Microscopic study of low-lying yrast spectra in <Superscript>100–108</Superscript>Mo isotopes

Variation-after-projection (VAP) calculations in conjunction with Hartree-Bogoliubov (HB) ansatz have been carried out for A=100−108 molybdenum (Mo) isotopes. In this framework, the yrast spectra with J _max ^π ≥10⁺, B(E2) transition probabilities, quadrupole (β₂) and hexadecapole (β₄) deformation parameters, moment of inertia (I) and square of cranking frequency (ω²) for even-even Mo isotopes have been obtained. The results of the calculation give an indication that it is important to include the hexadecapole-hexadecapole component of the two-body interaction for obtaining various nuclear structure quantities in these Mo isotopes.     

The Biot-Savart-Ampère law and the vacuum fieldB (3)

It is shown that the longitudinal vacuum fieldB ⁽³⁾ emerges from the Biot-Savart-Ampère law governing the motion of an electron with intrinsic spin moving at the speed of light, in which case the expression forB ⁽³⁾ is identical with that obtained from the Dirac equation of one electron accelerated to the speed of light by an electromagnetic field. Use of an O(3), non-Abelian, gauge geometry forB ⁽³⁾ identifies the quantized photon momentum appearing in the Dirac equation witheA ⁽⁰⁾, wheree is the charge on the electron andA ⁽⁰⁾ the amplitude of the vector potential. The condition =eA ⁽⁰⁾ can be obtained in turn from the relativistic Hamilton-Jacobi equation of an electron accelerated to the speed of light by an electromagnetic field.     

Non-abelian electrodynamics and the vacuumB (3)

By using an 0(3) gauge group, a non-Abelian theory of vacuum electrodynamics is developed in which the newly discovered longitudinal vacuum fieldsB ⁽³⁾ andi E ⁽³⁾ appear self-consistently with the usual plane wavesB ⁽¹⁾,B ⁽²⁾,E ⁽¹⁾, andE ⁽²⁾ in the circular basis (1), (2), (3), a complex representation of space. Using the charge quantization condition the vacuum Maxwell equations are given in the non-Abelian representation.     

Group theoretical aspects ofU B(6) ⊗U F(20) symmetry limits of IBFM related to theU B(5) andO B(6) limits of IBM

TheU ^B(6)⊗U ^F(20) Bose-Fermi dynamical symmetry of interacting boson-fermion model arises when the odd nucleon occupies single particle orbits withj=1/2, 3/2, 5/2, and 7/2. The subgroup structures ofU ^B(6)⊗U ^F(20) related to theU ^B(5) andO ^B(6) limits of sdIBM (U ^B(6)) are analysed. Broadly speaking,U ^B(6)⊗U ^F(20) admitsU ^BF(5)⊗U _s ^F (4), Spin^BF(5)⊗U _k ^F (5) andU ^BF(5)⊗U _s ^F (2) limits withU ^B(5) core and Spin^BF(6),O ^BF(5)⊗U _s ^F (4), Spin^BF(6)⊗U _k ^F (5) andO ^BF(6)⊗U _s ^F (2) limits withO ^B(6) core respectively. For each of these seven symmetry limits, group chains, quantum numbers labelling the basis states, generators and Casimir operators for the various subgroups and energy formulas are given. Recoupling coefficients (reduced Wigner coefficients) for constructing wavefunctions of low-lying states are tabulated and these will allow (together with sdIBMU ^B(5) andO ^B(6) limit results) one to calculateB(E2)’s,B(M1)’s, one and two nucleon transfer strengths etc. in the seven symmetry limits. Experimental examples for theU ^B(6)⊗U ^F(20) symmetry limits are briefly discussed.     

Multi-mode ground state interaction terms in C60-based electron donor-acceptor complexes

Quantum-chemical testing of donor-acceptor properties of binary molecular complexes, related to the singlet state, is suggested as QCh calculations of studied systems and their constituents by using both spin-nondependent (RHF) and spindependent (UHF) versions of the exploited computational tool. The avoided crossing of intermolecular interaction terms of neutral moleculesE _int (A ⁰ B ⁰) and molecular ionsE _int (A ⁺ B ⁻) causes a multi-mode character of the ground state term. The dependence of D-A complex properties on the type of the term, space positions of the term minimum, and the interrelation of the corresponding energies are discussed. The suggested approach has been applied to binary complexes C₆₀+X (X=TAE, TDAE, DMMA, COANP, 2Li, Mg).     

N2O+离子A2Σ+电子态高振动能级的转动结构分析

利用一束波长为36055nm的激光,通过(3+1)共振多光子电离方法制备纯净的且处于X²Π_1/2,3/2(000)态的N₂O⁺离子,用另一束激光激发所制备的离子到第一电子激发态A²Σ⁺的不同振动能级,然后解离,通过检测解离碎片NO⁺强度随光解光波长的变化,得到了转动分辨的N₂ 关键词： 2O⁺离子A²Σ⁺电子态')" href="#">N₂O⁺离子A²Σ⁺电子态 共振增强多光子电离 光解碎片激发光谱 光谱常数     

AsO+同位素离子X2∑+和A2∏电子态的多参考组态相互作用方法研究

采用包含Davidson修正多参考组态相互作用(MRCI)方法结合价态范围内的最大相关一致基As/aug-cc-pV5Z和O/aug-cc-pV6Z, 计算了AsO⁺ (X²∑⁺)和AsO⁺(A²∏)的势能曲线. 利用AsO⁺离子的势能曲线在同位素质量修正的基础上, 拟合出了同位素离子⁷⁵As¹⁶O⁺和⁷⁵As¹⁸O⁺的两个电子态光谱常数. 对于X²∑⁺态的主要同位素离子⁷⁵As¹⁶O⁺, 其光谱常数R_e, ω_e, ω_ex_e, B_e和α_e分别为 0.15770 nm, 1091.07 cm^-1, 5.02017 cm^-1, 0.514826 cm^-1和0.003123 cm^-1; 对于A²∏态的主要同位素离子⁷⁵As¹⁶O⁺, 其T_e, R_e, ω_e, ω_ex_e, B_e和α_e分别为5.248 eV, 0.16982 nm, 776.848 cm^-1, 6.71941 cm^-1, 0.443385 cm^-1和0.003948 cm^-1. 这些数据与已有的实验结果均符合很好. 通过求解核运动的径向薛定谔方程, 找到了J=0时AsO⁺(X²∑⁺)和AsO⁺(A²∏)的前20个振动态. 对于每一振动态, 还分别计算了它的振动能级、转动惯量及离心畸变常数, 并进行了同位素质量修正, 得到各同位素离子的分子常数. 这些结果与已有的实验值非常一致. 本文对于同位素离子⁷⁵As¹⁶O⁺(X¹∑⁺), ⁷⁵As¹⁸O⁺(X¹∑⁺), ⁷⁵As¹⁶O⁺(A¹∏)和⁷⁵As¹⁶O⁺(A¹∏)的光谱常数和分子常数属首次报导.     

Noether's theorem and the fieldB (3)

It is shown that the longitudinal, magnetic flux density,B ⁽³⁾ , of vacuum electromagnetic radiation can be accommodated rigorously within Noether's theorem, which relates fundamental spacetime symmetries to fundamental conservation laws. This demonstration linksB ⁽³⁾ to the canonical energy-momentum tensorT _µv that appears in Einstein's field equations of general relativity. Thus,B ⁽³⁾ provides a link between electromagnetism and gravitation which might eventually lead to an unified understanding of field theory.     

立方对称晶场中6S(3d5)态离子的磁相互作用及其自旋哈密顿参量的微观起源

基于完全对角化方法(complete diagonalization method, CDM), 研究了⁶S(3d⁵)态离子在立方对称晶场中的磁相互作用,分析了自旋哈密顿参量(a, g,Δg)的微观起源.研究中除了考虑研究者通常考虑的SO(spin-orbit)磁相互作用外,同时考虑了SS(spin-spin),SOO(spin-other-orbit),OO(orbit-orbit)磁相互作用.研究表明：⁶S(3d⁵)态离子在立方对称晶场中的自旋哈密顿参量起源于五种机理,即SO机理,SS机理,SOO机理,OO机理以及SO-SS-SOO-OO联合作用机理.文中研究了五种机理的相对重要性,结果表明：SO机理与SO-SS-SOO-OO联合作用机理在五种机理中最为重要.尽管SS,SOO,OO磁相互作用单独作用时对自旋哈密顿参量的贡献很小,但它们的联合作用SO-SS-SOO-OO机理对自旋哈密顿参量的贡献非常可观.此外研究表明：零场分裂参量a主要来自纯自旋四重态及自旋二重态与自旋四重态联合作用的贡献,而Zeemang(或者Δg)因子主要来自纯自旋四重态的贡献.纯自旋二重态对自旋哈密顿参量a与g(或者Δg)的贡献为零.在我们所选择的晶场区域,发现下列关系始终成立：a>0,a(-|Dq|)<a(|Dq|),g(-Dq)=g(Dq),a(-Dq,-ξ_d,B,C)=a(Dq,ξ_d, B,C),Δg(-Dq,-ξ_d, B, C)=Δg(Dq,ξ_d, B, C).作为本文理论的应用,研究了四种典型的Mn²⁺掺杂晶体材料,即Mn²⁺:KZnF₃,Mn²⁺: RbCdF₃,Mn²⁺: MgO,Mn²⁺: CaO,理论与实验测量符合很好. 关键词： 自旋哈密顿参量 6S(3d⁵)态离子')" href="#">⁶S(3d⁵)态离子 磁相互作用 完全对角化方法(CDM)     

用MRCI方法研究CS+同位素离子X2Σ+和A2Π态的光谱常数与分子常数

利用内收缩多参考组态相互作用方法和价态范围内的最大相关一致基aug-cc-pV6Z, 在0.05—0.60 nm的核间距范围内计算了CS⁺离子X²Σ+和A²Π态的势能曲线. 利用CS⁺离子的势能曲线并在同位素质量修正的基础上, 拟合出了X²Σ+和A²Π态的同位素离子^{1 关键词： 同位素识别 势能曲线 光谱常数 分子常数}     

SU(2)×SU(2) Electroweak Theory I: The B3 Field on the Physical Vacuum

Nonlinear optics confronts the U(1) theory of electrodynamics with the dilemma of the existence of nonlinear fields. The U(1) group is completely linear and Abelian and causes consideration of an SU(2) theory of electrodynamics. An SU(2) theory of electrodynamics, with a B ³ magnetic field, means that physics is forced to consider an SU(2) × SU(2) electroweak theory. It is then demonstrated that the B ³ field exists on the physical vacuum defined by the Higgs symmetry breaking of this extended electroweak theory.     

Shell-model calculation of51V using pairing-plus-surface-tensor-interaction

Employing⁴⁸Ca as the core, the structure of⁵¹V is studied in the framework of a conventional shell-model. A pairing-plus-surface-tensor-interaction is used as the effective two-body interaction. Besides all configurations arising from 1f _7/2 and 2p _3/2 single-particle orbits, configurations of the form wheren ₁+n ₂=3 (the number of extracore protons) andn ₂ = 1, 2 are also considered. Low-lying energy levels are calculated and a satisfactory agreement with the experimental values is obtained. Our calculated density of states is higher than that reported previously. We also present theB(E2) values for transitions between low-lying levels and the spectroscopic factors for the⁵⁰Ti (³He, d)⁵¹V reaction. The dependence of the interaction parameters on the mass number of the core nucleus is also studied.     

High spin yrast states in even platinum isotopes

The high spin yrast states up toJ=20⁺ in^{184, 186}Pt and^{190, 192, 194}Pt are studied in a microscopic approach of variation with number-conserved projected states. The energy spectra, quadrupole moments andB(E2) values are calculated by employing the Hamiltonian with quadrupole plus pairing interactions. The results of the calculations are in fair agreement with the available experimental data.     

High-resolution emission spectroscopy of the AΠ–XΣ system of AlH

The emission spectrum of the A²Π–X²Σ⁺ system of the AlH⁺ ion was investigated in the range of 27 000–29 000 cm⁻¹ by using a conventional spectroscopic technique. The AlH⁺ molecules were formed and excited in an aluminium hollow-cathode lamp with two anodes, filled with a mixture of Ne carried gas and a trace of NH₃. The emission from the discharge was observed with a plane grating spectrograph and recorded by a photomultiplier tube. The full rotational structure of the 0-0 and 1-1 bands has been observed for the first time (12 branches up to J″ = 36.5) and many new constants of the X²Σ⁺ state have been derived from the analysis. For the A²Π, v = 0 and 1 state a considerable irregularities of the Λ-doubling have been observed. The most reasonable explanation for this anomaly is an interaction with unstableness rotational levels of X²Σ⁺ state and perturbing of the A²Π state by the nearly lyingB²Σ⁺ state.     

The connection between photon mass andB (3) : The poincaré group

The longitudinal vacuum fieldB ⁽³⁾ is an experimental observable which produces by magnetization a well-defined square-root beam power density dependence. Its longitudinal polarization implies that the helicities of the photon are +1, 0, and –1, and that the little group of the Poincaré group is the rotation group 0(3) of a massive boson. The mass of the photon (m) is therefore related directly toB ⁽³⁾ through the Proca equation, and it is concluded that experimental evidence forB ⁽³⁾ is also evidence for finitem.     

Photon mass and the fieldB (3)

The connection between finite photon mass and the fieldB ⁽³⁾ is developed with reference to special relativity in the vacuum. The existence of the physical and longitudinal fieldB ⁽³⁾ implies that there are three degrees of polarization associated with the photon, which cannot therefore be a massless boson. The fieldB ⁽³⁾ can be observed experimentally through the magnetization of a plasma with microwave pulses, and this experiment serves to demonstrate unequivocally the existence of photon mass.     

High-Resolution Study of the BaI AΠ Electronic State

Near-infrared and visible spectra of the A²Π–X²Σ⁺, C²Π_1/2–A²Π_1/2, C²Π_1/2–B²Σ⁺, and C²Π_1/2–X²Σ⁺ band systems of the BaI molecule were recorded by using Fourier transform spectroscopy (FTS). The spectra were produced from the chemiluminescent reaction Ba + I₂ and also by using laser-induced fluorescence (LIF) technique in which the laser sources were a Ti:sapphire single-mode laser, a dye single-mode laser, and a Kr⁺ multimode ion laser. Resolved rotational data, originating from 19 vibrational levels (0 ≤ v ≤ 5 and 7 ≤ v ≤ 19) of the A²Π state, 24 vibrational levels (0 ≤ v ≤ 18 and 20 ≤ v ≤ 24) of the X²Σ⁺ state, and 8 vibrational levels (1 ≤ v ≤ 2 and 9 ≤ v ≤ 14) of the C²Π state, were used in the final analysis. Previously recorded data for the B²Σ⁺–X²Σ⁺ and C²Π–X²Σ⁺ systems, taken from R. F. Gutterres, J. Vergès, and C. Amiot, J. Mol. Spectrosc. 196, 29–44 (1999) and from C. A. Leach, A. A. Tsekouras, and R. N. Zare, J. Mol. Spectrosc. 153, 59–72 (1992), were added to the present work data field. Accurate and improved molecular constants, for the X²Σ⁺, B²Σ⁺, A²Π, and C²Π states, were derived from a simultaneous treatment of the whole data set.     

On the observability of the fieldB (3): Relativistic effects in magneto-optics

It is shown that the novel vacuum fieldB ⁽³⁾ is an experimental observable, and several methods of observation are suggested: these include the pulsed microwave magnetization of a plasma, the optical Aharonov-Bohm effect, and the microwave frequency optical Faraday effect. The effect ofB ⁽³⁾ is presented in the form of relativistically corrected semi-classical theory.     

Rotational Analysis of the 1–4 Band of the B 2Σ+–X 2Σ+ System of 14C16O+

ABSTRACT

High-resolution emission spectrum of the 1–4 band of the B ²Σ⁺–X ²Σ⁺ transition of ¹⁴C¹⁶O⁺ was observed for the first time by conventional emission spectroscopy. The band spectrum was excited in a water-cooled Geissler lamp filled with commercial gaseous carbon monoxide enriched in about 80% of the radiocarbon ¹⁴C. A rotational analysis has been carried out and obtained molecular constants have been merged with previously published data for the B ²Σ⁺–A ²Π_i and A ²Π_i–X ²Σ⁺ transitions. The principal equilibrium constants for the ground X ²Σ⁺ state obtained from this work are ω_e = 2121.7726(98), ω_e x _e = 13.9055(27), B _e = 1.815290(30), α_e = 1.6594(33) × 10^?2, and γ_e = ? 0.377(73) × 10^?4 cm^?1. Also, presently known experimental equilibrium molecular constants of the X ²Σ⁺ states of the CO⁺ isotopic molecules are summarized and isotopic dependence of the B _e and ω _e constants is discussed.