高强度均匀静磁场中氢原子能级的计算

采用一种简便的变分法，计算了在均匀高强度静磁场下氢原子的１１个低能态能级和平均半径，讨论了高强度磁场对能级和半径的影响。     

微扰法计算中等强磁场中氢原子的能级

本文在考虑氢原子轨道运动磁矩与磁场之间、自旋磁矩与磁场之间和感生磁矩与外磁场之间的相互作用的基础上,根据角动量和球谐函数的性质,应用简并态微扰方法研究了在中等强磁场中氢原子的能级,给出了计算中等强磁场中氢原子的一级近似能级的方法,具体计算了 T范围内氢原子 的各能级的数值,结果与有关文献给出的理论计算值是相近的,表明本文所给出的方法是简单的、计算结果是正确的。     

Effects of an electric field on the confined hydrogen atom in a parabolic potential well

Using the perturbation method, the confined hydrogen atom by a parabolic potential well is investigated. The binding energy of the confined hydrogen atom in a parabolic potential well is calculated as a function of the confined potential radius and as a function of the intensity of an applied electric field. It is shown that the binding energy of the confined hydrogen atom is highly dependent on the confined potential radius and the intensity of an applied electric field.     

在均匀强磁场中氢原子塞曼效应久期方程的简化公式

在均匀强磁场中,当氢原子的哈密顿量中B2项不能忽略时,氢原子的库仑场对称性遭到破坏,能级简并被全部解除.在应用变分法和数值法计算氢原子的能级过程中,计算十分复杂,而应用微扰法求解氢原子的能级,存在解久期方程的n2高阶行列式的困难.本文应用简并态微扰理论和球谐函数的性质,得到久期方程中非零微扰矩阵元普遍表达式.根据非零微扰矩阵元普遍表达式的性质,可以将氢原子塞曼效应久期方程的n2高阶行列式分解成1阶到n阶共n个低阶行列式的乘积,得到氢原子塞曼效应久期方程的简化公式,使得求解均匀强磁场中氢原子塞曼效应能级过程简化.而且由该公式可以得到氢原子在低能态时塞曼效应能级的解析解.根据该久期方程的简化公式计算了n=3氢原子塞曼效应一级近似能级.     

Quantum states of neutral atoms bound in the magnetic field of a Kepler-guide

The spectrum and the wave function of neutral atoms in the magnetic field of a Kepler-guide are presented by reducing a two-dimensional stationary Schrdinger equation to a one-dimensional hydrogen atom in Rydberg states. In addition, we set the scale for     

Control of dissipation of energy via reservoirs of coherent states

Dynamic profiles of various chemical reactivity indices like chemical potential, chemical hardness, electrophilicity, susceptibility, etc., within a confined environment during the interaction of atoms with strong oscillating time dependent magnetic fields have been studied. In the present study hydrogen and helium atoms in ground state (n = 1), as well as in excited state (n = 20) are considered. Time-dependent Schrödinger equations are solved for the ground and excited states of hydrogen atom and the Rydberg state of the helium atom while a generalized nonlinear Schrödinger equation is solved for the ground state of the helium atom. Dirichlet type boundary condition has been used to implement confinement to the systems. With an increase in the degree of confinement the system gets harder and hence becomes more stable. Keeping the confinement radius fixed, systems get more stabilized in strong field compared to weak field.     

Nuclear magnetic shielding of a hydrogen atom in an electric field

The nuclear magnetic screening constant of a hydrogen atom in a uniform electric field is calculated, neglecting any effect of electron spin. The screening is found to be reduced by the electric field for all directions of the applied magnetic field, the reduction being greatest if the two fields are perpendicular.     

均匀磁场中的二维氢原子

研究了二维氢原子在均匀磁场中的结构问题，随着磁场增强，能级出现分裂交叉和聚束的现象。     

正交非均匀电场中氢原子的高激发态

用数学软件Mathematica研究正交非均匀电场中氢原子两个高激发态(n=4和5)的能级和波函数.讨论能级分裂,并绘制零级近似下氢原子的电子概率角分布图.     

Resonances of a hydrogen atom in strong parallel electric and magnetic fields using B-spline basis sets

The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters $E_r}$ and $\Ga/2$ of a hydrogen atom in parallel electric and magnetic fields. The method can calculate the ground and higher excited resonances accurately and efficiently. The resonance parameters with accuracies of $10^{-9}-10^{-12}$ for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones. Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.     

Resonances of a hydrogen atom in strong parallel electric and magnetic fields using B-spline basis sets

The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters Er and Г/2 of a hydrogen atom in parallel electric and magnetic fields. The method can calculate the ground and higher excited resonances accurately and efficiently. The resonance parameters with accuracies of 10^-9 - 10^-12 for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones. Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.     

会聚线偏振强激光场中氢原子的能态变化

本文研究氢原子在会聚的线偏振强激光场中原子势的变化以及由此而引起的原子能级移位和波函数的空间扩展问题.结果表明,变化后的原子势等价于半径由外场决定而荷电量为核电荷的振荡球壳的势.在此势下,原子能级将变浅和分裂,波函数的空间分布将增大.     

超强激光场中氢原子辐射高次谐波蒙特卡罗模拟

运用蒙特卡罗方法，模拟和计算出在超强激光场中，氢原子在相对论领域的电离几率和辐射出的高次谐波，并且讨论了氢原子的电离几率和辐射出的高次谐波与激光场的电场和磁场的关系。     

氢原子的X射线新谱系的实验观测及其解释

 引出氢（氘）气放电产生的射线和粒子流打在非晶聚氘乙烯C₂D₄和有机玻璃C₅H₈O₂等靶上,测得其散射谱上有多条尖锐的X谱线,其中除一条外都是（不经散射的）原始谱中没有的。经反复证认,这些谱线不是靶中元素（如C或O）和可能包含的杂质元素的特征X射线,也不是原始谱中X射线的衍射线,更不可能是低能电子的轫致辐射经吸收后形成的峰,认为该谱线很可能是前所未知的一类新的原子态的X射线新谱系的一部分。用曾提出的一个“小氢原子”理论模型予以解释,即认为氢（氘）气放电中产生了“小氢原子”,其（在基态）电子轨道半径约为普通氢原子的玻尔半径的1/274,该小氢原子能级之间的跃迁能够很好地解释所测到的X射线新谱系。     

Semiclassical calculation of ionization rate for Rydberg hydrogen atoms near a metal surface

The ionization of Rydberg hydrogen atoms near a metal surface at different scaled energies above the classical saddle point energy has been discussed by using the semiclassical method. The results show that the atoms ionize by emitting a train of electron pulses. In order to reveal the chaotic and escape dynamical properties of this system in detail, the sensitive dependence of the ionization rate upon the scaled energy is discussed. As the scaled energy is close to the saddle point energy, the ionization process of the hydrogen atom is nearly the same as the case of hydrogen atom in an electric field. There is only a single pulse of electrons, with an exponentially decaying tail. With the increase of the scaled energy, the ionization rates are similar to the case of the hydrogen atom in parallel electric and magnetic field, a series of electron pulses appear in the ionization process. This is caused by classical chaos, which occurs for the metal surface. Our studies also suggest that the metal surface can play the role of both the electric and the magnetic fields. Our theoretical analysis will be useful for guiding experimental studies of the ionization of atoms near the metal surface.     

A hydrogen atom in a superstrong magnetic field and the Zeldovich effect

We consider the problem of a hydrogen atom in a superstrong magnetic field, B? B _a =2.35×10⁹ G. The analytical formulas that describe the energy spectrum of this atom are derived for states with various quantum numbers n_ρ and m. A comparison with available calculations shows their high accuracy for B?B _a . We note that the derived formulas point to a manifestation of the Zeldovich effect, i.e., a rearrangement of the atomic spectrum under the influence of strong short-range Coulomb potential distortion. We discuss the relativistic corrections to level energies, which increase in importance with magnetic field and become significant for B?10¹⁴ G. We suggest the parameters in terms of which the Zeldovich effect has the simplest form. Analysis of our precision numerical calculations of the energy spectrum for a hydrogen atom in a constant magnetic field indicates that the Zeldovich effect is observed in the spectrum of atomic levels for superstrong fields, B?5×10¹¹ G. Magnetic fields of such strength exist in neutron stars and, possibly, in magnetic white dwarfs. We set lower limits for the fields B_min required for the manifestation of this effect. We discuss some of the properties of atomic states in a superstrong magnetic field, including their mean radii and quadrupole moments. We calculated the probabilities of electric dipole transitions between odd atomic levels and a deep ground level.     

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.     

Donor-bound electron states in a two-dimensional quantum ring under uniform magnetic field

The electron states in a two-dimensional GaAs/AlGaAs quantum ring are theoretically studied in effective mass approximation. On-centre donor impurity and uniform magnetic field perpendicular to the ring plane are taken into account. The energy spectrum with different angular momentum changes dramatically with the geometry of the ring. The donor impurity reduces the energies with an almost fixed value; however, the magnetic field alters energies in a more complex way. For example, energy levels under magnetic field will cross each other when increasing the inner radius and outer radius of the ring, leading to the fact that the arrangement of energy levels is distinct in certain geometry of the ring. Moreover, energy levels with negative angular momentum exhibit the non-monotonous dependence on the increasing magnetic field.     

Perturbative approach to the hydrogen atom in a strong magnetic field

We consider states of the hydrogen atom with the principal quantum number n≤3 and zero magnetic quantum number in a constant homogeneous magnetic field ?. The perturbation theory series is summed using the Borel transformation and conformal mapping of the Borel variable. Convergence of the approximate energy eigenvalues and their agreement with the corresponding existing results are observed for external fields up to n³?/?₀～5, where ?₀ is the atomic magnetic field. The possibility of restoring the asymptotic behavior of energy levels using perturbation theory coefficients is also discussed.     

Relativistic theory of a hydrogen atom in a superstrong magnetic field

The Dirac equation for a hydrogen atom in a static, uniform magnetic field is transformed by a modified FWT transformation into a mixed form; relativistic for perpendicular motion and semi-relativistic for parallel motion. In this way the adiabatic approximation can easily be obtained.