high-energy cosmic photon spectrum should essentially cut off because of the strong absorption by the cosmic 3\ifmmode^\circ\else\textdegree\fi{}K blackbody photons, and at higher energies by the cosmic radio photons.

Optical Absorption Spectra of the Alkali Halides at 10°K

Abstract: The absorption spectra of all the alkali halides except LiF and LiI, measured in the range 5.0 to 12.0 eV at 10\ifmmode^\circ\else\textdegree\fi{}K, are presented. These data complement earlier measurements made at 80\ifmmode^\circ\else\textdegree\fi{}K. Identification of excition lines involving $d$-like electrons is made by a comparison of the crystal absorption and the absorption spectra of rare-gas atoms. From the positions of exciton states with $d$-like electrons, the energy of the second conduction band at $\ensuremath{\Gamma}$ is deduced for some of the alkali halides. The results of these deductions are compared with recent calculations of the conduction-band structure of KI and KCl.

Charge conversion of irradiated rare-earth ions in calcium fluoride. i.

Abstract: The mechanism by which the rare-earth ions in Ca${\mathrm{F}}_{2}$ can be reduced from the trivalent to the divalent state by exposure to x rays or $\ensuremath{\gamma}$ rays has been systematically studied for all the thirteen available ions in the lanthanide series. Each of the ions was irradiated at 77\ifmmode^\circ\else\textdegree\fi{}K and its temperature subsequently raised above room temperature. During the heating process the intensity of the thermoluminescence and the changes in the optical absorption spectrum were measured as a function of temperature. An accompanying paper describes the changes in the emission spectrum with temperature. In general, the temperatures at which significant changes in absorption occur, and for which there is simultaneous thermoluminescent emission, are independent of the particular rare-earth ion, while the emission spectra is characteristic of the rare earth. The absorption spectra have parts characteristic of the individual ions and parts independent of the ion. On the basis of these observations, it is possible to formulate a consistent model of the irradiation-induced charge-reduction process and the subsequent thermal reoxidation process. From 77 to about 330\ifmmode^\circ\else\textdegree\fi{}K the oxidation process is attributed to thermal activation of a variety of hole traps.

Theory of X-Ray Raman Scattering

Abstract: Inelastic scattering of X-rays by localized electrons, such as K -electrons, in solids is treated theoretically. The wave length of X-rays is chosen to be longer than the orbital radius of localized electrons, but still short enough so that the photon energy is much higher than the ionization energy. On the basis of reasonable approximations, it is found for polycrystals that the differential cross section is proportional to \begin{aligned} { u_{0}}^{2}t( u_{0}- u)(1+\cos^{2}\theta)\sin^{2}(\theta/2). \end{aligned} Here ν 0 and ν are respectively the frequencies of the incident and scattered X-rays, θ being the scattering angle. ν t (ν) is a quantity proportional to the cross section of absorption of the X-rays with frequency ν by the same electrons. The above expression has recently been confirmed experimentally.

Absorption and Luminescence of Excitons at Neutral Donors in Gallium Phosphide

Abstract: Absorption and photoluminescence spectra of excitons weakly bound to sulphur, selenium, and tellurium donors in gallium phosphide have been studied at 25\ifmmode^\circ\else\textdegree\fi{}K and below. Relatively weak satellite photoluminescence lines have been discovered. These photoluminescence satellites are phonon replicas, and some of the corresponding absorption satellites have been observed. Comparison with the intrinsic absorption-edge spectrum shows that some of these are the momentum-conserving (MC) phonons in the indirect transition. The more accurate estimates of these phonon energies provided from the bound exciton spectra are, (TA) 13.1\ifmmode\pm\else\textpm\fi{}0.1 meV, (LA) 31.5\ifmmode\pm\else\textpm\fi{}0.1 meV, (TO) 45.3\ifmmode\pm\else\textpm\fi{}0.1 meV (sulphur spectrum). Replicas associated with the zone-center optical phonons, of energy 45.4\ifmmode\pm\else\textpm\fi{}0.1 meV (TO) and 50.1\ifmmode\pm\else\textpm\fi{}0.1 meV (LO), are also prominent. Luminescence spectra associated with the relatively heavy donors selenium and tellurium also contain prominent 23- and 47-meV phonon replicas which do not appear in absorption. These bands are apparently associated with "in-band resonance" local modes occurring at possible regions of low density of thelattice modes. The relative intensity of adjacent Mc (LA) replicas is increased when the local modes are prominent. Apart from this apparent interference with the local modes, the intensities of the optical and acoustical (MC) phonon replicas vary together between spectra involving different donors, as do the intensities of the no-phonon line and the zone-center replicas. The binding energy of the exciton to the donor does not vary as expected with the ionization energy of the donor or with the strength of the coupling to the momentum-conserving phonons. An absorption satellite 40.6\ifmmode\pm\else\textpm\fi{}0.2 meV above the no-phonon lines for all three donors may also be a phonon replica, but is anomalously strong in the absorption spectra. Additional absorption satellites are apparently associated with excited states of the exciton-neutral-donor complex. The intensities of the satellites relative to the principal no-phonon line vary more than the relative transition energies between these three group-VI donors. The spectral positions of these excited states and the activation energy for thermal quenching of the luminescence intensity (29\ifmmode\pm\else\textpm\fi{}1.5 meV) suggest the liberation of free electrons and holes rather than free excitons from these complexes.

Structure and Optical Absorption of AgI Microcrystals

Abstract: Large corrections to the x-ray intensities of the standard powder diffraction pattern of hexagonal AgI are proposed Based on these intensities, it appears that some precipitates which have been described in the literature as pure hexagonal have actually contained about 30% of the cubic phase Hexagonal AgI was produced during precipitation only by slow crystallization and without an excess of either ${\mathrm{Ag}}^{+}$ or ${\mathrm{I}}^{\ensuremath{-}}$ Faster precipitations gave mixtures of the cubic and hexagonal phases, and crystals whose average diameter was as small at 150 \AA{} The Rayleigh scattering of these suspensions was sufficiently small that the absorption coefficients of the crystals could be readily measured The usually strong exciton absorption peak at about 420 m\ensuremath{\mu} was missing in the small crystals When the crystals were made to grow, the exciton peak appeared slightly below 420 m\ensuremath{\mu} for crystals which became more hexagonal as they increased in size, and somewhat above 420 m\ensuremath{\mu} for crystals which became more cubic The decrease in absorption for AgI in the exciton region was much more than for the absorption edge of AgBr for crystals of comparable small size Additional mechanisms for the loss of absorption in AgI compared with AgBr are apparently indicated It is suggested that the exciton radius in AgI is so large that the exciton cannot be formed close to the surface

Excitons and the Absorption Edge in ZnSe

Abstract: The optical absorption threshold at about 2.7 eV, near the lowest-energy fundamental edge, was investigated for cubic ZnSe single crystals. Absorption spectra are reported for temperatures between 2 and 200\ifmmode^\circ\else\textdegree\fi{}K, and absorption coefficients between 4 and 600 ${\mathrm{cm}}^{\ensuremath{-}1}$. Although contributions associated with defects dominated the results in most crystals, intrinsic absorption could be observed for $T\ensuremath{\gtrsim}60$\ifmmode^\circ\else\textdegree\fi{}K in the purest available crystals. This intrinsic absorption results from longitudinal-optical-phonon-assisted creation of excitons, as is shown by the good agreement between the observed magnitude, the temperature, and photon-energy dependence, and the absorption calculated for this mechanism. The relevant exciton states involve electrons and holes from band extrema near the center of the Brillouin zone; when created without phonon assistance, excitons from these same extrema also give the relatively very intense "direct transition" absorption lines. No evidence is found that any band gap is smaller than that at the zone center.

Range Measurements in Oriented Tungsten Single Crystals (0.1-1.0 MeV). I. Electronic and Nuclear Stopping Powers

Abstract: Range distributions of ${\mathrm{Na}}^{24}$, ${\mathrm{P}}^{32}$, ${\mathrm{K}}^{42}$, ${\mathrm{Cr}}^{51}$, ${\mathrm{Cu}}^{64}$, ${\mathrm{Br}}^{82}$, ${\mathrm{Kr}}^{85}$, ${\mathrm{Rb}}^{86}$, ${\mathrm{Sb}}^{122}$, ${\mathrm{Xe}}^{125}$, ${\mathrm{Xe}}^{133}$, ${\mathrm{W}}^{187}$, and ${\mathrm{Rn}}^{222}$ ions in the energy region 0.1-1.0 MeV have been measured in oriented tungsten single crystals by means of the electrochemical peeling technique. Wide-angle scattering of protons has, in some cases, been used to align the crystals to within \ifmmode\pm\else\textpm\fi{}0.1\ifmmode^\circ\else\textdegree\fi{}. The range distributions consist of two peaks---a broad one at approximately the depth predicted for an amorphous target, and a sharp one at a much larger depth. The latter, caused by channeling, falls off very sharply on the more penetrating side. This well-defined paximum range has approximately an ${E}^{\frac{1}{2}}$ dependence, characteristic of electronic stopping. From range-energy relations, electronic-stopping cross sections are derived at a constant velocity of 1.5\ifmmode\times\else\texttimes\fi{}${10}^{8}$ cm/sec. The electronic stopping is roughly $\frac{1}{3}$ of that predicted for amorphous tungsten, but exhibits a strongly oscillating dependence on ${Z}_{1}$. These ${Z}_{1}$ oscillations are much larger than those reported previously in amorphous foils. Alto, the range dispersion between the $〈100〉$ and $〈110〉$ directions exhibits an oscillating ${Z}_{1}$ dependence. For perfectly channeled Xe ions along the $〈100〉$ directions, electronic stopping is shown to dominate down to a few keV. The contributions from nuclear and electronic stopping become equal at about 4 keV, whereas the corresponding transition energy in amorphous tungsten would be \ensuremath{\sim}2.5 MeV. The nuclear stopping contribution can be fitted theoretically by means of the momentum approximation down to \ensuremath{\sim}0.5 keV. It is shown that, under certain conditions, range measurements in monocrystals provide information about amorphous ranges that is otherwise difficult to obtain. Good agreement between experiments and theoretical predictions is obtained. The present experiments also provide some information on the highly penetrating tail (supertail), earlier reported in tungsten. For comparison, a few range distributions have been measured in aluminum single crystals. The observed behavior is similar to that in tungsten, but the channeling is much less pronounced.

Radiation from the T 2 4 State of Cr 3 + in Ruby and Emerald

Abstract: The first appreciable decrease in the lifetime of the $^{2}E$ state of ${\mathrm{Cr}}^{3+}$ in ruby and emerald as the temperature is raised is shown to be the result of populating the shorter-lived $^{4}T_{2}$ level in thermal equilibrium with the metastable $^{2}E$. The direct transition from the $^{4}T_{2}$ to the ground $^{4}A_{2}$ state is shown to be mostly radiative. In both crystals, the emission peak of the $^{4}T_{2}\ensuremath{\leftrightarrow}^{4}A_{2}$ transition is shifted considerably toward longer wavelength compared to the absorption peak of that transition. The reduction in lifetime and quantum efficiency at very high temperatures is also considered.

Optical Absorption in Single-Domain Ferroelectric Barium Titanate

Abstract: The optical-absorption coefficients for polarized light have been measured for single-domain crystals of $n$-type BaTi${\mathrm{O}}_{3}$. The measurements were made over a wavelength range from approximately 0.4 to 12 \ensuremath{\mu}, and over a temperature range from 26 to 130\ifmmode^\circ\else\textdegree\fi{}C. This temperature range includes both the cubic and the ferroelectric tetragonal states. The most significant feature of the measurements is a broad peak in the optical-absorption coefficient $\ensuremath{\alpha}$ centered near a photon energy of 0.6 eV; the absorption exhibits a threshold at a photon energy of approximately 0.2 eV. In addition, a large anisotropy, comparable to that observed in the transport behavior, is noted in the infrared values of $\ensuremath{\alpha}$ in the tetragonal state. It is shown that a consistent explanation of the optical-absorption properties is that most of the absorption in the visible and near infrared is the result of optical excitation of electrons in impurity states approximately 0.2 to 0.3 eV below the conduction-band minimum, superimposed on a free-carrier and lattice-absorption background. The deep impurity states are probably associated with oxygen vacancies.

Phonon-Quasiparticle Interactions in Dilute Solutions of He 3 in Superfluid He 4 : I. Phonon Thermal Conductivity and Ultrasonic Attenuation

Abstract: Expressing the interaction between long-wavelength phonons and ${\mathrm{He}}^{3}$ quasiparticles in dilute solutions of ${\mathrm{He}}^{3}$ in ${\mathrm{He}}^{4}$ entirely in terms of macroscopic observables, we calculate the attenuation of first sound due to the ${\mathrm{He}}^{3}$ viscosity, and the rate of scattering of phonons from the ${\mathrm{He}}^{3}$. The results for the attenuation are in excellent agreement with recent experiments. In addition, we calculate the thermal conduction due to phonons for $T\ensuremath{\lesssim}0.6$ \ifmmode^\circ\else\textdegree\fi{}K; the conductivity is limited at very low temperatures by ultrasonic attenuation, while at higher temperatures it is predominantly limited by elastic phonon-quasiparticle scattering.

Study of Ionization-Induced Radiation Damage in MgO

Abstract: A study of the 2.3-eV absorption band in MgO crystals irradiated with electrons and gamma rays at 7, 80, and 305\ifmmode^\circ\else\textdegree\fi{}K has been made. This broad band, which has been designated as ${V}_{1}$, has a half-width of 0.96 eV at 5 and 78\ifmmode^\circ\else\textdegree\fi{}K and could be optically bleached even at liquid-helium temperature. When specimens were bleached with polarized light, it was found that there was no dichroism in any of the $〈100〉$, $〈110〉$, or $〈111〉$ directions at 5\ifmmode^\circ\else\textdegree\fi{}K. The colorability of the crystals was strongly dependent on their thermal treatment. The concentration of centers responsible for the 2.3-eV absorption could be enhanced by quenching the crystals from high temperature prior to irradiation and could be suppressed by slow cooling of the specimens to room temperature. The effects of these heat treatments were found to be reversible. The presence of certain impurities in the crystals was observed to suppress the 2.3-eV coloration, but no correlation between the ${\mathrm{Fe}}^{3+}$ concentration or the total Fe concentration and the maximum coloration in a quenched crystal was observed. The afterglow luminescence was also surveyed in the energy range 1.3-5.0 eV.

Far-Infrared Optical Properties of Ca F 2 , Sr F 2 , Ba F 2 , and Cd F 2

Abstract: The absorption coefficients and indices of refraction of pure Ca${\mathrm{F}}_{2}$, Sr${\mathrm{F}}_{2}$, Ba${\mathrm{F}}_{2}$, and Cd${\mathrm{F}}_{2}$ at 300, 200, 80, and 5\ifmmode^\circ\else\textdegree\fi{}K have been measured at all accessible frequencies between 300 Gc/sec and the transverse-optic (TO) frequencies of the crystals. The absorption has been interpreted in terms of 2-phonon difference processes involving high-energy phonons. The indices of refraction can be described by a harmonic rigid-ion approximation to the crystal. The temperature dependences of the long-wavelength dielectric constants and the TO frequencies have been measured and related to the Szigeti expression for the effective ionic charges.

Correlation of Electron Paramagnetic Resonance and Optical-Absorption Spectra of Ca F 2 : Yb 3 +

Abstract: An account is given of a combined optical and paramagnetic resonance investigation of trivalent ytterbium ions in ten different sites in calcium fluoride. Correlation between site geometry and optical absorption has been obtained for six of these by examining crystals prepared by different methods. A single optical-absorption line was observed for all but one of these sites, so that it was impossible to deduce the magnitudes of the Stark splittings. However, there is some evidence to indicate that they are large (of the order of hundreds of ${\mathrm{cm}}^{\ensuremath{-}1}$), rather than small, as suggested by Low. A new rhombic paramagnetic resonance is also reported and is thought to arise from pairs of ${\mathrm{Na}}^{+}$ and ${\mathrm{Yb}}^{3+}$ ions on adjacent ${\mathrm{Ca}}^{2+}$ sites.

Optical Properties of α − M n S

Abstract: Optical characteristics of $\ensuremath{\alpha}\ensuremath{-}\mathrm{M}\mathrm{n}\mathrm{S}$ have been determined from 0.02 to 14 eV. Single crystals were used for measurements above 0.05 eV. The shift with temperature of the $^{6}A_{1g}\ensuremath{\rightarrow}^{4}A_{1}$ crystal-field splitting peak is shown to be reasonably attributed to the effect of magnetic ordering. A broad weak band near 1 eV may be either an impurity band or the unallowed transition $\mathrm{Mn}(3{d}^{++})\ensuremath{\rightarrow}\mathrm{Mn}(3{d}^{+})$. The absorption edge at 2.8 eV is explained as due to transitions from the wide ${\mathrm{S}}^{2\ensuremath{-}}(3p)$ band to the narrow ${\mathrm{Mn}}^{+}(3d)$ band. Two tiny peaks in the edge at 2.96 and 3.05 eV are suggested to be zero-phonon spin-orbit-split exciton peaks associated with this transition. High-energy absorption structure taken from Kramers-Kronig analysis of ultraviolet reflectance data are assumed to be associated with wide-band to wide-band transitions as in nonmagnetic compounds. A simple band diagram is suggested to explain the electronic transitions. The reststrahlen reflectance on a pressed powder was analyzed and the following parameters obtained: low- and high-frequency dielectric constants, 20 and 6.8; longitudinal and transverse optical mode frequencies, 320 and 185 ${\mathrm{cm}}^{\ensuremath{-}1}$.

Optical Constants and Exciton States in KCl Single Crystals. I. The Low Temperature Properties

Abstract: Optical measurements were carried out on the reflectivity and absorption tails of KCl single crystals over the region 6.0 to 12 ev in the temperature range 10 to 573°K. With use of these data, Kramers and Kronig analysis was made on reflectivity spectra for three different temperatures 10, 78 and 295°K. The analysed spectra of important optical constants are presented in this article, and their properties are discussed in order to clarify the excitonic picture in a single crystalline lattice. The result is analysed along the theories of Toyozawa and Elliot. It was found that the first exciton line shape and the plateau in the higher energy side of the step are explained by them. The two overlapping components of the first band can be well separated at low temperatures in the case of single crystals, and this permits us to determine an oscillator strength for each component as 0.27 and 0.375 for \(\left(\frac{3}{2},\frac{1}{2}\right)\)- and \(\left(\frac{1}{2},\frac{1}{2}\right)\)-transition, respectively....

V K Centers and Recombination Luminescence in Rubidium Iodide and Sodium Iodide

Abstract: ${V}_{K}$ centers are introduced into both NaI and RbI by low-temperature irradiation of crystals containing electron-attaching impurities. These centers are identified by optical-absorption spectra and by the anisotropic absorption of oriented centers. ${V}_{K}$ centers are stable in NaI below about 58\ifmmode^\circ\else\textdegree\fi{}K, and in RbI below about 125\ifmmode^\circ\else\textdegree\fi{}K. These temperatures permit an estimate of the thermal activation energy for migration of the $\mathrm{I}_{2}^{}{}_{}{}^{\ensuremath{-}}$ as 0.15 and 0.32 eV, respectively. Recombination of electrons with ${V}_{K}$ centers in both crystals produces the "intrinsic" luminescence characteristic of the pure crystal. The connection with exciton states is discussed briefly.

Far Infrared Spectra of Al 2 O 3 : Cr 3 + and Al 2 O 3 : Ti 3 +

Abstract: The absorption sepctrum of ruby containing 1% ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ has been observed at 77\ifmmode^\circ\else\textdegree\fi{}K and below, over the range from 10 to 160 ${\mathrm{cm}}^{\ensuremath{-}1}$, using a large grating spectrometer. Although chromium ion pairs are known to have energy-level intervals in this region, no absorption lines were observed, even in a sample 15-cm long. Thus, these spin-changing transitions are, as might be expected, quite forbidden. In ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$:${\mathrm{Ti}}^{3+}$, levels were observed at 37.8 and 107.5 ${\mathrm{cm}}^{\ensuremath{-}1}$ with strong transitions connecting them. A broad lattice absorption was also observed. The position of the 37.8-${\mathrm{cm}}^{\ensuremath{-}1}$ level is in reasonable agreement with predictions from earlier microwave relaxation measurements in the ground state. The infrared linewidths are large, indicating a rapid relaxation without spin flip. The level spacings are smaller than predicted by crystal-field theory, indicating that the effective trigonal field and spin-orbit coupling are reduced by a dynamic Jahn-Teller effect.

Measurement of the Laser Transition Cross Section for Nd + 3 in Yttrium Aluminum Garnet

Abstract: This paper reports measurements of the room-temperature laser transition cross section of ${\mathrm{Nd}}^{+3}$ in yttrium aluminum garnet at 1.06 \ensuremath{\mu}. One method used is based on the measured upper-state lifetime and a determination of the fluorescence branching ratio for this state. The value thus determined is 3.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}19}$ ${\mathrm{cm}}^{2}$. The second method involves measurement of the ratio of fluorescent intensities from the upper laser level to the ground state and to the lower laser level, and measurement of the cross section in absorption of the transition which involves the ground state. The second method yields a value of 2.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}19}$ ${\mathrm{cm}}^{2}$. The difference represents the contribution of fluorescence to high-lying levels (not included in the determination of branching ratio) and nonradiative transitions. The probable experimental accuracy in both methods is \ifmmode\pm\else\textpm\fi{}15%.

Spin-Exchange Cross Sections for Rb 87 - Rb 87 and Rb 87 - Cs 133 Collisions

Abstract: In a hyperfine-optical-pumping experiment we employed the Franzen transient method to determine the total spin-exchange cross sections for ${\mathrm{Rb}}^{87}$-${\mathrm{Rb}}^{87}$ and ${\mathrm{Rb}}^{87}$-${\mathrm{Cs}}^{133}$ collisions at 78\ifmmode^\circ\else\textdegree\fi{}C. Values determined in this way were: $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Rb}}^{87})=(1.9\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$ and $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Cs}}^{133})=(2.3\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$. A large difference between the ground-state hyperfine populations was established by pumping with light absorbable by atoms in only one hyperfine level. In the presence of a second unpumped species, the resulting polarization relaxed with a characteristic rate of $\frac{1}{\ensuremath{\tau}}=\frac{1}{T}+\frac{1}{{T}_{S1}}+\frac{1}{{T}_{E1}}$, where $T$ is the non-spin-exchange relaxation time and ${T}_{S1}$ and ${T}_{E1}$ are the self- and cross-exchange times. Then $\ensuremath{\tau}$ was obtained by fitting the signal to a single exponential and applying a small correction ($\ensuremath{\approx}10%$) to account for the fact that the signal is only approximately proportional to the polarization (and hence to a single exponential). The relaxation measurement utilized rapid data accumulation with a Kerr-cell shutter and pulse-height analyzer. The cross section can be easily deduced from the relaxation times if the corresponding densities are known. Each density was measured by determining the integral over all frequencies of the absorption coefficient by means of a scanning Fabry-Perot interferometer. We describe how to remove the effect of the Fabry-Perot on the true emission and absorption profiles.

Optical Constants and Exciton States in KCl Single Crystals : II. The Spectra of Reflectivity and Absorption Constant

Abstract: The reflectivity between 6 eV and 12 eV and the absorption tails both in the intrinsic region and in the impurity bromine band region of KCl single crystals are studied as a function of temperature in the range 10°K to 573°K. The absorption measurement complements the earlier results reported in 1960 1) and 1961 2) in improving the wavelength scale and in extending the temperature range. The present data allow us to investigate the phonons interacting with \(\varGamma\)-exciton, yielding \(\hbar\omega{=}1.42{\times}10^{-2}\) eV (for (3/2, 1/2-component)) and =1.59×10 -2 eV (for (1/2, 1/2)-component)) for phonons effective to the peak shift and \(\hbar\omega{=}1.47{\times}10^{-2}\) eV for phonons taking part in the optical absorption processes in the intrinsic Urbach tail. The temperature dependence is presented on the absorption constant spectra up to 12 eV and dispersion spectra n up to the \(\varGamma\)-exciton region, each being derived by the Kramers and Kronig analysis with the use of the above data....

Paraelectric-Ferroelectric Phase Boundaries in Semiconducting Perovskite-Type Crystals

Abstract: The formation of first-order paraelectric-ferroelectric phase boundaries in semiconducting crystals of the ferroelectrics K${\mathrm{Ta}}_{0.65}$${\mathrm{Nb}}_{0.35}$${\mathrm{O}}_{3}$ and BaTi${\mathrm{O}}_{3}$ has been studied. It is shown that in crystals having carrier concentrations greater than ${10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, sharp first-order phase boundaries can form during the paraelectric-ferroelectric phase transformation, and that such a transformation results in the formation of reproducible single-domain crystals. The direction of the cubic-to-tetragonal phase boundary is found to differ from a {110} lattice plane by approximately 5\ifmmode^\circ\else\textdegree\fi{}, i.e., the boundary-plane normal is 40\ifmmode^\circ\else\textdegree\fi{} from the direction of the crystal $c$ axis. This result is in excellent agreement with existing crystallographic theories. Data are also presented on the infrared photo-ionization absorption anisotropy and the electrical resistance anisotropy measured on a single-domain semiconducting crystal of K${\mathrm{Ta}}_{0.65}$${\mathrm{Nb}}_{0.35}$${\mathrm{O}}_{3}$.

Theory of Tunneling, Including Photon-Assisted Tunneling, in Semiconductors in Crossed and Parallel Electric and Magnetic Fields

Abstract: Tunneling phenomena in crossed electric and magnetic fields cannot be properly described using the one-band effective-mass approximation. For this purpose, the two-band Hamiltonian is solved in the presence of crossed electric and magnetic fields and also in parallel fields. For crossed fields, two types of solutions are obtained. The first, for $ElH{(\frac{{\mathcal{E}}_{g}}{2{m}^{*}{c}^{2}})}^{\frac{1}{2}}$, are of the harmonic-oscillator type, with quantized energy levels. In this region there is no interband tunneling in a pure material. In the region of high electric field, where $EgH{(\frac{{\mathcal{E}}_{g}}{2{m}^{*}{c}^{2}})}^{\frac{1}{2}}$, the solutions are of the electric-field type with a continuous energy spectrum. The analogy of this model to the motion of free classical relativistic electrons in crossed fields is discussed. WKB solutions in the region of high electric field are used to calculate tunneling (Zener) current and photon-assisted tunneling [Franz-Keldysh (FK) effect]. The Hamiltonian is solved to obtain quasistationary solutions, neglecting a term which acts as the perturbation causing the Zener tunneling. The tunneling integrals are computed by the method of steepest descent. The results are nearly identical to those of Aronov and Pikus, obtained by a different method. In general, the magnetic field decreases both Zener and FK tunneling. The result for Zener tunneling predicts that the current will depend on $E$ and $H$ approximately as $\mathrm{exp}(\frac{{\ensuremath{-}H}^{2}}{{E}^{3}})$, in good agreement with experiment. In the FK effect, for photon energies close to that of the gap, the ratio of the absorption in crossed fields to that at $H=0$ varies with frequency and field approximately as $\mathrm{exp}[\frac{\ensuremath{-}{({\mathcal{E}}_{g}\ensuremath{-}\ensuremath{\hbar}\ensuremath{\omega})}^{\frac{5}{2}}{H}^{2}}{{E}^{3}}]$. This is confirmed experimentally, both in the frequency and field dependence, by Reine, Vrehen, and Lax. Thus the main features of electron tunneling in crossed fields can be explained by a WKB treatment which in addition provides a good physical picture of the tunneling process. In order to provide a unified picture of tunneling in crossed and parallel fields, we also obtain expressions for Zener and FK tunneling in parallel fields using WKB solutions to the two-band model. The results for FK tunneling are very similar to those of the preceding paper, in that the electron motion separates into quantized motion transverse to the magnetic field and nonquantized motion parallel to both fields. The magnetic field reduces the tunneling by increasing the effective energy gap by the energy of the transverse motion. Our expressions reduce to those of the preceding paper in the limit of large ${\mathcal{E}}_{g}$. The ratio of the absorption in parallel fields to that at $H=0$ varies approximately as $\mathrm{exp}[\frac{\ensuremath{-}{({\mathcal{E}}_{g}\ensuremath{-}\ensuremath{\hbar}\ensuremath{\omega})}^{\frac{1}{2}}H}{E}]$. The result for Zener tunneling predicts $\mathrm{exp}(\frac{\ensuremath{-}H}{E})$ behavior, in contrast to $\mathrm{exp}(\frac{\ensuremath{-}{H}^{2}}{{E}^{3}})$ for crossed fields. The model in the preceding paper does not predict any Zener tunneling.

Infrared Studies of Defect Production in n -Type Si: Irradiation-Temperature Dependence

Abstract: Infrared absorption measurements of electron-irradiated oxygen-doped $n$-type silicon are presented. The silicon samples were electron irradiated at carefully controlled irradiation temperatures between 75\ifmmode^\circ\else\textdegree\fi{}K and room temperature. Since the free Si vacancy, and presumably also the free Si interstitial, are mobile at these temperatures, intensity measurements of the vacancy-oxygen center, as well as of newly observed infrared absorption bands, provide a monitor of the intrinsic defect production. For irradiation temperatures below 100\ifmmode^\circ\else\textdegree\fi{}K, semilog plots of the intensities of the absorption bands for identical samples versus the reciprocals of their irradiation temperatures yield straight lines having the form $\ensuremath{\alpha}=\mathrm{const} {e}^{\frac{\ensuremath{-}\ensuremath{\Delta}E}{\mathrm{kT}}}$. On the basis of the slopes and intensities of these lines, the absorption bands can be divided into two groups. The more intense group, which includes the 836-${\mathrm{cm}}^{\ensuremath{-}1}$ ($A$-center) band and bands at 922, 932, and 865 ${\mathrm{cm}}^{\ensuremath{-}1}$, has a common energy $\ensuremath{\Delta}E=0.05\ifmmode\pm\else\textpm\fi{}0.005$ eV. Less intense bands at 936, 945, and 956 ${\mathrm{cm}}^{\ensuremath{-}1}$ are found to have a common energy $\ensuremath{\Delta}{E}^{\ensuremath{'}}=0.10\ifmmode\pm\else\textpm\fi{}0.02$ eV. These results are interpreted on the basis of a metastable interstitial-vacancy pair model in which the irradiation-temperature dependence of the formation of the defect-impurity complexes results from the temperature dependence of the production of intrinsic defects. On the basis of this model, the difference in the barriers to liberation and recombination of the metastable pair is 0.05 eV for $n$-type Si. The more intense infrared bands are concluded to be associated with complexes composed of a single vacancy or a single interstitial trapped at an oxygen impurity atom or group of atoms. Since the energies $\ensuremath{\Delta}{E}^{\ensuremath{'}}$ of the weaker infrared absorption bands are approximately twice those for the strong infrared bands, it is suggested that the weaker bands are associated with complexes composed of two intrinsic defects trapped at an oxygen impurity center.

Optical Properties of Gallium Arsenide-Phosphide

Abstract: The index of refraction of Ga (${\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x}$) is measured as a function of photon energy by the minimum-angle-of-deviation prism method at 300 and ${87}^{\mathrm{o}}$K. The dielectric constant in the optical region is found to vary linearly as a function of mole fraction of GaP between the values for GaAs and GaP. Curve-fit data are presented which allow calculation of index of refraction at 300 and ${87}^{\mathrm{o}}$K for a given crystal composition $x$ and photon energy. Transmission data on Ga (${\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x}$) are obtained at 300 and ${77}^{\mathrm{o}}$K. The reflectivity is calculated from the index of refraction and is used to calculate the absorption constant, assuming multiple internal reflections in the crystal. In the infrared, true free-carrier absorption is observed for degenerate GaAs-rich mixed crystals, whereas absorption due to transitions from donor levels to the conduction band is dominant in GaP-rich mixed crystals. The band-to-band absorption seen by Spitzer and Whelan in GaAs is observed in GaAs-rich alloys, and is thought to be due to transitions from the (0,0,0) minimum to minima in the $〈111〉$ directions. Finally, the absorption edge is investigated, and the Burstein shift of the absorption edge to higher energies with increased doping is observed, as well as shifts to lower energies due to compensation. In all cases, the fundamental absorption edge is found to exhibit an exponential dependence on photon energy.

Electron Paramagnetic Resonance of Copper in Beryllium Oxide

Abstract: Paramagnetic-resonance absorption of copper-doped single crystals of beryllium oxide has been investigated at 9 GHz. The best-fit values to a spin Hamiltonian with $S=\frac{1}{2}$ are $|{g}_{\ensuremath{\parallel}}|=1.709\ifmmode\pm\else\textpm\fi{}0.002$, $|{g}_{\ensuremath{\perp}}|=2.379\ifmmode\pm\else\textpm\fi{}0.001$, $|{A}_{\ensuremath{\parallel}}|=(50\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, $|{A}_{\ensuremath{\perp}}|=(108\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, and $|Q|=(11\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$, where the hyperfine values refer to the ${\mathrm{Cu}}^{63}$ isotope, for which $I=\frac{3}{2}$. The observations are interpreted as due to ${\mathrm{Cu}}^{2+}$ substitutional for beryllium at normal lattice sites. Crystal-field theory which incorporates covalent bonding has been used to interpret these results in terms of the $3{d}^{9}$ configuration of ${\mathrm{Cu}}^{2+}$ in ${C}_{3v}$ symmetry. The experimental results are shown to be consistent with the theory, which yields an orbital reduction factor of 0.6, and values for $〈{r}^{\ensuremath{-}3}〉$ and the contact hyperfine interaction close to those for the free ion. The results are also compared with some other cases of $3{d}^{9}$ ions in tetrahedral coordination.

Search for massive particles in cosmic rays

Abstract: A search for heavy particles with a mass greater than that of a nucleon, the existence of which has been suggested by higher-symmetry schemes, was performed with an apparatus set up at Echo Lake, Colorado (elevation 10 600 ft). The search was sensitive to strongly interacting particles with masses in the range 5-15 BeV, with no restriction imposed on their electric charge. The method used was to measure the time interval between the arrival of strongly interacting particles and accompanying air shower particles. This information, coupled with information from a measurement of the particle's energy and range of absorption in a total absorption spectrometer, enabled a distinction to be made between massive elementary particles, nucleons, and nuclei. In an operating period of 1542 h and with an aperture of 0.78 ${\mathrm{m}}^{2}$ sr, one delayed event was found whose behavior in the total absorption spectrometer was atypical of a nucleon or nucleus. If one considers this event to represent the arrival of a massive particle, then its mass, calculated assuming that its production occurred 1 km above the apparatus, is approximately 6.5 BeV. This one event corresponds to a flux of the order of ${10}^{\ensuremath{-}10}$ ${({\mathrm{cm}}^{2}\phantom{\rule{0ex}{0ex}}\mathrm{s}\mathrm{e}\mathrm{c}\phantom{\rule{0ex}{0ex}}\mathrm{s}\mathrm{r})}^{\ensuremath{-}1}$, where a correction for detection efficiency has been included. As there is also an 8% probability that this event was a nucleon, we do not regard this as significant evidence for the existence of a massive elementary particle, but rather as setting an effective upper limit to the flux of such particles.