It is shown that the appearance of a fixed-point singularity in the kernel of the two-electron Cooper problem is responsible for the formation of the Cooper pair for an arbitrarily weak attractive interaction between two electrons. This singularity is absent in the problem of three and few superconducting electrons at zero temperature on the full Fermi sea. Consequently, such three- and few-electron systems on the full Fermi sea do not form Cooper-type bound states for an arbitrarily weak attractive pair interaction.
In the present work we develop a theoretical study to analyze how the image charges effects can modify the electronic properties in Si and SrTiO3-based quantum wells. We have used the method based on the calculation of the image charge potential by solving Poisson equation in cylindrical coordinates. The numerical results show that the electron-heavy hole recombination energy can be shifted by more than 200 meV due to the combination of charge image and SiO2 (SrTiO3) interface thickness effects.
Reflection electron energy loss spectra have been measured for silver using incoming electrons with energies between 5 and 40 keV, in a surface and volume-sensitive geometry. Bulk and surface loss functions are extracted from these data and various consis
We present experimental and theoretical differential cross sections for elastic electron scattering from xenon. Two independent measurements were carried out at (1) Chungnam National University for incident electron energies of 10, 20, 30, 50 and 100 eV a
The ionization of Mg 3s and 2p and He 1s has been studied in (e, 2e) experiments at about 1000 eV incident energy and 20 eV ejected electron energy for a momentum transfer between 0.5 and 2.1 au. The comparison with the predictions of the distorted wave B
A new experimental technique has been applied to measure absolute scattering cross sections for electron impact excitation of the n ≤ 2, 3 states of helium at near-threshold energies. The experimental results are compared with predictions from recent st
An octopus program is demonstrated to generate electron energy levels in
three-dimensional geometrical potential wells. The wells are modeled to have
shapes similar to cone, pyramid and truncated-pyramid. To simulate the electron
energy levels in quantum mechanical scheme like the ones in parabolic band
approximation scheme, the program is run initially to find a suitable electron
mass fraction that can produce ground-state energies in the wells as close to
those in quantum dots as possible and further to simulate excited-state
energies. The programs also produce wavefunctions for exploring and determining
their degeneracies and vibrational normal modes.; Comment: 6 pages, 8 figures
We derive the Landau energy levels for twisted N-enlarged Newton-Hooke
space-time, i.e. we find the time-dependent energy spectrum and the
corresponding eigenstates for an electron moving in uniform magnetic as well as
in uniform electric external fields.; Comment: 10 pages, no figures
At low temperatures the phase diagram for the quantum Hall effect has a
powerful symmetry arising from the Law of Corresponding States. This symmetry
gives rise to an infinite order discrete group which is a generalisation of
Kramers-Wannier duality for the two dimensional Ising model. The duality group,
which is a subgroup of the modular group, is analysed and it is argued that
there is a quantitative difference between a situation in which the spin
splitting of electron energy levels is comparable to the cyclotron energy and
one in which the spin splitting is much less than the cyclotron energy. In the
former case the group of symmetries is larger than in the latter case. These
duality symmetries are used to constrain the scaling functions of the theory
and, under an assumption of complex meromorphicity, a unique functional form is
obtained for the crossover of the conductivities between Hall states as a
function of the external magnetic field. This analytic form is shown to give
good agreement with experimental data.
The analysis requires a consideration of the way in which longitudinal
resistivities are extracted from the experimentally measured longitudinal
resistances and a novel method is proposed for determining the correct
normalisation for the former.; Comment: 22 pages...
The physical consequences of the relativistic and nonrelativistic approaches
to describe the energy levels of electrons which propagate in a static
homogeneous magnetic field are considered. It is shown that for a given
strength of the magnetic field, the quantized energy levels of the electrons
calculated by nonrelativistic and relativistic equations differ substantially,
up to few orders of magnitude for a magnetic field of about 1 Tesla.
Experimental verification to resolve the discrepancy would be very welcome.; Comment: & pages
We derive an approximate expression for a "radiative potential" which can be
used to calculate QED strong Coulomb field radiative corrections to energies
and electric dipole (E1) transition amplitudes in many-electron atoms with an
accuracy of a few percent. The expectation value of the radiative potential
gives radiative corrections to the energies. Radiative corrections to E1
amplitudes can be expressed in terms of the radiative potential and its energy
derivative (the low-energy theorem): the relative magnitude of the radiative
potential contribution is ~alpha^3 Z^2 ln(1/(alpha^2 Z^2)), while the sum of
other QED contributions is ~alpha^3 (Z_i+1)^2, where Z_i is the ion charge;
that is, for neutral atoms (Z_i=0) the radiative potential contribution exceeds
other contributions ~Z^2 times. The advantage of the radiative potential method
is that it is very simple and can be easily incorporated into many-body theory
approaches: relativistic Hartree-Fock, configuration interaction, many-body
perturbation theory, etc. As an application we have calculated the radiative
corrections to the energy levels and E1 amplitudes as well as their
contributions (-0.33% and 0.42%, respectively) to the parity non-conserving
(PNC) 6s-7s amplitude in neutral cesium (Z=55). Combining these results with
the QED correction to the weak matrix elements (-0.41%) we obtain the total QED
correction to the PNC 6s-7s amplitude...
We perform electron momentum spectroscopy studies of a Li2O film using the (e, 2e) spectrometer of the Australian National University. This technique provides a direct observation of the electron motion through measurement of the energy-momentum resolved
The effects of Rashba spin-orbit interaction (SOI) on the energy levels of parabolically confines quantum dot were analyzed. The spin-polarized electronic states were obtained in a weakly confined dot, when SOI was greater than a critical value of the SOI strength. It was observed that in high magnetic fields, the spectra of low-lying states exhibited features of Fock-Darwin levels and Landau levels. It was also observed that the effective SOI in the system was decreasing with increasing magnetic field and confining potential of the dot.
The second-order Born theoretical model developed for describing simultaneous ionization excitation and double ionization of a two-electron atomic shell by a fast charged-particle impact, was discussed. The model measured the projectile-target interaction to the second order, whereas the interaction of the two target electrons ejected into continuum was treated nonperturbatively by the convergent close-coupling (CCC) method. The model was used to describe two-electron ionization processes with large projectile velocity, small momentum transfer, and small to intermediate energy of the ejected electrons. The model was also applied to ionization excitation and double ionization of He by electron and positron impact in kinematics.
First order distorted wave Born approximation (DWBA) triple differential cross sections are reported for low-energy electron-impact ionization of the inner 3s and outer 3p shells of argon. Previous DWBA works have demonstrated that experiment and theory are not in accord for low energy ionization of inert gases and here we investigate the importance of exchange scattering. Different approximations for treating exchange scattering are investigated. It is shown that exchange scattering is particularly important for 3s ionization. Even with a proper treatment of exchange, the first order calculations are still not in satisfactory agreement with experiment. Consequently higher order effects will have to be included to achieve a satisfactory description of the low-energy ionization process. We also investigated both the Hartree-Fock and optimized potential methods for calculating atomic wavefunctions and static potentials and found that both methods produced almost the same cross sections.
Absolute differential cross sections for elastic electron scattering by water vapour have been measured at nine incident electron energies between 4 to 50 eV and over scattering angles between 10° and 180°, using a crossed-beam electron spectrometer. A
Absolute measurements of the differential cross section for elastic electron scattering from benzene (C6H6) are reported, for the first time, for incident electron energies of 8.5 and 20 eV. The angular distributions are discussed in terms of known negative ion resonance features and a favourable comparison is made with a recent model potential calculation.
We review recent theoretical results on the double photoionization and ionization with excitation of two-electron atomic targets obtained with the convergent close coupling (CCC) method. The method proved to be capable of producing accurate total ionization cross-sections for H-, He, and Li+ in a wide photon energy range from the double ionization threshold to 10 keV where the results go over continuously to the non-relativistic limit of infinite photon energy. By applying scaling laws these results can be extrapolated to all two-electron systems with an arbitrary nucleus charge Z. Present theory can also describe accurately the angular correlation in the two-electron continuum in the form of the fully-resolved triple-differential cross-section (TDCS). The latest results for the TDCS on He agree very well with recent absolute measurements with linearly polarized light.
We determine, both experimentally and theoretically, the fully resolved fivefold differential cross section (5DCS) of double ionization of helium by 5.6 keV electron impact. Symmetric energy sharing between the two ejected electrons is investigated at the excess energy of 8 and 20 eV with 0.22 and 0.24 au momentum transfer, respectively. Absolute 5DCS are determined by normalizing the experimental data to the well established single-ionization cross sections. The calculation is performed by using the convergent close-coupling method for the interaction between the two slow ejected electrons, together with the first Born approximation for the interaction of the fast incident electron with the atom. Experimental and theoretical 5DCS tend to agree in shape but disagree in magnitude by factors of three and 14 for the 20 and 8 eV excess energies, respectively. The small momentum transfer invites absolute comparison of the present electron-impact double-ionization results with the corresponding double-photoionization experiment and theory. Theoretically, the momentum transfer is sufficiently close to zero to show the scaling between the two scattering processes. This smallness of the momentum transfer also makes the calculated 5DCS nearly invariant with respect to simultaneous inversion of the momenta of the two ejected electrons.
Integral and backward scattering cross sections are reported for the scattering of electrons from C6H5F, C6H5Cl, C6H5Br and C6H5I over the energy range between 10 and 20 meV to 10 eV. The measurements were made in transmission experiments using a synchrotron radiation photoionization apparatus with an energy resolution in the incident electron beam of approx. 3.5 meV (FWHM). The absolute accuracy of the cross sections is limited by experimental difficulties with respect to strong rotationally inelastic forward scattering, due to the dipolar nature of the target molecules. Integral scattering cross sections are found to rise to more than 1500 angstrom2 at the lowest energies in C6H5F, C6H5Cl and C6H5Br and to more than 2000 angstrom2 in C6H5I due to an additional contribution from electron attachment. At low energy, both integral and backward scattering cross sections are very similar in C6H5F, C6H5Cl and C6H5Br. Data are interpreted in terms of rotationally inelastic scattering, with values of cross sections essentially dictated by the correspondingly similar dipole moments (1.6-1.7 D) of these three species. The Born model for rotationally inelastic scattering consistently underestimates the experimental cross sections and overestimates the degree of forward scattering. Our data illustrate the limitations of the Born model for the estimation of low-energy scattering cross sections for plasma modelling.