椭球坐标下求解强磁场中的氢原子

在椭球坐标系下,采用B样条基组方法计算了磁场范围在0-1000 a.u.下氢原子低能态能量以及实验室磁场下(几个特斯拉)氢原子里德堡态的能级,并与文献中的精确结果进行了比较.对1s0态,磁场γ≤100 a.u.时,本文计算结果有12位有效数字的精度,γ=1000 a.u.时有11位有效数字的精度.对2p-1低激发态,γ≤100 a.u.时,能量至少有11位有效数字的精度;γ=1000 a.u.时,有9位有效数字的精度.对原子高激发态,我们计算了实验室磁场下(磁场为4.7特斯拉)氢原子里德堡态(主量子数n=23)的抗磁谱,得到了至少10位有效数字精度的能谱.本文方法既适用于超强磁场下低能态的计算,同样适合原子高里德堡态抗磁谱的计算,为精确计算强磁场下原子能谱提供了一个新的可行方案.此外,讨论了本文方法推广到平行及交叉电磁场下原子能谱计算的可行性.     

磁场对异质界面上D-中心的影响

势阱中的类氢杂质的能级问题一直为学术界所长期关注。讨论了异质界面上中性施主D⁰和负施主离子D^-的能量随垂直于界面的磁场的变化情况,同时将磁场和势阱结合起来考虑其对类氢杂质的影响。研究发现随磁场的增大,其对D⁰基态能的影响越来越大,对其束缚能的影响逐渐变小,而对D^-中心,磁场的作用使得D^-由非束缚态转变为束缚态。计算中分别选取了两种不同的波函数,分析了这两种波函数的适用范围,利用变分的方法得到此结构中D⁰中心的基态能量和束缚能与D^-中心角动量L=-1自旋三重态的本征能量和束缚能随磁场的变化关系,找到了此三重态由非束缚态转变到束缚态对应磁场的阈值。     

Anisotropic features of two-dimensional hydrogen atom in magnetic field

The aim of this study is the numerical research of anisotropic characteristics of a two-dimensional (2D) hydrogen atom induced by a magnetic field. The ground state energy (GSE) of the 2D hydrogen atom and the corresponding wavefunction have been numerically calculated in the Born–Oppenheimer approximation and taking into account the finite proton mass. The nonlinear dependence of the GSE on angle α between the magnetic field vector and the normal to the electron motion plane has been found in a wide range of the magnetic field. The effect of a significant reduction of the GSE (up to 1.9-fold) is observed with increasing the angle α up to 90°. The agreement with experimental data has been demonstrated. The dependences of the GSE of a 2D exciton in GaAs/Al_0.33Ga_0.67As have been determined for various tilt angles and magnetic fields.     

Polarization operator of a photon in a magnetic field

The polarization operator of a photon in a static uniform magnetic field has been studied at photon energies both above and below the threshold of electron–positron pair production by a photon. In the first order of the fine-structure constant α, expressions for the refractive index of a photon with a certain polarization in both low and high fields as compared to the critical field H₀ = 4.41 × 10¹³ G have been obtained. Both the purely quantum range of photon energies, where the particles of a pair are produced at the lowest Landau levels, and the region of applicability of the semiclassical approximation in the case of the population of high energy levels have been considered. A general spectral integral formula has been obtained with divergent threshold terms separated in an explicit form.     

The Gaussian Atomic Orbital Multiplied by a Field-Dependent Gauge Phase for the Hydrogen Molecular Ion in Non-aligned Magnetic Fields

We multiply the anisotropic Gaussian atomic orbital by a field-dependent gauge phase to describe the wave function for the hydrogen molecular ion in non-aligned magnetic fields. With the kind of basis set, the convergence of the total energy at the equilibrium distance for the 1 _u state is much improved compared to the same atomic orbital without the gauge phase. For 2.35 × 10⁴ ≤ B ≤ 10⁷ T, better total energies of the 1 _u state at the corresponding equilibrium are obtained for the deviations 15°–90° of the magnetic field relative to the molecular axis. The result also shows that, there is a transition of the equilibrium configuration from the vertical orientation to the parallel orientation with increasing field strength.     

Isomerization of C3H3NO isomers: ab initio study

The structures and isomerization process of C₃H₃NO species have been explored at the MP2/6–311++G(d,p) level of theory of the ab initio method. Eleven minima and four interconversion transition states have been identified. The zero-point vibrational energy corrections were made to predict reliable energies. We predict a five-membered ring-like structure to be the lowest energy isomer, which is 177.73?kcal?mol^?1 more stable than the least stable isomer X found on the potential energy surface. The transition states and minima isomers were verified by frequency calculation. Intrinsic reaction coordinate (IRC) calculations have been performed to confirm that each transition state is linked by the desired reactants and products. The isomer stabilities have been studied using the relative energies, chemical hardness and chemical potential. The MHP principle could not predict the order of stability for C₃H₃NO isomers as arrived at with the relative energies. The role of intramolecular hydrogen bonds on the equilibrium structure has been discussed. The energy barrier and reaction enthalpy have been calculated during isomerization.     

Scattering of low-energy positrons by the hydrogen molecular ion

A first application of the Kohn method is made to the calculation of scattering parameters for positron collisions with the hydrogen molecular ion below the positronium formation threshold at 9.45 eV. Phase shifts from the two-centre Coulomb value are obtained for the lowest spheroidal partial wave of _g ⁺ symmetry. For energies as low as 1.2 eV, it is found that a very flexible trial function must be used if accurate results are to be obtained.     

High resolution neutron scattering study of low-energy magnetic excitations in Nd2-xCexCuO4

The low-energy magnetic excitations (?ω ≤ 2 meV) of polycrystalline samples of Nd_2-xCe_xCuO₄ with x = 0, 0.1 and 0.15 have been measured with high resolution inelastic neutron scattering using time-of-flight technique at temperatures below 0.3 K. All observed scattering originates from transitions within the ground state doublet of Nd³⁺. For Nd₂CuO₄ the response is inelastic, and shows at least three different modes, of which one is almost dispersionless. For x = 0.1 the excitation spectrum shifts towards lower energies, but the main features of the undoped compound are still visible, whereas for x = 0.15 the response is mainly quasi-elastic but remains localised in Q-space around the first magnetic Bragg point (0.5 0.5 1). A comparison with data obtained on a triple-axis-spectrometer on single crystals with x = 0.0 and x = 0.15 reveals that the response of the doped sample in the [0 0 1] direction is still inelastic.     

Dynamical deformations of the electron density in an H2 molecule under strong,oscillating magnetic fields: an application of time-dependent quantum fluid density functional theory

Following the time-dependent quantum fluid density functional theory developed in our laboratory, the present quantum-mechanical, dynamical study of the H₂ molecule under strong, oscillating magnetic fields reveals a coexistence of both slow and fast dynamics, as seen earlier in the cases of hydrogen and helium atoms. Using the Deb–Chattaraj equation of motion we find that, contrary to the situation with static magnetic fields, the electron density now transiently expands. Consequently, the fate of the H–H bond under such strong TD magnetic fields has been addressed through detailed and accurate TD density profiles computed by direct numerical solution of the real-time evolution equation. A detailed interpretation of the slow dynamics has been made.     

Donor electron in a quantum well under the influence of an electric field

The ionization energies and the polarizabilities of a donor in an isolated well of a quasi two dimensional (Q2D) GaAs/Ga_1−x Al _x As heterostructure have been obtained for different well widths including electron-lattice coupling. A wave function that properly reduces to the hydrogenic function in the limiting case has been used. For fields of the order of 10⁵ V/m, the ionization energies decrease slightly with electric fields for all well widths (10 nm to 50 nm) studied. Also for a given electric field, as the well width increases, the ionization energy decreases. For fields of the order of 10⁷ V/m and for smaller well widths (<10 nm), the ionization energy generally increases with electric field. The results also show that for electric fields of this order, no donor bound state associated with the lowest subband is possible for well widths greater than 20 nm. The polarizabilities estimated using the expression for the dipole operator show that as the well width increases, the polarizability values also increase and do not show any abnormal behaviour.     

Ground states of the hydrogen molecule and its molecular ion in the presence of a magnetic field using the variational Monte Carlo method

ABSTRACT

By using the variational Monte Carlo (VMC) method, we calculated the 1sσ_g-state energies, the dissociation energies, and the binding energies of the hydrogen molecule and its molecular ion in the presence of an aligned magnetic field regime between 0 and 10?a.u. The present calculations are based on using two types of compact and accurate trial wave functions, which are put forward for consideration in calculating energies in the absence of a magnetic field. The obtained results are compared with the most recent accurate values. We conclude that the applications of the VMC method can be successfully extended to cover the case of molecules under the effect of a magnetic field.     

Magnetic excitations of HoAl2 in a magnetic field

The ground state spin wave excitation energies of single crystalline HoAl₂ have been studied at T= 4.2 K in external magnetic fields up to 7 T by means of inelastic neutron scattering. The results have been interpreted in terms of a cubic crystalline electric field using the parameters determined by magnetization measurements and an exchange interaction with the exchange parameters taken from the zero field measurements.     

Theoretical study of magnetic susceptibility of orbitally unquenched compound KCoF3

The effect of residual orbital magnetic moment of Co²⁺ in KCoF₃ on the magnetic susceptibility has been studied. For the calculation for both the ordered state and the paramagnetic state we have applied the correlated effective field approximation developed by Lines. An excellent value of the Néel temperature is obtained and, except near the Néel temperature, the calculated susceptibility agrees well with the experimental results over the whole temperature range.     

Stabilization of electron-hole liquid in uniaxially strained germanium in a strong magnetic field

Luminescence spectra of uniaxially and uniformly strained high-purity germanium crystals at liquid-helium temperatures in a magnetic field of up to 14 T have been investigated. In strongly strained Ge crystals, a new line has been detected on the low-energy side of the excitonline in magnetic fields higher than 4 T. Studies of this line’s characteristics as functions of pressure, temperature, and magnetic field have led us to conclude that its presence is due to recombination of electron-hole pairs in an electron-hole liquid. The experimental data suggest that the metallic electron-hole liquid is stabilized in a strong magnetic field. By approximating the shape of the newly detected line using the model of metallic electron-hole liquid, we have obtained the electron-hole liquid density n _EHL(B) and Fermi energies E _Fe,h of electrons and holes. The liquid binding energy ø as a function of magnetic field has been estimated.     

Theoretical study of the hydrogen abstraction reaction of CH3OH with NCO

A direct dynamics method is employed to study the mechanism and kinetics of the hydrogen abstraction reaction of CH₃OH with NCO. The optimized geometries and frequencies of the stationary points and the minimum-energy paths (MEPs) are obtained at the MP2/6-311G(d,p) level. In order to obtain more accurate potential energy surface (PES) information and provide more credible energy data for kinetic calculation, the single-point energies along the MEPs are further computed at QCISD(T)/6-311+G(d,p) and G3MP2 levels. The rate constants for two channels, the methyl-H abstraction channel and hydroxyl-H abstraction channel, are calculated by canonical variational transition state theory (CVT) with small-curvature tunneling (SCT) contributions over the wide temperature region 220–1500?K. The theoretical overall rate constants are in good agreement with the available experimental data. For the title reaction, the methyl-H abstraction channel is dominant, while the hydroxyl-H abstraction channel is negligible over the whole temperature region.     

Positronium formation for positron scattering from metastable hydrogen

Positronium(Ps) formation for positron impact on metastable hydrogen in 2s state has been studied by using the twochannel, two-center eikonal final state-continuum initial distorted wave(EFS-CDW) method. The differential, integrated,and total cross sections for Ps formation in different states have been calculated from each channel opening thresholds to high energy region. The results are compared with other theoretical calculations available in the literature. For Ps formation in s-state at intermediate and high energies, our results are in good agreement with the prediction of distorted wave theory.Those formed in p-states and the total Ps formation cross sections are reported for the first time. It is shown that the total Ps formation cross sections for positron scattering from H(2s) state are significantly larger at relatively low energies, while smaller at high energies, compared with those obtained from hydrogen in ground state.     

Electromodulation spectroscopy of excitons: High field regime

The effects of electric field on excitons have been investigated experimentally by means of electroabsorption (EA). The behavior of excitons with ionization fields F_I of the same order of magnitude as or smaller than typical applied fields is reported. EA spectra associated with excitons in TlBr, PbI₂, BiI₃, trigonal Se, and α-monoclinic Se will illustrate this case. In this situation the EA signal arises principally from the effect on the exciton ground state, and no finer structure could be detected. The exciton ground state undergoes a shift to higher energies with the applied field. Characteristic dependences with field of the sizes, energy position of the peaks, and zero crossing points of the EA signals have been found. Estimates of exciton parameters can be readily obtained from the EA spectra. Unusual features of the exciton EA spectra PbI₂ are discussed. Qualitatively, at least, theoretical predictions are obeyed.     

A pulsed NMR study of hydrogen diffusion in hydrides of group IVa transition metals

Activation energies E_A for hydrogen diffusion in hydrides of Group IVa transition metals have been determined by ¹H nuclear magnetic resonance measurements of spin lattice relaxation in both the laboratory (T₁) and rotating (T_1p) frames. For the HfHx system both activation energies obtained from T₁ data, and the value of T₁ at the minimum appear to be insensitive to hydrogen content x in the range 1.58 ? x ? 1.98. For hydrides of titanium and zirconium of approximately stoichiometric composition MH₂ (where M = metal), there is excellent agreement between activation energies obtained from T₁ and T_1p data. Mean activation energies obtained were 0.51 eV for TiH_1.98 and 0.83 eV for ZrH_1.96, consistent with a single diffusion mechanism in each case over the temperature range 260–600K and 400–800K respectively. In the case of HfH_1.98 the agreement was less good, values of 0.64 and 0.55 eV being obtained from T₁ and T_1p respectively.     

On the role of the magnetic dipolar interaction in cold and ultracold collisions: numerical and analytical results for NH(3Σ−) + NH(3Σ−)

We present a detailed analysis of the role of the magnetic dipole-dipole interaction in cold and ultracold collisions. We focus on collisions between magnetically trapped NH molecules, but the theory is general for any two paramagnetic species for which the electronic spin and its space-fixed projection are (approximately) good quantum numbers. It is shown that dipolar spin relaxation is directly associated with magnetic-dipole induced avoided crossings that occur between different adiabatic potential curves. For a given collision energy and magnetic field strength, the cross-section contributions from different scattering channels depend strongly on whether or not the corresponding avoided crossings are energetically accessible. We find that the crossings become lower in energy as the magnetic field decreases, so that higher partial-wave scattering becomes increasingly important below a certain magnetic field strength. In addition, we derive analytical cross-section expressions for dipolar spin relaxation based on the Born approximation and distorted-wave Born approximation. The validity regions of these analytical expressions are determined by comparison with the NH + NH cross sections obtained from full coupled-channel calculations. We find that the Born approximation is accurate over a wide range of energies and field strengths, but breaks down at high energies and high magnetic fields. The analytical distorted-wave Born approximation gives more accurate results in the case of s-wave scattering, but shows some significant discrepancies for the higher partial-wave channels. We thus conclude that the Born approximation gives generally more meaningful results than the distorted-wave Born approximation at the collision energies and fields considered in this work.     

强磁场中氢原子的能级结构

发展了一套简单高效的非微扰理论方法研究强磁场中的原子能级结构.作为例子,给出了磁场强度从0到1000个原子单位,氢原子基态和低激发态的结合能以及四极矩等重要原子能级结构参数.结果表明:相对于其他的高精度计算方法,该方法不仅能计算出高精度的能级位置而且可方便给出精确的电子波函数.此外,该法还具有很强的普适性,可直接推广到原子与任意方向的交叉电磁场相互作用的研究. 关键词： 强磁场 CWDVR谱方法 氢原子能级结构 四极矩