Hund's rules,jj coupling and the gn electron configurations

The role of Hund's rules for the determination of the ground states of superheavy elements is considered.     

Channel-facilitated molecular transport across membranes: attraction, repulsion, and asymmetry

Transport of molecules across membrane channels is investigated theoretically using exactly solvable discrete stochastic site-binding models. It is shown that the interaction potential between molecules and the channel has a strong effect on translocation dynamics. The presence of attractive binding sites in the pore accelerates the particle current for small concentrations outside the membrane, while for large concentrations, surprisingly, repulsive binding sites yield the most optimal transport. In addition, the asymmetry of the interaction potential also strongly influences the channel transport. The mechanism underlying these phenomena is discussed using the details of particle dynamics at the binding sites.     

Molecule-type phases and Hund's rule in vertically coupled quantum dots

We study the ground state of two vertically coupled quantum dots as a function of the interdot distance within the spin density functional theory. The tunneling between the dots is included. For small and large interdot distances the atomic phases are recovered. For intermediate distances new molecule-type phases are predicted which can be observed experimentally in the addition energies. The results are interpreted in terms of an effective single particle picture and we find that Hund's rule breaks down for 11 and 12 electrons. The results are summarized in a phase diagram in which spin and isospin blockade regions are also found.     

Metal-insulator transitions: influence of lattice structure, jahn-teller effect, and Hund's rule coupling

We study the influence of the lattice structure, the Jahn-Teller effect, and the Hund's rule coupling on a metal-insulator transition in A(n)C60 (A = K,Rb). The difference in the lattice structure favors A3C60 (fcc) being a metal and A4C60 (bct) being an insulator, and the coupling to H(g) Jahn-Teller phonons favors A4C60 being nonmagnetic. The coupling to H(g) ( A(g)) phonons decreases (increases) the value U(c) of the Coulomb integral at which the metal-insulator transition occurs. There is an important partial cancellation between the Jahn-Teller effect and the Hund's rule coupling.     

The interaction energy of three molecules united in a nanocluster by long-range attraction forces with account for Coulomb repulsion

The interaction energy of three neutral molecules that form a nanocluster is studied. It is assumed that one molecule (M₀) has a dipole moment, while the other two (M₁ and M₂) are nonpolar. The molecule interaction energy in such a nanocluster is determined by the sum of dispersion interaction energies of each pair of molecules and the sum of inductive energies of the molecules. Analytical expressions for these energies as functions of the distance between the centers of mass of the molecules have been obtained. A method for the determination of damping functions which takes the contribution of repulsive forces into account has been developed. Analytical expressions for the molecule interaction energies for a two-molecule cluster in an external field of the third molecule have been obtained. A nanocluster consisting of a molecule of polar isomer pentene C₅H₁₀ and a nonpolar molecule of polycyclic aromatic hydrocarbon pyrene C₁₆H₁₀ in the external electrostatic field of another pyrene molecule is considered. The calculation showed that the interaction energy of the two-molecule nanocluster increases by a factor of 1.5 if this cluster is in the field of the induced dipole moment of an external pyrene molecule.     

Hund's rules and the interpretation and common misinterpretation of energy differences

With a Z expansion formalism which is exact in non-relativistic quantum mechanics it has been shown that for multiplets of neutral atoms and of many positive ions the state of the highest energy has the lowest expectation value for the interelectronic repulsion energy. This reversed order of the repulsion energy occurs for cases which obey Hund's first rule as well as for cases which obey the second of Hund's rules. It can be shown that the energy differences are in all cases dominated by the difference in electron nuclear attraction energy and not by the difference in electron repulsion energy.

The lowest ¹Π _u and ³Π _u states of the H₂ molecule have similar features. At many internuclear distances, including the equilibrium ones, the ¹Π _u state has the highest energy but the lower kinetic energy and electron repulsion energy but again the higher electron nuclear attraction energy. These results contradict clearly the usual theories for energy differences between spectroscopic states in atoms and molecules.     

Microscopic conditions favoring itinerant ferromagnetism: Hund's rule coupling and orbital degeneracy

The importance of Hund's rule coupling for the stabilization of itinerant ferromagnetism is investigated within a two-band Hubbard model. The magnetic phase diagram is calculated by finite-temperature quantum Monte-Carlo simulations within the dynamical mean-field theory. Ferromagnetism is found in a broad range of electron fillings whereas antiferromagnetism exists only near half filling. The possibility of orbital ordering at quarter filling is also analyzed. Received: 26 February 1998 / Accepted: 17 April 1998     

Leptodermous expansion of nuclear ground state energies and the anomaly in the nuclear curvature energy

The leptodermous expansion of the total ground state energy of a nucleus into volume, surface, curvature and gauss curvature contributions has been studied starting from a semi-classical energy density formalism of extended Thomas Fermi type. A numerical procedure was used to obtain the surface energy and curvature energy contributions from surface moments of energy density profilesH(r) for a sequence of nuclei withN=Z and neglecting the coulomb interaction for the three Skyrme forces. A transition to the liquid drop model type expansion in increasing powers ofA ^−1/3 is then made, taking into account the dependence of the central density and the surface structure on the mass of the nucleus. It is found that there is no inconsistency between the curvature contribution to the total energy in the leptodermous expansion and theA ^−1/3 term contribution in the liquid drop model expansion. It has been shown that the earlier apparent anomaly between the above two methods arises due to the use of semi-infinite approximation and the mass dependence of the central density and the surface structure of finite nuclei.     

Quench dynamics of two one-dimensional harmonically trapped bosons bridging attraction and repulsion

ABSTRACT

We unravel the nonequilibrium quantum dynamics of two harmonically confined bosons in one spatial dimension when performing an interaction quench from finite repulsive to attractive interaction strengths and vice versa. A closed analytical form of the expansion coefficients of the time-evolved two-body wavefunction is derived, while its dynamics is determined in terms of an expansion over the postquench eigenstates. For both quench scenarios the temporal evolution is analysed by inspecting the one- and two-body reduced density matrices and densities, the momentum distribution and the fidelity. Resorting to the fidelity spectrum and the eigenspectrum we identify the dominant eigenstates of the system that govern the dynamics. Monitoring the dynamics of the above-mentioned observables we provide signatures of the energetically higher-lying states triggered by the quench.     

Anomalous non-coincidence effects in liquids: separation of attraction and repulsion contributions

A method enabling one to separate the contributions of repulsion and attraction forces resulting in frequency non-coincidences in liquids is presented.     

Dependence of the knock-on electron cross-section on muon energy in high,medium and low Z elements

Using the recent experimental results of various authors the dependence of the knock-on electron cross-section on primary muon energy has been studied in detail. It is found that the knock-on production cross-section increases with primary muon energy upto at least 32 GeV in accordance with Bhabha's theory for energy transfers greater than 15 MeV.     

用原子核结合能公式估算Z的取值范围

利用原子核液滴模型的结合能公式得出了最重的原子核的Z值和偏离稳定线最远的原子核的Z值,从而确定了核素存在的范围.     

The flavour liquid state and Hund‘s rule effects in spin systems with orbital degeneracy

In order to understand the properties of the spin system with orbital degeneracy, we first generalize the linearized semiclassical spin wave method for the SU(2) generators into the SU(4) case, and then investigate the elementary excitations of the orbital-spin systems in the SU(4) limit. The results show that, due to the reduction of the dimensionality of the excitations, the ordered state of the SU(4) spin-orbital model is unstable. Secondly, we study the effects of the Hund interaction on the flavour liquid state of the system. Our mean-field results suggest that, for a small Hund interaction, the flavour liquid state is still stable against the generalized spin-density wave state, but with sufficient deviation from the SU(4) limit, the long-range order may be attained in two-dimensional systems. Finally, the implications for the experimental observations on the material LiNiO₂ are discussed.     

Mass, energy, and the electron

The two-component solutions of the Dirac equation currently in use are not separately a particle equation or an antiparticle equation. We present a unitary transformation that uncouples the four-component, force-free Dirac equation to yield a two-component spinor equation for the force-free motion of a relativistic particle and a corresponding two-component, time-reversed equation for an antiparticle. The particle-antiparticle nature of the two equations is established by applying to the solutions of these two-component equations criteria analogous to those applied for establishing the four-component particle and antiparticle solutions of the four-component Dirac equation. Wave function solutions of our two-component particle equation describe both a right and a left circularly polarized particle. Interesting characteristics of our solutions include spatial distributions that are confined in extent along directions perpendicular to the motion, without the artifice of wave packets, and an intrinsic chirality (handedness) that replaces the usual definition of chirality for particles without mass. Our solutions demonstrate that both the rest mass and the relativistic increase in mass with velocity of the force-free electron are due to an increase in the rate of Zitterbewegung with velocity. We extend this result to a bound electron, in which case the loss of energy due to binding is shown to decrease the rate of Zitterbewegung.