基于严格交换势的低能电子与H2分子碰撞振动激发散射截面的研究

严格交换势用于研究低能电子与H₂分子的弹性和非弹性散射截面,线性代数方法和R-矩阵传播子相结合求解基于振动密耦合方法的积分-微分耦合方程组,由此得到收敛的(0→0,0→1,0→2)散射微分截面和积分截面.理论计算结果与目前优秀的实验值和其他理论计算值进行了比较,表明基于振动密耦合方程的严格交换势在低能电子与H₂分子振动激发散射中有重要作用. 关键词： 严格交换势 2分子振动激发')" href="#">H₂分子振动激发 微分截面 积分截面     

运用球高斯分布极化势研究低能电子与H2 分子碰撞的振动激发动量迁移散射截面

用最近改进的球高斯分布(distributed spherical Gaussian,DSG)极化势模型,在振动密耦合框架下和基于量子力学从头计算的静电势、交换势的基础上,研究了低能电子与H₂分子碰撞振动激发的动量迁移散射截面(momentum transfer cross section,MTCS).通过包含18个振动波函数、5个分波和16个分子对称性,得到了0<E≤10 eV时收敛性很好的ν=0→ν'=0,1,2,3等几个振动跃迁通道和总的MTCS,并与其他实验和理论得到的值进行了比较和分析. 关键词： 2分子碰撞')" href="#">H₂分子碰撞 动量迁移散射截面 振动激发 球高斯分布极化势     

低能电子与H_2分子碰撞振动激发动量迁移散射截面的研究

采用振动密耦合方法及基于量子力学从头计算的静电势、交换势和相关极化势,研究了低能电子与H2分子碰撞振动激发的动量迁移散射截面.通过包含18个振动波函数、8个分波和16个分子对称性,得到了收敛性很好的ν=0→ν′=0,1,2,3,4等几个振动跃迁通道的动量迁移散射截面值,并在入射电子能量1eVE≤10eV时给出了比以前的理论研究更为合理的总的动量迁移散射截面.     

低能电子与氢分子碰撞的振动激发积分散射截面的研究

采用振动密耦合方法,研究了低能电子与H₂分子碰撞的振动激发积分散射截面.研究表明,使用18个Morse振动波函数、5个分波和4个对称性可以得到收敛的0→0,0→1,0→2和0→3积分散射截面;而且振动波函数的性质和振动能级的精确性会直接影响振动激发散射势能和振动激发积分散射截面.计算结果与实验符合得很好. 关键词： 电子散射 振动激发 2分子')" href="#">H₂分子 积分截面     

低能电子与N2分子碰撞的振动共振激发散射截面的密耦合研究

使用经孙卫国教授改进后的振动密耦合散射方法和基于量子力学从头计算得到的静电、交换与极化散射作用势,研究了低能电子与N2分子的振动激发散射截面.研究表明在振动密耦合计算中使用18个振动波函数和12个分波数目,可以得到收敛的0→5,1→5等高激发散射的积分和微分截面.     

中高能电子被O2及CF4分子散射的微分截面、弹性积分截面及动量转移截面

利用可加性规则，使用Roothaan-Hartree-Fock波函数，采用由束缚原子概念修正过的复光 学势，在300—1000eV内若干个能量点处计算了电子被O₂及CF₄分子 散射的微分截面、 弹性积分截面及动量转移截面，并将计算结果与实验结果及其他理论计算结果进行了比较. 比较的结果表明，利用被束缚原子概念修正过的复光学势及可加性规则进行计算，所得微分 散射截面的精度要比利用未修正的复光学势及可加性规则进行计算得到的结果准确得多；同 时，计算得到的弹性积分截面及动量转移截面也比较接近实验值.因此，在复光学势中采用 束缚原子概念可提高电子被分子散射的微分截面、弹性积分截面及动量转移截面的计算准确 度. 关键词： 电子散射 可加性规则 微分截面 弹性积分截面     

中、高能电子被SO2分子散射的微分截面、动量转移截面及弹性积分截面

在考虑分子内成键原子间的电子云重叠效应的基础上, 提出了一种能够准确计算“中、高能电子-分子”散射的微分截面、动量转移截面及弹性积分截面的修正势方法. 利用可加性规则、使用Hartree-Fock波函数并采用被这一方法修正过的复光学势, 在100—1000eV内对电子被SO₂分子散射的微分截面、动量转移截面及弹性积分截面进行了计算, 并将计算结果与实验及其他理论结果进行比较. 结果表明, 利用这一修正过的复光学势及可加性规则获得的微分截面比利用未修正的复光学势及可加性规则得到的结果准 关键词： 可加性规则 微分截面 动量转移截面 电子散射     

低能电子与Kr、Xe弹性碰撞截面的计算

本文利用原子的解析波函数,导出了电子与第四,五周期元素原子相互作用势的解析形式,并用文献提出的物理模型与计算方法,对低能电子被Kr和Xe散射的截面进行了计算,得到了入射电子能量从0.01eV到100eV范围内弹性散射总截面,动量转移截面和微分散射截面的大量数据。计算结果与实验符合得很好。同时利用计算的结果,对低能电子被惰性气体原子散射的规律性进行了探讨。     

高离化态Cu18+离子的双电子复合及共振转移激发过程的理论研究

在准相对论理论框架下计算了Cu¹⁸⁺离子的双电子复合截面，分析了组态相互作用对截面的影响.基于这些数据，在冲量近似下，通过对靶原子中电子动量分布的卷积，进一步得到了Cu¹⁸⁺与H₂碰撞过程中的共振转移激发截面，并与已有的实验结果作了比较，符合得很好.A 关键词： 双电子复合 共振转移激发     

Cd+离子5s2S1/2→5p2P3/2电子碰撞激发截面和退激辐射光子极化度的理论研究

本文采用全相对论扭曲波方法计算了Cd⁺离子5s²S_1/2 → 5p²P_3/2电子碰撞激发总截面、磁能级的激发截面以及退激辐射光子极化度. 详细讨论了电子关联效应对激发截面以及退激辐射光子极化度的影响. 我们发现, 在低能碰撞部分(<10 eV), Core-价关联对电子碰撞激发截面的贡献非常重要, 与不考虑Core-价关联的结果相比, Core-价关联的计算结果使得激发截面降低了1/2到2/3; 在高能碰撞部分(>80 eV), Core-价关联的贡献不是非常明显, 但与不考虑Core-价关联的结果相比, 其激发截面也降低了15%. 然而, 对于退激辐射光子极化度, Core-价关联的贡献非常小, 其影响是可以忽略的.     

Bound states of the Schrdinger equation for the Pschl-Teller double-ring-shaped Coulomb potential

Põschl--Teller double-ring-shaped Coulomb (PTDRSC) potential, the Coulomb potential surrounded by Põschl--Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in φ, θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrõdinger equation with PTDRSC potential are presented. The normalized φ, θ angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of Laguerre polynomials are presented. Energy spectrum equations are obtained. Wave function and energy spectrum equations of the system are related to three quantum numbers and parameters of PTDRSC potential. The solutions of wave functions and corresponding eigenvalues are only suitable for the PTDRSC potential.     

Effective potentials and the onset of quantization in ultrasmall MOSFETs

The connection between the minimum size of an electron wavepacket, and the introduction of an effective potential is discussed. The effective potential approach has a long history of use in trying to transition the gap between classical mechanics and quantum mechanics. An effective potential is one in which the quasi-classical regime is approximated through a density which arises from the effective potential W(x) through exp[ − βW(x)]. The generation of the effective potentialW (x) gives the effects of the onset of quantization in the system. In this paper, we study the use of the effective potential in a triangular well formed between the oxide and the depletion field of the semiconductor. We determine the quantization energy of the carriers in the potential well and their mean set-back from the interface. Finally, we show the connection between the effective potential and the Bohm-derived quantum potentials that have become of interest in simulations.     

Non perturbative effective potentials of quantum oscillators

Non perturbative analogues of the Gaussian effective potential (GEP) are defined for quantum oscillators obeyingq—or (q,p)—deformed commutation relations. These are called the non perturbativeq-effective potential (NP _q EP) and the non perturbativeqp effective potential (NP _qp EP), in the respective cases. A system-specific effective potential (SSEP) is also introduced by means of an additional minimization with respect to theq orq andp parameters. The method is applied toq and (q,p) oscillators of the quartic and sextic types. The SSEP in the case of ground states of theq-oscillators corresponds toq=1, which is the ordinary bosonic limit. A potential shape transition that involves the conversion of a double well to a single well or vice versa, is seen to exist in the case of quantum oscillators sitting in a double well potential.     

高次正幂与逆幂势函数的叠加的径向薛定谔方程的解析解

当薛定谔方程中出现高次非谐振子势，电偶极矩势，分子晶体势，极化等效势等高次正幂与逆幂势函数以及它们的叠加时，薛定谔方程的求解变得非常复杂，采用奇点邻域附近的级数解法与求解渐近解相结合，在多种相互作用幂函数紧密耦合的条件下，得到势函数为V(r)=a₁r⁶+a₂r²+a₃r^{-4关键词： 级数解法 幂势函数 径向波函数 渐近解}     

Explicit form of the effectiveN-N potential from the quark cluster model

We derive an effectiveN-N potential from a microscopic quark Hamiltonian using the quark cluster model. We construct it in an explicit analytical form, which is expressed only by nuclear variables and which can be used in nuclear structure calculations. To this end we first solve the equation of motion for the six-quark system with a microscopic quark Hamiltonian that includes the quadratic-confinement, one-gluon-, and one-pion-exchange potentials. We then eliminate the quark (internal) degrees of freedom explicitly and express them implicitly in terms of an effectiveN-N potential. The equation of motion for the two-nucleon system is then described by a Schrödinger equation with an effectiveN-N potential. In addition to the one-pion-exchange potential, this effectiveN-N potential contains thequark-exchange potential, which represents the quark-exchange processes associated with a gluon or a pion exchange. This quark-exchange potential is incorporated into the effectiveN-N potential through nonlocal and isospin-dependent terms, which produce a short-range repulsion in theN-N interaction. We give the explicit analytical form of this quark-exchange potential so that it can be used in the nuclear structure calculations.Supported by the DFG under contract number Fa 67/10-5Dedicated to Prof. Erich Schmid on the occasion of his 60th birthday     

Inverse Spectral Problem with Partial Information¶on the Potential: The Case of the Whole Real Line

The Schrödinger operator -d²/dx²+q(x)-d^2/dx^2+q(x) is considered on the real axis. We discuss the inverse spectral problem where discrete spectrum and the potential on the positive half-axis determine the potential completely. We do not impose any restrictions on the growth of the potential but only assume that the operator is bounded from below, has discrete spectrum, and the potential obeys q(-|x|) 3 q(|x|)q(-|x|)\geq q(|x|). Under these assertions we prove that the potential for xS 0 and the spectrum of the problem uniquely determine the potential on the whole real axis. Also, we study the uniqueness under slightly different conditions on the potential. The method employed uses Weyl m-function techniques and asymptotic behavior of the Herglotz functions.     

类Quesne环状球谐振子势场中的赝自旋对称性

提出了一种新的类Quesne环状球谐振子势,应用二分量方法求解1/2-自旋粒子满足的Dirac方程, Dirac哈密顿量由标量和矢量类Quesne环状球谐振子势构成.在Σ=S(r)+V(r)=0的条件下,得到了Dirac旋量波函数下分量的束缚态解和能谱方程, 显示出类Quesne环状球谐振子势场中的赝自旋对称性.讨论了束缚态波函数和能谱方程的有关性质. 关键词： 类Quesne环状球谐振子势 Dirac方程 赝自旋对称性 束缚态     

An Algebraic Approach to the Generalized Symmetrical Double-Well Potential

We have obtained the energy eigenvalues and the corresponding eigenfunctions for the generalized double-well potential in the non-relativistic Schr?dinger equation. We have calculated the creation and annihilation operators directly from the eigenfunction and we have shown these operators satisfy the commutation relation of the SU(2) group. We have expressed the Hamiltonian in terms of the su(2) algebra. Some interesting result including the standard symmetrical double-well potential, reflectionless-type potential and V ₀tanh ²(r/d) potential are also discussed.     

XF2(X=B,N)分子基态的结构与势能函数

基于Gaussian03计算软件利用QCISD方法,选用不同基组对XF₂(X=B,N)分子基态结构进行了几何优化,在此基础上选出最优基组D95(df,pd)和D95+(df,pd)分别对BF₂和NF₂分子的谐振频率、力常数等进行了计算.推导出XF₂(X=B,N)分子基态的多体展式势能函数,同时根据势能函数绘制了XF₂(X< 关键词： 2')" href="#">BF₂ 2')" href="#">NF₂ 结构 势能函数     

On the Semiclassical Propagator for Any One-Dimensional Admissible Potential

This paper shows that by choosing suitably the general fundamental invariantI=f(I₁) as a new canonical momentum, we can find the semiclassical propagator for any one-dimensional admissible potential, whereIis a certain function of the fundamental invariantI₁. We apply this method to the case of quartic potential and point out few applications of the propagator for this potential.