Mixed Symmetry States in Even—Even ^96—108Mo Nuclei

Excitation energies and electromagnetic transition strengths in even-even ^96-108Mo nuclei have been described systematically be using the proton-neutron interacting boson model (IBM-2).It appears that the properties of low-lying levels in these isotopes,for which the comparison between experiment and theory is possible,can be satisfactorily described by the IBM-2 model,provided proper account is taken of the presence at low energy of states having a mixed-symmetry character.It seems possible to identify,in each isotope,a few states having such a character,the lowest ones being either 22^ or 23^ levels.It is found that these nuclei are in the transition from U(5) to SU(3).     

Description of Even–Even 114–134Xe Isotopes in the Transitional Region of IBM

Properties of ^114–134Xe isotopes are studied in the U(5)?SO(6) transitional region of Interacting Boson Model (IBM-1). The energy levels and B(E2) transition rates are calculated via the affine SU(1,1) Lie Algebra. The agreement with the most recent experimental is acceptable. The evaluated Hamiltonian control parameters suggest a spherical to γ-soft shape transition and propose the ¹³⁰Xe nucleus as the best candidate for the E(5) symmetry.     

Homoclinic Bifurcation for Boussinesq Equation with Even Constraint

The exact homoclinic orbits and periodic soliton solution for the Boussinesq equation are shown. The equilibrium solution u0 = -1/6 is a unique bifurcation point. The homoclinic orbits and solitons will be interchanged with the solution varying from one side of-1/6 to the other aide. The solution structure can be understood in general.     

Backbending Phenomena in Even–Even $${}^{\boldsymbol{162{-}172}}$$ Hf Isotopes

Physics of Atomic Nuclei - This study probes the backbending phenomena in even–even $${}^{162{-}172}$$ Hf isotopes. Experimental ground-state rotational energies up to $$J^{\pi}=36^{+}$$...     

Even and odd coherent states are “shadowed-like” states

Shadowed states were introduced recently in the literature. It was shown that these states always exhibit nonclassical effects [R. Srinivasan and C.T. Lee, Phys. Lett. A 218 (1996) 151]. Here we show that the well known even and odd coherent states are shadowed-like states, whose differences and similarities are discussed.     

Influence of 1h11/2 Orbit on the Shapes of Even Even Nuclei Around A～100 Region

Using modified surface delta interaction, the deformed Hartree-Fock calculations for twenty two nuclei such as ^102—114Ru, ^102—116Pd,^104—116Cd etc. are performed in the gds and gdsh configuration space, respectively. Prolate and oblate configurations are obtained. It is shown that there exist shape transitions for the nuclei with the mass number from 102 to 116, the resultant single-particle energy spectrum is changed not only with the mass number but also with the configuration, and the results, by considering the 1h_11/2 orbit, are quite different from those obtained in the gds configuration space. Moreover, the number of protons in the nucleus and filling up the 1h_11/2 orbit, especially with neutrons, play important roles in the single-particle energy spectrum and the shape transition.     

Landau–Khalatnikov–Fradkin Transformation and Even $$\zeta$$ Functions

Physics of Atomic Nuclei - An exact formula that relates standard $$\zeta$$ functions and so-called hatted $$\zeta$$ ( $$\hat{\zeta}$$ ) functions in all orders of perturbation theory is presented....     

Properties of Amplitude N th-power Squeezing of Even and Odd qs-Coherent States

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Even and Odd Schrödinger Cat States in the Probability Representation of Quantum Mechanics

Journal of Russian Laser Research - We consider even and odd coherent states (Schrödinger cat states) in the probability representation of quantum mechanics. The probability representation of...     

Nonclassicality Generated by Applying Hermite–Polynomials Photon-Added Operator on the Even/Odd Coherent States

We examine nonclassical properties of the quantum state generated by applying Hermite polynomials photon-added operator on the even/odd coherent state (HPECS/HPOCS). Explicit expressions for its nonclassical properties, such as quantum statistical properties and squeezing phenomenon, are obtained. It is interesting to find that the HPECS/HPOCS exhibits sub-Poissonian distribution, anti-bunching effects and negative values of the Wigner function. Thus, we confirm the HPPECS/HPPOCS is a new nonclassical state. Finally, we reveal that the HPPECS/HPPOCS is a novel intelligent state by its squeezing effects in position distribution and quadrature squeezing.     

First Eigenvalue of the Dirac Operator for a Kähler Manifold of Even Complex Dimension: The Limiting Case

K. D. Kirchberg has given a minoration of the absolute value of the eigenvalues of the Dirac operator for a compact Kähler spin manifold (W,g) with positive scalar curvature and has introduced, in this context, the notion of Kähler twistor-spinor. We prove here that if dim_C W = p 4 is even, in the limiting case, (W, g) is the Kähler product of an odd-dimensional limiting case compact Kähler spin manifold of complex dimension (p-1), by a flat Kähler manifold which is a compact quotient of C.     

Quantum Even Spheres Σ<Superscript><Emphasis Type="Italic">2n</Emphasis></Superscript><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript> from Poisson Double Suspension

We define even dimensional quantum spheres ²ⁿ _q that generalize to higher dimension the standard quantum two-sphere of Podle and the four-sphere ⁴ _q obtained in the quantization of the Hopf bundle. The construction relies on an iterated Poisson double suspension of the standard Podle two-sphere. The Poisson spheres that we get have the same kind of symplectic foliation consisting of a degenerate point and a symplectic ²ⁿ and, after quantization, have the same C ^* –algebraic completion. We investigate their K-homology and K-theory by introducing Fredholm modules and projectors.