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The polarization of the luminescence light shows the importance of the thermalization time for electrons, excited in the conduction band by circularly polarized light of energy larger than the band gap. The influence of the thermalization time on the oscillations of the light polarization as a function of the excitation energy is discussed and applied to GaSb and GaAs. Besides, the effect of a transverse magnetic field (”Hanle effect„) in a three level atomic system is extended to a semiconductor. This allows to explain the Hanle effect that had not yet been interpreted for such an energy of excitation in a semiconductor. A new form of Hanle line is predicted and the experimental conditions to observe it are specified. La polarisation de la lumiere de luminescence montre l'importance du temps de thermalisation des electrons, cree s dans la bande de conduction par une lumidre polarisee circulaire d'energie superieure a celle de la bande interdite. L'influence du temps de thermalisation sur les oscillations de la polarisation de la lumiere en fonction de l'energie d'excitation est discutee et appliquee au GaSb et ail GaAs. De plus, l'effet d'un champ magnetique transverse („effet Hanle) dans un systeme atomique a trois niveaux est etendu iL un semiconducteur. Ceci nous permet d'expliquer l'effet Hanle, qui n'avait pas encore ete interprete pour une excitation de cette energie dans un semiconducteur. Nous prevoyons une nouvelle forme pour la raie correspondant a l'effet Hanle et precisons les conditions experimentales necessaires pour I'observer.

On the basis of earlier works by Gross et al., we have studied and compared the excitation spectra of three main types of samples : « pur » « impur » and surface-polluted. This lead us to distinguish two main channels for the transfer of excitation in the crystal, when exciting . energy is greater than the gap. The main channel is creation of free electron-hole pairs which may be bound to form excitons. But the straight forward creation of excitons in their band is possible, with longitudinal optical phonon participation. This contribution to the excitonic luminescence becomes the most important when only a few free pairs are bound into excitons, a situation which happens in doped material. From this point of view, the surface-polluted samples form a surprizing intermediate case between pur and doped samples. ' Then, it comes out that the created excitons lose very quickly a kinetic energy NfiO, where f 1 . Q is the energy of one LO phonon ; and that the thermalization does not occur, because the total lifetime of excitons is shorter than the interactions time with acoustical phonons. This gives rise to peaks in the spectra, separated by fifi. A rather simple calculation corroborates this point of view and reproduces the correct ratio of the intensities of the peaks. One deduces informations about the mechanisms of energy relaxation, binding on impurities, and radiative recombination of excitons. From a more geaeral point of view, this study points out first the validity of the notion of exciton band, even at kinetic energies much greater than the binding energy ; second, the opposition between electron-hole pairs (where the two particles behave without any coherence) and the excitons, characterized by a « memory of their excitation conditions ». This notion happens to be of most importance in the experiments of spin orientation by optical pumping. (*) Laboratoire associe au C.N.R.S. ; Universite de Paris VII, 2, place Jussieu, Paris 5e. (**) G.P.E.C. Departement de Physique, 70, route Leon-Lachamp, 13009 Marseille. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974313 C3-84 R. PLANEL, C. BENOIT A LA GUILLAUME ET A. BONNOT

The main characteristics of the current obtained when photo-injecting electrons into glassy 3-methylpentane have been investigated: decrease of the thermalization range during glass configurational relaxation, space charge build-up inside the sample due to deeply trapped electrons in the glass and effect of the excitation light wavelength. The thermalization range is found to be ≈ 80A.

The modulation of low temperature (2°K) molecular crystal phosphorescence by submicrosecond duration heat pulses is discussed in connection with the study of rates of triplet energy transfer and trap thermalization. A phenomenological discussion of the dynamics of heat pulse propagation in molecular solids is presented and estimates of the thermal relaxation time of the lattice are obtained. It is suggested that these times are sufficiently short to permit investigation of the dynamics of exciton energy transport in molecular crystals. The details of the technique are discussed and results from several experiments are presented. Additionally, heat pulse modulation of the electron paramagnetic spin distribution of radiative triplet states is discussed and some preliminary results presented.

In this review we discuss the different aspects of positron annihilation in metals that involve the dynamics of positron motion before annihilation. The emphasis is on the theory, but also some experimental evidence is quoted. The topics covered are: slowing down and thermalization, effective mass, temperature dependence of positron vacancy trapping, positron channeling, and escape of low energy positrons from metal surfaces.

The propagation of thermal neutron waves has been studied in four beryllium parallelepipeds. The transverse bucklings of these parallepipeds ranged from 0·0497 to 0·2572 cm−2, values which are greater than the critical buckling (0·00116 cm−2). From the space-time profiles, the dispersion law for beryllium was deduced over the frequency range 0 < ω < 1000 Hz. For the larger systems good agreement was found with calculations based on thermalization theory at frequencies less than 600 Hz. The effect of continuum contamination was apparent in all the systems but in the larger blocks this contamination had about the same magnitude and attenuation as the discrete modes. For the smaller systems, the continuum contamination was associated with neutrons having energies below the Bragg cut-off and was manifested by oscillations in the complex inverse relaxation lengths at the higher frequencies.

The local aspect of the thermalization of thermal radiation due to the interaction of thermal radiation with matter is explored. It is shown that for absorption and emission interactions some well-known phenomenological statements of irreversible thermophysics are indeed relevant. For scattering interactions the entirely different picture that emerges is also briefly discussed. The local analysis is based on the concepts of temperature and entropy of nonequilibrium thermal radiation fields, as originally introduced by Planck, and shows that these concepts are susceptible of a very natural thermodynamic interpretation.

The entropy generated in an expanding gas-filled universe is calculated for an expansion that takes place in a series of steps during which the gas is collisionless. At the end of each step the gas is allowed to thermalize before undergoing its next expansion step. The results of the calculation show that entropy is generated only during a brief period in the evolution of the gas and that the total dimensionless entropy per baryon generated (∼10) is insufficient to explain the existence of the 108 per baryon of dimensionless entropy that appears to exist in the universe.

Measurements indicate a thermalization of a trapped electron beam. The resulting hot beam-plasma system is unstable for new waves. The succession of instabilities leads to a stepwise diffusion in velocity space of beam particles to smaller velocities.

We investigate the importance of positron phonon interaction for the many body effects observed in positron annihilation in metals. The interaction is formulated as the screened Coulomb interaction of the positron with the polarization charge of the metal produced by lattice vibrations. The phonon contribution to the effective mass is found negligibly small. Due to the interaction with phonons the equilibrium positron momentum distribution deviates from a Boltzmann distribution leading to a larger thermal smearing of the annihilation curves than expected from the rather small effective mass. The positron energy loss in the thermalization process due to phonon excitation is discussed and found comparable to the energy loss due to the excitation of electron hole pairs in the experimentally interesting temperature range.

A high flux fast neutron was produced by the (d, n) reaction of a lithium metal target. A thick lithium layer for the target was prepared by a simple method of melt-coating on a copper plate. The fast neutron (>9 MeV) flux at a distance of 6mm from the target was (9.0±1.6)×l06 n/cm2·sec·μA with use of a 2.0 MeV deuteron beam. A flux of 2.7×109 n/cm2·sec was obtained by bombarding the target with the deuteron beam of 300 μA.

The time, energy and space-dependent Boltzmann equation has been studied in order to obtain information on the diffusion-cooling coefficient and other pulsed neutron parameters. In order to interpret experiments correctly it is essential to know what is meant by buckling in an energy-dependent system. It is shown by an exact spatial analysis of the energy spectrum that this can be identified with the square of the infinite medium Fourier transform variable only if the extrapolated endpoint Z0 is itself a function of buckling. The value of Z0(B2) has been calculated, together with the average energy of the spectrum across the system.

A theoretical study of the pulsed neutron problem and of steady-state neutron spectra has been made in mixtures of H2O and D2O in the temperature range 253 to 4°K. Mixtures with D2O content of 0, 5...

The ultraviolet photoejection of electrons from ferrocyanide, in various water—alcohol mixtures, was studied by using N2O as a scavenger. The quantum yields of solvated electrons were obtained. The results can not be interpreted in terms of a single parameter of the solvent such as dielectric constant, relaxation time, or diffusion coefficient. Mozumder's theory was chosen as a possible way of interpretation. The agreement between the calculated and experimental results is good, provided enough care is taken in choosing the relaxation times. The thermalization length of the ejected electrons was found to be 30 A, independent of the particular water—alcohol mixture.

The dependence of the total luminescence light emitted under excitation at 90 °K and of the total thermoluminescent glow light after excitation of a KCl:Tl crystal on the photon excitation energy in the range 7.0 to 10.5 eV have been investigated. The role of the displacement of the electron–hole pair components before thermalization in the luminescence and energy accumulation processes is considered. [Russian Text Ignored].

Some lattice versions of the wind‐tree model of Ehrenfest are introduced and studied. They include two versions in which overlapping of tree particles is forbidden, a third in which it is allowed, and a fourth in which it is allowed but results in a finite repulsive force. In every case it is found that the mean‐square displacement Δ(t) of the wind particles at time t is bounded independently of t at sufficiently high density of the trees. This is in sharp contrast with the Einstein relation Δ(t) = O(t) as t → ∞, which might be expected to hold at low densities. Randomization of the initial velocity of a wind particle is also shown to occur in a certain sense, and upper bounds on a recurrence time are obtained at high density. On the other hand, it is shown that thermalization does not occur even at low densities.

The formalism of the reproducing kernel method is used to evaluate exponents of bounded operators. Reproducing kernels are built with interpolating properties that do take into account any approximate knowledge of the spectrum. The explicit solution of linear evolution equations is reduced to the solution of a few static problems.

Secondary emission results show that the energy needed to create an electron-hole pair by low-energy electron bombardment of anthracene crystals is less than 75 eV, and that the thermalization distance of a secondary is such that initial recombination cannot account for the low yield of one pair per 400 eV obtained by Delany and Hirsch. It is suggested that columnar recombination accounts for at least part of the difference. Preliminary results of characteristic losses of 41 keV electrons in anthracene are reported. The dominant loss, in the range 14–25 eV, is a solid state effect, tentatively assigned to collective oscillations of the π electrons. The free path for excitation of these oscillations by low-energy electrons should be very short and electron-hole pair creation would proceed largely through ionization of these plasmons. The small value of the pair-creation energy suggests that radiative recombination inside a column could play a large role in fast scintillation processes in anthracene.

A model describing the kinetics of electron and hole (exciton) recombination at isoelectronic impurities is presented. The model considers three separate occupation states for the isoelectronic center, i.e., empty, electron (hole) occupied, and exciton occupied As a result, it generalizes the conventional two-state Shockley-Read-Hall (SRH) model which cannot be applied to recombination at isoelectronic centers. A detailed analysis is given of the time-dependent behavior of the radiative recombination at iseolectronic centers. Included in the analysis are the effects of nonradiative Auger and thermalization process. It is shown that under steady-state conditions the recombination at isoelectronic centers can be described by the SRH model, provided that the temperature is not so high that thermalization of the electron (hole) occupied state becomes important. The radiative decay time is shown to depend at low temperatures on thermal dissociation of excitons bound to the centers, and at high temperatures on Auger processes and thermalization of the electron (hole) occupied state. Using the model, a good fit is obtained to the measured time decay of the red luminescence from p-type Zn,0-doped GaP for $0lTl440\ifmmode^\circ\else\textdegree\fi{}$K. On the basis of the agreement between calculated and measured time-decay curves, values are given for the Auger parameters, and for the electron and hole-capture lifetimes of the isoelectronic Zn-O trap.

The fluorescence intensities and lifetimes of various no-phonon lines in ruby samples with 2.1 and 0.94% ${\mathrm{Cr}}^{3+}$ were studied from 13 to 700\ifmmode^\circ\else\textdegree\fi{}K. The temperature dependences of the intensities of numerous lines were used to determine the energy levels of two pair systems. The relative intensities of the single-ion ($R$) lines and the pair ($N$) lines are proportional to Boltzmann factors ${e}^{\frac{\ensuremath{-}\ensuremath{\Delta}E}{\mathrm{kT}}}$, where $\ensuremath{\Delta}E$ is the difference in energy of the metastable states, at high temperatures but not at low temperatures. The deviation from this law is greater and occurs at higher temperatures in the less concentrated sample. The fluorescence decays of the $R$ and $N$ lines are pure exponentials in the temperature region where the $N$ lines follow a Boltzmann law; at low temperatures the $N$ lines have an initial rise in fluorescence and then a decay. These results are interpreted in terms of coupled fluorescence systems consisting of single ions and pairs. A phonon-assisted cross-relaxation coupling process is suggested which allows for thermalization of the systems at high temperatures and direct pumping of the pair systems by the single-ion system at low temperatures. Energy transfer from single-ion to multi-ion systems was also observed.

The thermalization time of hot photoexcited holes in $p$-type germanium has been investigated. This was accomplished by studying the mobility and recombination properties in a series of copper-doped-germanium samples, in which the carrier lifetime was systematically varied. Recombination-center densities were varied over five orders of magnitude, so that the transition from a thermalized to a hot photocarrier distribution was observed as the carrier lifetime became shorter. The carrier lifetime was measured directly from the photoresponse signal decay, for several samples, to establish the recombination cross section. A theory, assuming energy loss via optical- and acoustic-phonon emission, correctly predicts the increase in the average photoexcited-carrier energy as the recombination-center density is increased.

Excitation into the charge-transfer states (CTS) of Eu +3 directly feeds certain 4f states whose energies are brought into resonance with the CTS by nuclear rearrangement. In Y 2 O 2 S and La 2 O 2 S, the emitting 5 D states are directly fed; in Y 2 O 3 , higher 4f states are fed. In either case, the CTS are positioned such that the preferred 4f states are in resonance near the CTS minimum, as if thermalization within the CTS precedes 4f feeding. The low energy of the CTS in the oxysulfides (the CTS minimum is near that of 5 D 3 allows the 5 D states to come into thermal contact with the CTS. The resultant thermal emptying of the 5 D states via the CTS produces a sequential quenching of the 5 D emissions. Placements of the CTS derived from 5 D quenching data and from CTS absorption data agree.

The moderation and thermalization of ions by a hot plasma is treated by a method which is a generalization of the age theory of continuous slowing down. Formulas are given for the slowing down coefficients of an ion in a hot plasma. The method is illustrated by calculating the thermalization of a monoenergetic pulse of ions injected into a plasma and by a calculation of the T-D reaction probability when high-energy tritons are injected into a deuterium plasma.

The neutron flux in the case of pulsed finite moderator assemblies has been expanded in powers of B2, following the method of Nelkin and Beckurts. Expressions for the diffusion cooling coefficient and the coefficient of B2 term have been derived both on diffusion and transport theory. Using the Nelkin kernel in the incoherent approximation and transport cross sections as given by Singwi, these parameters have been evaluated for BeO moderator. Numerical calculations have been done with an energy mesh of 0·9 meV and cut-off energy of 0·3 eV. The theoretical value of 3·4 × 105 cm5 sec−1 for the diffusion cooling coefficient is on the lower side of the experimental value which lies between (3·5–6) × 105 cm4 sec−1. In view of the large experimental errors on F-coefficient, no conclusion could be drawn. On the basis of the theoretically calculated negative F-value, one concludes that the thermalization power for BeO decreases with a decrease in neutron temperature.

The thermalization time required for positrons in argon is estimated by separating the energy range of positrons into the three regions (i) E > 0.01 MeV, (ii) 0.01 MeV > E > Eexc and (iii) E < Eexc (Eexc is the first excited level of the argon atom). The elastic collision cross sections determined by Marder et al. are re-evaluated. The thermalization time in region (iii) is not negligible compared with the free annihilation lifetime and most of the free positrons will be annihilated before being thermalized.

The absorption of light and subsequent thermalisation of the absorbed energy can be significantly affected by the presence of non-equilibrium population distributions in gases. The phenomenon of thermal blooming in gases is discussed from this standpoint. It is shown that a transient phenomenon of “absorption cooling” can occur, leading to a focusing rather than defocusing of an incident laser beam. Flux densities causing saturation in air and pure CO2 are calculated. For vibrational saturation in air, I > 3.66 kw/cm2, for pure CO2, I > 4.58 kw/cm2. For rotational saturation, in either gas, I > 840 kw/cm2.

The thermalization of neutrons was experimentally measured for the purpose of testing Kushneriuk's thermalization calculation in a cylindrical shell of moderator surrounding a fuel rod in a thermal reactor. The basis of the study was the measurement of activations for a set of five detectors--/sup 55/Mn, /sup 197/Au, /sup 115/In, / sup 239/Pu, and /sup 176/Lu-- inside the central fuel rod and the surrounding moderator at 20-cm hexagonal lattice pitch in the Atomic Energy of Canada Ltd.'s (AECL's) heavy-water-moderated, natural uranium critical reactor, ZEEP. The neutron flux distribution, calculated by Kushneriuk's method (first-order and exact solutions), was used in calculating detector activations. When compared, the measured detector activations and those calculated showed good agreement in the moderator, with the exception of points near and inside the fuel rod. The measured detector activations were also compared with the predicted values obtained from the HAMMER code. In this instance, the agreement was generally better than that obtained between measured and calculated values based on Kushneriuk' s method. (auth)

In an earlier paper we extracted an asymptotic series solution in half-integral powers of (kTE) from the Boltzmann transport equation for neutrons coming into thermal equilibrium with a moderating material. In this paper we consider the series in detail for moderators having simple crystalline structure, or in which vibrational modes predominate, and give the coefficients of the series explicitly in terms of moments of the frequency spectrum of crystal vibrations. Our calculations indicate that the neutron density in the asymptotic region increases as one hardens the spectrum of crystal vibrations, whence the “hardness” of the neutron spectrum increases, too. We also discuss some aspects of the mass-expansion for these systems, and compare our calculations with those of other workers, and with typical experimental data for thermalization in water. Finally, we discuss the asymptotic expansion for moments of the scattering kernel and for ξσ_s, the slowing down power.

The neutron thermalization process for an incident neutron pulse in a moderating assembly has so far been treated by solving the Boltzmann equation in the diffusion approximation with scattering kernel based on theoretical models. In this paper, the mean energy, E (t) and average logarithmic energy decrement, ξ for an infinite medium of graphite at room temperature has been studied by time-step and Monte Carlo methods for incident neutron energies of 0·11 and 0·01 eV, using the experimental values of Egelstaff for the scattering kernel. From the mean energies, the slowing down (τs) and heating up (τH) relaxation time constants have been evaluated. It is observed that the slowing down relaxation time constant of 187 μsec is not very much different from the heating up relaxation time constant τH of 198 μsec. The calculated value of τs is in good agreement with the earlier experiments but differs from the recent ones. The average logarithmic decrement, ξ decreases with decreasing energy due to binding effects.

Three methods of studying ionospheric photoelectron thermalization, in which transport effects are evaluated in different ways, are outlined and compared. One method uses a diffusion equation formulation, the second proceeds from a two-stream approximation to the general particle transfer equation, and the third employs a Monte Carlo technique to simulate electron paths. The methods are compared by applying them to identically prepared models. The methods are in close agreement for altitudes in the region of local energy loss, but higher altitudes reveal a discrepancy of as much as a factor of 2 in the net flux of photoelectrons. The discrepancy is removed by appropriately modifying the computational techniques.

An approximate method given by Bonalumi and extended in this paper is used to calculate the collision probabilities in a cylindrical cell with the fuel in the form of concentric annuli of arbitrary cross sections; these are used to derive one-group flux distributions across the cell. Comparisons are given with exact collision-probability calculations and with Carlson Sn calculations. It is concluded that the method gives results of acceptable accuracy in normal fine-structure problems. Programmed for the Ferranti Mercury computer the method is faster than existing transport theory codes and is well suited to routine calculations, for example as a subroutine in a thermalization code.

The damping of the giant resonances in heavy and medium-heavy nuclei can be described by thermalization and cooling-off processes. The direct emission of particles, which is strongly inhibited by Coulomb and centrifugal barriers is neglected here. In the damping process, which begins with the thermalization, the 1p-1h giant resonance states induced by the incoming electromagnetic field are scattered inelastically due to the presence of two-body residual forces into other 1p-1h and 2p-2h states. In heavy nuclei there exist, at the energy of the giant resonance, several hundreds of such 2p-2h states. The 1p-1h dipole and quadrupole basis states for the diagonalization of the Hamiltonian are obtained from a spherical Nilsson potential. The density of the 2p-2h states obtained from the same potential are then used to determine the energy dependence of the widths of the giant resonances.

The spectral line shapes, or signature profiles, of O( 1 S) proceeding from the dissociative recombination of O2+(2πg) in the upper atmosphere have been optically observed in the nightglow at the geomagnetic equator with a Fabry-Perot spectrometer. The results indicate that the recombination leading to O( 1 S), O( 3 P) and 2.79 eV excess energy is favored relative to that leading to O( 1 S), O( 1 D) and 0.83 eV. excess energy by at least a factor of 5 to 1. Partial thennalization of the profile was observed indicating energy exchange with the medium. From this, a relaxation time of about 3 sec, or a collision cross section of about 6 × 10−16 cm2 can be derived depending on the mechanism invoked for thermalization.

The triplet state of tetramethylparaphenylenediamine (TMPD) dissolved at 10−5M in aliphatic hydrocarbons was photoionized with light of photon energy ≤3.86 eV at room temperature. A combination of transient photocurrent measurements, transient absorption measurements, and temperature effects permitted evaluation of the pertinent kinetic parameters. A representative thermalization range of the low‐energy photoejected electron was estimated to be 180 A and the absorption coefficient connecting triplet to continuum between 320–410 nm was estimated as 1 × 10−18 cm2.

We discuss the behaviour of the asymptotic thermal flux in the “pulsed” and “exponential” experiments. In particular, we give a pair of theorems which bear upon the possibility of measuring λ0 and ...

The effect of applied forward bias upon the photocurrent observed in p-n heterojunctions has been investigated in the systems GaAs-Ga(AsP) and (GaIn)As-GaAs. In all the heterodiodes measured the photocurrent was found to cut-off sharply at a well defined bias and this cut-off voltage proved extremely sensitive to temperature. The observation that the excess photocurrent is simply related to the dark-current leads to a model in which photo electrons may rapidly thermalize in the conduction band notch if the equilibrium injected population is sufficiently large. Es wurde der Einflus einer Vorspannung in Durchlasrichtung auf den Photostrom in p-n-Heteroubergangen der Systeme GaAs-Ga(AsP) und (GaIn)As-GaAs untersucht. In alien untersuchten Heterodioden wurde gefunden, das der Photostrom bei einer wohldefinierten Vorspannung scharf abfallt und diese Grenzspannung sehr empfindlich von der Temperatur abhangt. Die Beobachtung, das der zusatzliche Photostrom in einfacher Beziehung zum Dunkelstrom steht, fuhrt zu einem Modell, in dem die Photoelektronen schnell in den Leitungsbandeinschnitt thermalisiert werden, wenn die injizierte Gleichgewichtsbesetzung hinreichend gros ist.

The neutron diffusion and integral scattering properties of graphite have been measured by the pulsed-neutron-source technique. Measurements were performed on assemblies with geometric bucklings fr...

A general mathematical formalism for the energy transfer moments and their associated integrals, whrch is useful in the study of neutron thermalization, is presented. This formalism is employed to obtain these quantities for the general Doppler approximation' case, which represents a large number of approximations that belong to the Doppler class. An exact formula for M/sub 2/ (the second energy transfer moment welghted by the Maxwellian distribution) is given ln terms of binding parameters for the general Doppler case. A Doppler approximation, which satisfies the Detailed Bal ance theorem and is based upon the Debye-Waller factor and the specific heat integral, is also formulated. A comparative study is undertaken of this approximation and three other Doppler cases (the monatomic-gas-model, the effective-temperature, and the Krieger-Nelkin approximations for rotating molecules) in terms of the validity of the Detailed Balance theorem and the asymptotic scatterrng behavior. Numerical results based upon the Debye ffrequency distribution of vibrational modes in the Doppler approximation are presented. (auth)

In a previous paper some general properties of the Boltzmann equation governing the transient behavior of neutron distributions were developed. The experimental consequences of these considerations are examined and some reported experimental results are discussed. It is found that in some cases theoretical restrictions on time-decay constants and diffusion lengths are apparently violated. (auth)

The heating of solar-wind protons cannot be explained by the thermalization of those protons arising from the ionization of neutral hydrogen atoms traveling in the general direction of the sun. By requiring the heating to satisfy the experimental results of the T sub p versus V sub sw correlation, an efficiency function of thermalization of these incoming protons is obtained, and a value of the 'hot component' of the hydrogen population is about 0.05 per cu cm near 1 AU. This hot component hydrogen density is too high compared to recent estimates by satellite experiments of Lyman alpha radiation and other experiments, and therefore the suggested solar-wind heating mechanism is unimportant in explaining the T sub p versus V sub sw correlation.