E. Nadjakov

Modes in diffused optical waveguides (parabolic and Gaussian models)

A simple analytical description of diffused optical waveguides by a Gaussian refractive index profile is proposed and compared to a parabolic one. Propagation constants and fields are obtained in terms of well-known functions only. The models are experimentally verified by measuring the mode spectrum of waveguides formed by thermal diffusion of silver ions into glass. These models yield a method to obtain guide parameters from mode spectrum.

The feeding times and lifetimes of high-spin levels in ytterbium doubly even isotopes

Abstract The intensities, lifetimes and feeding times of rotational bands with spins up to 10–20ħ have been measured for four doubly even isotopes, 160–166 Yb, formed in the reactions 124–130 52 Te ( 40 18 Ar, 4n), using the recoil-distance Doppler-shift method. The obtained values of rotational level lifetimes, τ I , are compared with the predictions of the rigid-rotor model. For the isotopes 164, 166 Yb a small retardation (by a factor of 1.2–1.4) of transitions in the backbending region is found. Intrinsic quadrupole moments and deformation parameters are deduced as a function of spin for all the four isotopes. The results are discussed in terms of different backbending concepts. The meansquare angular momenta of the levels populated are obtained. Some conclusions on the nature of the γ-ray cascade leading to the feeding of rotational bands are drawn.

Feeding and lifetimes of yrast levels in Hf nuclei

Abstract Feeding intensities and times, as well as lifetimes of yrast levels in doubly even 166, 168, 170 Hf nuclei have been measured. The reactions 122, 124 Sn( 48, 50 Ti, 4n) 166–170 72 Hf have been investigated using the recoil-distance Doppler-shift method. The lifetimes, and hence the B ( E 2) values measured, show the same trends of rather small deviations from the rigid rotor as in the known 68 Er and 70 Yb cases. In addition to the fast feeding component, showing behaviour rather similar to that of the Yb nuclei, another type of slow feeding, related to the low spin yrast levels, is observed.

Determination of refractive index profiles in diffused optical waveguides

An improved method for the reconstruction of diffused waveguide index profiles from experimental mode spectra is proposed. The method uses a parabolic approximation between successive points. It is tested on the example of an exponential profile, and applied to the reconstruction of index profiles in Ag+ ion-exchanged waveguides from measured mode spectra. This method appears to work well also in the cases of very few mode wave-guides.

Theory of coupled rotational bands in nuclei: (I). General

Abstract An RPA type approach to nuclear rotation and its coupling to other modes is proposed, giving both energies and transition rates in deformed nuclei. It is based on a general expansion of any multipole operator, in terms of earlier introduced elementary transition operators, acting in and between nuclear rotational bands. The expansion is formally obtained by using symmetry properties only. The matrix element of any expansion term is calculated from the algebraic properties of the transition operators. Applied to the Hamiltonian it gives a phenomenological model, accounting for vibrations and rotation with coupling between these modes, together with the prescription for evaluation of the model parameters. Applied to a multipole transition inducing field, it leads to a model-independent derivation of the spin (I)-dependent corrections to adiabatic unified model transition rates. A microscopic procedure for calculating the model-dependent expansion coefficients is proposed. The latter are expressed in terms of the elementary transition operators, or in terms of an extended density matrix involving these operators, giving their quasiparticle structure. The procedure is based on a generalized equations-of-motion method for the density matrix. The method is illustrated by the example of coupled ground-state (g), beta (β)-state and gamma (γ)-state rotational bands in even-even nuclei. Results for E2 non-adiabatic transition rate corrections inside the g-band and for transitions from the γ- and β-bands to the g-band are obtained. This example is to be developed in the following paper towards numerical applications and an extension of the description to high-spin states.

Description of the nuclear rotational bands by the collective variable method

Abstract The method of a collective variable canonically conjugated to the angular momentum operator is generalized to describe the energy spacings between all the states of the rotational band. Formulae giving the energy dependence on the angular momentum are obtained for a quantal model of a doubly even nucleus rotating in a plane. These formulae generalize the Inglis formula for the moment of inertia.

Theory of coupled rotational bands in nuclei: (II). Application to even-even nuclei

Abstract The method developed in the preceding paper is applied to study the basic parameters of the states belonging to the ground, β- and γ-rotational bands in even-even deformed nuclei. The parameters of the model Hamiltonian and the expansion coefficients of the physical operators are calculated within a microscopic model, including pairing and quadrupole-quadrupole interactions in an average field of the Woods-Saxon type. One obtains the energies of the states and the non-adiabatic corrections to the different multipole moments in the charge and density distributions of nuclei, and electromagnetic transition probabilities. The agreement of the theoretical results with the known experimental data is generally good. Some conclusions are drawn concerning the deformability of the rotating nuclei in the region of angular momenta critical for the exisience of pairing correlations.

Microscopic determination of band interaction in 154Gd and 164Er

Abstract Microscopic equations describing the direct coupling of the ground state band with the beta-, gamma- and K π = 1 + (responsible for the RAL effect) rotational bands are solved and the interaction strengths are obtained using a Woods-Saxon potential and P + QQ residual forces. The calculated non-adiabatic characteristics are found to be in good agreement with experimental data and are compared to other theories.

Systematic behavior ofB(E2) values in the yrast bands of doubly even nuclei

The experimental information onB(E2) transition rates in the yrast bands of doubly even nuclei (126≦A≦184) is systematized. The strength functionSexp≡B(E2,I→I−2)×E(I→I−2) is found to reveal characteristic behavior significant for structure studies of yrast bands. The energy-weightedB(E2,I→I−2) values (Sexp) and 2ℐ/ℏ2(ℐ: moment of inertia) are plotted versus the rotational frequency squared ℏ2ω2 for each nucleus. In strongly deformed nuclei (N≧90), theSexp curves smoothly increase for low rotational frequencies suggesting that up to spin valuesI≈8 the ratioQ02ℐ is nearly constant (Q0: quadrupole moment). This is not the case in nuclei with a soft core (N≦88). In the relevant discussion, the hydrodynamical model as well as the CAP effect are considered. The results in the backbending region are qualitatively discussed in terms of the two-band crossing model. Evidence is found supporting the prediction of an oscillating behavior of the yrast-yrare interaction.

Particle and subparticle quantum models

Extensions of the Dyson mapping for products of any numbers of fermion and boson operators are suggested. Their general importance in obtaining the relationship between particle and subparticle quantum models and in particular between particle and subparticle nuclear models is discussed. An application in nuclear physics is demonstrated by introducing an interacting spinor model of the nucleus using a new type of supersymmetry and by showing its ability to unify and derive dynamic symmetry nuclear models. Another application is demonstrated by suggesting a quark nuclear-plasma model and by showing that it is possible to give a foundation for such system models, including the transition from quark condensate into nucleons (nucleus) in one limit and quark chaotic behaviour (plasma) in another.