It is proved that the mapping, time-dependent
potential-->time-dependent density, is not invertible, in general,
over the class of all potentials expandable in a Taylor series with
respect to time coordinates. However, an invertible mapping does exist
between the time-dependent potential and time-dependent current density.
To explore this in detail, a one-body time-dependent problem is examined
in an attempt to seek a time-dependent current-density-functional
formalism.
The time-dependent density-functional theory of Runge and Gross [Phys.
Rev. Lett. 52, 997 (1984)] is reexamined on the basis of its
limitations, and the criticisms raised by Xu and Rajagopal [Phys. Rev. A
31, 2682 (1985)] are addressed, within the imposition of natural
boundary conditions of vanishing density and potential at infinity.
Also, for a single-particle system characterized by an arbitrary
time-dependent potential, the uniqueness of the density-to-potential
mapping is established explicitly for both bound and scattering states.
Experimental determinations of correlation functions typically involve events of differing particle number. In order to interpret such data, it is important to relate these measurements to fixed-number correlations. We exhibit the total correlation function in terms of fixed {ital n} correlations and fluctuations with respect to the average. We note that moments, constructed as integrals of the appropriate correlation functions, can be dominated in the case of broad distributions by cumulant moments constructed from single-particle density fluctuations.
We address the problem of identifying an operational prescription for quantum phase measurements. As is known, different experiments can lead to different measured phase operators. However, we show that ambiguities of interpretation can arise even if a single experiment, such as that of Noh, Fougères, and Mandel [Phys. Rev. Lett. 67, 1426 (1991)], is chosen as defining a phase measurement. We show by reference to a simple but fundamental example that it is not possible to deduce a unique phase difference from the measurements.
Most developments of Cherenkov Radiation are in terms of the Fourier components of the fields and power emitted by a single electron. When many electrons in a compact bunch are emitted from an accelerator, the bunch radiates coherently and at a lower frequency than for a single electron. The theory for the time structure of the fields arising from a charge bunch is developed, and it is shown that the source of the radiation is di/dt. Present detector technology should be able to resolve these fields.
A generalization of linear-response theory is attempted, within the framework of information theory [Y. Alhassid and R. D. Levine, Phys. Rev. A 18, 89 (1978); D. Otero et al., Phys. Rev. A 26, 1209 (1982)], with the idea of developing a formalism capable of dealing with small deviations from a previously well-described situation. The ensuing approach is applied to diverse physical situations that illustrate its flexibility.
We have measured the position of the Zeeman level crossing between the (J,M) = (0,0) and (1,1) sublevels of the 3 /sup 3/P state of helium. The result, 15.756 195(22) MHz (NMR frequency in water), is in good agreement with earlier, less precise measurements. This value, together with our previous measurement of the (2,2)-(0,0) level crossing, is used to calculate the zero-field fine-structure splitting. We find E/sub 02/ = 8772.517(16) MHz between the J = 0 and 2 states, E/sub 12/ = 658.548(69) MHz between the J=1 and 2 states, and E/sub 01/ = 8113.969(80) MHz between the J = 1 and 0 states.
We have measured the position of the magnetic field level crossing of the J = 2, M = 2, and the J = M = 0 sublevels of the 3 /sup 3/P state of helium. Time-resolved level-crossing spectroscopy, coupled with photoionization detection, were used to achieve accuracy of 1.5 ppm. The result, quoted in NMR frequency in water, is 9695.023(15) kHz, in good agreement with earlier, less precise measurements.
We have measured ({ital e},2{ital e}) energy spectra in cadmium for the 4{ital d}{sup 9}5{ital s}{sup 2}5{ital p} {ital J}=1 autoionizing region. The ejected-electron energy range investigated was from 2.6 to 4.8 eV with an incident electron energy of 150 eV and a scattering angle of 3{degree}. Small differences were found in spectra taken at ejected-electron directions 180{degree} apart. We ascribe these differences to interference terms arising from coherent excitation of the {ital J}=1 and overlapping 5{ital pnp} {ital J}=0,2 autoionizing levels. A calculation of these effects is presented that agrees quite well with the experimental data. We obtain experimental excitation amplitude ratios and assign a previously undetected autoionizing level to 5{ital p}6{ital p} {sup 3}{ital D}{sub 2}.
A many-body-theory (MBT) formulation for electron scattering by excited
electronic states is applied to excitation from the 2 1,3S
metastable states of helium. The lowest-order MBT for these transitions
involves a ``chanel coupling'' to the ground state of helium as well as
a distortion of the free-electron wave function by the ground state of
the target, while the distorted-wave approximation (DWA) involves a
distortion of the incident and scattered electron wave functions by the
initial and final target states, respectively. Results using the
first-order many-body theory and DWA are reported here for integral and
differential cross sections for excitation from the 2 1,3S
states to (2,3) 1,3P, 3 1,3S, and 3
1,3D states, and are compared with published experimental and
theoretical data.
The rotational excitation of N2 and Cl2 molecules on electron impact is investigated over a wide range of incident electron energies (0.01-1000 eV). Two different excitation mechanisms are reported, the importance of which depends on the impact energy. At low electron energies only a few rotational quanta are exchanged, and the differential cross section decreases exponentially with Deltaj. At high electron energies the excitation spectrum shows a rotational rainbow, i.e., the differential cross secton has a maximum at a relatively high Deltaj. The location of this maximum depends on electron energy E and scattering angle theta. For intermediate energies there is an interplay of these two mechanisms. It can be seen that the contributions of both mechanisms can roughly be added to yield the cross section for the observed process.
Equilibrium charge distributions have been measured for 18 kinds of ions passing through a carbon foil in the energy region of 1-6 MeV/u for light ions and of 0.2-1 MeV/u for heavy ions. By combining the data obtained at present with those reported for other energies or ion species, an attempt is made to find the systematics for charge fraction F(q), mean charge q¯, and distribution width d over the wide range of ion species Z and energy E. Strong correlation has been found between the shell structure of ions and the variation of q¯ or d with Z or E. The analysis for this correlation enables the evaluation of rather reliable values of q¯, d, or F(q) for ion species 4
The equation of state and the transport coefficients of shear viscosity, thermal conductivity, thermal diffusion, and mutal diffusion are estimated for a binary, equimolar mixture of hard spheres having a diameter ratio of 0.4 and a mass ratio of 0.03 at volumes in the range 1.7[ital V][sub 0] to 3[ital V][sub 0] ([ital V][sub 0]=1/2 [radical]2 N[ital tsum][sub [ital a]x[ital a]][sigma][sub [ital a]][sup 3], where [ital x][sub [ital a]] are the mole fractions, [sigma][sub [ital a]] are the diameters, and [ital N] is the number of particles), complementing and, in some cases, improving earlier low-density results through Monte Carlo, molecular-dynamics calculations using the Green-Kubo formulas. Calculations are reported for 108 to 2048 particles, so that both finite-system and, in the case of the transport coefficients, long-time tail corrections can be applied to obtain accurate estimates of the pressure and the transport coefficients in the thermodynamic limit. Corrections of both types are found to be increasingly important at higher densities, for which the pressure is observed to become nonlinear in 1/[ital N] over the range covered. The Mansoori-Carnahan-Starling-Leland (MCSL) equation is found to account for the pressure with considerable accuracy for [ital V][ge]1.7[ital V][sub 0]; the difference between the observed (infinite-system) pressure and the MCSL prediction increases monotonically with density, reaching 0.4% at [ital V]=1.7[ital V][sub 0]. For volumes below 2[ital V][sub 0] the pressure in excess of the MCSL prediction is found to soften'' slightly in its dependence on the density.
The transport coefficients of shear viscosity, thermal conductivity, thermal diffusion, and mutual diffusion are estimated for a binary, equimolar mixture of hard spheres having a diameter ratio of 0.4 and a mass ratio of 0.03 at volumes of 5V0, 10V0, and 20V0 (where V0=1/2 &surd;2 N tsuma xasigma3a, xa are mole fractions, sigmaa are diameters, and N is the number of particles) through Monte Carlo, molecular-dynamics calculations using the Green-Kubo formulas. Calculations are reported for as few as 108 and as many as 4000 particles, but not for each value of the volume. Both finite-system and long-time-tail corrections are applied to obtain estimates of the transport coefficients in the thermodynamic limit; corrections of both types are found to be small. The results are compared with the predictions of the revised Enskog theory and the linear density corrections to that theory are reported. The mean free time is also computed as a function of density and the linear and quadratic corrections to the Boltzmann theory are estimated. The mean free time is also compared with the expression from the Mansoori-Carnahan-Starling-Leland equation of state.
The charge-state distribution of neon recoil ions produced by ion-atom collisions has been investigated with ${\mathrm{Ni}}^{\mathrm{p}+}$, ${\mathrm{Cu}}^{\mathrm{p}+}$, and ${\mathrm{N}}^{2+}$ projectiles. The dependence of recoil-ion production on the ionization state of the primary ions has been investigated for two projectile energies in an intermediate velocity range not previously studied. Absolute net-ionization and charge-specific cross sections have been determined and are compared with other experiments and with theoretical predictions.
Electron transfer and excitation in 0.05- to 20-keV/amu He++Na(3s) collisions is studied theoretically within the close-coupling method with two-electron molecular- and atomic-orbital expansion basis sets. Results agree with the trend of other information on this system. Remaining discrepancies that are larger than those in similar contemporary studies of one-electron systems are discussed with reference to the convergence of this two-electron study. Results for the integral alignment parameter A20 are also presented as a guideline for future experimental study.
After compressing electron bunches with a half-meter long, four-dipole chicane at 8 MeV, we have measured full width at half maximum (FWHM) bunch lengths of less than 1 ps for charges from 0.1 to 1.1 nC. The uncompressed FWHM bunch lengths varied from 10 to 20 ps, and we achieved compression ratios in excess of 40 and peak currents greater than 1 kA. Bunch lengths for low charges were measured using a transversely deflecting rf cavity; bunch lengths for high charges were inferred from the energy spread induced in the beam by its longitudinal space-charge force as it drifted from the end of the compressor to the spectrometer. {copyright} {ital 1996 The American Physical Society.}
In this work, we study the formation of doubly excited projectile states near the double-escape threshold in collisions of 0.1-MeV/u Ag4+ ions with He, H2, and Ar gas targets under single-collision conditions. We detect projectile states in which one electron occupies a high Rydberg state and a second electron occupies a low-lying continuum state. The cross sections for producing these doubly excited projectile states are on the order of 10-20 cm2. The production probabilities are measured as a function of the continuum-electron laboratory-frame energy with the detected Rydberg electrons arising from a fixed band of energy levels. The width of the continuum-electron energy distribution measured in coincidence with a Rydberg electron is smaller than the width of the energy distribution measured without the coincidence requirement for H2 and Ar targets but not for He targets. The width of the continuum-electron energy distribution measured in coincidence with a Rydberg electron decreases as the fraction of doubly excited states formed by projectile double excitation and ionization decreases and the fraction formed by double-target-electron capture increases.
Electron-capture and deexcitation processes in collisions of excited Na*(3p) atoms with He+ ions are studied in the energy range 0.1-7 keV/u by using the molecular-orbital-expansion method within the semiclassical framework. The integral alignment (A20), alignment angle (gamma), and orientation (O) parameters of excited He(2 1P,2 3P) orbitals resulting from electron capture are also determined. Furthermore, the effects of the initial alignment of the Na*(3pm) orbital on the cross sections, O, and gamma parameters are investigated. The present results show that the ratio of theoretical cross sections for electron capture by the He+ ion in collisions with the Na*(3p) atom and the ground state Na(3s) atom, respectively, is nearly equal to unity in the energy range studied here. The results also show that the O and gamma parameters are significantly different for the singlet and triplet manifolds, implying that different collision dynamics for He(2p) formation govern in each manifold. These parameters can be effectively controlled by adjusting the initial alignment of the Na*(3p) orbitals.
Partial cross sections for electron capture into specific n states are reported for 0.1- and 0.25-MeV/nucleon Iq+-H2 collisions (q=12–18). The measured cross sections show pronounced differences when compared to theoretical calculations based on a number of models for bare incident ions on atomic hydrogen.
Cross sections for production of electrons which are moving with near-zero velocity in the projectile frame in pure-target-ionization and transfer-ionization events were measured for 12.7-MeV I13+ ions incident on He and H2 gas targets. These cusp-electron-production cross sections were found to be nearly equal for pure-target-ionization and transfer-ionization events in both targets. The cross section for cusp-electron production in transfer ionization from He targets comprised only 0.04% of the total transfer-ionization cross section and in pure target ionization comprised only 0.12% of the total pure-target-ionization cross section. Similar results were obtained for H2 targets except that all respective cross sections were larger than for He. The experiment shows that most of the free electrons released in pure-target- and transfer-ionization events for 0.1-MeV/u I13+ incident on He and H2 gas targets are not low-energy electrons in the projectile frame.
Elastic differential, integral, and momentum-transfer cross sections are calculated for the electron-NH3 system in the energy range of 0.1-1.0 keV. A parameter-free spherical optical potential is constructed from near-Hartree-Fock one-center expansion ammonia wave functions. A parameter-free spherical optical potential for the system is treated exactly in a partial-wave scheme to determine the final cross sections. The optical potential includes polarization effects. Several versions are employed of parameter-free polarization and exchange potentials. The calculated differential cross sections compare very well with the available experimental data.
The electron emission spectra observed following collisions of heavy ions with heavy atoms is often dominated by electrons with a continuous range of energies. The impact-parameter dependence for the emission of these electrons from Kr-Kr and Kr-Xe collisions has been measured for collision energies from 0.1 to 3.2 MeV and for scattering angles from 3° to 10° by measuring the emitted electrons in coincidence with the scattered ions. These data indicate that most of the ionization (often 20 to 25 electrons from the collision system) resulting from these heavy-ion-atom collisions occurs during the collision on a time scale of 10-16-10-17 sec, as opposed to Auger decay in the separated atoms following the collision. For each combination thresholds were observed for electron production as a function of the collision's distance of closest approach. These excitation thresholds agree well with promoted molecular orbitals calculated within the framework of the Fano-Lichten model and indicate that this model is useful beyond its expected range of applicability.
We report ab initio calculations for the electron-CH4 elastic scattering around the Ramsauer-Townsend (RT) minimum region (0.1-1.0 eV). A model potential approach, in the fixed-nuclei and one-center-expansion formalism, is employed in which the total optical potential is composed of three interaction terms: an accurate static potential of the Hartree-Fock level, an exchange interaction in the Hara free-electron-gas-exchange approximation (plus the orthogonalization), and a semiempirical polarization of the form &) 6, where rc is an adjustable parameter. The final results on the total and momentum-transfer cross sections compare reasonably well with experimental data. In particular, a shallow RT structure rather than a pronounced dip in the total cross section is reproduced, which is in good agreement with recent measurements. We also determine the scattering length to be a=-3.4 a.u. by extrapolating our very-low-energy eigenphases (E~=0.001 eV) to the limit of zero energy: From a simple s-wave analysis, this value gives the RT minimum position around 0.4 eV, which is in close agreement with the correct value.
Electron-CHâ scattering is investigated in a wide energy range (0.1--500 eV) by using a previously proposed spherical model (A. Jain, J. Chem. Phys. 81, 724 (1984)). The study is divided into three energy regions: the 0.1--1.0-eV region, where a well-known minimum occurs in the total cross section (Ramsauer-Townsend (RT) effect), between 2 and 20 eV, with a d-wave broad structure around 7--8 eV, and from 20 to 500 eV, where inelastic channels (mainly ionization and dissociation) dominate over the elastic process. It is shown that a simple model, in which the total optical complex potential is spherical, is capable of reproducing qualitative features in the total, differential, and momentum-transfer cross sections in the present energy region.
