Transverse Ward-Takahashi identities and full vertex functions in different representations of QED_3

We derive the transverse Ward-Takahashi identities(WTI) of N-dimensional quantum electrodynamics by means of the canonical quantization method and the path integration method, and subsequently attempt to prove that QED_3 is solvable based on the transverse and longitudinal WTI, indicating that the full vector and tensor vertices functions can be expressed in terms of the fermion propagators in QED_3. Further, we discuss the effect of different γ matrix representations on the full vertex function.     

Approximation of a general singular vertex coupling in quantum graphs

The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints is joined by an edge carrying a δ potential and a vector potential coupled to the “loose” edges by a δ coupling. It is shown that if the lengths of the connecting edges shrink to zero and the potentials are properly scaled, the limit can yield any prescribed singular vertex coupling, and moreover, that such an approximation converges in the norm-resolvent sense.     

Strong coupling constants of light pseudoscalar mesons with heavy baryons in QCD

We calculate the strong coupling constants of light pseudoscalar mesons with heavy baryons within the light cone QCD sum rules method. It is shown that sextet–sextet, sextet–antitriplet and antitriplet–antitriplet transitions are described by one universal invariant function for each class. A comparison of our results on the coupling constants with the predictions existing in literature is also presented.     

单分子磁体中交换常数计算的新方法

采用基于密度泛函理论(DFT)的第一性原理计算方法,在现有的单分子磁体交换耦合常数计算方法的基础上提出了一种新的计算方法.采用新方法计算两个原子之间的交换耦合常数时,首先分别设置这两个原子的自旋取向,然后再同时设置两个原子的自旋取向,计算出总能即可,而不用选取不同的自旋组态并求解线性方程组.方法特别适合含有数目很大的磁性原子的单分子磁体交换耦合常数的计算.采用新方法计算了Fe7和Fe20配合物分子的交换耦合常数.结果表明,Fe7和Fe20分子中的交换常数都为负,即反铁磁耦合时能量更低,这与类似分子的相关研究相一致.     

单分子磁体中交换常数计算的新方法

采用基于密度泛函理论(DFT)的第一性原理计算方法,在现有的单分子磁体交换耦合常数计算方法的基础上提出了一种新的计算方法.采用新方法计算两个原子之间的交换耦合常数时,首先分别设置这两个原子的自旋取向,然后再同时设置两个原子的自旋取向,计算出总能即可,而不用选取不同的自旋组态并求解线性方程组.方法特别适合含有数目很大的磁性原子的单分子磁体交换耦合常数的计算.采用新方法计算了Fe7和Fe20配合物分子的交换耦合常数.结果表明,Fe7和Fe20分子中的交换常数都为负,即反铁磁耦合时能量更低,这与类似分子的相关研究相一致.     

A set of new nucleon coupling constants and the proto neutron star matter

Using a new set of nucleon coupling constants CZ11 the properties of a proto neutron star are examined within the framework of the relativistic mean-field theory for the baryon octet system.It is found that the relative number density of Λ,Ξ-,and Ξ0 for CZ11 are all smaller than those for GL97 and for both CZ11 and GL97,Σ-,Σ0,and Σ+ do not appear.It is also found that the pressure and the maximum mass for CZ11 are all smaller than those for GL97.The maximum mass for CZ11 decreases by approximately 9 percent compared with that for GL97.     

Sum rules for the baryon20, baryon20′ and meson 16-plet coupling constants in broken SU (4) and SU (3) symmetry

Sum rules for the coupling constants for D (20), B (20′) and P (16) are given taking into account first order breaking of SU (4) and SU (3) symmetries. The D (20) and B (20′) contain the usual 3/2⁺ baryon decuplet and 1/2⁺ baryon octet of SU (3), while the P (16) contains the usual pseudoscalar octet of pions, etc. These sum rules generalize the decuplet → octet + octet sum rules of broken SU (3 to a broken SU (4) symmetry scheme, in particular the charm SU (4) for hadrons. It is pointed out that, of the many sum rules, it may be possible to check some of them experimentally (see Section 5) and thus provide a test for an underlying SU (4 symmetry for strong interactions.     

IFSERF, an isotope-filtered SERF experiment for the precise measurement of proton-proton coupling constants between chemically equivalent protons

An isotope-filtered selective refocusing (IFSERF) experiment is presented for the sensitive and precise measurement of the proton-proton coupling constant between chemically equivalent protons. The 2D NMR method combines an initial doubly selective isotope filter based on heteronuclear cross-polarization followed by a selective J-resolved block. The coupling topologies obtained from several 2D variants of the IFSERF experiment are described for the simultaneous measurement of both proton-proton and proton-carbon coupling constants in the involved AA'XX' spin system. Application on the determination of the relative configuration of double bonds in symmetrical molecules is illustrated.     

Microwave spectra, inversion splittings and quadrupole coupling constants of NHDCl and ND2Cl

The microwave spectra of monochloroamine (NH₂Cl) and its isotopic species have been observed by Cazzoli et al. [G. Cazzoli, D.G. Lister, P.G. Favero, J. Mol. Spectrosc. 42 (1972) 286-295; G. Cazzoli, D.G. Lister, J. Mol. Spectrosc. 45 (1973) 467-474]. We observed microwave spectra of four isotopic species of ¹⁴NHD³⁵Cl, ¹⁴NHD³⁷Cl, ¹⁴ND₂³⁵Cl, and ¹⁴ND₂³⁷Cl produced by the direct reaction of ammonia gas-d₃ or ammonium hydroxide-d₅ with N-chlorosuccinimide. The microwave spectra of NHDCl (d₁-species) and ND₂Cl (d₂-species) were observed in the frequency range from 8.0 to 60 GHz. The inversion splitting (ΔE_o) of ¹⁴NHD³⁵Cl and ¹⁴NHD³⁷Cl in the ground vibrational state are shown to be 11.46(15) and 11.44(15) MHz for K_a = 0 ← 1, and 10.49(15) and 10.26(15) MHz for K_a = 1 ← 2, respectively. However, the inversion splitting of the d₂-species could not be observed in our spectrometer. Only small J and K-dependence of the inversion splitting of d₁-species was observed. The rotational constants of ¹⁴NHD³⁵Cl were determined to be A = 187895.44(18), B = 13353.343(15) and C = 12859.794(15) MHz for the 0⁺ ← 0⁻ state, which means the transition from the lower inversion level to the upper one, and A = 187918.52(18), B = 13353.345(15) and C = 12859.798(14) MHz for the 0⁻ ← 0⁺ state. The rotational and centrifugal distortion constants of ¹⁴ND₂³⁵Cl were determined to be A = 141030.885(72), B = 12594.481(6) and C = 12055.356(6) MHz, and Δ_J = 18.342(23), Δ_JK = 318.15(56), Δ_K = 2219.3 (fixed), δ_J = 0.8717(17) and δ_K = 157.78(61) kHz. The values of the planar moments P_bb = (I_b − I_a − I_c)/2, of ¹⁴ND₂³⁵Cl and ¹⁴ND₂³⁷Cl were found to be 2.68898(2) and 2.68890(2) u Å², respectively, which are about twice as large as those of normal species (P_bb = 1.3548(6) and 1.3544(16) u Å², respectively). It was found that the bond length of r(N-Cl) of NH₂Cl was longer than that of Cl-NCO by 0.045(12) Å, and was almost the same as that of CH₂N-Cl, while it was much shorter than those of Cl-NO₂ and Cl-NO, by 0.092(6) and 0.227(6) Å, respectively.     

A comprehensive approach for accurate measurement of proton-proton coupling constants in the sugar ring of DNA

Stereo-selectivedeuteration has been explored as an approach for improving the accuracy of NMR-derived, three-bond vicinal proton-proton coupling constants in the 12-base-pair DNA Dickerson sequence [d(CGCGAATTCGCG)(2)]. The coupling constants are useful for DNA structure determination in restrained molecular dynamics calculations. Specifically, the A5 and A6 residues were prepared with the H2" proton stereo-selectively replaced with a deuteron. Deuteration of the H2" leads to a 42-fold reduction in the transverse cross-relaxation rate of the H2' spin, effectively negating the contribution of transverse cross relaxation to the cross peak frequencies and phases. Calculated linewidth and polarization transfer functions indicated that the reduced dipolar interaction is also expected to result in a significant increase in intensity for all cross peaks involving the H1', H2', or H3' spin. The spectral complexity is also reduced by selective deuteration. Time-shared homonuclear decoupling of passive spins during acquisition was implemented, reducing the spin system, in some cases, to an effectively isolated two-spin system. This enables the use of a 90 degrees mixing pulse instead of the 35 degrees pulse commonly used in standard P.E.COSY experiments, leading to an additional 75% increase in signal intensity. Selective excitation pulses were used to reduce the number of increments required in the indirect dimension by as much as a factor of 4. The cumulative improvement in sensitivity is striking, approaching three orders of magnitude per unit time. Separate experiments, referred to as Stripe-COSY and Superstripe-COSY, were optimized for each coupling constant measured. Finally, J-doubling was used to obtain the most accurate peak separations. This comprehensive approach shows promise as an effective method for extracting highly accurate homonuclear vicinal coupling constants in DNA.     

Weak decay constants of light and heavy pseudoscalar mesons

We investigate the weak leptonic decays of light and heavy pseudoscalar mesons in a relativistic quark model of independent quarks. We perform a static calculation of the decay constantf _M purely on grounds of simplicity. In order to minimize the possible uncertainty in the static calculation, we estimate the ratios of the decay constants which are found to be in good agreement, in the heavy flavor sector, with the predictions of other models available in the literature and existing experimental data. However, there is a noticeable discrepancy in the current prediction for pion decay constant which demonstrates the inherent limitations of the static approximation in the study of non-strange light mesons.     

1H-detected double-J-modulated INEPT-INADEQUATE for simultaneous determination of one-bond and long-range carbon-carbon connectivities and the measurement of all carbon-carbon coupling constants

We describe a new NMR experiment, (1)H-detected double-J-modulated (DJM)-INEPT-INADEQUATE, for tracing out the carbon skeleton of molecules. This experiment allows simultaneous correlation of directly bonded carbon atoms and those separated by multiple bonds, while at the same time also providing the values of all J(CC) coupling constants. This is achieved by replacing both fixed carbon-carbon coupling evolution intervals of the INEPT-INADEQUATE experiment by variable time intervals, which are incremented in concert with the DQ evolution period (t(1)). We show that the analysis of the fine structure of cross-peaks in DJM-INEPT-INADEQUATE spectra leads to accurate values of coupling constants and give guidelines for the proper usage of the method. The proposed experiment is two times less sensitive that the original INEPT-INADEQUATE experiment. We show that, using a 600-MHz cryoprobe and 20 mg of a monosaccharide, spectra that are suitable for the analysis of coupling constants as small as 2 Hz can be obtained within 24 h. Instead of performing multiple experiments, a single DJM-INEPT-INADEQUATE experiment can thus provide a wealth of information for the structural analysis of small molecules.     

Vertex function and coupling constant for the virtual decay of7Li

The alpha-triton relative wave function with various nucleon exchange contributions and their asymptotic normalization are considered in the framework of the generator coordinate method (GCM). The asymptotic normalization of relative wave function provide the estimate of the coupling constant. The relative wave function is also used to obtain⁷Li-α-t vertex function in the virtual decay of⁷Li. The extrapolation of vertex function for negative values ofq ² up to the alpha-triton pole provide the vertex constant, which is compared with the experimentally determined estimates 0.67 FM and 0.72 FM. Our calculated value is 0.656 FM which is in close agreement with the above estimates.     

Boundary correlation functions of the six and nineteen vertex models with domain wall boundary conditions

Boundary correlation functions of the six and nineteen vertex models on an N×N lattice with domain wall boundary conditions are studied. The general expression of the boundary correlation functions is obtained for the six vertex model by the use of the quantum inverse scattering method. For the nineteen vertex model, the boundary correlation functions are shown to be expressed in terms of those for the six vertex model.     

库仑波函数的束缚连续跃迁矩阵元的解析计算公式和递推关系

给出了库仑波函数的束缚连续跃迁矩阵元的解析计算公式,并获得了不同幂次矩阵元之间所满足的递推关系.这些结果可广泛的用于原子和分子的散射问题.     

H, C NMR and JCH coupling constants investigation of 4-Phenylpyridine: A combined experimental and theoretical study

Proton coupled and uncoupled ¹³C, ¹H, DEPT, COSY and HETCOR NMR spectra of 4-Phenylpyridine (4-Phpy) have been reported for the first time except for its ¹H NMR spectrum. In order to provide a precise structural elucidation for carbon atoms those have very close chemical shifts to each other, the magnitude of ⁿJ_CH (n=1,2,3) coupling constants of 4-Phpy (C₁₁H₉N) have also been investigated. ¹³C, ¹H NMR chemical shifts and ^1-3J_CH coupling constants of 4-Phpy have been calculated by means of B3LYP density functional method with 6-311++G(d,p) basis set. Moreover, the optimized parameters (bond lengths, bond and torsion angles) of 4-Phpy have been calculated with B3LYP at 6-31G(d) level in methanol (ε=32.63). Comparison between the experimental and the theoretical results indicates that density functional B3LYP method is able to provide satisfactory results for predicting NMR properties.     

SO＋离子b4∑-态光谱常数和分子常数研究

采用考虑Davidson修正的内收缩多参考组态相互作用方法和相关一致基aug—CC—pV5Z，在0．103—1．083nm的核间距内计算了SO＋离子b4∑-态的势能曲线．采用态相互作用方法和非收缩全电子aug．CC—pCVTZ基组、利用完全Breit—Pauli算符计算了旋轨耦合效应对光谱常数的影响．为提高势能曲线和旋轨耦合常数的计算精度，考虑了核价相关效应和相对论效应对势能曲线的影响．核价相关效应是使用CC—pCVTZ基组计算的；相对论效应是在-cc-pV5Z基组水平上使用三级Douglas．Kroll．Hess哈密顿算符计算的．利用得到的势能曲线，计算了各种情况下的光谱常数，并进行了详尽的分析和讨论．结果表明：在MRCI＋Q／aug—cc—pV5Z＋CV＋DK理论水平获得的光谱常数总体上最接近实验值．在MRCI＋Q／aug-cc-pV5Z＋CV＋DK理论水平，用全电子aug—cc—pCVTZ基组计算旋轨耦合修正时得到的旋轨耦合常数为1cm^-1．利用MRCI＋Q／aug-cc-pV5Z＋CV＋DK理论水平得到的势能曲线，通过求解核运动的振转Schr6dinger方程，计算了无转动SO＋离子b4∑-态前20个振动态的G（v），Bv和Dv等分子常数．其值与已有的实验结果一致．本文得到的光谱常数和分子常数达到了很高精度，能为进一步的光谱实验和理论研究提供可靠参考．文中的大部分光谱常数和分子常数均属首次报道．