Showing papers on "Energy (signal processing) published in 1985"

Acceleration of Electrons by the Interaction of a Bunched Electron Beam With a Plasma

Abstract: A new scheme for accelerating electrons, employing a bunched relativistic electron beam in a cold plasma, is analyzed. We show that energy gradients can exceed 1 GeV/m and that the driven electrons can be accelerated from ${\ensuremath{\gamma}}_{0}m{c}^{2}$ to $3{\ensuremath{\gamma}}_{0}m{c}^{2}$ before the driving beam slows down enough to degrade the plasma wave. If the driving electrons are removed before they cause the collapse of the plasma wave, energies up to $4{\ensuremath{\gamma}}_{0}^{c}m{c}^{2}$ are possible. A noncollinear injection scheme is suggested in order that the driving electrons can be removed.

Plasma Distribution Function in a Superthermal Radiation Field

Abstract: A plasma which is immersed in superthermal radiation suffers velocity-space diffusion which is enhanced by the photon-induced Coulomb-field fluctuations. This enhanced diffusion universally produces a power-law distribution ${(\frac{E}{{E}_{0}})}^{\ensuremath{-}\ensuremath{\kappa}}$ at energy $E$ larger than a critical energy ${E}_{0}$ where the transition energy ${E}_{0}$ and the power $\ensuremath{\kappa}$ are inversely proportional to the photon-field intensity.

Gravitational radiation from cosmic strings

Abstract: Gravitational radiation from oscillating loops of string is studied both analytically and numerically. The total radiated power is found to be P=\ensuremath{\gamma}G${\ensuremath{\mu}}^{2}$, where \ensuremath{\mu} is the mass density of the string and \ensuremath{\gamma} is a numerical coefficient \ensuremath{\sim}100. The intensity and the spectrum of the stochastic gravitational-wave background produced by the loops are calculated. Gravitational radiation from asymmetric loops carries not only energy, but also momentum; the loop recoils and accelerates like a rocket. The momentum radiation rate from loops is calculated and it is shown that cosmological loops formed with sufficiently small initial velocities are slowed down by dynamical friction and do not rocket away.

Nuclear Bragg diffraction of synchrotron radiation in yttrium iron garnet.

Abstract: Monochromatization of synchrotron radiation down to about ${10}^{\mathrm{\ensuremath{-}}8}$ eV at an energy of 14.4 keV has been achieved by double nuclear Bragg diffraction from $^{57}\mathrm{yttrium}$ iron garnet single-crystal films set for the electronically forbidden {200} reflection. The monochromatized \ensuremath{\gamma} quanta have been analyzed with respect to time delay and capabiltiy of resonance absorption. By setting of appropriate energy and time windows a pure beam of resonant \ensuremath{\gamma} quanta at a rate of about 1 Hz is available.

A structure preserving energy function for power system transient stability analysis

Abstract: A new model is proposed for the study of transient stability where the load is modeled as a PQ bus. Flux decay of the generator field winding is included. The original network topology is maintained explicitly. An energy function is proposed which differs from the traditional one in that it includes additional terms corresponding to the energy stored in the loads and field winding. A characterization of the stability region is derived based on this energy function.

Theory of high-field electron transport in silicon dioxide

Abstract: A Monte Carlo technique is employed to simulate the electron transport in ${\mathrm{SiO}}_{2}$ at high electric fields (from 1.5\ifmmode\times\else\texttimes\fi{}${10}^{6}$ to 12\ifmmode\times\else\texttimes\fi{}${10}^{6}$ V/cm). Both the polar and the nonpolar electron-phonon scattering processes are considered. We show that the nonpolar interaction with the acoustic and band-edge phonons is a mechanism which must be included in order to explain the experimental evidence of a steady-state electron-transport regime at high average electron energy (\ensuremath{\simeq}3--4 eV) at these high fields. The LO phonons alone cannot prevent the electrons from running away at fields above 2\ifmmode\times\else\texttimes\fi{}${10}^{6}$ V/cm, while at higher fields the main effect of the nonpolar scattering is that of randomizing the electron momenta via large-angle scattering, thus stabilizing the electron-energy distributions. The average energies and the energy relaxation distances obtained from the Monte Carlo simulation agree very well with the experimental data, particularly when collisional broadening effects are introduced in the simulation. Internal photoemission of electrons from an aluminum or a silicon electrode into ${\mathrm{SiO}}_{2}$ is also simulated, and the results agree with the well-known data indicating an effective relaxation length of about 3 nm for electrons in ${\mathrm{SiO}}_{2}$. Comparison is also made between the experimental and theoretical electron-energy distributions at high fields (\ensuremath{\gtrsim}8\ifmmode\times\else\texttimes\fi{}${10}^{6}$ V/cm). The results indicate that at very high electron energies the band structure of ${\mathrm{SiO}}_{2}$ and quantum transport effects may reduce the effective scattering rates. While the semiclassical Monte Carlo solution seems to be reasonably valid for electron energies up to about 4 eV, more sophisticated approaches are needed to investigate the high-energy tails of the electron distributions.

Effect of magnetic field on the energy levels of a hydrogenic impurity center in GaAs/Ga1-xAlxAs quantum-well structures.

Abstract: We have calculated the binding energies of the ground (1s-like) and excited (2${p}_{\ifmmode\pm\else\textpm\fi{}}$-like) states of a hydrogenic donor associated with the first subband in a GaAs quantum well, sandwiched between two semi-infinite layers of ${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As. Results have been obtained as a function of the potential-barrier height (or equivalently of Al concentration x) and the size of the quantum well in the presence of an arbitrary magnetic field. We have considered the two cases of donor at the center and at the edge of the well. The applied magnetic field is taken to be parallel to the axis of growth of the quantum-well structure. We have used a variational approach in which the trial wave functions are expanded in terms of appropriate Gaussian basis sets. For a given value of the magnetic field, the binding energies are found to be larger than their values in a zero magnetic field.

Exact results for the fractional quantum Hall effect with general interactions

Abstract: Laughlin's state ${\ensuremath{\psi}}_{m}$ is shown to be the exact nondegenerate ground state for repulsive interactions of vanishing range. In this limit, his quasihole states are not exact, and some previously proposed states are ruled out. An experimental prediction is made concerning the competition of ${\ensuremath{\psi}}_{m}$ with charge-density waves. Several exact properties are shared by systems with interactions of shorter range than ${r}^{\mathrm{\ensuremath{-}}2}$, for which the center-of-mass motion separates from the other degrees of freedom. These include new invariant subspaces, an operator that creates exact eigenstates, and a subset property of the energy eigenvalues.

Double occupancy of the f orbital in the Anderson model for Ce compounds

Abstract: The Anderson model at zero temperature is studied as a function of the f-level position ${\ensuremath{\varepsilon}}_{f}$ and the f-level--conduction-electron hopping matrix element V. The f-f Coulomb interaction U is assumed to be finite, and double occupancy of the f level is taken into account. For a large value of the f-level degeneracy ${N}_{f}$, there is an important asymmetry between ${f}^{0}$ and ${f}^{2}$ configurations. Even for ``symmetric'' parameters, 2${\ensuremath{\varepsilon}}_{f}$+U=2${\ensuremath{\varepsilon}}_{F}$=0, the ${f}^{2}$ weight is much larger than the ${f}^{0}$ weight if V is small. The effect of this asymmetry on other properties is studied for ${N}_{f}$\ensuremath{\rightarrow}\ensuremath{\infty}. The static susceptibility is primarily determined bythe ${f}^{0}$ weight, while the shape of the valence photoemission spectrum close to the Fermi energy ${\ensuremath{\varepsilon}}_{F}$ also has an important dependence on the ${f}^{2}$ weight. The valence photoemission spectrum can have a pronounced two-peak character, with one peak close to ${\ensuremath{\varepsilon}}_{f}$ and a second structure close to ${\ensuremath{\varepsilon}}_{F}$. For ${\ensuremath{\varepsilon}}_{f}$ well below ${\ensuremath{\varepsilon}}_{F}$ (``spin-fluctuation'' limit) the weight of the second structure can be strongly enhanced compared to the U=\ensuremath{\infty} limit, and its shape and position depends on the conduction density of states. This structure can therefore have a peak below ${\ensuremath{\varepsilon}}_{F}$. The bremsstrahlung isochromat spectroscopy spectrum shows an ${f}^{1}$ peak with an energy separation from ${\ensuremath{\varepsilon}}_{F}$ which is determined by the ``Kondo'' temperature. The tail of this peak contributes to the structure in the valence photoemission spectrum below ${\ensuremath{\varepsilon}}_{F}$.Ground-state properties are calculated variationally, treating 1/${N}_{f}$ as a small parameter. A new technique for performing these calculations is developed. This technique makes it possible to include such a large basis set that accurate results are obtained for the ground-state energy and the f-level occupancy in the limit ${N}_{f}$=1. To calculate the spectra we introduce a time-dependent method which facilitates the inclusion of f2 configurations in the valence photoemission spectrum.

Band-gap renormalization in semiconductor quantum wells containing carriers

Abstract: A theoretical calculation is presented of the so-called ``gap renormalization'' due to free carriers for the quasi-two-dimensional (2D) electrons or holes confined in a semiconductor quantum well. A general theory of the effect is developed assuming parabolic subbands, the Hubbard approximation (random-phase approximation) for the correlation energy, and a model potential containing the well thickness for the effective 2D Coulomb interaction. Results are presented for gap renormalization versus carrier density for GaAs wells of 81 and 217 A\r{} thickness. An experimental measurement of gap renormalization is presented which is based on an analysis of the excitation and luminescence spectra of a p-type modulation-doped Ga(${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$)As multilayer sample of well width 107 A\r{} and hole density 5.3\ifmmode\times\else\texttimes\fi{}${10}^{10}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$. The calculated value is in excellent agreement with the experimental value (6.3 meV) in this case.

Spin-polarized angle-resolved photoemission study of the electronic structure of Fe(100) as a function of temperature.

Abstract: By spin- and angle-resolved photoemission with synchrotron radiation the electronic structure of Fe(100) has been tested between room temperature and the Curie temperature ${T}_{C}$ for photon energies in the range 20\char21{}70 eV. The spin-resolved energy-distribution curves (SREDC's) reflect the dispersions of the ${\ensuremath{\Delta}}_{5}^{\ensuremath{\uparrow}}$,\ensuremath{\downarrow}-symmetry initial-state bands. This manifests in an abrupt change in spin character of the peak near ${E}_{F}$ from predominantly minority spin to majority spin when tuning the photon energy across 33 eV. The non-spin-resolved EDC's thereby remain nearly unchanged. Upon heating to 0.85T/${T}_{C}$, depending on photon energy, qualitative different changes in the SREDC's are observed: At h\ensuremath{ u}=60 eV, ${\ensuremath{\Gamma}}_{25}^{\mathcal{'}\ensuremath{\uparrow}}$ is found to be stationary in energy upon heating, and the spin-summed intensity decreases by less than 5%. At ${\ensuremath{\Gamma}}_{25}^{\mathcal{'}\ensuremath{\downarrow}}$, a strong loss of intensity occurs. In contrast, at h\ensuremath{ u}=31 and 21 eV, an increase in minority-spin (and total) photocurrent upon heating is observed. This is interpreted as resulting from a decrease of the exchange splitting with temperature near H.

Semiconductor drift chambers for position and energy measurements

Abstract: Semiconductor drift chambers have been recently suggested and feasibility tests performed. This paper presents the first operative silicon drift detectors for position and energy measurements. Design criteria and experimental results in the laboratory and on an accelerator beam are reported.

Energy levels of two- and three-dimensional polarons in a magnetic field.

Abstract: The influence of the electron-phonon interaction on the Landau levels of two- (2D) and three-dimensional (3D) electrons are studied within second-order perturbation theory. It is found that polaron effects in ideal 2D systems are larger than in 3D systems which agrees with recent results of Das Sarma and Larsen. Analytical and numerical results are presented for the electron-phonon correction to the different Landau levels (n) below the LO-phonon continuum. Special attention is paid to the small and large magnetic-field limit and to the splitting of the Landau levels which occurs at n${\ensuremath{\omega}}_{c}$\ensuremath{\approxeq}${\ensuremath{\omega}}_{0}$ (${\ensuremath{\omega}}_{c}$ is the cyclotron frequency and ${\ensuremath{\omega}}_{0}$ is the LO-phonon frequency). Existing results are rederived and generalized.

Photoemission from activated gallium arsenide. I. Very-high-resolution energy distribution curves.

Abstract: The energy distribution curves (EDC's) of the photoelectrons emitted from the (100) face of a p-type doped (\ensuremath{\sim}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$) GaAs crystal, activated to negative electron affinity in ultrahigh-vacuum conditions, is investigated. The study is performed at 300 and 120 K under well-focused ${\mathrm{Kr}}^{+}$-laser excitation and with a very-high-energy resolution (20 meV). The analysis of the EDC's as a function of the photon energy, mainly at low temperature, is shown to provide a very direct picture of the GaAs band structure away from the Brillouin-zone center. The experimental results are well fitted by a spherical, nonparabolic k\ensuremath{\rightarrow}\ensuremath{\cdot}p\ensuremath{\rightarrow} perturbation calculation of the coupled conduction and valence bands, for electron kinetic energies up to 1 eV in the central \ensuremath{\Gamma} valley. The essential role played by the subsidiary L and X minima in the energy relaxation and photoemission processes is evidenced. The main contribution to the total emitted current is due to electrons which were thermalized in the bulk \ensuremath{\Gamma} minimum and have lost an average energy \ensuremath{\simeq}130 meV in the band-bending region prior to emission into vacuum. The band-bending value is shown to be \ensuremath{\ge}0.5 eV. The yield and time evolution of GaAs photocathodes are discussed. This detailed study leads to a reexamination of the pioneer work of L. W. James and J. L. Moll [Phys. Rev. 183, 740 (1969)] and to a good understanding of the photoemission properties of activated GaAs.

Dissipative quantum tunneling in a biased double-well system at finite temperatures.

Abstract: We study quantum tunneling in a biased double-well potential in the presence of Ohmic dissipation with a friction coefficient $\ensuremath{\alpha}g1$. The tunneling rate out of the metastable well is calculated in real time as a function of the temperature $T$ and bias energy $\ensuremath{\epsilon}$. The $T=0$ result agrees with a droplet-model calculation in imaginary time. At low temperatures we find an enhancement to the $T=0$ rate varying as ${(\frac{T}{\ensuremath{\epsilon}})}^{2}$.

Kohn-Sham exchange potential exact to first order in ρ(K→)/ ρ 0

Abstract: The Kohn-Sham exchange potential may be written, exact to first order in \ensuremath{\rho}(K\ensuremath{\rightarrow})/${\ensuremath{\rho}}_{0}$, ${V}_{x}^{\mathrm{KS}}$=-(3/2) (3/\ensuremath{\pi}${)}^{1/3}$${\ensuremath{\rho}}_{0}^{\mathrm{\ensuremath{-}}2/3}$ ${\mathcal{J}}_{\mathrm{K}\ensuremath{\rightarrow}}^{\mathcal{'}}$\ensuremath{\rho}(K\ensuremath{\rightarrow})F(K)${e}^{i\mathrm{k}\ensuremath{\rightarrow}\ensuremath{\cdot}\mathrm{r}\ensuremath{\rightarrow}}$. We here evaluate the universal function F(K/${k}_{F}$) for all K/${k}_{F}$ and find large corrections to the local-density approximation which should result in much improved values for semiconductor energy gaps.

Many-body effects on the cyclotron resonance in a two-dimensional electron gas.

Abstract: We consider optical absorption by an interacting two-dimensional electron system, with impurities, in a strong perpendicular magnetic field, at electron densities such that an integral number of Landau levels is filled. The Coulomb energy ${e}^{2}$/\ensuremath{\epsilon}${l}_{0}$ is assumed to be smaller than the cyclotron energy \ensuremath{\Elzxh}${\ensuremath{\omega}}_{c}$, and correlation effects are treated exactly to lowest order in (${e}^{2}$/\ensuremath{\epsilon}${l}_{0}$)/\ensuremath{\Elzxh}${\ensuremath{\omega}}_{c}$. The impurity scattering is treated in a self-consistent approximation for several different impurity potentials. The cyclotron resonance line is found to be significantly altered by electron-electron interactions. The line is shifted to lower frequencies and a line narrowing due to correlation effects is found.

Comparison of fully relativistic energy bands and cohesive energies of MoSi 2 and WSi 2

Abstract: After correcting small errors in our previous ${\mathrm{WSi}}_{2}$ calculations, we compare the equilibrium bond length and symmetric optical phonon frequency of ${\mathrm{MoSi}}_{2}$ and ${\mathrm{WSi}}_{2}$ calculated self-consistently using the semirelativistic norm-conserving pseudopotential. At the equilibrium bond length, fully relativistic calculations of the energy bands, projected densities of states, cohesive energy, bonding charge density, and Fermi surfaces are compared.

Current and current density limitations in existing electron storage rings

Abstract: Storage rings dedicated for synchrotron light sources must show good beam performances in order to obtain high flux and brilliance. In particular bunch length, energy spread, beam intensity and transverse emittances have to satisfy special requirements. We intend here to briefly overview twenty years of experience obtained with small and medium size storage rings which were initially built as high energy physics facilities. The limiting effects will be extensively discussed by comparing theoretical models with systematic experimental studies. The possible means to remedy the inconveniences are also mentioned.

Exact and approximate results for the ground-state energy of a Fröhlich polaron in two dimensions.

Abstract: The ground-state energy of a two-dimensional (2D) Fr\"ohlich polaron is calculated to second order in the coupling constant (\ensuremath{\alpha}) and gives E/\ensuremath{\Elzxh}${\ensuremath{\omega}}_{s}$=-(\ensuremath{\pi}/2)\ensuremath{\alpha}-0.063 97${\ensuremath{\alpha}}^{2}$ with \ensuremath{\Elzxh}${\ensuremath{\omega}}_{s}$ the surface optical-phonon energy. In the strong-coupling limit the adiabatic approximation is used and E/\ensuremath{\Elzxh}${\ensuremath{\omega}}_{s}$=-0.4047${\ensuremath{\alpha}}^{2}$ is found to leading order in \ensuremath{\alpha}. The Feynman path-integral approximation, the Gaussian approximation, and the modified Lee-Low-Pines unitary transformation approximation to the polaron ground-state energy all satisfy the scaling relation ${E}_{2\mathrm{D}}$(\ensuremath{\alpha})=(2/3)${E}_{3\mathrm{D}}$(( 3\ensuremath{\pi}/4)\ensuremath{\alpha}), where ${E}_{2\mathrm{D}}$ (${E}_{3\mathrm{D}}$) is the ground-state energy of the 2D (3D) polaron.

Analysis of polaron effects in the cyclotron resonance of n-GaAs and AlGaAs-GaAs heterojunctions

Abstract: Cyclotron resonance (CR) was measured at high magnetic fields in three-dimensional bulk n-GaAs and in the two-dimensional (2D) electron system of an AlGaAs-GaAs heterojunction, at a number of far-infrared laser lines, up to energies close to the longitudinal optical phonon energy, \ensuremath{\Elzxh}${\ensuremath{\omega}}_{\mathrm{LO}}$. A quantitative analysis of the CR as a function of magnetic field is presented, taking into account dimensionality, band nonparabolicity, and polaron effects. It is found that screening is important in 2D systems, and from an analysis of polaron effects in the CR of the AlGaAs-GaAs heterojunction, a value for the screening strength in a 2D electron system is obtained. Our analysis of data very close to resonance with the optical phonon shows that band nonparabolicity has to be included explicitly in the calculation of polaron corrections to obtain the proper asymptotic limit \ensuremath{\Elzxh}${\ensuremath{\omega}}_{\mathrm{LO}}$ for the CR transition energy.

Weak localization and anharmonicity of phonons

Abstract: The problem of localization of phonons in disordered materials is studied in the framework of the weak-localization theory. Quantum correction to phonon diffusion is calculated by the resummation technique of maximally crossed diagrams in two and three dimensions. The strong energy dependence of the elastic mean free path---the Rayleigh-Klemens scattering---is responsible for the existence of a threshold frequency ${\ensuremath{\omega}}_{3}^{\mathrm{*}}$ where the diffusion constant vanishes. The value of ${\ensuremath{\omega}}_{3}^{\mathrm{*}}$ depends only on the local fluctuation of masses and on the Debye frequency in three dimensions. This threshold describes the phenomenon of localization of phonon density fluctuations or second sound. The self-energies of the phonons are strongly affected by this quantum correction via the anharmonic interactions. The two basic anharmonic couplings contribute to the one-phonon renormalization and provide shortening of the mean lifetime as well as excess of spectral density in the vicinity of the threshold. In two dimensions, as for the electrons, the dynamical quantum correction diverges logarithmically when the frequency goes to zero. A procedure of convergence is used by cutting off the low-frequency contributions at the inelastic relaxation rate. Renormalization of phonons are obtained in a self-consistent way. Finally a tentative application of the previous results to the low-temperature properties of glasses is discussed. In particular the existence of a plateau in thermal conductivity accompanied by excess specific heat in all the glasses measured so far could be understood as the manifestation of localization of acoustic-phonon density at the critical threshold ${\ensuremath{\omega}}_{3}^{\mathrm{*}}$. .AE

Threshold excitation of short-lived atomic inner-shell hole states with synchrotron radiation.

Abstract: The Xe ${L}_{3}\ensuremath{-}{M}_{4}{M}_{5} (^{1}G_{4})$ Auger spectrum, photoexcited in the vicinity of the ${L}_{3}$ edge, has been measured as a function of photon energy. The $\mathrm{nd}$ spectator-electron satellite lines show resonant behavior. The diagram line exhibits the larges (\ensuremath{\gtrsim} 1 eV) post-collision interaction shift yet observed. For comparison with the data, the first fully quantum-mechanical calculation of the post-collision interaction in deep inner-shell Auger decay is performed, based on a resonant-scattering approach that involves a complete summation over intermediate ${L}_{3}$ one-hole states.

Energy dependence of inelastic electron scattering cross section by surface vibrations: Experimental measurement and theoretical interpretation.

Abstract: We report on the first comparison of the inelastic cross section of Ni(001) surface phonons for an extended energy range with a dynamical scattering theory. Both theory and experiment indicate large modulations in the loss cross section as a function of incident energy. The intensity ratio of the ${S}_{4}$ and ${S}_{6}$ surface phonons on Ni(001) is best fitted with a 1.7%-3.3% contraction in the outer-most interlayer spacing.

Bound states of heavy Q 2 Q¯ 2 systems

Abstract: The Born-Oppenheimer approximation for heavy quarks in the MIT bag is extended to the ${Q}^{2}$Q${\ifmmode\bar\else\textasciimacron\fi{}}^{2}$ system, where the glue plus volume energy becomes an operator in color space. Taking its lowest eigenvalue as the approximate potential energy, the four-body Schr\"odinger equation is solved variationally for the ground-state energy. With this approximation, it is found that heavy-quark systems such as ${c}^{2}$c${\ifmmode\bar\else\textasciimacron\fi{}}^{2}$ are stable against breakup into two \ensuremath{\psi} (cc\ifmmode\bar\else\textasciimacron\fi{}) mesons. It is necessary to solve the coupled-channel (in color space) problem to confirm this result.

New form of the time-energy uncertainty relation

Abstract: A new form of the time-energy uncertainty principle is presented. It has the form \ensuremath{\tau} \ensuremath{\Delta}E\ensuremath{\ge}3\ensuremath{\pi}${5}^{1/2}$/25, where \ensuremath{\tau} is the average lifetime of a decaying state, and \ensuremath{\Delta}E is the energy spread of the state computed from \ensuremath{\Delta}${E}^{2}$=〈${E}^{2}$〉-〈E${〉}^{2}$. The particular state for which the above relationship becomes an equality is identified, and it is proved that all other states give a greater \ensuremath{\tau} \ensuremath{\Delta}E product. This general result should have a wide range of applications.

Direct reaction description of sub- and above-barrier fusion of heavy ions.

Abstract: A new approach to calculation of the fusion cross section ${\ensuremath{\sigma}}_{F}$, based on the direct reaction concept, is presented. The method is to define a fusion potential ${W}_{F}$ [with r\ensuremath{\le}${R}_{F}$=${r}_{F}$(${A}_{1}^{1/3}$+${A}_{2}^{1/}$ 3)] as a part of the imaginary potential of the usual optical model. The ${\ensuremath{\sigma}}_{F}$ is then obtained as that part, due to only ${W}_{F}$, of the total absorption cross section. It is seen that, if ${r}_{F}$ is chosen as 1.40--1.50 fm, the value of ${\ensuremath{\sigma}}_{F}$ computed as described fits the experimental ${\ensuremath{\sigma}}_{F}$ very well, in both sub- and above-barrier regions, and for a variety of fusing nuclear pairs ${A}_{1}$ and ${A}_{2}$. In most cases, it is sufficient to consider only the incident (elastic scattering) channel. In a few cases, in which some specific nuclear structure effects are involved, it is found necessary to perform coupled-channel calculations. Then absorption due to other channels is also taken into account explicitly. It is shown that adding these contributions is the key to getting good fits to data, under the above-mentioned special circumstances. A possible relation of what the present approach describes, particularly when it is used in the sub-barrier region, to (spontaneous) fission is also discussed.

Resonance scattering of electrons from N 2 adsorbed on a metallic surface

Abstract: The energy and width of the $^{2}\mathrm{\ensuremath{\Pi}}$ shape resonance in e-${\mathrm{N}}_{2}$ collisions are calculated for ${\mathrm{N}}_{2}$ molecules physisorbed on a metallic surface. The breaking of the molecular symmetry by the surface is found to increase the resonance width as compared to that for collisions in the gas phase. The metallic image potential is found to broaden the resonance and lower its energy. The calculated broadening and energy shift agree in order of magnitude with the observed values.

Time-dependent Hartree-Fock calculations of 4 He + 14 C, 12 C + 12 C ( 0 + ), and 4 He + 20 Ne molecular formations

Abstract: Time-dependent Hartree-Fock calculations for head-on collisions of $^{4}$He${+\mathrm{}}^{14}$C, $^{12}$C${+\mathrm{}}^{12}$C${(0}^{+}$), and $^{4}$He${+\mathrm{}}^{20}$Ne have been performed at bombarding energies near the Coulomb barrier. The results are interpreted in terms of their classical quasiperiodic and chaotic behavior. The position of the time-dependent Hartree-Fock collective path with respect to the multidimensional energy surface of the compound nuclear system is shown. Dynamical collective degrees of freedom are identified and classical frequencies associated with each degree of freedom are calculated. For $^{24}\mathrm{Mg}$ we calculate molecular frequencies of about 0.8 and 1.0 MeV and a characteristic moment of inertia of 15 ${\mathrm{MeV}}^{\mathrm{\ensuremath{-}}1}$.

Stochastic Theory for Nonadiabatic Level Crossing with Fluctuating Off-Diagonal Coupling

Abstract: A simple stochastic model is presented describing the nonadiabatic transitions in the level crossing with fluctuating off-diagonal coupling, in which the fluctuation is assumed to obey the Markoffian Gaussian process. The probability P that the transition occurs from one diabatic state to another is calculated exactly in the two limiting situations: In the slow fluctuation limit, P is given by \(P{=}1-\{1+(4{\pi}J^{2}/\hbar|v|)\}^{-1/2}\), where J is the averaged amplitude of the off-diagonal term and v is the velocity of the change of the energy difference between the crossing levels. In the rapid fluctuation limit, P is given by \(P{=}\{1-{\exp}(-4{\pi}J^{2}/\hbar|v|)\}/2\). The intermediate case is studied numerically by the Wiener-Hermite expansion method. Generally, P approaches not 1 but 1/2 in the limit of slow passage, namely, v →0.