Coupling of one and two quasiparticles to a Bohr-Mottelson core in195,196,197,198Hg

A new model for coupling the motion of particles to that of a quadrupole collective core with rotations andβ andγ vibrations is proposed. The Hamiltonian describing the core is obtained by quantising the classical Hamiltonian associated with the quadrupole degrees of freedom. The inertial parameters and the deformation energy surface are determined microscopically. The spherical shell model particles interacting among themselves by pairing are coupled to the core by aλ ²-pole (λ=0, 2, 4) potential. The theory is applied to^195–198Hg. The predicted results agree very well the experimental data. A comparison of the present model to the other formalism is also given.     

Ultrasonication--a complementary 'green chemistry' tool to biocatalysis: a laboratory-scale study of lycopene extraction

Lycopene is bequeathed with multiple bio-protective roles, primarily attributed to its unique molecular structure. The concomitant exploitation of two of the green chemistry tools viz., sonication and biocatalysis is reported here for the laboratory scale extraction of lycopene from tomato peel. The coupled system improved the extraction by 662%, 225% and 150% times over the unaided, only cellulase ‘Onozuka R-10’ treated and only sonication treated samples respectively. The sonication parameters (duration, cycle and amplitude) during the coupled operation were optimized using response surface methodology (RSM). Derivative UV-visible spectra (i.e., dA/dλ and d²A/dλ² against λ), FTIR analysis, and DPPH scavenging test suggested that the reported extraction protocol did not affect the molecular structure and bioactivity of the extracted lycopene. The influence of sonication on the probable structural modulation (through UV-visible spectral analysis) and activity of the enzyme were also analyzed. A plausible mechanism is proposed for the enhanced extraction achieved via the coupled system.     

Coupling of two quasiparticles to coherent cores in the Pt isotopes

A model for coupling the motion of particles to that of a quadrupole-collective core is proposed. The quadrupole vibrations and rotations of the core are described by angular momentum projected coherent states. The spherical shell model particles interact among themselves by pairing and surface delta interactions. The particles are coupled to the core through a multipole-multipole interaction. The method is applied to several even mass isotopes of Pt. The agreement with experimental data of the excitation energies, gyromagnetic factors andE2 probabilities is very good.     

Description of odd transitional nuclei in terms of core-quasiparticle models

A general core-quasiparticle coupling (CQPC) formalism is presented that properly accounts for the particle-hole structure in odd-A transitional nuclei. The method is a consequent generalization of the Coriolis-coupling approach. The formalism is applied to the coupling of a quasiparticle to the γ = 30° triaxial rotor and to a γ-unstable core. A comparison with the experimental ¹⁹¹Pt spectrum shows that the odd particle is not a sufficiently sensitive probe to distinguish between the two core models.     

Carbon monoxide oxidation over well-defined Pt/ZrO2 model catalysts: Bridging the material gap

Four different Pt/ZrO₂/(C/)SiO₂ model catalysts were prepared by electron beam evaporation. The morphology of these samples was examined before and after the catalytic reaction by Rutherford back-scattering (RBS), transmission electron microscopy (TEM) and grazing-incidence small-angle scattering (GISAXS). The catalytic behavior of such model catalysts was compared to a conventional Pt/ZrO₂ catalyst in the CO oxidation reaction using different oxygen excess (λ = 1 and 2). The so-called material gap was observed: model catalysts were active at higher temperature (620-770 K) and resulted in higher activation energy values (E_a = 77-93 kJ mol⁻¹ at λ = 1 and 129-141 kJ mol⁻¹ at λ = 2) compared to the powdered Pt/ZrO₂ catalyst (370-470 K, E_a = 74-76 kJ mol⁻¹). This material gap is discussed in terms of diffusion limitations, reaction mechanism and apparent compensation effect. Diffusion processes seem to limit the reaction on planar samples in the reactor system that was shown to be appropriate for the evaluation of the catalytic activity of powder samples. Kinetic parameters obeyed the so-called apparent compensation effect, which is discussed in detail. Langmuir-Hinshelwood-type of reaction, between CO_ads and O_ads, was proposed as the rate-determining step in all cases. Pt particles deposited on planar structures can be used for modeling conventional powdered catalysts, even though some limitations must be taken into account.     

Band crossing in184Pt

The levels in the ground band of¹⁸⁴Pt are identified up to the member with spin 20 in an in-beam spectroscopy experiment on theγ-rays following the¹⁷⁷Hf(¹²C, 5n)¹⁸⁴Pt reaction. In contrast to the situation in the heavier Pt isotopes, where the 10⁺ to 12⁺ level spacing is very small, the transition energies in¹⁸⁴Pt show a monotonie increase with spin. However, between spin 10⁺ and 14⁺ the moment of inertia grows quite rapidly and this appears to be reminiscent of the much more pronounced irregularity encountered in the isotopes of larger mass. This property of the moment of inertia is discussed within a model where twoi _13/2 neutron quasiparticles or twoh _9/2 orh _11/2 proton quasiparticles may be excited and coupled to the rotation of the core.     

Study of Pt isotopes in the core excited interacting boson model 1

The core exited IBM model was applied to the Pt isotopes. It was found that the energy spectra of the high-spin states as well as those of the low-spin states can be reproduced quite well. Also, it was found that there is a structure transition between ¹⁸⁶Pt and ¹⁸⁸Pt. The B(E2) values of ¹⁸⁴Pt were calculated and compared with recent experimental data. It was found that the general features of the B(E2) values can be reproduced qualitatively. The need of more boson core excitations is also discussed.     

Hartree-Fock calculations for finite nuclei with equivalent nonlocal potentials

The method of constructing equivalent regular two-body potentials by a unitary transformation of the two-body Hamiltonian has been generalized to spin-parity dependent nuclear potentials containing tensor- and spin-orbit terms. Starting from the Gammel-Christian-Thaler potential, which includes tensor forces, we obtained a class of equivalent regular, but nonlocal potentials depending on a parameterλ — the range of nonlocality. — These potentials have been used in a Hartree-Fock calculation for the closed-shell nuclei He⁴, C¹², O¹⁶, Si²⁸, S³², Ca⁴⁰. The calculated binding energies show a slowλ-variation with a minimum in the region of 0.7 f. The nuclear radii decrease with increasingλ and are in general too small. The sequence of single particle levels of the nuclei with closedl- shells is in agreement with that obtained with the usual nuclear shell model potential including spin-orbit coupling.     

Eigenvalues of theµx 2 +λx 2m interaction

The even and odd parity eigenvalues for the bounded potentialμx ² +λx ^2m with both positive and negative values ofμ andm=2, 3, 4, 5, 6 are obtained by the method of series solution for any positive value of the coupling constantλ. Whenμ is negative the lower order eigenvalues are closely bunched in pairs in the low-λ regime (λ≪1). The results agree well with existing results.     

Deformation properties of the neutron-deficient odd-A Pt and Hg nuclei

Nuclear and atomic spectroscopy measurements have provided a great number of data on the neutron-deficient Pt and Hg nuclei. The odd-A Pt and Hg with A<186 have a prolate shape, and the even-even isotopes have a triaxial shape, while the nuclear shape of the odd-A Pt and Hg with A>186 is still an open question. The energy of the low-lying levels and the nuclear moments have been calculated in the framework of a semimicroscopic “axial-rotor + 1 quasiparticle” coupling model. The predictions are compared with the experimental data and discussed. The results strongly suggest a prolate shape for the negative-parity low-lying states of the odd-A ^187–191Pt and ^187–193Hg isotopes.     

Study of transitional odd-odd mass nuclei

The low lying high spin states in the transitional odd-odd mass nuclei are studied systematically in the framework of gamma deformed rotor model. The two odd particles, a proton and a neutron, are treated as the BCS quasi particles moving in a triaxially deformed field. The calculations are confined to smallβ-deformation which is typical of the transitional nuclei. Moreover, we consider only the case where two odd particles are in singlej-shells. Results for the excitation energy covering the various physical situations are presented as a function of theβ-deformation, the asymmetryγ, and the Fermi energiesλ _p andλ _n . Electromagnetic transitions and moments are also calculated. Certain features well known in the odd mass nuclei are shown to persist also in the odd-odd mass system. Trends in the level systematics and the electromagnetic properties are predicted for the case where both particles decouple or remain strongly coupled, and for the case where one decouples and the other couples strongly with the core. Measurements which are getting now available show encouraging agreement with the theoretical results.     

Synchronization of oscillators coupled through an environment

We study synchronization of oscillators that are indirectly coupled through their interaction with an environment. We give criteria for the stability or instability of a synchronized oscillation. Using these criteria we investigate synchronization of systems of oscillators which are weakly coupled, in the sense that the influence of the oscillators on the environment is weak. We prove that arbitrarily weak coupling will synchronize the oscillators, provided that this coupling is of the ‘right’ sign. We illustrate our general results by applications to a model of coupled GnRH neuron oscillators proposed by Khadra and Li [A. Khadra, Y.X. Li, A model for the pulsatile secretion of gonadotropin-releasing hormone from synchronized hypothalamic neurons, Biophys. J. 91 (2006) 74-83.], and to indirectly weakly-coupled λ-ω oscillators.     

A Timoshenko beam reduced order model for shape tracking with a slender mechanism

We consider a flexible bio-inspired slender mechanism, modeled as a Timoshenko beam. It is coupled to the environment by a continuous distribution of compliant elements. We derive a reduced order model by projecting the governing partial differential equations along the linear modal basis of the Timoshenko beam. The coupling with the substrate allows us to formulate the problem in a control framework, and eventually to treat the system as a sensor to reconstruct the profile of the substrate through the deformation of the body. The coupling is modeled in the framework of two parameters elastic foundations. The convergence of the reduced order model with increasing number of basis functions is addressed in a suitable H¹ error norm. A closed loop force control is simulated for shape morphing when the system is coupled with a smooth substrate.     

The Wightman axioms and the mass gap for weakly coupled (ϕ4)3 quantum field theories

We show that for sufficiently small coupling constant λ the λ?⁴ model in three spacetime dimensions exists and satisfies all the Wightman axioms. We also establish the existence of a nonzero mass gap.     

Low-energy spectrum of one-neutron halo nucleus 11Be

We investigate the low-energy spectrum of the one-neutron halo nucleus ¹¹Be using the complex scaled coupled channel method for a ¹⁰Be + n model, paying attention to the effects of the deformation of the ¹⁰Be-core and the Pauli principle between the core and a valence neutron. For positive parity states of ¹¹Be, our calculation well reproduces the experimental results, but for negative parity states, not so well. With reducing the coupling between the core deformation and a valence neutron, the negative parity levels of the ¹¹Be nucleus are much improved.     

Large R-parity violating couplings and grand unification

We consider the possibility that R-parity violating interactions of particles which do not involve the first generation have large (up to 1) coupling constants, λ. Such couplings, if they exist, could have a number of phenomenological consequences: renormalization of the b − τ mass ratio, generation of ν_τ mass in the MeV region, etc. In grand unified models, where B- and L-violating couplings appear simultaneously, proton decay can be forbidden in virtue of the hierarchical flavor structure of λ. However, due to Cabibbo-Kobayashi-Maskawa mixing this decay is induced already at one loop. Present experimental data give the upper bound λ ⪅ 10⁻⁸ (or |λ′λ″| ⪅ 7 × 10⁻¹⁶, on products of certain L- and B-violating coupling constants, in a more general context). The bound can be avoided if there is an asymmetry between the L- and B-violating couplings of the usual matter fields. In the SU(5) model the asymmetry can be related to the doublet-triplet splitting.     

Dephasing in the semiclassical limit is system-dependent

Dephasing in open quantum chaotic systems has been investigated in the limit of large system sizes to the Fermi wavelength ratio, L/λ_F 〉 1. The weak localization correction g ^wl to the conductance for a quantum dot coupled to (i) an external closed dot and (ii) a dephasing voltage probe is calculated in the semiclassical approximation. In addition to the universal algebraic suppression g ^wl ∝ (1 + τ_D/τ_?)^?1 with the dwell time τ_D through the cavity and the dephasing rate τ _? ^?1 , we find an exponential suppression of weak localization by a factor of ∝ exp[? $\tilde \tau $ /τ_?], where $\tilde \tau $ is the system-dependent parameter. In the dephasing probe model, $\tilde \tau $ coincides with the Ehrenfest time, $\tilde \tau $ ∝ ln[L/λ_F], for both perfectly and partially transparent dot-lead couplings. In contrast, when dephasing occurs due to the coupling to an external dot, $\tilde \tau $ ∝ ln[L/ξ] depends on the correlation length ξ of the coupling potential instead of λ_F.