Vortex formation in quantum dots in high magnetic fields

We study electronic structures of two-dimensional quantum dots in high magnetic fields using the density-functional theory (DFT) and the exact diagonalization (ED). With increasing magnetic field, beyond the formation of the totally spin-polarized maximum density droplet (MDD) state, the DFT gives the ground-state total angular momentum as a continuous function with well-defined plateaus. The plateaus agree well with the magic angular momenta of the ED calculation. By constructing a conditional wave function from the Kohn–Sham states we show that vortices enter the quantum dot one-by-one at the transition to the state with the adjacent magic angular momentum. Vortices are also observed outside the high-density region of the quantum dot. These findings are compared to the ED results and we report a significant agreement. We also study interpretations and limitations of the density functional approach in these calculations.     

On number and angular momentum projection from Hartree-Bogoliubov states

Rotational spectra, calculated by angular momentum projection from Hartree-Bogoliubov states may be completely distorted by particle number nonconservation. A simple method for correcting this is presented, which brings them close to the number projected spectra. It is also shown that by a slight modification of the usual number projection operator this projection may then be executed two times faster and with better numerical accuracy. We study the effect ofJ- and/orN projection before the variation in a constrained Hartree-Bogoliubov model. It is demonstrated that only simultaneous projection of both particle number and angular momentum before the variation is meaningful. Then a more gradual antipairing effect is found than known from previous work. We conclude however that the diagonalization of the Hamiltonian in a space of appropriately chosen generator wave functions is preferable to projection before the variation. In all cases the examples are nuclei in thesd-shell, calculated selfconsistently without separating off and inert core. The nucleon-nucleon force is the Hamada-Johnston potential.     

Theory of higher-order stark effect of symmetric top molecules

The Stark effect formula for symmetric top molecules, which is correct to the fifth order of an external electric field, is given. The formula is applicable to linear molecules without or with electronic angular momenta coupled in Hund;s case a. Numerical tables are given for the special case of linear molecules without any electronic angular momentum. The effect of centrifugal stretching is considered to the first order. It is shown that our perturbation formula, which is correct to the sixth order of an external electric field, is good even when μE/B is about 1.     

NMR shifts in paramagnetic systems: A nonmultipole expansion method

NMR shifts arising from the electron orbital angular momentum and the electron spin dipolar-nuclear spin angular momentum interactions using a nonmultipole expansion method are examined for a d electron in a crystal field of octahedral symmetry and with a tetragonal component. Bonding with the paramagnetic center is included. The NMR shifts are illustrated as isoshielding contour maps, and the results are compared with the multipole expansion method. It is shown that even when experimental data are successfully fitted by considering the NMR shifts as arising from the Fermi contact and the dipolar interactions, such an interpretation may lead to incorrect conclusions about the interactions within the paramagnetic system.     

The NMR isoshielding diagram for an f-electron system in a crystal field environment of octahedral symmetry

A general expression using a nonmultipolar expansion technique is derived for the NMR shift resulting from the f-electron orbital angular momentum and the f-electron spin dipolar-nuclear spin angular momentum interaction, where the f electron is in a crystal field environment of octahedral symmetry. From this expression all the multipolar terms are determined. For both the f¹ and f¹³ ions in a crystal field of octahedral symmetry the exact solution for the NMR shift, ΔB, is compared with various approximations such as the effect of neglecting the crystal field and the magnetic field mixing of the two J levels and the multipolar terms. In addition an analysis of the temperature dependence of the exact solution further illustrates that considerable care must be taken in interpreting NMR results in paramagnetic systems. Finally, the variations in the isoshielding diagram is interpreted in terms of the predominant energy level of the ground state and this is governed primarily by the crystal field parameters.     

Semiweak production of a top quark accompanied by a bottom quark and 2 jets at hadron colliders

We present a computation for the process of semiweak production of a top and a bottom quark accompanied by two jets. The calculation is performed using spinor techniques generalized to include massive fermions. The obtained matrix element squared allows for an accurate simulation of single top quark production in hadronic interactions with realistic transverse momentum and angular distributions for the jets in the event.Differential cross-sections are compared with previously obtained distributions from calculations.     

Analysis of relaxation phenomena in heavy-ion collisions

The transfer of mass, as well as the dissipation of relative kinetic energy and relative angular momentum in deeply inelastic heavy-ion collisions are studied as functions of time. Based on the determination of a parametrized deflection function from the experimental angular distributions, a classical model for the calculation of the mean interaction time as a function of initial relative angular momentum is presented. The method allows to include also those processes which correspond to long interaction times. The model is applied to determine mass transport coefficients from experimental mass (or element) distributions. The resulting mass drift and diffusion coefficients are accurate within less than 30% and compare well with the systematics obtained from the microscopic transport theory. The energy loss as function of interaction time is consistent with the following picture: Fast dissipation of the radial part of the kinetic energy accompanied by the loss of angular momentum with a larger relaxation time.     

Traces of products of angular momentum operators

Traces of products of angular momentum operators in a spherical or cartesian basis are common in the theory of atomic levels in fields, in the theory of nuclear orientation and of asymmetric top moments. Conventional angular momentum techniques lead to difficult and cumbersome calculations. In the present paper Schwinger's coupled boson representation is used in straightforward calculations of angular momentum and spherical tensor traces, of matrix elements and of asymmetric top moments. Only simple algebra, elementary multiplication and summation of integers are necessary. The method considerably simplifies calculations with angular momentum operators.     

杂质对量子环上荷负电激子的影响

讨论了在杂质电荷的电场影响下,量子环上荷负电激子X-的能-光谱及其Aharonov-Bohm振荡.当轨道总角动量不守恒的情况下,提出如何按轨道角动量分类构成基矢组并用典型的对角化方法求解体系的本征值和本征矢的方案.该方案计算简单,计算结果令人满意.还讨论了运用等效电荷变换公式和变换图,把位于三维空间的杂质简化为二维平面(或x轴上)的杂质处理,使计算变得更简单,对结果的分析也更明晰.     

采用量子含时波包方法研究H/D+Li_2→LiH/LiD+Li反应

采用量子波包方法和二阶分裂算符方法对H/D+Li_2→LiH/LiD+Li反应在0.01到0.4 eV的碰撞能范围内进行了动力学计算.在态分辨的理论水平上计算了反应概率、积分截面、微分截面等动力学性质并与之前的理论结果进行了比较.结果表明:由于本文的计算中包含了总角动量J在体固定坐标轴上的所有投影所得,结果更加精确;此外,当H原子被重的同位素原子D取代,反应概率、积分截面增大,然而这并没有对反应机理产生大的影响.前后对称的微分截面表明插入反应机理在反应过程中占据主导地位.     

Microscopic study of the 12C + 16O system

An angular momentum projected microscopic calculation is performed for the ¹²C + ¹⁶O system with an effective nuclear force and the exact Coulomb interaction. The ¹²C wave function is projected on a 0⁺ state. Parametrizations of the Coulomb interaction between the nuclei are fitted. The L-projected energy curves present a quite complicated structure especially for the negative parity states. The role played by critical angular momenta is put into evidence. A generator coordinate calculation gives several bands of bound, quasibound and virtual states. Excellent agreement in energy and angular momentum is obtained with the 13.7 MeV (J = 9), 19.7 MeV (J = 14), 22.7 MeV (J = 15) and other resonances.     

Angular-momentum-projected cranked hfb approach to the study of nuclear rotations

Employing a pairing-plus-quadrupole interaction hamiltonian and projecting out good angular momentum states from the cranked Hartree-Fock-Bogoliubov (CHFB) intrinsic wave functions the yrast spectra of ¹⁵⁸Dy and ¹⁶⁸Yb are calculated up to moderately high spins (I_max = 16) as to include the backbending region. Then the variation of pairing correlation, g-factor and rotational alignment of neutron spin as a function of total angular momentum is studied. The effect of particle number projection on the spin-projected CHFB wave functions is also investigated and is found to be unimportant for the calculation of g-factors. On the other hand, corrections of the excitation energies for number fluctuations in the CHFB wave functions are essential. Furthermore, looking at the distribution of the total projection quantum number K in various cranking wave functions we are able to throw some light on the K ≠ 0 nature of the aligned s-band.A variation-after-spin projection calculation strictly for the axial shape, without cranking, is also carried out for both the nuclei considered here. In the low-spin region this numerically “cheaper” scheme produces energy spectra similar to that of the CHFB method, and may thus be used to readjust the interaction parameters.     

Properties of the transition amplitude for two-nucleon transfer reactions

A general discussion is given of the angular momentum structure of the transition amplitude for two-nucleon transfer, particularly in light-ion-induced reactions. For example, it is shown that, within the model which is usually assumed, the relative phase between simultaneous and sequential transfer parts of the amplitude, for a given two-nucleon configuration, cannot depend upon the value of J, the total angular momentum transfer. A dependence on the oddness or evenness of J can emerge when there are additional sources of angular momentum transfer. Some of these are indicated.     

Orientation of O(3) and SU(2)⊗CI representations in cubic point groups (Oh,Td) for application to molecular spectroscopy

We propose a detailed method for the symmetrization of the standard O(3) or SU(2)⊗C_I basis |j_τ,m〉 (τ=g or u) into the O_h or T_d point group. This is realized by means of an orientation matrix called G. The oriented basis obtained in this way allows matrix element calculations for rovibronic spectroscopic problems concerning octahedral or tetrahedral molecules. Particular attention has been put on careful phase choices. A numerical calculation of all the G matrix elements for both integer and half-integer j values up to 399/2 has been performed. Such high angular momentum values are necessary for the case of heavy molecules with high rotational excitation. To calculate the G coefficients with high precision at high j values we pre-calculated the necessary Wigner functions using symbolic MAPLE software and made then the numerical calculations with quadruple precision. The complete list of these coefficients can be obtained freely at the URL: http://www.u-bourgogne.fr/LPUB/group.html. As an illustration, we also present briefly an application to two typical spectroscopic calculations: the pure rotational levels of SF₆ in its ground vibrational state and the ν₃ band of ReF₆ (an open-shell molecule with an odd number of electrons and a fourfold degenerate electronic ground state).     

The electronic structures of Mg,Al and Si in octahedral coordination with oxygen from SCF Xα MO calculations

Molecular orbital calculations performed using the SCF Xα Scattered Wave Cluster method are presented for the octahedral oxyanions MgO₆^?10, AlO₆^?9 and SiO₆^?8. The AlO₆^?9 results are used to assign and interpret the X-ray photoelectron spectra (XPS), X-ray emission (XES) and u.v. spectra of Al₂O₃. Agreement between calculation and experiment is good for valence band and fair for conduction band orbitais. The SCF Xα results for MgO₆^?10 are also in good agreement with observed valence band energies in MgO, but in this case the lowest energy features in the u.v. spectrum are not assignable in terms of either the calculations or the X-ray spectral results. The substantial increase in covalency expected between the Mg and Si oxides is evidenced in the calculations by an increase in valence region width from 2.6 to 5.3 eV and an increase in valence-conduction band separation from 5.2 to 10.0 eV. The calculated trends are in reasonable agreement with u.v. spectral data and with absolute valence orbital binding energies derived from X-ray spectra. A comparison of the SiO₆^?8 calculation with the analogous tetrahedral SiO₄^?4 calculation shows the valence band in the octahedral oxyanion to be much simpler in structure and somewhat narrower than that in the tetrahedral oxyanion. Using the orbital structure calculated for the valence bands of tetrahedral and octahedral oxides, a method is presented for calculating atomization energies directly from X-ray spectral data for SiO₂, Al₂O₃ and MgO. Results are in good agreement with experiment but the method involves an empirical parameter which is not presently understood in detail. Studies of trends in p-type bonding orbital binding energies derived from experimental data provide a qualitative explanation for the preferred coordination numbers in the Mg, Al and Si oxides.     

Relativistic calculation for the reactions\bar p d → 5πp and\bar p d → 3πp at rest

We present a fully relativistic calculation for ¯pd → 5πp and ¯pd → 3πp that includes angular momentum and spin dynamics. We calculate the inclusive proton distributions from two diagrams: the leading “tree” diagram, and the diagram for pion rescattering. Pion-nucleon rescattering proceeds through the Δ, in the RaritaSchwinger formalism, thus preserving the correct angular dependence. We use realistic parameterizations of the deuteron, keeping both theS andD states. The loop integrations for the rescattering amplitude and the phase space integrations have been done numerically. We find that the combined effects of a correct treatment of the rescattered pion and relativity are small in comparison with a simple non-relativistic calculation.     

The peripheral partial waves in pion-nucleon scattering from two pion exchange

A detailed and critical calculation is presented of the partial-wave amplitudes with large angular momentum in pion-proton scattering up to a lab momentum of 3 GeV/c.     

The peripheral partial waves in kaon-nucleon scattering

A detailed and critical calculation is presented of the partial-wave amplitudes with large angular momentum in kaon-proton scattering up to a lab momentum of 3.2 GeV/c.