Series expansion for mesonic masses in multicolor QCD

A systematic procedure for the calculation of mesonic masses in QCD with large number of colors is proposed. The masses are expanded in terms of an auxiliary parameter α, which is set to 1 at the end of the calculation. The expansion coefficients are expressed in general in terms of the Feynman integrals of QCD.The terms of order αⁿ involve diagrams with n loops. Explicit expressions are found up to α³. These terms appear to be rather small, so that one may try to extrapolate to α = 1. The qualitative properties of the spectrum are plausible, but for quantitative predictions further calculations are required.     

Dimensional renormalization of scalar field theory in curved space-time

The regularization and renormalization of an interacting scalar field φ in a curved spacetime background is performed by the method of continuation to n dimensions. In addition to the familiar counter terms of the flat-space theory, c-number, “vacuum” counter terms must also be introduced. These involve zero, first, and second powers of the Reimann curvature tensor R_αβψδ. Moreover, the renormalizability of the theory requires that the Lagrange function couple φ² to the curvature scalar R with a coupling constant η. The coupling η must obey an inhomogeneous renormalization group equation, but otherwise it is an arbitrary, free parameter. All the counter terms obey renormalization group equations which determine the complete structure of these quantities in terms of the residues of their simple poles in n ? 4. The coefficient functions of the counter terms determine the construction of φ² and φ⁴ in terms of renormalized composite operators 1, [φ²], and [φ⁴]. Two of the counter terms vanish in conformally flat space-time. The others may be computed from the theory in purely flat space-time. They are determined, in a rather intricate fashion, by the additive renormalizations for two-point functions of [φ²] and [φ⁴] in Minkowski space-time. In particular, using this method, we compute the leading divergence of the R² interaction which is of fifth order in the coupling constant λ.     

Contribution of electric quadrupole and dipole-quadrupole interference terms in Coulomb breakup of 15C

The effects of electric quadrupole (E2) and dipole-quadrupole interference (E1–E2) terms in the Coulomb breakup of ¹⁵C have been investigated within the framework of eikonal approximation. The sensitivity of Coulomb breakup cross section, differential in relative energy and Longitudinal Momentum Distribution (LMD) of core fragments, towards these terms have been examined. A very small (1% of E1) contribution of E2 transition has been predicted in integrated Coulomb breakup cross section. Further it is also found that the inclusion of E2 and E1–E2 terms introduces a small asymmetry in the peak of relative energy spectrum and also increases the peak height of the spectrum. The contribution of dipole-quadrupole interference terms is clearly shown in LMD, as it introduces an asymmetry in the shape of LMD and enhances the matching between the data and predictions.     

Accuracy and convergence of a variational theory of nuclear matter for ν6 models

A number of higher-order terms in a previously proposed variational theory of nuclear matter are examined to establish the accuracy and convergence of the method. Numerical results for four semirealistic ν₆ model interactions, which include central, spin, isospin and tensor components, are reported. Although individual higher-order terms are substantial (> 1 MeV) they are much smaller than the corresponding lower-order terms, indicating good convergence of the theory. The higher-order terms also tend to cancel out, and three of the four ν₆ models show little net change in their E(k_F) curves, compared to previous work. The method is believed to have an error ?1 MeV for k_F ≦ 1.6 fm^?1.     

ΔE-effect due to magnetization rotation in nickel

The change in the elastic modulus Cγ = (C₁₁ ? C₂₂) of nickel due to stress induced rotation of the domain magnetic moments is predicted in terms of well-known material properties. Large stresses produce γ representation strain mixing terms Cγ,^ik which are also given.     

Regge extrapolation to the resonance region

The structure of dual amplitudes (beta functions) suggests that in non-exotic channels one should add to the usual Regge terms a second term which drops off as exp (?π Im α(s)) at large s but which is important for s?5 GeV². This “dual correction” multiplies the usual Regge imaginary part by an oscillating complex factor. With inclusion of such extra terms, it is possible to match πp amplitudes from phase-shift analyses significantly better than if the terms are omitted. The partial waves of a modified fit using the leading N, Δ, ?, f trajectories with a fixed-pole pomeron show much more of the correct resonant structure than do those of an unmodified fit.     

Second-order corrections to correlations in muon capture

Muon capture by a nucleus with an arbitrary spin is considered. Second-order terms in 1/M in the effective weak-interaction Hamiltonian are taken into account. New terms in the Hamiltonian associated with the nucleon-nucleus potential are found. A general expression for the angular distribution of neutrinos (recoil nuclei) is derived for polarized muons and oriented target nuclei. Second-order contributions to the amplitudes M _u (k) are obtained. This allows one to calculate second-order corrections to any integral and correlation characteristics in muon capture that are expressed in terms of M _u (k).     

Error compensation for mirror symmetry absolute test

A method is proposed to compensate intrinsic error in mirror symmetry absolute test. Because of the limitation of rotation times of flat A, intrinsic error of CNθ terms occurs in reconstructed wavefronts of flats A, B and C. If flat A is rotated to a new azimuthal position, and the wavefront difference between two measurements before and after rotation is calculated, the Zernike coefficients of CNθ terms can be obtained by solving coefficient equations due to rotation invariability of the form of Zernike polynomials in polar coordinates. Therefore, the intrinsic error of CNθ terms may be compensated. Because the amount of CNθ terms is infinite, the compensated terms are decided in terms of the balance between intrinsic error reduction and computational effort. Computer simulation proves the validity of the proposed method.     

Applications of reciprocity to non-linear extended thermodynamics kinetic equations

Reciprocity relations and integrability conditions can be used in non-linear extended irreversible thermodynamics to calculate forces and phenomenological coefficients uniquely in terms of parameters in kinetic equations derived from a model. One assumes a set of n even variables α_i and corresponding η = α_i, with an equation from the model for η_i. η-independent thermodynamic forces terms are assumed known. Comparison of powers of η in the model equation with corresponding powers in the canonical Onsager-Casimir formalism yields equations to determine all quantities in the latter save the higher η-dependence of entropy which is affected by uncertainties in measurement. By introducing a phenomenological ansatz, one can relate these higher entropy terms to corresponding terms in the model equation. A numerical illustration is made for a relaxing scalar structural parameter appropriate to a simple liquid.     

Strong coupling polaron theory and translational invariance

We develop a systematic, manifestly translation invariant, strong coupling theory for nonrelativistic Hamiltonians of the polaron type. As in earlier strong coupling theories, the position of the polarization well is a collective coordinate. The field is expanded in a set of basis functions centered about the well with three amplitudes deleted. A particle coordinate relative to the polarization center is introduced. The new coordinates are introduced using a point canonical transform leading to a Hermitian Hamiltonian, with properly normalized wavefunctions, and with a Jacobian that is evaluated in closed form. All subsequent approximations to the states are manifestly translation invariant. For the ground state the energy of the recoil terms to leading order depend on the coupling constant g as g^?4. The intrinsic part of the Hamiltonian determines the energy terms of order g⁴ and g⁰. An adiabatic canonical transformation is used to calculate all terms through order g^?4. The coefficients depend on the Green's function for the electron in a static potential well. We determine the first three terms in the inverse coupling constant expansion of the effective mass.     

Core hole satellites in Ni and Au Ni

The 2p core hole satellite structure in Ni and 5% Ni in Au are compared and discussed in terms of recent theoretical models. The large differences found for these two materials are explained in terms of the large differences in the Ni 3d band, and virtual bound state widths. The satellite structure for Au Ni is found to agree with the multiplet splitting of the free atom in a 2p⁵3d⁹ configuration.     

Intertwining operators and S matrix

The class of one-dimensional many-body systems related to semisimple Lie groups G is studied. The Hamiltonians of these systems are expressed in terms of Casimir operators (or, equivalently, Laplace-Beltrami operators on symmetric spaces) of underlying symmetry groups G. It turns out that the S matrix for all these problems is related to the intertwining operators for groups G. This connection provides immediately the functional form of the S matrix. Moreover, this connection allows one to prove that multiparticle S-matrix elements can be expressed in terms of two-particle ones.     

On the role of the Δ(1232) on the transverse nuclear response in the (e,e′) reaction

The transverse nuclear response to an electromagnetic probe which is limited to create (or destroy) a particle-hole (ph) or delta-hole (Δh) pair is analyzed. Correlations of the random phase approximation (RPA) type and self-energy insertions are considered. For RPA correlations we have developed a scheme which includes explicitly the Δ and the exchange terms. Self-energy insertions over ph and Δh bubbles are studied. Several residual interactions based on a contact plus a (π + ϱ)-meson exchange potential are used. All calculations are performed in non-relativistic nuclear matter. The main effect of the Δ is to reduce the intensity over the nuclear quasi-elastic peak. Exchange RPA terms are very important, while the terms with self-energy insertions depend strongly on the residual interaction employed. Our results are compared with data for ⁴⁰Ca at momentum transfer q = 410 and q = 550 MeV/c, where the longitudinal response is also briefly discussed.     

Wk structure of A SU(2)-level k from covariant construction of Kac-Moody algebras

The W_k structure underlying the transverse realization of affine SU(2) at level k is analyzed. The extension of the equivalence existing between the covariant and light-cone gauge realization of an affine Kac-Moody algebra to W_k algebras is given. Higher spin generators are extracted by the less singular terms in the operator product expansion of the parafermions constructed by means of the projection of the covariant on the light-cone gauge. These fields can be written in terms of only one free boson compactified on a circle.     

Exact asymptotic solution of the Della Sala-Görling integral equation for the exchange-only potential for Be-like atomic ions at large Z

Della Sala and Görling (DSG) have written an integral equation for the exchange-only potential Vx(r) in terms of the Dirac density matrix. Here, an exact asymptotic solution of this integral equation is presented, for the ground state of Be-like atomic ions, in terms of γ(r,r^′) plus the 2s HOMO orbital. In the large Z limit of such ions, the DSG integral equation corrects the asymptotic form −e²/r of Vx(r) by exponentially decaying terms. This amounts to setting the polarizability equal to zero.     

A strangeonium potential model with completeO(v 2/c 2) hyperfine splittings

We model the strangeonium system by numerically solving the Schrödinger equation with a Coulomb plus linear scalar confining potential. All hyperfine terms toO(v ²/c ²) are treated in detail; we show that neglect of spin-independent terms is unjustified. The model is fit to the ?(1019.6) andf′ (1516), and masses for excitedss states are predicted: the strangeonium parameters are contrasted with the values found in charmonium.     

Higher order solutions of Lieb-Liniger integral equation

We study higher order solutions of Lieb-Liniger integral equation for a one-dimensional δ-function Bose gas. By use of the power series expansion method, the integral equation is solved and the correction terms which improve the Bogoliubov theory are calculated analytically in the weak coupling regime. Physical quantities such as the ground state energy and the chemical potential are represented by a dimensionless parameter γ=c/ρ, where c is the interaction strength and ρ is the number density of particles while the quasi-momentum distribution function is expressed in terms of a dimensionless parameter λ=c/K, where K is the cut-off momentum.     

Optical and physical properties of different composition of InxSe1−x thin films

Thin film binary alloys of In_xSe_1−x (0.05?x?0.30) have been prepared by the thermal evaporation technique. The optical transmission and reflection spectrum of these films were measured in the range 300-1100 nm. Both refractive index, n and extinction coefficient k have been determined from transmission and reflection measurements in terms of Murmann's equations. The dispersion of the refractive index is discussed in terms of the single-oscillator Wemple-DiDomenico model. The width of band tail is determined and the optical absorption edge is described using the ‘non-direct transition’ model proposed by Tauc. Finally, the relationship between the optical gap and chemical composition in In_xSe_1−x amorphous system is discussed in terms of the average heat of atomization H_s and average coordination number N_c. The results of these calculations can be used rationalize the observed optical properties of these materials. Finally, the chemical bond approach has been also applied to interpret the decrease of the glass optical gap with increasing In content.