Possible alternatives to tri-bimaximal mixing

Possible alternatives to tri-bimaximal mixing are presented based on other symmetry principles, and their predictions for |U _e3|, sin ² θ ₁₂ and sin ² θ ₂₃ are compared to the present neutrino mixing data. In some cases perturbations are required to give better agreement with the data, and the use of a minimal approach is illustrated. Precise experimental determinations of the mixing parameters will be required to decipher the correct mixing pattern and to pin down the appropriate flavor symmetry.     

Application of the Keating Bendings to ALCL3 and SO3: Preliminary Communication

Force fields from literature for the degenerate (E') vibrations of AlCl₃ and SO₃ are transferred from the valence symmetry coordinates to the central- and Keating symmetry coordinates. In both cases it is found |F ₁₂ ^k| > |F ₁₂| > |F ₁₂ ^c|.     

A basis-free approach to time-reversal for symmetry groups

We develop a basis-free approach to time-reversal for the quantal angular momentum group,SU2, and apply these methods to the physical symmetrySU2_isospin,SU3_flavor,SU3_nuclear and the nuclear collective symmetry groupSL(3,R) of Gell-Mann and Tomonaga.     

Gamow-Teller transitions from 58Ni to discrete states of 58Cu

Under the assumption that isospin is a good quantum number, symmetry is expected for the transitions from the ground states of T = 1, T _z = ±1 nuclei to the common excited states of the T _z = 0 nucleus situated between the two nuclei. The symmetry can be studied by comparing the strengths of Gamow-Teller (GT) transitions obtained from a (p, n)-type charge-exchange reaction on a target nucleus with T _z = 1 with those from the β-decay of the T _z = - 1 nucleus. The A = 58 system is the heaviest for which such a comparison is possible. As a part of the symmetry study, we measured the GT transitions from ⁵⁸Ni (T _z = 1) to ⁵⁸Cu (T _z = 0) by using the zero-degree (³ He, t) reaction at 150 MeV/nucleon. With the achieved resolution of 50 keV, many hitherto unresolved GT states have been identified. The GT transition strengths were obtained for states up to 8 MeV excitation, i.e., near to the Q window limitation ( Q _EC = 9.37 MeV) of the β-decay from ⁵⁸Zn (T _z = - 1) to ⁵⁸Cu. The strength distribution is compared with that from shell-model calculations. Received: 24 November 2001 / Accepted: 30 January 2002     

Representations ofSO(p+q) andO(p) with an application to the shapes of8,9Li

It is easy to show that the symmetry groups governing a system ofZ protons andN neutrons areSO(p+q) andO(p), wherep, q are related toZ, N and the symmetry groups are transitive on a Grassmann manifoldG _p,q. In this paper the general representations ofSO(p+q) andO(p) are found and used to describe the geodesics onG _p,q for the nuclear manifolds of the neutron rich-elements^8,9Li.     

Axial-vector symmetry breaking and the mass generation of the singlet pseudoscalar meson

The Fabri-Picasso formulation of the spontancous breaking of theSU _A (3) symmetry is applied to theU _A (1) symmetry. It is argued that the notion of the spontaneous breaking of theU _A (1) symmetry is different from that of theSU _A (3) symmetry. In contrast to the octet sector, absence of the massless Goldstone mode amounts to the existence of an exotic vacuum-like degenerated state.     

Pseudoscalar Mesons as Goldstone Bosons in Chiral SU(4) ⊗ SU(4) Symmetry

We study the pseudoscalar mesons in the framework of broken chiral SU(4) SU(4) symmetry when the symmetry-breaking Hamiltonian, H_SB, is taken as –(u₀ + cu₈ + du₁₅) and the symmetry of the Hamiltonian is realized in Goldstone-Nambu way. An interesting property of two chimeral SU(4) subgroups and the Goldstone nature of some of the pseudoscalar mesons in certain symmetry limits are exploited to obtain some mass relations and the ratio c/d.     

Chirality and Symmetry Breaking in a Discrete Internal Space

In previous papers the permutation group S ₄ has been suggested as an ordering scheme for quarks and leptons, and the appearance of this finite symmetry group was taken as indication for the existence of a discrete inner symmetry space underlying elementary particle interactions. Here it is pointed out that a more suitable choice than the tetrahedral group S ₄ is the pyritohedral group A ₄×Z ₂ because its vibrational spectrum exhibits exactly the mass multiplet structure of the 3 fermion generations. Furthermore it is noted that the same structure can also be obtained from a primordial symmetry breaking S ₄→A ₄. Since A ₄ is a chiral group, while S ₄ is achiral, an argument can be given why the chirality of the inner pyritohedral symmetry leads to parity violation of the weak interactions.     

Unambiguous evidence for extended s-wave pairing symmetry in hole-doped high-temperature superconductors

We have analysed data from angle-resolved photo-emission spectroscopy, Fourier transform scanning tunneling spectroscopy, and low-temperature thermal conductivity for optimally doped Bi₂Sr₂CaCu₂ O _8+y in order to discriminate between d-wave and extended s-wave pairing symmetry. The combined data are inconsistent with d-wave symmetry, but quantitatively consistent with extended s-wave symmetry with eight line nodes. We also explain all phase-sensitive experiments in a consistent manner.     

N = 1 Dualities for Exceptional Gauge Groups and Quantum Global Symmetries

We discuss our attempts to generalize the known examples of dualities in N = 1 supersymmetric gauge theories to exceptional gauge groups. We derive some dual pairs from known examples connected to exceptional groups and find an interesting phenomenon: sometimes the full global symmetry is “hidden” on the magnetic side. It is not realized as a symmetry on the fundamental fields in the Lagrangian. Rather, it emerges as a symmetry of the quantum theory. We then focus on an approach based on self-dual models. We construct duals for some very special matter content of E₇, E₆ and F₄. Again we find that the full global symmetry is not realized on the fundamental fields.     

Analysis of the Resonance Raman Scattering Spectra and Line Spectra of Tetrabenzoporphin Metal Complexes

On the basis of the calculations of normal vibrations of Zn– and Cu–tetrabenzoporphin, the literature spectra of resonance Raman scattering of the above compounds and the fluorescence spectra of Zn–tetrabenzoporphin are interpreted. The nonmirror character of the fluorescence and fluorescence excitation spectra is noted for some B _1g symmetry type vibrations of the point group of symmetry D _4h caused by the symmetry breakdown of a molecule in its electronic state S ₁ due to the Jahn–Teller effect.     

New Symmetries for the Uq(slN) 6-j Symbols from the Eigenvalue Conjecture1

In the present paper, we discuss the eigenvalue conjecture, suggested in 2012, in the particular case of U_q(sl_N) 6-j The eigenvalue conjecture provides a certain symmetry for Racah coefficients and we prove that the eigenvalue conjecture is provided by the Regge symmetry for U_q(sl_N) 6-j, when three representations coincide. This in perspective provides us a kind of generalization of the Regge symmetry to arbitrary U_q(sl_N) 6-j.

     

Jahn–Teller distortions considered as steady state bifurcations

The steady state bifurcation model can be used to determine the Jahn–Teller distortion modes of a molecule having symmetry point group G to lower symmetry structures having symmetry point groups H _j ???G. In order to find such distortion modes, the trace formula arising from bifurcation theory is applied to all subgroups H _j of G to give a sum of irreducible representations Γ(G?→?H _j ) corresponding to the possible distortion modes of G to H _j . These subgroups H _j correspond to epikernel subgroups of G for any irreducible representation of G found in Γ(G?→?H _j ). This method has been applied to Jahn–Teller distortions of square (D _{4 h} ), octahedral (O _h ), and icosahedral (I _h ) molecules leading to lower symmetry structures.     

The symmetry properties and collinearity of the magnetogyric,hyperfine splitting and magnetic susceptibility tensors

The symmetry properties of g and A cannot be elicited using invariance properties, due to their special nature, and are found using the properties of a Kramers doublet. It is shown that the collinearity of g and A depends on the molecule having at least C ₂ with σ _v or C ₂′ symmetry elements. The symmetry properties of x are found from those of g. The conditions for collinearity of the tensors and the consequences of non-collinearity are discussed, with examples.     

A relativistic approach to the equation of state of asymmetric nuclear matter

The properties of asymmetric nuclear matter for a wide range of densities and asymmetric parameters are investigated within the lowest-order-constrained variational (LOCV) method by employing the relativistic Hamiltonian with a potential which has been fitted relativistically to N-N phase shifts ( [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} and to the AV₁₄interaction. Like our previous work on symmetric nuclear matter, the boost interaction corrections as well as the relativistic one-body and two-body kinetic corrections are calculated. The various properties of asymmetric nuclear matter such as the symmetry energy, the saturation energy and the validity of the a² \alpha^{2}_{} law, etc., are examined. The symmetry energy is reduced by about 7MeV when we use [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} instead of its non-relativistic version, i.e. the AV₁₄interaction. The results are compared with other many-body calculations.     

The spin-isospin decomposition of the nuclear symmetry energy from low to high density

The energy per particle BA in nuclear matter is calculated up to high baryon density in the whole isospin asymmetry range from symmetric matter to pure neutron matter.The results,obtained in the framework of the Brueckner-Hartree-Fock approximation with two-and three-body forces,confirm the well-known parabolic dependence on the asymmetry parameterβ=(N?Z)/A(β^2 law)that is valid in a wide density range.To investigate the extent to which this behavior can be traced back to the properties of the underlying interaction,aside from the mean field approximation,the spin-isospin decomposition of BA is performed.Theoretical indications suggest that theβ^2 law could be violated at higher densities as a consequence of the three-body forces.This raises the problem that the symmetry energy,calculated according to theβ^2 law as a difference between BA in pure neutron matter and symmetric nuclear matter,cannot be applied to neutron stars.One should return to the proper definition of the nuclear symmetry energy as a response of the nuclear system to small isospin imbalance from the Z=N nuclei and pure neutron matter.     

Si80笼状分子的结构研究

采用基于密度泛函的第一性原理计算方法,构建了Si₈₀笼状分子的模型,并对其结构和电学特性进行了考察. 研究发现,经过结构优化计算,Si₈₀分子从I_h高对称性下降为T_h,但仍然保持较好的笼状结构. 对Si₈₀笼状分子的稳定性、轨道分布和电荷分布等性质进行了分析和讨论. 关键词： 80')" href="#">Si₈₀ 富勒烯 结构     

Temperature dependent study of the single crystal electronic spectrum of octahedral Ni2+ ion subjected to distortions in weak fields

Electronic spectra of two high spind ⁸ nickel complexes, Ni(en)₃Cl₂.2H₂O and Ni(OAc)₂.4H₂O, are reported. Polarized spectra were measured at 298 K. Temperature dependent spectra were measured using unpolarized light down to 20 K. The spectra at 20 K are well resolved revealing the features of spin-forbidden transitions and vibrational fine structure on some of the bands. Some of the spectra are deconvoluted to separate out the overlapping bands. The assignments are made usingD ₃ symmetry for Ni(en)₃Cl₂.2H₂O complex whileD ₄ symmetry is used for Ni(OAc)₂.4H₂O. The energies of the spectroscopic states are calculated and compared with the observed transition energies. The distortion parameters are determined.     

The effect of relaxation on the symmetry of N.M.R. spectra

The effect of nuclear relaxation on the symmetry properties of N.M.R. spectra is examined in terms of the properties of the relaxation matrix elements R_ijkl . It is found that the symmetry relations R_ijkl = R_jilk = R_klij = Rlkij obtain for one or more dominant relaxation mechanisms under ‘extreme narrowing’ conditions. Further, the symmetry relation R_ijkl = R_{λi, λj, λk, λl} , where λ is a spin inversion operator, is shown to obtain for (a) only one dominant relaxation mechanism or (b) two dominant relaxation mechanisms which have the same commutation properties with λ. This latter symmetry relation does not obtain for two dominant relaxation mechanisms with the same order of spatial dependence and different commutation properties with λ. The effect of nuclear relaxation can therefore yield unsymmetrical first-order spectra; the application of this analysis to the determination of the absolute sign of the spin-spin coupling constants is proposed.     

Local structures around Cu2+ and Zn2+ions related to cooperative jahn-teller distortions in dilute systems of K2Cu x .Zn1F4

The structural properties of the dilute systems of K₂Cu _x Zn_{1 x} F4 have been studied by means of X-ray absorption fine structure (EXAFS) for the Cu-K edge and Zn-K edges. It is found that there are rigid-like Jahn-Teller distortions of the CuF₆ octa-hedra in the region of 0.0 < x ≤ 1.0. It is also found that, in dilute systems, the ZnF₆ octahedra at least show two kinds of shapes, of which one is characterized to have a 2-fold symmetry axis and the other to have a 4-fold symmetry axis in the (x-y) plane. Thus, the inner strains induced by the replacement of the Zn atoms by the Cu atoms are localized around the Zn atoms, and can be reduced by the appearance of the former ZnF₆ octahedra showing a pseudo Jahn-Teller distortion.