测量薄膜微粗糙度的总积分散射仪

介绍了一种检测光学薄膜表面总积分散射（TIS）分布的总积分散射仪。对仪器的基本结构、理论基础、测量原理以及系统性能等进行了阐述，提出了抑制系统噪音和提高测量精度的有效措施。利用该仪器对K9基底上的银（Ag）膜和氧化锆（ZrO2）薄膜进行了测量，并根据标量散射理论得到了表面均方根（RMS）粗糙度。利用光学轮廓仪和原子力显微镜（AFM）分别测量了上述Ag膜和ZrO2薄膜的表面均方根粗糙度，并与总积分散射仪所得的粗糙度进行了比较。结果表明，根据测量的薄膜表面总积分散射计算得到的表面均方根粗糙度与光学轮廓仪及原子

光学表面的标量散射理论

简要论述了标量散射理论的研究进展做,着重介绍了Beckman的一维标量散射理论和几种典型的多层膜散射模型-非相关表面粗糙度模型、附加表面粗糙度模型和非相关体内不均匀模型,比较了这些模型在中心波长为632.8nm的11层高反膜的散射特性.结果表明,非相关体内的不均匀性引起反射能带边缘散射,反射能带内的散射主要由附加表面粗糙度引起.理想粗糙度对膜系反射带内的散射影响很小,对反射带边缘几乎无影响.预测了标量散射理论的应用领域及前景.

电子束蒸发氧化锆薄膜的粗糙度和光散射特性

利用电子束蒸发工艺，以Ag层为衬底，沉积了中心波长为632．8nm的氧化锆（ZrO2）薄膜，膜层厚度在80-480nm范围内变化．研究了不同厚度样品的粗糙度变化规律和表面散射特性．结果发现，随着膜层厚度的逐渐增加．其表面均方根（RMS）粗糙度和总积分散射（TIS）均呈现出先减小后增大的趋势．利用非相关表面粗糙度的散射模型对样品的TIS特性进行了理论计算，所得结果与测量结果相一致．

Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

NONLINEAR SCALAR COUPLING MODELS AND PROTON-NUCLEUS SCATTERING OBSERVABLES

The effects of nonlinear scalar field couplings on elastic proton-nucleus scattering observables are investigated using a relativistic impulse approximation. Nonlinear couplings affect in a nontrivial way the effective nucleon mass and the nuclear scalar and vector densities. Modifications on the densities might have observable consequences on scattering observables. Our investigation indicates that the description of the observables for the reactions p-O-16 and p-Ca-40 at 200 MeV are not greatly modified with the use of nonlinear models in comparison with the description using linear models.

Scattering and bound states of fermions in a mixed vector-scalar smooth step potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

I. Non-linear effects in a self-consistent calculation of SU_3 symmetry breaking in strong interaction coupling constants. II. Direct-channel reggeization of strong interaction scattering amplitudes

The thesis is divided into two parts. Part I generalizes a self-consistent calculation of residue shifts from SU₃ symmetry, originally performed by Dashen, Dothan, Frautschi, and Sharp, to include the effects of non-linear terms. Residue factorizability is used to transform an overdetermined set of equations into a variational problem, which is designed to take advantage of the redundancy of the mathematical system. The solution of this problem automatically satisfies the requirement of factorizability and comes close to satisfying all the original equations.

Part II investigates some consequences of direct channel Regge poles and treats the problem of relating Reggeized partial wave expansions made in different reaction channels. An analytic method is introduced which can be used to determine the crossed-channel discontinuity for a large class of direct-channel Regge representations, and this method is applied to some specific representations.

It is demonstrated that the multi-sheeted analytic structure of the Regge trajectory function can be used to resolve apparent difficulties arising from infinitely rising Regge trajectories. Also discussed are the implications of large collections of "daughter trajectories."

Two things are of particular interest: first, the threshold behavior in direct and crossed channels; second, the potentialities of Reggeized representations for us in self-consistent calculations. A new representation is introduced which surpasses previous formulations in these two areas, automatically satisfying direct-channel threshold constraints while being capable of reproducing a reasonable crossed channel discontinuity. A scalar model is investigated for low energies, and a relation is obtained between the mass of the lowest bound state and the slope of the Regge trajectory.

Studies on scattering and thermodynamics of black holes in f(R) theory and Einstein's theory

One of the interesting consequences of Einstein's General Theory of Relativity is the black hole solutions. Until the observation made by Hawking in 1970s, it was believed that black holes are perfectly black. The General Theory of Relativity says that black holes are objects which absorb both matter and radiation crossing the event horizon. The event horizon is a surface through which even light is not able to escape. It acts as a one sided membrane that allows the passage of particles only in one direction i.e. towards the center of black holes. All the particles that are absorbed by black hole increases the mass of the black hole and thus the size of event horizon also increases. Hawking showed in 1970s that when applying quantum mechanical laws to black holes they are not perfectly black but they can emit radiation. Thus the black hole can have temperature known as Hawking temperature. In the thesis we have studied some aspects of black holes in f(R) theory of gravity and Einstein's General Theory of Relativity. The scattering of scalar field in this background space time studied in the first chapter shows that the extended black hole will scatter scalar waves and have a scattering cross section and applying tunneling mechanism we have obtained the Hawking temperature of this black hole. In the following chapter we have investigated the quasinormal properties of the extended black hole. We have studied the electromagnetic and scalar perturbations in this space-time and find that the black hole frequencies are complex and show exponential damping indicating the black hole is stable against the perturbations. In the present study we show that not only the black holes exist in modified gravities but also they have similar properties of black hole space times in General Theory of Relativity. 2 + 1 black holes or three dimensional black holes are simplified examples of more complicated four dimensional black holes. Thus these models of black holes are known as toy models of black holes in four dimensional black holes in General theory of Relativity. We have studied some properties of these types of black holes in Einstein model (General Theory of Relativity). A three dimensional black hole known as MSW is taken for our study. The thermodynamics and spectroscopy of MSW black hole are studied and obtained the area spectrum which is equispaced and different thermo dynamical properties are studied. The Dirac perturbation of this three dimensional black hole is studied and the resulting quasinormal spectrum of this three dimensional black hole is obtained. The different quasinormal frequencies are tabulated in tables and these values show an exponential damping of oscillations indicating the black hole is stable against the mass less Dirac perturbation. In General Theory of Relativity almost all solutions contain singularities. The cosmological solution and different black hole solutions of Einstein's field equation contain singularities. The regular black hole solutions are those which are solutions of Einstein's equation and have no singularity at the origin. These solutions possess event horizon but have no central singularity. Such a solution was first put forward by Bardeen. Hayward proposed a similar regular black hole solution. We have studied the thermodynamics and spectroscopy of Hay-ward regular black holes. We have also obtained the different thermodynamic properties and the area spectrum. The area spectrum is a function of the horizon radius. The entropy-heat capacity curve has a discontinuity at some value of entropy showing a phase transition.

An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons

In recent years nonpolynomial finite element methods have received increasing attention for the efficient solution of wave problems. As with their close cousin the method of particular solutions, high efficiency comes from using solutions to the Helmholtz equation as basis functions. We present and analyze such a method for the scattering of two-dimensional scalar waves from a polygonal domain that achieves exponential convergence purely by increasing the number of basis functions in each element. Key ingredients are the use of basis functions that capture the singularities at corners and the representation of the scattered field towards infinity by a combination of fundamental solutions. The solution is obtained by minimizing a least-squares functional, which we discretize in such a way that a matrix least-squares problem is obtained. We give computable exponential bounds on the rate of convergence of the least-squares functional that are in very good agreement with the observed numerical convergence. Challenging numerical examples, including a nonconvex polygon with several corner singularities, and a cavity domain, are solved to around 10 digits of accuracy with a few seconds of CPU time. The examples are implemented concisely with MPSpack, a MATLAB toolbox for wave computations with nonpolynomial basis functions, developed by the authors. A code example is included.

A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces

We propose a Nystr¨om/product integration method for a class of second kind integral equations on the real line which arise in problems of two-dimensional scalar and elastic wave scattering by unbounded surfaces. Stability and convergence of the method is established with convergence rates dependent on the smoothness of components of the kernel. The method is applied to the problem of acoustic scattering by a sound soft one-dimensional surface which is the graph of a function f, and superalgebraic convergence is established in the case when f is infinitely smooth. Numerical results are presented illustrating this behavior for the case when f is periodic (the diffraction grating case). The Nystr¨om method for this problem is stable and convergent uniformly with respect to the period of the grating, in contrast to standard integral equation methods for diffraction gratings which fail at a countable set of grating periods.

Effects Due to a Scalar Coupling on the Particle-Antiparticle Production in the Duffin-Kemmer-Petiau Theory

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the relationship between a 2 x 2 matrix and second-order scalar spectral problems for integrable equations

A simple proof is given that a 2 x 2 matrix scheme for an inverse scattering transform method for integrable equations can be converted into the standard form of the second-order scalar spectral problem associated with the same equations. Simple formulae relating these two kinds of representation of integrable equations are established.

Low-Energy Scattering of Heavy-Light Mesons from Nucleons

We study the low-energy scattering of charmed (D) and strange (K) mesons by nucleons. The short-distance part of the interaction is due to quark-gluon interchanges derived from a model that realizes dynamical chiral symmetry breaking and confines color. The quark-gluon interaction incorporates a confining Coulomb-like potential extracted from lattice QCD simulations in Coulomb gauge and a transverse hyperfine interaction consistent with a finite gluon propagator in the infrared. The long-distance part of the interaction is due to single vector (rho, omega) and scalar (sigma) meson exchanges. We show results for scattering cross-sections for isospin I = 0 and I = 1.

Static potential in scalar QED(3) with non-minimal coupling

Here we compute the static potential in scalar QED(3) at leading order in 1/Nf. We show that the addition of a non-minimal coupling of Pauli-type (is an element of(mu nu alpha)j(mu)partial derivative(nu)A(alpha)), although it breaks parity, it does not change the analytic structure of the photon propagator and consequently the static potential remains logarithmic ( confining) at large distances. The non-minimal coupling modifies the potential, however, at small charge separations giving rise to a repulsive force of short range between opposite sign charges, which is relevant for the existence of bound states. This effect is in agreement with a previous calculation based on Moller scattering, but differently from such calculation we show here that the repulsion appears independently of the presence of a tree level Chern-Simons term which rather affects the large distance behaviour of the potential turning it into a constant.

Polarization in fermion scattering

The behaviour of the helicity of an initially left-handed beam of massive fermions first interacting with a Coulomb field and then with a charged scalar particle via a photon exchange is analysed. It is found that in both cases the massive fermions have their helicity flipped, while massless fermions seeem to be unaffected by the electromagnetic field as far as their helicity is concerned.