The potential for which E n 1 ′ 12=E n 2 ′ l1 in nonrelativistic quantum mechanics

The answer is provided to the question ‘What is the potential for which E _{n 1} ^′ l₂=E _{n 2} ^′ l₁ in nonrelativistic Quantum Mechanics?’     

Energies, Auger and radiative probabilities of the doubly-excited 1s23l3l′ states for Be-like neon

Energy levels, Auger decay and radiative transition rates of the doubly-excited 1s ²3l3l′ states for Be-like neon are calculated using relativistic Multiconfiguration Dirac-Fock (MCDF) method. Electron correlation and relaxation effects are taken into account. The magnitude of Auger rates for the 35 doubly-excited states and their decay channels are discussed. Present calculated values are in agreement with the latest experimental electron spectra as well as other theoretical results.     

类镍等电子系列离子M1,M2,E2禁戒跃迁特性的理论研究

利用基于全相对论框架下的多组态Dirac-Fock理论方法发展起来的程序包GRASP92和新发展的处理辐射跃迁过程的程序REOS99,计算了类镍等电子系列离子(Z=45-95)的基组态3s23p63d10 1S0以及低激发组态3s23p63d94l,3s23p53d104l和3s3p63d104 l(l=s,p,d,f)的能级及其向基态的M1,M2,E2禁戒跃迁概率.通过分析高离化类镍离子在特定的原子序数范围内由于存在能级交叉而产生的强组态相互作用,解释了高离化类镍离子禁戒跃迁概率的反常变化现象,探讨了禁戒跃迁概率受强组态相互作用影响而变化的一般规律.     

Theoretical calculation of atomic spectrum for 1s23l4l′ states of beryllium-like ions

Using the saddle-point variation and saddle-point complex-rotation methods, energies, radiative, and Auger rates are calculated for the doubly-excited states 1s²3l4l′ of beryllium-like ions. The total wave function is expanded by the restricted variation method to saturate the functional space and improve the nonrelativistic energy. Relativistic corrections and mass polarization effects are taken into account by the first-order perturbation theory. The partial Auger rates for these states are studied. The calculated Auger electron energies are compared with the experimental results which are observed in high resolution electron spectroscopy. The total radiative rates and the total Auger rates for these doubly-excited states 1s²3l4l′ in the beryllium-like ions are also analyzed along with the increase of atomic number Z. Calculated results show that the total Auger rates are several orders of magnitude larger than the total radiative rates for these low-Z systems.     

High temperature superconductivity in (M1−xM′x)2CuO4−δ and related compounds (M = Y,La, Eu,Sm; M′ = Ba,Sr)

Compounds of the form (M_1−xM′_x)₂CuO_4−δ and related compounds where M and M′ are Y, various rare earths from La to Lu, and the alkaline earths Sr and Ba, have been investigated in connection with high temperature superconductivity. High temperature superconductivity is confirmed for the system (La_1−xBa_x)₂CuO_4−δ, (La_1−xSr_x)₂CuO_4−δ and (Y_1−xBa_x)₂CuO_4−δ with superconducting transition temperature T_c onsets of 30 K, 38 K and 90 K, respectively. We have found that the related systems (Eu_1−xBa_x)₂CuO_4−δ and (Sm_1−xBa_x)₂CuO_4−δ also exhibit high temperature superconductivity with T_c onsets of 95 K and 65 K, respectively. The highest T_c onset observed in this investigation was 97 K for a sample with the nominal composition of the spinel structure Y_0.33Ba_0.67Cu₂O_4−δ. Measurements of the specific heat C as a function of temperature T on a La_0.8Sr_0.2CuO_4−δ sample reveal a break in slope in the C/T vs T curve at the T_c midpoint, but no clearly discernable jump in C at T_c. A linear term ≈ λ′T in C was observed at low temperature in the superconducting state.     

Theoretical Investigation on Excitation,Ionization and Capture in H（1s, 2s） ＋ H（1s, 2s） Collisions

Cross sections of electron-loss in H（1s）＋ H（1s） collisions and total collisional destruction of H（2s） in H（1s） 4- H（2s） collisions are calculatted by four-body classical-trajectory Monte Caylo （CTMC） method and compared with previous theoretical and experimental data over the energy range of 4-100 keV. For the former a good agreement is obtained within different four-body CTMC calculations, and for the incident energy Ep 〉 10 keV, comparison with the experimental data shows a better agreement than the results calculated by the impact parameter approx- imation. For the latter, our theory predicts the correct experimental behaviour, and the discrepancies between our results and experimental ones are less than 30%. Based on the successive comparison with experiments, the cross sections for excitation to H（2p）, single- and double-ionization and H- formation in H（2s）＋H（2s） collisions are calculated in the energy range of 4-100 keV for the first time, and compared with those in H（1s）＋H（1s） and H（1s）＋U（2s） collisions.     

Calculated conversion rate of E′4 centers into E′2 centers in alpha quartz

Recent cluster calculations by Rudha et al. [1] are used to obtain a pseudo-Jahn-Teller adiabatic energy profile for the interconversion between E′₄ centers and E′₂ centers based on the structural models proposed therein. Reasonable values are obtained for the underlying parameters which lends some further support to the models. A reaction rate method is next used to compute the temperature dependence of the conversion rate in either direction, as well as of the rate for reorientational flopping of Fowler's E′₁ center. Thermally-activated tunneling is found to be the main factor controlling the conversions in most of the temperature range of any practical interest.     

Weak- and hyperfine-interaction-induced 1s2s ~1S_0→ 1s~2 ~1S_0 E1 transition rates of He-like ions

Weak- and hyperfine-interaction-induced 1s2s1S0→ 1s2 1S0E1 transition rates for the isoelectronic sequence of Helike ions have been calculated using the multi-configuration Dirac–Hartree–Fock(MCDHF) and relativistic configuration interaction methods. The results should be helpful for the future experimental investigations of parity non-conservation effects.     

在周期场中类氢原子的1s,2s,2p基态的能级

取1/Z/(me~2)为长度单位,Z~2(me~4/~2)为能量单位,则类氢原子的波函数ψ(r)满足 -1/2ψ-1/rψ=Eψ。 (1)在周期场中,采用Wigner-Seitz近似,以等体积原子球代替原子多面体,则在半径r_0处基态ψ满足边界条件(由ψ的周期性质和对称性质得到) (ψ/r)_r_0=0,对1s,2s; (2) (ψ)_r_0=0,对2p。(3) 根据严格的合流超几何函数的波函数,利用Slater的表和库伦波函数表,可以得到能量与原子球半径r_0的数值关系(见表1)。     

Electric-dipole allowed （El） and forbidden （E2, M1 and M2） transition probabilities of 4f for N＋

By applying systematically enlarged multi-configuration Dirac-Fock wavefunction, the transitions for electricdipole allowed （E1） and forbidden （E2, M1 and M2） lines are studied among 4f pair coupling and low-lying configurations for singly ionized nitrogen. Most important effects of relativity, electron correlation, the rearrangement of electron density, Breit interaction, and quantum electrodynamic effects are included in the computation. Then, allowed （E1） and forbidden （E2, M1 and M2） transition probabilities of 4f for N＋ are obtained and compared with experimental results. Good agreement with available experimental results is found and most of the data of 4f are presented for the first time.     

稀土区奇A核M1和E2跃迁的性质

利用推广的粒子-转子模型研究了稀土区奇A核的M1和E2跃迁的性质,指出核心的十六极形变、转动哈密顿量中的二级科里奥利作用对M1(ΔI=1)和E2跃迁几率的Signature依赖性以及对Signature的平均值有着不容忽略的影响.对¹⁵⁷Ho的计算得到了能谱的Signature分离、B(M1;ΔI=1)值和[B(E2;ΔI=1)/B(E2;ΔI=2)]^1/2比值都同实验定性相符的结果.     

为什么可用l（l＋1）代替l~2

为什么可用ｌ（ｌ＋１）代替ｌ￣２Ｐ．Ｗ．Ｍｉｌｏｎｎｉ在量子力学中为什么可以用ι（ι１）代替ι￣２？这里ι是角动量量子数．在一些导论性的教科书中这个特别的结果是作为一种特殊的量子力学效应提出的，即空间量子化（问题的确如此）．但似乎没有很容易的方法理解...     

Fuzzy Kaluza-Klein induced M2?s from a single M5

We propose an algorithmic procedure of obtaining multiple M2 brane dynamics starting with an action of a single M5 brane. The procedure involves a novel Kaluza-Klein reduction. First, the M5 brane action is truncated to keep a few leading terms in the derivative expansion. Then 3+3 splitting of dimensions is carried out. With expansion in terms of the S² spherical harmonics, the fields are associated with SU(N) (or its infinite extension) gauge algebra. We present an elaborate reduction procedure that leads to ABJM theory when the fuzzy spherical harmonics are replaced by SU(N) gauge generators.     

Identification of E6-generated Z′ from combined charm II,LEP 1, SLC high-precision measurements

We show that a combined analysis of three specific longitudinal polarization asymmetries in electron-positron annihilation on Z₀ resonance, of the mass ratio M_w/M_z and of the neutrino-electron neutral cross-section ratio, which could be measured in the near future at SLC, LEP, ACOL and CHARM II, would lead to a well-defined identification of a single new E₆-generated Z′. In particular, it might be possible to disentangle a superstring-inspired model from other currently considered possibilities down to values of the mixing angle θ_η = 0.02 and, at the same time, to fix the mass ratio ε = M_Z²/M_Z′² with known accuracy.     

Two Dimensional 1HNMR Studies on 2′5′-Dideoxyadenosylcobalamin

The ¹HNMR spectrum of 2′,5′-dideoxyadenosylcobalamin, a Coenzyme B₁₂(5′-deoxyadenosylcobalamin) analogue, has been assigned by 2D COSY. Its proton coupling constants have also been measured by J-resolved experiment. The comparison between the analogue and Coenzyme B¹² was made.     

类铍离子1s22s2p 3P1, 2 能级之间的磁偶极跃迁

用多组态Dirac-Fock和相对论组态相互作用的扩展优化能级方法,在计算中包含了Breit相互作用,真空极化,自能以及有限核质量修正,计算了核电荷数从Z=6到80的类铍离子等电子序列的1s22s2p 3P1, 2的精细结构能级,磁偶极跃迁几率和振子强度。结果与目前可靠的结果在其不确定度范围内符合得很好,另外也得到一些与其他早期理论计算不同的结果。     

类铍离子磁四极M2 2s2 1S0-2s2p 3 P2(Z=10-103)禁戒跃迁

利用全相对论多组态:Dirac-Fock方法系统地计算了高离化类铍离子的磁四极M2 2s2 1S0-2s2p3P2 (Z=10-103)自旋禁戒跃迁的能级间隔、跃迁概率和振子强度,计算中考虑了重要核的有限体积效应,Breit修正和QED修正,所得结果和最近的实验数据以及理论值进行了比较,结果表明:高原子序数的高电荷离子(Z≥70)磁四极M2自旋禁戒跃迁几乎可以和中性原子的光学允许跃迁相比拟,不仅在天体等离子体中,在ICF和MCF高温激光等离子体中,磁四极自旋禁戒跃迁和其他自旋禁戒跃迁(磁偶极、电四极)一样不容忽视,在双电子复合、不透明度、自由程等理论计算中应该考虑其影响.     

CoⅩⅧ离子2s~22p~53l2s2p~63l、2s~22p~54l组态的能级及跃迁波长计算

本文用相对论多组态Dirac-Fock广义平均能级(MCDF-EAL)模型,计算了可能形成超真空紫外区相干辐射的类氖等离子体激光工作物质的CoXVⅢ离子2s~22p~53l、2s2p~63l、2s~22p~54l组态精细结构能级的能量值,以及3l、4l-2p~6(~1S_0)、3l-3l＇、3l-4l＇、4l-4l＇多重态之间的跃迁波长值。3l、4l-2p~6(~1S_0)跃迁波长计算值与已知观测值符合相当好。     

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Using the fully relativistic configuration interaction (RCI) method and the multi-configuration Dirac-Fock (MCDF) method and taking quantum electrodynamical (QED) effect and Breit correction into account, wavelengths, transition probabilities and oscillator strengths were calculated for electric dipole (E1) transitions and magnetic dipole (M1) transitions in Au⁵⁰⁺ ion. The obtained energy levels of some excited states and wavelengths of transitions in Au⁵⁰⁺ ion from the method were compared with other theoretical and experimental results, and a good agreement with other results was shown. The calculated transition probabilities and oscillator strengths in E1 transitions using the velocity and length gauges respectively confirmed the accuracy of our calculations. The calculation results indicated that for high-Z highly ionized atom, some forbidden transitions could be very important.