Representations of quantumso(8) and related quantum algebras

We study irreducible representations of the quantum groupU (so(8)) when ^* is a primitivel ^th root of unity. By a theorem of De Concini and Kac, there is a finite number of such representations associated to each point of a complex algebraic variety of dimension 28 and the generic representation has dimensionl ¹².We give explicit constructions of essentially all the irreducible representations whose dimension is divisible byl ⁸. In addition, we construct all cyclic representations of minimal dimension. This minimal dimension isl ⁵, in accordance with a conjecture of De Concini, Kac and Procesi.Partially supported by the NSF, DMS-9115984     

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3s²3p⁶3d¹⁰¹S₀以及低激发组态3s²3p⁶3d⁹4l,3s²3p⁵3d¹⁰4l和3s3p⁶3d¹⁰4l(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.     

High-Resolution Infrared Spectra of the ν2, ν3, ν4, and 2ν3 Bands of SO3

New measurements are reported for the infrared spectrum of sulfur trioxide, ³²S¹⁶O₃, with resolutions ranging from 0.0015 cm⁻¹ to 0.0025 cm⁻¹. Rovibrational constants have been measured for the fundamentals ν₂, ν₃, and ν₄ and the overtone band 2ν₃. Comparisons are made with the earlier high-resolution measurements on SO₃, and the high correlation among some of the constants related to the Coriolis coupling of the ν₂ and ν₄ levels is discussed in order to understand the areas of disagreement with the earlier work. Splittings of some of the levels are observed and the splitting constant for K=3 of the ground state is determined for the first time. Other observed splittings include the K=1 levels of 2ν₃ (l=2), the K=2 levels of ν₃ and ν₄, and the K=3 levels of ν₂. The analysis shows that there are level crossings between the l=0 and l=2 states of 2ν₃ that allow one to determine the separation of the subband centers for these two states even though access to the l=0 state from the ground state is electric-dipole forbidden. This is a generalized phenomenon that should be found for many other molecules with the same symmetry. The l-type resonance constant, q₃, that causes the splitting of the l₃=±1, k=±1 levels of ν₃ also couples the l₃=0 and 2 states of 2ν₃.     

Electronic transition moments and oscillator strengths for polyatomic molecules: the (2B1-2A1) transition in BH2

A series of potential energy curves and electronic transition moments characterizing the ² A ₁ and ² B ₁ states of BH₂ are presented. The transition moments are computed in both the position and momentum representations, and a number of alternative expressions for the calculation of oscillator strength are examined. The implications of transition moment variation as a function of the vibrational coordinate and the Franck-Condon principle are also discussed.     

类氖等电子系列离子基态的双电子复合速率系数研究

使用全相对论组态相互作用方法, 能级-能级细致计算了0.1 E_I ≤ kT_e≤ 10 E_I (E_I是类钠离子基态的第一电离能) 温度范围内类氖离子基态双电子复合(DR)速率系数, 双激发自电离能级考虑了(2s2p)⁷3ln'l', (2s2p)⁷4l4l' 以及(2s2p)⁷4l5l'组态. 对于(2s2p)⁷3ln'l'双激发自电离组态, 轨道角量子数l' >8 的(2s2p)⁷3ln'l'双激发自电离态对双电子复合速率系数的贡献可以忽略不计; (2s2p)⁷3ln'l'双激发自电离组态的高里德堡态对双电子复合速率系数的贡献满足 n'^-3组态-组态外推法, 并且核电荷数越大, 趋于n'^-3标度的n'值越小; 对细致能级计算得到的类氖离子基态的总DR速率系数进行了拟合, 得到类氖离子基态的总DR速率系数随核电荷数 Z和电子温度变化的经验公式, 该拟合公式与细致计算结果的偏差在2%以内, 能较准确的计算任意核电荷数Z的类氖离子在0.1E_I ≤ kT_e ≤ 10E_I电子温度范围的DR速率系数. Burgess-Merts(BM)近似公式不适用于估算低温(kT_e<0.3 E_I)类氖离子的DR速率系数, 在高温(kT_e>2E_I)时, 类氖离子的DR速率系数可以用BM近似公式表示.     

Induced Representations and Invariant Integral Operators for SU (2, 2)

The elementary representations (ER) of SU (2, 2) induced from the three non-trivial parabolic subgroups P₀, P₁, P₂ are explicitly constructed in two equivalent realizations. We exhibit a one-to-one correspondence between the P₀ and P₂ induced representations. The corresponding representations are equivalent. We also exhibit a two-to-one correspondence between the P₁ ERs and a subset of the P₀ ERs; however, the corresponding representations are only partially equivalent. The Knapp-Stein integral intertwining operators are explicitly given for all representations in consideration.     

Spectral moments of the rotational correlation functions for the first- and second-rank tensors of asymmetric top molecules

A method of evaluating the spectral moments M^l _2k of the rotational correlation functions for the first- and second-rank tensors of rigid asymmetric top molecules is developed. It is based on the calculation of the coefficients of a Taylor series expansion of the vector and tensor orientational correlation functions about t = 0 with the help of angular momentum theory, and is applicable to a pair intermolecular interaction potential with arbitrary dependence on the angular variables. Equations for the second (M^l ₂), fourth (M^l ₄), and sixth (M^l ₆) spectral moments are obtained as a demonstration of the ability of the method. The results for (M^l ₂) and M^l ₄ coincide with previously known values and the equation for M^l ₆ is new. As particular cases, the theory contains the results for classical ensembles of symmetric tops, spherical tops, and linear molecules.     

The electrostatic persistence length of polymers beyond the OSF limit

We use large-scale Monte Carlo simulations to test scaling theories for the electrostatic persistence length l _e of isolated, uniformly charged polymers with Debye-Hückel intrachain interactions in the limit where the screening length κ^-1 exceeds the intrinsic persistence length of the chains. Our simulations cover a significantly larger part of the parameter space than previous studies. We observe no significant deviations from the prediction l _e∝κ^-2 by Khokhlov and Khachaturian which is based on applying the Odijk-Skolnick-Fixman theories of electrostatic bending rigidity and electrostatically excluded volume to the stretched de Gennes-Pincus-Velasco-Brochard polyelectrolyte blob chain. A linear or sublinear dependence of the persistence length on the screening length can be ruled out. We show that previous results pointing into this direction are due to a combination of excluded-volume and finite chain length effects. The paper emphasizes the role of scaling arguments in the development of useful representations for experimental and simulation data. Received 12 February 2002     

The 2ν8 Band of CH3CN

The overtone band 2ν⁰₈ of CH₃CN around 720 cm⁻¹ has been measured on a Bruker Fourier transform spectrometer at a resolution of 0.003 cm⁻¹. Only the parallel band was observed, but due to the l(2, 2) resonance, ΔK = −2 lines leading to the v₈ = 2, l₈ = −2 levels with K = 1-3 could be seen. More information for the l₈ = ±2 component of the vibrational state v₈ = 2 was evaluated from the hot band 2ν^±2₈ - ν^±1₈. Altogether more than 1000 lines were assigned. In the fit pure rotational lines from literature were also combined. Among the results the anomalous A₀ - A′ values 4.6722(13) × 10⁻³ cm⁻¹ for the 2ν⁰₈ band and 7.0324(32) × 10⁻³ cm⁻¹ for the 2ν^±2₈ band are striking.     

关于B0→π－l+ν l衰变过程分支比的计算

通过构造适当的关联函数,计算B→π跃迁形状因子f⁺_Bπ(q²),f _{Bπ(q²)和标量形状因子f⁰(q²),从而就能研究轻子质量对B⁰→π ^{关键词： B介子半轻衰变 形状因子 分支比}}     

Two Peculiar Classes of Solvable Systems Featuring 2 Dependent Variables Evolving in Discrete-Time via 2 Nonlinearly-Coupled First-Order Recursion Relations

In this paper we identify certain peculiar systems of 2 discrete-time evolution equations,

which are algebraically solvable. Here l is the “discrete-time” independent variable taking integer values (l = 0, 1, 2, . . .), x_n ≡ x_n(l) are 2 dependent variables, and are the corresponding 2 updated variables. In a previous paper the 2 functions F⁽ⁿ⁾(x₁, x₂), n = 1, 2, were defined as follows: F⁽ⁿ⁾(x₁, x₂) = P₂ (x_n, x_n+1), n = 1, 2 mod[2], with P₂(x₁, x₂) a specific second-degree homogeneous polynomial in the 2 (indistinguishable!) dependent variables x₁(l) and x₂(l). In the present paper we further clarify some aspects of that model and we present its extension to the case when a specific homogeneous function of arbitrary (integer) degree k (hence a polynomial of degree k when k > 0) in the 2 dependent variables x₁(l) and x₂(l).     

Quadratic spherical bessel functions and the inverse scattering problem

In the course of inverting the partial-wave Born approximation, a new expression for the inverse function ofj _l ² (ρ) was obtained. Using this result, one can also derive two expressions involving the binomial coefficients. Finally, a particular differential operator whose effect onj _l ² (ρ) was previously investigated by Mavromatis and Jalal is shown to have similar effects onn _l ² (ρ) andn _l (ρ)j _l (ρ).     

Free energy and orientational phase transition in solid C60

On the basis of a microscopic model, the free energy of the orientationally disordered fcc crystalline phase of C₆₀-fullerite is derived up to fourth order in the rotational density fluctuations. The order parameter variables are symmetry adapted rotator functions which belong to thel=6 andl=10 manifolds. They are basis functions ofT _2g representations of the cubic group. The phase transition to thePa3 structure is discussed, and is found to be of first order. The orientationally ordered phase is described in terms of condensed rotator functions.     

Properties of the skeleton of aggregates grown on a Cayley tree

We discuss and analyze a family of trees grown on a Cayley tree, that allows for a variable exponent in the expression for the mass as a function of chemical distance, M(l)l ^dl . For the suggested model, the corresponding exponent for the mass of the skeleton,d _l ^s , can be expressed in terms ofd _l asd _l ^s = 1,d _l d _l ^c = 2;d _l ^s = d _l –1,d ₁ d _l ^c = 2, which implies that the tree is finitely ramified ford _l 2 and infinitely ramified whend _l 2. Our results are derived using a recursion relation that takes advantage of the one-dimensional nature of the problem. We also present results for the diffusion exponents and probability of return to the origin of a random walk on these trees.     

Intercepts of the momentum correlation functions in the $ \mu$ -Bose gas model and their asymptotics

The so-called μ-deformed oscillator (or μ-oscillator) introduced by A. Jannussis, though it possesses rather exotic properties with respect to other better known deformed oscillator models, also has a good potential for diverse physical applications. In this paper, the corresponding μ-Bose gas model based on μ-oscillators is developed. Within this model, the intercepts l⁽²⁾ \lambda^{{(2)}}_{}(K) and l⁽³⁾ \lambda^{{(3)}}_{}(K) of two- and three-particle momentum correlation functions are calculated with the goal of possible application for modeling the non-Bose-type behavior of the intercepts of two- and three-pion correlations, observed in the experiments on relativistic heavy-ion collisions. In the derivation of intercepts, a fixed order of approximation in the deformation parameter μ is assumed. For the asymptotics of the intercepts l⁽²⁾ \lambda^{{(2)}}_{}(K) and l⁽³⁾ \lambda^{{(3)}}_{}(K) , we derive exact analytical formulas. The results for l⁽²⁾ \lambda^{{(2)}}_{}(K) are compared with experimental data, and with earlier known results drawn using other deformed Bose gas models.     

Action of monoatomic cations on the structure and spectra of Mx(1)M1-x(2)UO2(NO3)3 crystals

The action of the monovalent M⁺ cations on the luminescent properties of the mixed M _x ⁽¹⁾ M _1-x ⁽²⁾ UO₂(NO₃)₃ crystals, where M is Na, K, Rb, Cs, or NH₄ , has been investigated. It has been established that the spectral positions of the bands of vibronic transitions depend linearly on the ratio between the concentrations of the M⁽¹⁰⁾ and M⁽²⁾ cations. It is shown that the crystals considered are composed of l[RbUO₂(NO₃)₃]n[CsUO₂(NO₃)₃] clusters, where l/n = x/(1 - x). The spectral regularities revealed are determined by the partial contributions of the M⁽¹⁾ and M⁽²⁾ cations to their combined, polarizing action on the uranyl complex and are explained by the ligand nature of its highest occupied molecular orbital.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 827–830, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

On mass corrections to the decay <Emphasis Type="Italic">P</Emphasis> → <Emphasis Type="Italic">l</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">l</Emphasis><Superscript>−</Superscript>

The Mellin-Barnes representation is used to improve the theoretical estimate of mass corrections to the width of a light pseudoscalar meson decay into a lepton pair, P → l ⁺ l ⁻. The full resummation of the terms ln(m _l ²/Λ²)(m _l ²/Λ²) ⁿ and (m _l ²/Λ²) ⁿ to the decay amplitude is performed, where m _l is the lepton mass and Λ ≈ m _ρ is the characteristic scale of the P → γ*γ* form factor. The total effect of the mass corrections for the e ⁺ e ⁻ channel is negligible and, for the μ⁺μ⁻channel, its order is of a few percent. The text was submitted by the authors in English.     

Ab initio calculation of force constants for the linear molecules HCN,FCN, (CN)2 and the ion N2F+

Force constants have been calculated from ab initio Hartree-Fock wave-functions by the force method, using 7s3p/1 and 5s2p/1 gaussian basis sets for HCN, FCN, C₂N₂ and FN₂ ⁺. Agreement of the quadratic and some cubic force constants with experiment is good for HCN and FCN. The influence of anharmonicity upon the l-type doubling constant of FCN is estimated. Both the experimental l-type doubling constant and the ab initio calculations indicate that the quadratic stretch, stretch coupling constant is positive in FCN, contrary to recent results of Wang and Overend, obtained from the Anderson potential function. There is good agreement for the CN, C′N′ coupling in C₂N₂ but the calculated CN, CC coupling, although positive, is much lower than in two recent experimental force fields. The calculated FN, NN coupling in FN₂ ⁺ is small and positive. The predicted geometry of FN₂ ⁺ is r _NF = 1·28 Å, r _NN = 1·10₅ Å. The validity of the Anderson potential function is discussed.     

The Spectrum of D = 11 Supergravity via Harmonic Expansions on S4 X S7

We derive the complete particle spectrum of the d = 11 supergravity compactified on AdS X S⁷, by analytically continuing AdS to S⁴, and using the Salam-Strathdee method of harmonic expansion on S⁴ X S⁷. The spectrum is arranged into supermultiplets labelled by an integer l = 0, 1, 2,. The massless supermultiplet corresponds to l = 0. For the l'th supermultiplet we find a relation, involving the eigenvalues of the second order Casimir operators of SO(3, 2) and SO(8), given by 2C₂[SO(3, 2)] + C₂[SO(8)] = 3/2(l + 2) (l + 4).     

Relations between nonlinear kernels of the collision integral

Previously, to solve the Boltzmann equation by the moments method with expansion of the distribution function by spherical Hermit polynomials, a new computational method was suggested which allowed to construct nonlinear matrix elements of the collision integral with very large indices. This made it possible to substantially advance in construction of the distribution function. Limitations to convergence of the distribution function that appear in moment method are eliminated if we come to expansion by spherical harmonics from expansion by spherical Hermit polynomials. In this case, a complex five-fold collision integral is replaced by a set of comparatively simple integral operators, and kernels G _l1,l2 ^l (c, c ₁, c ₂) of these operators become the analog of matrix elements. We found the relations between expansions of the distribution function in the reference frames with various velocities of motion along marked axis. Starting from the invariance condition of the collision integral with respect to selection of such reference frames, we derived recurrent relations between the kernels with various indices. These relations allow us to construct any nonlinear kernel G _{l1, l2} ^l (c, c ₁, c ₂), if the kernel G _0,0⁰(c, c ₁, c ₂) is known.