Spherical Potential Well Research Articles

Photoionization of Ca 4s in a spherical attractive well potential: dipole, quadrupole and relativistic effects

A study of the outer 4s subshell of the Ca atom in a spherical attractive potential well (SAW) of variable depth is performed to determine the effect of an external potential on dipole (E1) and quadrupole (E2) photoionization processes. As the depth of the potential well increases, dramatic changes are observed in the 4s cross-section, as well as in the photoelectron angular distribution. The existence of Cooper minima in the 4s dipole channels give rise to very significant effects of quadrupole interactions, even at extremely low energies, in the vicinity of the E1 Cooper minimum. It is shown that the entrapment of Ca in a spherical attractive well (Ca@SAW) further enhances the importance of quadrupole interactions determining the photoionization parameters. The complicated behavior of both dipole and quadrupole Cooper minima, as functions of well depth, is delineated, along with the importance of relativistic effects.

A quantum Carnot engine in three-dimensions

A simple quantum engine is designed which makes use of the closed- form solution for the energy eigenvalues of the Schrodinger equation under an infinite three-dimensional spherical potential well. A reversible cycle is defined for this system and made to operate in such a way that equations of state can be formulated for it on each leg of its cycle. For a closed, reversible cycle, a quantum Clausius equation can be obtained.

Exchange and spin states in quantum dots under strong spatial correlations. Computer simulation by the Feynman path integral method

The fundamental laws in the behavior of electrons in model quantum dots that are caused by exchange and strong Coulomb correlations are studied. The ab initio path integral method is used to numerically simulate systems of two, three, four, and six interacting identical electrons confined in a three-dimensional spherical potential well with a parabolic confining potential against the background of thermal fluctuations. The temperature dependences of spin and collective spin magnetic susceptibility are calculated for model quantum dots of various spatial sizes. A basically exact procedure is proposed for taking into account the permutation symmetry and the spin state of electrons, which makes it possible to perform numerical calculations using modern computer facilities. The conditions of applicability of a virial energy estimator and its optimum form in exchange systems are determined. A correlation estimator of kinetic energy, which is an alternative to a basic estimator, is suggested. A fundamental relation between the kinetic energy of a quantum particle and the character of its virtual diffusion in imaginary time is demonstrated. The process of natural “pairing” of electron spins during the compression of a quantum dot and cooling of a system is numerically reproduced in terms of path integrals. The temperature dependences of the spin magnetic susceptibility of electron pairs with a characteristic maximum caused by spin pairing are obtained.

Newly Synthesized Silicon Quantum Dot–Polystyrene Nanocomposite Having Thermally Robust Positive Charge Trapping

Striving to replace the well known silicon nanocrystals embedded in oxides with solution-processable charge-trapping materials has been debated because of large scale and cost effective demands. Herein, a silicon quantum dot-polystyrene (SiQD-PS) nanocomposite (NC) was synthesized by post-functionalization of hydrogen-terminated silicon quantum dots (H-SiQDs) with styrene using a thermally induced surface-initiated polymerization approach. The NC contains two miscible components: PS and SiQD@PS which, respectively, are polystyrene and polystyrene chains-capped SiQDs. Spin-coated films of the nanocomposite on various substrate were thermally annealed at different temperatures and subsequently used to construct metal-insulator-semiconductor (MIS) devices and thin film field-effect transistors (TFTs) having a structure of p-Si++/SiO2/NC/pentacene/Au source-drain. Capacitance-voltage (C-V) curves obtained from the MIS devices exhibit a well-defined counterclockwise hysteresis with negative fat band shifts, which was stable over a wide range of curing temperatures (50-250 °C). The positive charge trapping capability of the NC originates from the spherical potential well structure of the SiQD@PS component while the strong chemical bonding between SiQDs and polystyrene chains accounts for the thermal stability of the charge trapping property. The transfer curve of the transistor was controllably shifted to the negative direction by varying applied gate voltage. Thereby, this newly synthesized and solution processable SiQD-PS nanocomposite is applicable as charge trapping materials for TFT based memory devices.

Photoionization of confined Ca in a spherical potential well

Photoionization of confined Ca in a spherical potential well

A THEORETICAL APPROACH FOR INVESTIGATING THE NONRELATIVISTIC REPULSIVE OPTICAL POTENTIAL INVOLVED IN NEUTRON–NUCLEUS SCATTERING

For the first time, we present a theoretical formulation to determine the nonrelativistic repulsive optical potential relative to neutron–nucleus interaction in terms of the s-wave coherent scattering amplitude and the radius of the nucleus which is regarded as a spherical infinite potential well. Within this context, the Fermi velocity is determined in excellent agreement with the Fermi velocity obtained from considerations relative to nuclear density obeying the Saxon–Woods distribution. Assuming this distribution, the force relative to the neutron–nucleus interaction is calculated. Aspects related to the involved chemical potential are discussed. Our results are consistent with previous work.

ON THE OPTICAL POTENTIAL OF AN ATTRACTIVE NONRELATIVISTIC DEGENERATE ELECTRON GAS INTERACTING WITH NUCLEAR MATTER

The optical potential of an attractive nonrelativistic electron gas interacting with nuclear matter is determined on the basis of the concept of degenerate Fermi gas. In fact, the involved electrons are treated as three-dimensional quantum harmonic oscillators confined at the surface of a spherical (approximately ideal) potential well. Within this picture, the Fermi velocity is calculated as well as the spatial electron density at the surface of the potential well and the attractive force between the electron gas and the nuclear matter. In addition, considerations related to the Lippmann–Schwinger model are made.

Dirac particle in a spherical scalar potential well

In this paper we investigate a solution of the Dirac equation for a spin-$\frac{1}{2}$ particle in a scalar potential well with full spherical symmetry. The energy eigenvalues for the quark particle in ${s}_{1/2}$ states (with $\ensuremath{\kappa}=\ensuremath{-}1$) and ${p}_{1/2}$ states (with $\ensuremath{\kappa}=1$) are calculated. We also study the continuous Dirac wave function for a quark in such a potential, which is not necessarily infinite. Our results, at infinite limit, are in good agreement with the MIT bag model. We make some remarks about the sharpness value of the wave function on the wall. This model, for finite values of potential, also could serve as an effective model for the nucleus where $U(r)$ is the effective single particle potential.

A semi-classical approach of the relationship between simple cells' size and their living temperature limits based on number fluctuations of water coherence domains

Starting from the concepts of the quantum electrodynamics (QED) theory of coherence domains (CD) in water we propose a model aimed to evaluate the relationship between the size and the living temperature limits for simple, small cells. Cells are described as spherical potential wells with impenetrable walls, with CDs moving inside. The radius of the spherical potential well was estimated for physiological temperatures and the results match to bacteria and yeasts cells' size. As a CD in the spherical cell exerts a force upon the membrane, a 'gas' formed by CDs bears a pressure on the walls. A classical statistical stability condition relates this pressure to cell volume and to the relative fluctuations of the CD number, allowing the evaluation of an upper temperature limit as a function of cellular volume. Assuming further that the CDs in the living cell form together a coherent state, the number-phase incertitude relationship (Heisenberg limit) applies. The maximum coherence between CDs is found in the ground state, a picture consistent also to Fröhlich's postulate. For a given phase dispersion, a lower temperature limit as a function of the cell volume is found. Although we neglected the rod-like shape of certain bacteria and the presence of nucleus in yeasts, the biological data of volume and optimal living temperature intervals fit well to our model's predictions. Moreover the larger the cell volume, the higher are the number of CDs and the coherence of their system. In addition we suggest a new classification criterion for small cells based on model's parameters, which show discontinuities between Gram negative and positive microorganisms as well as between prokaryotes and the smallest eukaryotes.

Theoretical and numerical investigation of the size-dependent optical effects in metal nanoparticles

We further develop the theory of quantum finite-size effects in metallic nanoparticles, which was originally formulated by F. Hache, D. Ricard, and C. Flytzanis [J. Opt. Soc. Am. B 3, 1647 (1986)] and (in a somewhat corrected form) by S. G. Rautian [Sov. Phys. JETP 85, 451 (1997)]. These references consider a metal nanoparticle as a degenerate Fermi gas of conduction electrons in an infinitely high spherical potential well. This model (referred to as the HRFR model below) yields mathematical expressions for the linear and the third-order nonlinear polarizabilities of a nanoparticle in terms of infinite nested series. These series have not been evaluated numerically so far and, in the case of nonlinear polarizability, they cannot be evaluated with the use of conventional computers due to the high computational complexity involved. Rautian has derived a set of remarkable analytical approximations to the series but direct numerical verification of Rautian's approximate formulas remained a formidable challenge. In this work, we derive an expression for the third-order nonlinear polarizability, which is exact within the HRFR model but amenable to numerical implementation. We then evaluate the expressions obtained by us numerically for both linear and nonlinear polarizabilities. We investigate the limits of applicability of Rautian's approximations and find that they are surprisingly accurate in a wide range of physical parameters. We also discuss the limits of small frequencies (comparable to or below the Drude relaxation constant) and of large particle sizes (the bulk limit) and show that these limits are problematic for the HRFR model, irrespective of any additional approximations used. Finally, we compare the HRFR model to the purely classical theory of nonlinear polarization of metal nanoparticles developed by us earlier [G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, Phys. Rev. Lett. 100, 47402 (2008)].

Peculiarities of the amplitude of elastic subbarrier impurity scattering

A formula for the amplitude of electron elastic subbarrier (in the domain of imaginary momenta) scattering by an impurity modeled as a spherical potential well is derived. An equation is obtained to find the features (poles) of this amplitude in a complex energy plane in the close vicinity of which the energy spectrum of quantum resonant percolation trajectories in M-I-M contacts (M = N (normal metal) or S (superconductor) and I is an insulator) with weak (low impurity concentration) structural disorder in the I layer is concentrated [1–4].

Characteristic Energies and Shifts in Optical Spectra of Colloidal IV−VI Semiconductor Nanocrystals

We investigate structural, electronic, and optical properties of colloidal IV-VI semiconductor quantum dots (QDs) using an ab initio pseudopotential method and a repeated supercell approximation. In particular, rhombo-cuboctahedral quantum dots consisting of PbSe, PbTe, and SnTe with a pseudohydrogen passivation shell are investigated for different QD sizes. The obtained dependence of the confinement energy on the QD size questions the use of three-dimensional spherical potential well models for small QD structures. The predicted band gaps are almost in agreement with measured values. The calculated Franck-Condon shifts vary significantly with the QD size. Only for PbSe they may explain the Stokes shift between optical absorption and emission. For the tellurides, spectral properties such as the oscillator strength are more important.

Weakly bound electrons in an external magnetic field

The electron behavior in a spherical symmetric potential well in the presence of an external magnetic field is studied. The transcendental equation for the energy spectrum is derived. The energy of the bound state is approximately calculated. The electron wave function and the probability current are found.

Exciton recombination energy in spherical quantum dots on Ga1−xInxAsySb1−y/GaSb grown by liquid-phase epitaxy

Photoluminescence and photoreflectance responses at 12 K of Ga1−xInxAsySb1−y films grown over GaSb single-crystal substrates by liquid-phase epitaxy do not exhibit the same energy values. The photoluminescence peak shifts to 20 meV in relation to the photoreflectance response, indicating a possible electronic confinement in some parts of the growth heterostructure. The possibility of low-dimensional structures is investigated herein. They are possibly formed during the growth process and are responsible for this energy shift. The optical emission spectra associated with transitions between the first conduction and valence-band levels in spherical Ga1−xInxAsySb1−y/GaSb quantum dots, using x and y values in the range of 0.11–0.15 and 0.10–0.14, respectively, are studied here. These ranges were chosen according to experimental results obtained from the samples under study. Spherical potential wells of finite depth determined by the discontinuity in the conduction band ΔEC for electrons and the discontinuity in the valence band ΔEV for holes were used. In the calculations, the variational procedure within the effective-mass approximation was used and electrons and holes in a type-I band alignment formed by two semiconductors with similar parabolic conduction bands were considered. From these results, it was concluded that higher electronic confinements such as quantum dots were possibly formed during the growth process in some areas of the heterostructure.

A Helium Atom Confined by a Spherical Gaussian Potential Well

The helium atom confined by a non-impenetrable spherical box, i.e., a spherical Gaussian potential well which possesses finite height and range, is studied employing the exact diagonalization method. Total energies of the ground and three low-excited states are obtained as a function of the confined potential radii. We find that the confinement may cause accidental degeneracies between levels with different low-excited states and the inversion of the energy values. The results for the three-dimensional spherical potential well and the two-dimensional disc-like potential well are compared with each other: in general, the energies of the states decrease and the energy intervals between states increase with the reduction of the space dimensions.

A Study of Confined Helium Atom

The helium atom confined by a spherical parabolic potential well isstudied employing the adiabatic hyperspherical approach method. Total energiesof the ground and three low-excited states are obtained as a function of theconfined potential radii. We find that the energies of a spherical parabolicpotential well are in good agreement with those of an impenetrable sphericalbox for the larger confined potential radius. We find also that theconfinement may cause accidental degeneracies between levels with differentlow-excited states and the inversion of the energy values. The results forthe three-dimensional spherical potential well and the two-dimensionaldisc-like potential well are compared with each other. We find that theenergy difference between states in a two-dimensional parabolic potential isalso obviously larger than the corresponding levels for a sphericalparabolic potential.

Interpreting electron transmission spectroscopy and negative ion mass spectrometry data using a spherical potential well model

Experimental data obtained using electron transmission spectroscopy and negative ion mass spectrometry based on resonance electron capture are interpreted within the framework of a spherical potential well model in application to a series of chloro-and bromoalkane molecules. Allowance for the scattering of a single partial p-wave of the incoming electron makes possible (i) reproduction of the ratio of a resonance peak width to the electron energy observed in the electron transmission spectra and (ii) establishment of a relation between the total cross section of electron scattering on a molecule and the dissociative electron attachment cross section. The proposed model offers a radical simplification of the approach developed previously based on the Fashbach-Fano resonance theory.

Computer simulation of the collision frequency of two particles in optical tweezers

Optical tweezers have been successfully used in the study of colloid science. In most applications people are concerned with the behaviour of a single particle held in the optical tweezers. Recently, the ability of the optical tweezers to simultaneously hold two particles has been used to determine the stability ratio of colloidal dispersion. This new development stimulates the efforts to explore the characteristics of a two-particle system in the optical tweezers. An infinite spherical potential well has been used to estimate the collision frequency for two particles in the optical trap based on a Monte Carlo simulation. In this article, a more reasonable harmonic potential, commonly accepted for the optical tweezers, is adopted in a Monte Carlo simulation of the collision frequency. The effect of hydrodynamic interaction of particles in the trap is also considered. The simulation results based on this improved model show quantitatively that the collision frequency drops down sharply at first and then decreases slowly as the distance between the two particles increases. The simulation also shows how the collision frequency is related to the stiffness of the optical tweezers.

Exciton States in Spherical Gaussian Potential Wells**The project supported by National Natural Science Foundation of China under Grant No. 10275014

The exciton L = 0 and L = 1 states of a spherical GaAs quantum dot with a Gaussian confining potential are calculated by using the matrix diagonalization method. The size dependence of the exciton levels and the influence of the depth of the confining potential well in the spherical quantum dots are investigated. The same calculations performed with the parabolic approximation of the Gaussian potential lead to the results, which are qualitatively and quantitatively different.

Study on the coupled multiple nanocrystal quantum-dot system

We have studied excess electron filling rule in the coupled multiple nanocrystal quantum-dot systems, i.e. quantum chain and quantum pattern, by the unrestricted Hartree–Fock–Roothaan method. Assuming each quantum dot of quantum pattern to be confined in a three-dimensional spherical potential well of finite depth, we have studied the intradot and interdot electron Coulomb and exchange interactions. By varying the center distance d between the coupled quantum dots, the transition from the strong- to weak-coupling situation is realized. For the systems in question, our results show that, with the filling of excess electrons into the quantum pattern, the corresponding chemical potentials form quasi-band structure, which is similar to the energy-band structure of crystal material. In each chemical-potential band of quantum pattern, the number of chemical-potential curves is equal to the number of quantum dots, and the distributions of them depend strongly on the quantum-dot arrangement structure of quantum pattern.