Interelectron Interaction Research Articles

Exactly Solvable Model Mimicking the H2 Molecule in the Limit of Large Nuclear Masses

Avoiding the limitations of the Born-Oppenheimer approximation remains an issue of continuing importance in molecular physics. If we take the H 2 molecule as a prototype, then one uses, in some sense, the ratio of electron mass in to nuclear mass M as an expansion parameter, sometimes cited to be explicitly (m/M) 1/4 . Here, we employ a model of such a two-electron diatomic molecule set up by Makarewicz [Am. J. Phys. 54 (1986) 178] to study the exact ground-state wave function obtained by treating electrons and nuclei on the same footing, Of course, to obtain such a wave function analytically means adopting model force laws, both for confinement and for the interelectronic interaction. From the exact wave function and ground-state energy, contact is finally established with the large nuclear mass limit.

Dependence of the vortex structure in quantum dots on the range of the inter-electron interaction

The internal structure of a composite fermion is investigated for a two dimensional parabolic quantum dot containing three electrons. A Yukawa screened Coulomb interaction is assumed, which allows us to discuss the evolution of the electron-vortex correlations from the Coulomb interaction limit to the contact potential limit. The vortex structure approaches the Laughlin limit non-monotonically through the formation of intermediate composite fermions in which a flip of the spatial orientation of the vortices with respect to the position of the electrons is observed. Only when we limit ourselves to the lowest Landau level (LLL) approximation the flip appears through the formation of an intermediate giant vortex at specific values of the screening length. Beyond the LLL approximation antivortices appear in the internal structure of the intermediate composite fermions which prevent the nucleation of giant vortices. We also studied the system of five electrons and show that the mechanism of the flip of the vortex orientation found for three-electron system is reproduced for higher number of electrons.

Parametrizations and dynamical analysis of angle-integrated cross sections for double photoionization including nondipole effects

Similarly to differential cross sections for one-electron photoionization, the doubly differential cross section for double photoionization (DPI) may be conveniently described by four parameters: the singly differential (with respect to energy sharing) cross section $({\ensuremath{\sigma}}_{0})$, the dipole asymmetry parameter $(\ensuremath{\beta})$, and two nondipole asymmetry parameters ($\ensuremath{\gamma}$ and $\ensuremath{\delta}$). Here we derive two model-independent representations for these parameters for DPI from a $^{1}S_{0}$ atomic bound state: (i) in terms of one-dimensional integrals of the polarization-invariant DPI amplitudes and (ii) in terms of the exact two-electron reduced matrix elements. For DPI of He at excess energies, ${E}_{\mathrm{exc}}$, of 100 eV, 450 eV, and 1 keV, we present numerical results for the asymmetry parameters within the framework of the convergent close-coupling theory and compare them with results of lowest-order (in the interelectron interaction) perturbation theory (LOPT). The results for ${E}_{\mathrm{exc}}=1\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ exhibit a nondipole asymmetry that is large enough to be easily measured experimentally. We find excellent agreement between our LOPT results and other theoretical predictions and experimental data for total cross sections and ratios of double to single ionization cross sections for $K$-shell DPI from several multielectron atoms.

Optical Signatures of Spin-Orbit Interaction Effects in a Parabolic Quantum Dot

We demonstrate here that the dipole-allowed optical absorption spectrum of a parabolic quantum dot subjected to an external magnetic field reflects the interelectron interaction effects when the spin-orbit (SO) interaction is also taken into account. We have investigated the energy spectra and the dipole-allowed transition energies for up to four interacting electrons parabolically confined, and have uncovered several novel effects in those spectra that are solely due to the SO interaction.

Spin precession in a fractional quantum Hall state with spin-orbit coupling

In order to investigate the fundamental question of whether inter-electron interactions are important in planar electron-based spintronics devices, we have carried out a many-body study of the spin configuration in a quantum Hall state in the presence of Bychkov-Rashba-type spin-orbit interaction. We find that the spin orientation is position dependent and can be tuned via the applied electric field. We propose that this and other properties of such a system are ideally suited for exploitation in spin devices, and that the performance can be further optimized by a careful choice of the growth orientation.

Ballistic chaotic quantum dots with interactions: A numerical study of the Robnik-Berry billiard

In previous work we have found a regime in ballistic quantum dots where interelectron interactions can be treated asymptotically exactly as the Thouless number $g$ of the dot becomes very large. However, this work depends on some assumptions concerning the renormalization group and various properties of the dot obeying Random Matrix Theory predictions at scales of the order of the Thouless energy. In this work we test the validity of those assumptions by considering a particular ballistic dot, the Robnik-Berry billiard, numerically. We find that almost all of our predictions based on the earlier work are borne out, with the exception of fluctuations of certain matrix elements of interaction operators. We conclude that, at least in the Robnik-Berry billiard, one can trust the results of our previous work at a qualitative and semi-quantitative level.

Third-order negative-energy contributions to transition amplitudes in heliumlike ions

It is shown that third order (second order in the interelectron interaction and first order in the interaction with the electromagnetic field) contributions to transition amplitudes in heliumlike ions with one negative-energy intermediate state (NES) vanish in QED but not in relativistic many-body perturbation theory (RMBPT) in which the summation over NES states replaces one summation over positive-energy states with the same sign. An all-order RMBPT procedure based on QED for evaluating transition amplitudes in heliumlike ions that takes this result into account is formulated and used to evaluate 1s2s {sup 3}S{sub 1}{yields}1s3s {sup 3}S{sub 1} M1 transitions for heliumlike ions with Z=2-10.

Evaluation of quasidegenerate energy levels of two-electron configurations for multicharged ions

We present an accurate QED calculation of the interelectron interaction corrections to the energy of the (1s2p)1P1 and (1s2p)3P1 two-electron configurations for ions with nuclear charge 10⩽Z⩽92. When the fully relativistic treatment based on j–j coupling scheme is employed, the corresponding energy levels become quasidegenerate in the region Z⩽40. To evaluate the energies of these configurations within the framework of QED we utilize the line profile approach. The numerical results we have obtained are compared with available experimental data and with different calculations.

Nondipole effects in the triply differential cross section for double photoionization of He

Lowest-order nondipole effects are studied systematically in double photoionization (DPI) of the He atom. Ab initio parametrizations of the quadrupole transition amplitude for DPI from the {sup 1}S{sub 0} state are presented in terms of the exact two-electron radial matrix elements. Analytic expressions for these matrix elements within lowest-order perturbation theory (LOPT) in the interelectron interaction are also given. The corresponding parametrizations for the dipole-quadrupole triply differential cross section (TDCS) are presented for the case of an elliptically polarized photon. A general analysis of retardation-induced asymmetries of the TDCS including the circular dichroism effect at equal energy sharing is presented. Numerical LOPT estimates of nondipole asymmetries in photoelectron angular distributions for the cases of linear and circular polarization and of the circular dichroism effect at equal energy sharing are presented. We find that experimental observation of nondipole effects at excess energies of the order of tens to hundreds of eV should be feasible in TDCS measurements. Our numerical results exhibit a nondipole forward-backward asymmetry in the TDCS for DPI of He at an excess energy of 450 eV that is in qualitative agreement with existing experimental data.

Effects of interaction on an adiabatic quantum electron pump

We study the effects of interelectron interactions on the charge pumped through an adiabatic quantum electron pump. The pumping is through a system of barriers, whose heights are deformed adiabatically. (Weak) interaction effects are introduced through a renormalisation group flow of the scattering matrices and the pumped charge is shown to always approach a quantized value at low temperatures or long length scales. The maximum value of the pumped charge is set by the number of barriers and is given by ${Q}_{\mathrm{max}}={n}_{b}\ensuremath{-}1$. The correlation between the transmission and the charge pumped is studied by seeing how much of the transmission is enclosed by the pumping contour. The (integer) value of the pumped charge at low temperatures is determined by the number of transmission maxima enclosed by the pumping contour. The extra dissipation at finite temperatures leading to the nonquantized values of the pumped charge scales as a power law with the temperature $(Q\ensuremath{-}{Q}_{\mathrm{int}}\ensuremath{\propto}{T}^{2\ensuremath{\alpha}})$, or with the system size $(Q\ensuremath{-}{Q}_{\mathrm{int}}\ensuremath{\propto}{L}_{W}^{\ensuremath{-}2\ensuremath{\alpha}})$, where $\ensuremath{\alpha}$ is a measure of the interactions, and vanishes at $T=0({L}_{W}=\ensuremath{\infty})$. For a double barrier system, our result agrees with the quantisation of pumped charge seen in Luttinger liquids.

New Shell Structures and Their Ground Electronic States in Spherical Quantum Dots (II) under Magnetic Field

We theoretically studied the electronic structure of the three-dimensional spherical parabolic quantum dot (3D-SPQD) under a magnetic field. We obtained the quantum dot orbitals (QDOs) and determined the ground state by using the extended UHF approach where the expectation values of the z component of the total orbital angular momentum <\\hatLz> are conserved during the scf-procedure. The single-electron treatment predicts that the applied magnetic field (B) creates k-th new shells at the magnetic field of Bk=k(k+2)/(k+1)ω0 with the shell-energy interval of \\hbarω0/(k+1), where ω0(=\\hbar/m*l02) is the characteristic frequency originating from the spherical parabolic confinement potential. These shells are formed by the level crossing among multiple QDOs. The interelectron interaction breaks the simple level crossing but causes complicated dependences among the total energy, the chemical potential and their differences (magic numbers) with the magnetic field or the number of confinement electrons. The ground state having a higher spin multiplicity is theoretically predicted on the basis of the quasi-degeneracies of the QDOs around these shells.

Electron correlations in a quantum dot with Bychkov-Rashba coupling

We report on a theoretical approach developed to investigate the influence of the Bychkov-Rashba interaction on a few interacting electrons confined in a quantum dot. We note that the spin-orbit coupling profoundly influences the energy spectrum of interacting electrons in a quantum dot. Interelectron interaction causes level crossings in the ground state and a jump in magnetization. As the coupling strength is increased, that jump is shifted to lower magnetic fields. Low-field magnetization will therefore provide a direct probe of the spin-orbit coupling strength in a quantum dot.

Plasma modes in low-dimensional electron system over surface of liquid helium

The collective plasma modes in a quasi-two-dimensional (Q2D) electron system located over the free surface of liquid helium are studied theoretically within many-body dielectric formalism. The dispersion of modes is considered both over bulk liquid and over helium film where the essential modification of interelectron interaction occurs due to screening effects in the substrate with a large value of dielectric constant. It is shown that the plasma spectrum consists of longitudinal and transverse branches which dispersion laws depend on the values of the dielectric constant of helium and the film thickness. For the helium film covering metal, the longitudinal mode is acoustic differing of that for the surface electron (SE) system over bulk helium.

Calculation of quasidegenerate energy levels of two-electron ions

Accurate QED calculations of the interelectron interaction corrections for the $(1s2p){2}^{1}{P}_{1}$ and $(1s2p){2}^{3}{P}_{1}$ two-electron configurations for ions with nuclear charge numbers $10\ensuremath{\leqslant}Z\ensuremath{\leqslant}92$ are performed within the line profile approach. Total energies of these configurations are evaluated. Employing the fully relativistic treatment based on the $j\ensuremath{-}j$ coupling scheme these energy levels become quasidegenerate in the region $Z\ensuremath{\leqslant}40$. To treat such states within the framework of QED we utilize the line profile approach. The calculations are performed within the Coulomb gauge.

Power-law dependence of the angular momentum transition fields in few-electron quantum dots

We show that the critical magnetic fields at which a few-electron quantum dot undergoes transitions between successive values of its angular momentum (M), for large M values follow a very simple power-law dependence on the effective inter-electron interaction strength. We obtain this power law analytically from a quasi-classical treatment and demonstrate its nearly-universal validity by comparison with the results of exact diagonalization.

The interelectron interaction corrections to the hyperfine structure of the 2p3/2 state in Li-like, B-like and N-like 20983Bi ions

The lowest-order interelectron interaction corrections to the hyperfine structure intervals for the 2p3/2 state in Li-like, B-like and N-like 20983Bi ions are calculated. The contributions of the magnetic dipole, electric quadrupole and magnetic octupole moments are included. The ‘dynamical’ model of hyperfine interaction is employed, where the electron is assumed to interact with the valence proton in the 20983Bi nucleus via the exchange of a virtual photon. Within this model the magnetic and electric moment distributions inside the nucleus are taken into account simultaneously.

The contribution of the central region of the electron energy spectrum to the total double photoionization cross section of helium in the asymptotic nonrelativistic energy region

The double photoionization of helium at high photon energies is considered using a nonrelativistic approach. The central region of the energy spectrum and its contribution to the total process cross section and to the ratio between the double and single ionization cross sections are studied. Interelectronic interaction in the initial state is included exactly, whereas the interaction between the fast outgoing electrons is calculated by perturbation theory. A detailed derivation of the expression for the cross section ratio between double and single ionizations is given. The corresponding results obtained by other authors are analyzed and corrected.

Theoretical studies of photodetachment

A short survey of the model and ab initio many electron approaches applied to the study of negative ion photodetachment is presented. Primarily, attention is paid to the manifestation of dynamic many electron effects such as interference between different channels, polarization interaction, core relaxation and screening of the interelectron interaction in one-photon photodetachment processes.

Hyperfine structure of the2p3/2state of Li-like, B-like, and N-like83209Biions

The lowest-order interelectron interaction and electron self-energy radiative corrections to the hyperfine structure intervals for the ${2p}_{3/2}$ state of Li-like, B-like, and N-like ${}_{83}^{209}\mathrm{Bi}$ ions are calculated. The contributions of the magnetic dipole, electric quadrupole, and magnetic octupole moments are included. The ``dynamical'' model of the hyperfine interaction is employed, where the electron is assumed to interact with the valence proton in ${}_{83}^{209}\mathrm{Bi}$ nucleus via the exchange of a virtual photon. Within this model the magnetic and the electric moment distributions inside the nucleus are simultaneously taken into account.

Evaluation of the low-lying energy levels of two- and three-electron configurations for highly charged ions

Accurate QED evaluations of the interelectron interaction for low lying two- and three-electron configurations for ions with nuclear charge numbers 60⩽Z⩽93 are presented. The three-photon interaction is also partly taken into account. The results are compared with available experimental data and with different calculations. A detailed investigation of the behaviour of the energy levels of the configurations 1s1/22s1/21S0, 1s1/22p1/23P0 near the crossing points Z=64 and Z=92 is carried out. The determination of the crossing points is important for the future experimental search for parity non-conserving effects in highly charged ions.