Session J13: Few-Body Systems (Atomic)

Characterization by spectroscopic Ellipsometry, the physical properties of silver nanoparticles.

Physicists are able to change their minds through their experiments. I think it is time to go kick the curse and go further in research if we want a human future. I work in the Nano-Optics and Plasmonics research. I defined with ellipsom\`{e}trie the structure of new type of Nano particles of silver. It's same be act quickly to replace the old dirty leaded electronic-connexion chip and by the other hand to find a new way for the heath care of cancer disease by nanoparticles the next killers of bad cells. Silver nanoparticle layers are obtained by Spark Plasma Sintering are investigated as an alternative to lead alloy based material for solder joint in power mechatronics modules. These layers are characterized by mean of conventional techniques that is the dilatometry technique, the resistivity measurement through the van der Pauw method, and the flash laser technique. Furthermore, the nanoparticles of silver layer are deeply studied by UV-Visible spectroscopic ellipsometry. Spectroscopic angles parameters are determined in function of temperature and dielectric constants are deduced and analyzed through an optical model which takes into account a Drude and a Lorentz component within the Bruggeman effective medium approximation (EMA). The relaxation times and the electrical conductivity are plot in function of temperature. The obtained electrical conductivity give significant result in good agreement to those reported by four points electrical measurement method.   

Two-body problem in graphene

The description of excitons in graphene as a bound electron and hole using two dimensional Dirac equation is presented. We introduce a transformation to decouple the center-of-mass motion and the relative motion and analyze the two body problem with action-at-a-distance inter-particle Coulomb potential in a gapped graphene sheet. Then turn to a problem of two Dirac particles in two-layer graphene sheets separated by a dielectric, assuming that exciton in this system is formed by the electron located in the one graphene sheet and the hole located in the other. Assuming that interaction potential and both relative and center-of-mass kinetic energies are small compared to the gap energy, the analytical solution for the wave functions and energy spectrum of the exciton are found. The advantage of the consideration of exciton formed by an electron and a hole from two different graphene layers, separated by an insulating slab, is that the dielectric slab creates the barrier for the electron-hole recombination which increases the life-time of the exciton compared to the exciton formed by an electron and a hole in a single graphene layer.   

The ground state of $(2e 3Z)$ system (the ${\rm H}_3^+$ molecular ion): a physics behind

The Coulomb problem of two electrons in a field of three fixed equal charges $Z=1$ forming the equilateral triangle at equilibrium is studied. Five physics mechanisms of interaction leading to binding of $(2e 3Z)$ system (thus, forming the ${\rm H}_3^+$ molecular ion at equilibrium) are identified. Each mechanism is realized in form of variational trial function and their respective total energies are calculated. Each of them provides subsequently the most accurate approximation for the Born-Oppenheimer (BO) ground state energy among (two-three-seven)-parametric trial functions being correspondingly, $(2e 2Z)$-system plus $Z$ (two variational parameters), $(e 2Z)$-system plus $(e Z)$-system (three variational parameters) and generalized Guillemin-Zener (seven variational parameters). These trial functions are chosen following a criterion of physical adequacy, they assume two-charge potential is in the form $\sim \frac{\gamma}{r}$, hence, $\Psi \sim \exp{(\gamma r_{12})}$, where $\gamma$ is a variational parameter. Superposition of three mechanisms: generalized Guillemin-Zener plus (H$_2$ -molecule plus proton) plus (H$_2^+$ -ion plus H) (fourteen parameters) leads to the total energy which deviates from the best known BO energy ($\sim$ 7000 terms) to $\sim 0.0004$ a.u.   

Triexciton as a system of the three dipoles in a trap

Multi exciton production is a process that can occur in two dimensional (2D) quantum dots (QD) by which the energy of an absorbed photon can be used to create one or more additional excitons instead of being wasted as heat. This effect has received considerable interest because it has the potential to significantly improve the performance of solar cells, nanocrystal lasers, and high speed electronic devices. Cooling the excitons has become possible by confining electrons and holes in separate two dimensional (2D) quantum wells, which extensively increases their lifetime. In coupled quantum wells where the electrons and holes are separated in the two adjacent layers, all the indirect, the exchange effects are significantly covered up by the dipole-dipole repulsion, so dipole excitons can be treated as Bose particles. In the frame of indirect excitons, biexciton (2X) is a two body system which is well studying and triexciton (3X) is a three body system. To our best knowledge quantum three body systems of two-dimensional trapped dipoles no further were not well studied. In this presentation binding energy and structure of indirect three dipolar bosons in a parabolic trap will be investigate using the hyperspherical functions method and study how the Efimov and crystal- like phases are formed in the system.   

Two charges on plane in magnetic field

Two Coulomb charges on a plane subject to a constant magnetic field $B$ perpendicular to the plane are considered. Major emphasis is given to three particular cases: the Hydrogen atom, the Positronium and two electrons (quantum dot), at zero pseudo-momentum. It is shown that in addition to global integrals, pseudo-momentum and angular momentum, a particular integral appears for a certain values of magnetic field. The particular integral implies the existence of closed trajectories (in classical case) and polynomial eigenfunctions (in quantum case). Combining for the phase of wavefunction the WKB expansion at large distances and the perturbation theory at small distances a compact uniform approximation for lowest eigenfunctions is constructed. For the lowest states at magnetic quantum numbers $s=0,1,2$ this approximation gives not less than $7$ s.d., $8$ s.d., $9$ s.d. for the total energy $E(B)$ for magnetic fields 0.049\, a.u. $<$ B $<$ 2000\, a.u. (Hydrogen atom), 0.0125\, a.u. $<$ B $<$ 500.6\, a.u. (Positronium) and 0.025\, a.u. $\leq$ B $\leq$ 1000\, a.u. (two electrons), respectively. In framework of convergent perturbation theory the corrections to proposed approximations are evaluated.   

Test of the Unruh Effect Using Atomic Electrons

We propose a test for the circular Unruh effect using the electrons of atomic fluorine and oxygen. For these atoms the centripetal acceleration of the outer shell electrons implies an effective Unruh temperature in the range 1000 - 2000 K. This range of Unruh temperatures is large enough to shift the population of the outer electrons in low lying energy levels above the ground state. Examining these atoms at low ambient temperatures and finding a population of electrons in low lying excited states beyond what is expected via background thermal excitation would provide experimental evidence for the Unruh effect.