Magnetic field effect on state energies and transition frequency of a strong-coupling polaron in an anisotropic quantum dot

By employing a variational method of the Pekar-type, which has different variational parameters in the x–y plane and the z-direction, we study the ground and the first excited state energies and transition frequency between the ground and the first excited states of a strong-coupling polaron in an anisotropic quantum dot (AQD) under an applied magnetic field along the z-direction. The effects of the magnetic field and the electron–phonon coupling strength are taken into account. It is found that the ground and the first excited state energies and the transition frequency are increasing functions of the external applied magnetic field. The ground state and the first excited state energies are decreasing functions, whereas transition frequency is an increasing function of the electron–phonon coupling strength. We find two ways of tuning the state energies and the transition frequency: by adjusting (1) the magnetic field and (2) the electron–phonon coupling strength.     

磁场对石墨烯中弱耦合极化子性质的影响

研究了磁场作用下石墨烯中电子与表面光学声子弱耦合情况下的极化子的性质。采用线性组合算符和Pekar变分法分别推导出了石墨烯中弱耦合极化子的基态能量E₀、第一激发态能量E₁和跃迁频率ω随磁场强度B和德拜截止波数k_d之间的变化关系。数值计算结果表明,极化子的基态能量E₀随磁场强度B变化的曲线（k_d一定时）和E₀随k_d的变化曲线（B一定时）均会分裂成对称的两条,并且当B一定时E₀的绝对值随k_d的增加而增加。在k_d一定时,极化子的第一激发态能量E₁和跃迁频率ω均为磁场B的增函数;在B一定时,E₁和ω均随k_d的增加而增大。     

Calculation of Excited States of He Atoms in a Strong Magnetic Field

A recently developed B-spline algorithm is extended and utilized to calculate excited states of He atoms in the presence of strong magnetic fields. Binding energies are presented for He in the five excited atomic states 2¹0⁺, 1¹0^-, 2¹0^-, 1¹(-1)⁺, and 2¹(-1)⁺ with magnetic field strength ranging from 0.0001 to 10 a.u. The obtained energies are compared with available theoretical data, and found to be in good agreement. We investigate influence of magnetic fields on atomic structures of multielectron atoms, and illustrate that how electron probability density distributions change with increasing magnetic field strength. The current approach is directly applicable to simulations of discrete spectra for He atoms in the atmospheres of magnetized white dwarf stars.     

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.     

Specific features of Zeeman structure of configurations 2p55g of Ne I and 3p55g of Ar I

The energies of Zeeman sublevels of the 2p ⁵5g configuration of the neon atom and the 3p ⁵5g configuration of the argon atom are calculated for different values of the magnetic quantum number M (mainly for M = 0, ±1, and ±2) and magnetic field strength that vary in the range of 0–100 kOe. Values of the fields of crossings (ΔM = ±1 and ±2) and anticrossings (ΔM = 0) of magnetic components are determined. The regions of the strong nonlinearity of the dependence of Zeeman sublevel energies on the magnetic field strength are revealed. The gyromagnetic ratios are determined from the level splitting in the linear region (H ∼ 0.05 Oe).     

Sodium in a strong magnetic field

We investigate the effects of a magnetic field with low to intermediate strength on several spectroscopic properties of the sodium atom. A model potential is used to describe the core of sodium, reducing the study of the system to an effective one-particle problem. All states with principal quantum numbers n = 3, 4, 5, 6 and 7 are studied and analysed. A grid of twenty values for the field strength in the complete regime B = 0 - 0.02 a.u. is employed. Ionisation energies, transition wavelengths and their dipole oscillator strengths are presented. Received 5 November 2002 Published online 4 February 2003     

外场下压力及屏蔽对无限深量子阱中施主结合能的影响

考虑外加磁场、压力及屏蔽效应,利用变分方法数值计算GaN/AlxGa1-xN无限深量子阱系统中的杂质态结合能。给出结合能随磁场和阱宽的变化关系,同时讨论了有无屏蔽时的区别。结果表明:在磁场和压力作用下,结合能随阱宽的增大而减小;阱宽和压力一定时,结合能随磁场的增大而增大。屏蔽效应使得有效库仑吸引作用减弱而导致杂质态结合能显著下降。屏蔽效应对结合能的影响随压力增大而增强,随磁场强度增大而减弱。     

X-ray-line diagnostic of magnetic field strength for high-temperature plasmas

An x-ray line diagnostic for use in magnetic field measurements in high-temperature plasmas has been identified. The intensity of the otherwise strictly forbidden 1s(2)2s(2)2p(1/2)2p(4)(3/2)3s(1/2) 3P0-->1s(2)2s(2)2p(6) 1S0 transition in neonlike ions is shown to depend on the magnetic field strength. The field dependence is illustrated between one and 3 T in the Ar8+ spectrum. The line is well resolved, bright, and close to reference lines, making it an experimentally simple to use diagnostic.     

ODD parity donor levels of germanium in a magnetic field

The lowest three odd parity states of Ge donors are calculated in the effective mass approximation as functions of magnetic field strength for fields in the (111) and (100) directions. This extends our earlier calculations of 1s and 2s-like Ge donor states. No simplifying assumptions are introduced —we attempt to take explicitly into account the lack of cylindrical symmetry of the effective mass Hamiltonian in our choice of trial functions. Our results appear to agree reasonably well with measured transition energies of Nisida and Horii.     

三价铕离子配合物的激光光谱研究

利用高灵敏度的时间辨激光光谱技术研究了在配位场作用下Ｅｕ＾３＾＋的直接激发与发特性。Ｅｕ＾３＾＋的直接激发光谱（特别是７Ｆ０－５Ｄ０的超灵敏跃迁）及其发射光谱随不同的配合物的变化，同时观测到与配位对称性及配位强度有联系的７Ｆ１－５Ｄ０磁偶极跃 迁的分裂。在对７Ｆ０－５Ｄ０跃迁共振与非共振的１０ｐｓ激光脉冲的激励下，都可以立即观察到５Ｄ０－７ＦＪ（Ｊ＝２，３，４）的发射，说明Ｅｕ＾３＾＋的５Ｄ０能态     

Theory of the magnon-phonon interaction in magnetic field induced ferromagnet

The dependence of the elementary excitation energies and sound velocities on the magnetoelastic coupling and the magnetic field strength has been theoretically investigated in field-induced ferromagnets.It has been shown that near the field intensities, where the long range magnetic order appears, the acoustic quasi-phonon velocities and, in consequence, some elastic constants turn to zero. Such a behaviour has been interpreted as result of a structural phase transition.     

Lattice relaxation of graphene under high magnetic field

We investigate the n = 0 Landau level (LL) in monolayer graphene with high magnetic field. We find that the energy gap is opened in the n = 0 LL by the magnetic-field-dependent lattice relaxation originating from the interactions between the electrons (holes) and longitudinal-deformation-acoustic phonon. Both the linear and square-foot dependence of the energy gap on the magnetic field are obtained depending on the choice of the Debye cut-off wave number for the acoustic phonon. The relations of the Huang-Rhys parameter (lattice relaxation strength) and the transition linewidths with the magnetic field are also discussed. Our results agree with the current experiments on graphene in high magnetic field, and provide an alternative explanation for the experimental measurements.     

Relativistic calculations of 3s2 1S0-3s3p 1P1 and 3s2 1S0-3s3p 3P1,2 transition probabilities in the Mg isoelectronic sequence

Using the multi-configuration Dirac-Fock self-consistent field method and the relativistic configuration-interaction method,calculations of transition energies,oscillator strengths and rates are performed for the 3s 2 1 S 0-3s3p 1 P 1 spinallowed transition,3s 2 1 S 0-3s3p 3 P 1,2 intercombination and magnetic quadrupole transition in the Mg isoelectronic sequence(Mg I,Al II,Si III,P IV and S V).Electron correlations are treated adequately,including intravalence electron correlations.The influence of the Breit interaction on oscillator strengths and transition energies are investigated.Quantum electrodynamics corrections are added as corrections.The calculation results are found to be in good agreement with the experimental data and other theoretical calculations.     

Properties of a Magneto-Exciton in a Quantum Well

The ground state energies of an exciton in a GaAs/Ga_1-xAl_xAs quantum well structure for perpendicular magnetic field of arbitrary strength are studied. The results show that the energy of the magneto exciton will be increased with the increase of quantum well width and magnetic field strength.     

Impurity-related electronic properties in quantum dots under electric and magnetic fields

This paper presents a systematic study of the ground-state binding energies of a hydrogenic impurity in quantum dots subjected to external electric and magnetic fields.The quantum dot is modeled by superposing a lateral parabolic potential,a Gaussian potential and the energies are calculated via the finite-difference method within the effectivemass approximation.The variation of the binding energy with the lateral confinement,external field,position of the impurity,and quantum-size is studied in detail.All these factors lead to complicated binding energies of the donor,and the following results are found:(1) the binding energies of the donor increase with the increasing magnetic strength and lateral confinement,and reduce with the increasing electric strength and the dot size;(2) there is a maximum value of the binding energies as the impurity placed in different positions along the z direction;(3) the electric field destroys the symmetric behaviour of the donor binding energies as the position of the impurity.     

Hydrogen atom in strong magnetic field: a high accurate calculation in spheroidal coordinates

A B-spline-type basis set method for the calculation of hydrogen atom in strong magnetic fields in the frame of spheroidal coordinates has been introduced. High accurate energy levels of hydrogen in the magnetic field, with strength ranging from 0 to 1000 a.u., have been obtained. For the ground state, 1s₀, energies with at least 11 significant digits have been obtained. For the low-lying excited state, 2p₋₁, energies with at least 9 significant digits are obtained. The method has also been applied to the calculation of hydrogen Rydberg states in laboratory magnetic fields. Energy spectra with at least 10 significant digits are presented. A comparison with other results in the literatures has been performed. Our results are comparable to the most accurate one up to date. A possible extension to the cases of parallel and crossed electric and magnetic fields have been discussed.     

Stability of the director profile of a nematic liquid crystal around a spherical particle under an external field

We study numerically the effect of an external magnetic or electric field on the director profiles of a nematic liquid crystal around a spherical particle. We pay particular attention to the stability of a hyperbolic hedgehog defect accompanying the particle, which transforms into a Saturn-ring defect encircling the particle under a sufficiently strong external field. We focus on the particle size dependence of the two important threshold field strengths: the “thermodynamic-transition” field strength H₁ at which the hedgehog and the Saturn-ring configurations have the equal free energy, and the critical field strength H₂ at which the hedgehog loses its (meta)stability. Our numerical results demonstrate that while H₁ is non-monotonically dependent on the particle radius R₀, H₂ monotonically increases with R₀ and the dependence of H₂ is weak for large R₀. The non-monotonic dependence of H₁ on R₀ can be explained by comparing the energies of the two configurations and assuming the dependence of those energies on a rescaled field. A crude argument of the energetics of a hyperbolic hedgehog defect under an external field shows that for an asymptotically large R₀ the critical field strength is independent of R₀, which agrees with our numerical finding.     

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。     

Zeeman effects on d-wave superconductor and tunneling spectrum in normal-metal/d-wave superconductor tunnel junction

We study the Zeeman effect on the d-wave superconductor and tunneling spectrum in normal-metal(N)/d-wave superconductor(S) junction by applying a Zeeman magnetic field to the S. It is shown that: (1) the Zeeman magnetic field can lead to the S gap decreasing, and with the increase in Zeeman energy, the superconducting state is changed to the normal state, exhibiting a first-order phase transition; (2) the Zeeman energy difference between the two splitting peaks in the conductance spectrum is equal to2h0 (h0 is the Zeeman energy); (3) both the barrier strength of interface scattering and the temperature can lower the magnitudes of splitting peaks, of which the barrier strength can lead to the splitting peaks becoming sharp and the temperature can smear out the peaks,however, neither of them can influence the Zeeman effect.     

Quenching of SO2 phosphorescence by a magnetic field

Phosphorescence excitation spectra of the ã³B₁← [Xtilde]¹A₁ transition of SO₂ were measured in the absence and presence of a magnetic field (B = 0?44 T², P(SO₂) = 0?7 Torr). The absorption and phosphorescence excitation spectra of the ã³B₁← [Xtilde]¹A₁ transition of SO₂ measured in the absence of a magnetic field show that the relative intensity of the bands of the phosphorescence excitation spectrum is smaller than the relative intensity of the corresponding bands of the absorption spectrum beginning with the (0, 2, 0) band. In the presence of a magnetic field, the intensity of the phosphorescence excitation band falls, for ν_exc> 26400 cm^-1. Under the direct excitation of the ã³B₁← [Xtilde]¹A₁ transition, the dependence of the magnetic quenching of the SO₂ phosphorescence on the excitation frequency (ν_exc) was studied at P(SO₂) = 0?7 Torr and B = 0?44 T. The dependence of the magnetic field effect on ν_excshows that only the vibrationally excited levels of the ã³B₁ state are sensitive to an external magnetic field. The magnetic field strength and the pressure dependence of the magnetic field effects were studied under indirect excitation of the ã³B₁← [Xtilde]¹A₁ transition at λ_exc = 308 nm. The magnetic field and the pressure dependence were investigated for pure SO₂ and for SO₂ + RH (RH n-C₅H₁₂) mixtures. It was found that the magnetic field effect was saturated at B ? 0?25 T. The saturation value (Gr = l(0?3 T)/l(0)) increases with increasing gas pressure. The magnetic field, the pressure and the excess vibrational energy (ν_excess) dependence of the magnetic quenching of SO2 phosphorescence show that the data observed can be explained by an indirect mechanism within the framework of a low level density approximation.