arXiv subjects
Publications and source records attributed to Z. Papp.
We studied the level shifts in the $K^- p$ system caused by the interplay of strong nuclear and long range Coulomb potentials. We observed a level rearrangement in the system and found that the $1s$ shift of kaonic hydrogen is in fact ``attractive''. In addition, we demonstrated that absorption in the strong antikaon-nucleon interaction does not destroy the level rearrangement.
We solve the Goldstone-boson-exchange (GBE) relativistic constituent quark model of light and strange baryons by using the Faddeev approach. The model reproduces the vacuum mass spectrum of light and strange baryons below $2$ GeV reasonably well. To test the sensitivity of the model to possible medium-induced effects, we vary the masses of the constituent quarks and the exchange bosons, the confinement strength, and the quark-meson coupling constant. In a parametric study, we consider a set of power law scaling relations for these parameters, including some motivated by constituent quark level current algebra relations. We find that the baryon spectrum is most sensitive to the quark-meson coupling constant, and generally observe a decrease in baryon mass with decreasing constituent quark mass. We qualitatively estimate the impact of these mass shifts on ideal-gas baryon yields and yield ratios. Absolute yields can change significantly already for mass shifts of a few $10$~MeV, whereas yield ratios are strongly modified only when the compared baryons have different constituent-quark-mass dependence.
The Feshbach-Villars version of the relativistic quantum mechanics can be extended for two-body systems in such a way that the center-of-mass motion is separated off. The procedure results in an equation of Feshbach-Villars-type in terms of the relative coordinate.
We propose method for studying relativistic spin-$1/2$ particles by solving the corresponding Feshbach-Villars equation. We have found that the Feshbach-Villars spin-$1/2$ equations can be formulated as spin-coupled Feshbach-Villars spin-$0$ equations, that results in a Hamiltonian eigenvalue problem. We adopted an integral equation formalism. The potential operators are represented in a discrete Hilbert space basis and the relevant Green's operator has been calculated by a matrix continued fraction.
The problem of a hydrogen atom in a strong magnetic field is a notorious example of a quantum system that has genuinely different asymptotic behaviors in different directions. In the direction perpendicular to the magnetic field the motion is quadratically confined, while in the direction along the field line the motion is a Coulomb-distorted free motion. In this work, we identify the asymptotically relevant parts of the Hamiltonian and cast the problem into a Lippmann-Schwinger form. Then, we approximate the asymptotically irrelevant parts by a discrete Hilbert space basis that allows an exact analytic evaluation of the relevant Green's operators by continued fractions. The total asymptotic Green's operator is calculated by a complex contour integral of subsystem Green's operators. We present a sample of numerical results for a wide range of magnetic field strengths.
A computational method is proposed to calculate bound and resonant states by solving the Klein-Gordon and Dirac equations for real and complex energies, respectively. The method is an extension of a non-relativistic one, where the potential is represented in a Coulomb-Sturmian basis. This basis facilitates the exact analytic evaluation of the Coulomb Green's operator in terms of a continued fraction. In the extension to relativistic problems, we cast the Klein-Gordon and Dirac equations into an effective Schr\"odinger form. Then the solution method is basically an analytic continuation of non-relativistic quantities like the angular momentum, charge, energy and potential into the effective relativistic counterparts.
We propose a solution method for studying relativistic spin-$0$ particles. We adopt the Feshbach-Villars formalism of the Klein-Gordon equation and express the formalism in an integral equation form. The integral equation is represented in the Coulomb-Sturmian basis. The corresponding Green's operator with Coulomb and linear confinement potential can be calculated as a matrix continued fraction. We consider Coulomb plus short range vector potential for bound and resonant states and linear confining scalar potentials for bound states. The continued fraction is naturally divergent at resonant state energies, but we made it convergent by an appropriate analytic continuation.
We re-examine the series of resonances found earlier in atomic three-body systems by solving the Faddeev-Merkuriev integral equations. These resonances are rather broad and line-up at each threshold with gradually increasing gaps, the same way for all thresholds and irrespective of the spatial symmetry. We relate these resonances to the Gailitis mechanism, which is a consequence of the polarization potential.
The Feshbach-Villars equations, like the Klein-Gordon equation, are relativistic quantum mechanical equations for spin-$0$ particles. We write the Feshbach-Villars equations into an integral equation form and solve them by applying the Coulomb-Sturmian potential separable expansion method. We consider bound-state problems in a Coulomb plus short range potential. The corresponding Feshbach-Villars Coulomb Green's operator is represented by a matrix continued fraction.
The inverse of an $\infty \times \infty$ symmetric band matrix can be constructed in terms of a matrix continued fraction. For Hamiltonians with Coulomb plus polynomial potentials, this results in an exact and analytic Green's operator which, even in finite-dimensional representation, exhibits the exact spectrum. In this work we propose a finite dimensional representation for the potential operator such that it retains some information about the whole Hilbert-space representation. The potential should be represented in a larger basis, then the matrix should be inverted, then truncated to the desired size, and finally inverted again. This procedure results in a superb low-rank representation of the potential operator. The method is illustrated with a typical nucleon-nucleon potential.
The fishbone potential of composite particles simulates the Pauli effect by nonlocal terms. We determine the $n-\alpha$ and $p-\alpha$ fish-bone potential by simultaneously fitting to the experimental phase shifts. We found that with a double Gaussian parametrization of the local potential can describe the $n-\alpha$ and $p-\alpha$ phase shifts for all partial waves.
The fishbone potential of composite particles simulates the Pauli effect by nonlocal terms. We determine the $\alpha-\alpha$ fishbone potential by simultaneously fitting to two-$\alpha$ resonance energies, experimental phase shifts and three-$\alpha$ binding energies. We found that essentially a simple gaussian can provide a good description of two-$\alpha$ and three-$\alpha$ experimental data without invoking three-body potentials.
A method is presented that allows to solve the Faddeev integral equations of the semirelativistic constituent quark model. In such a model the quark-quark interaction is modeled by a infinitely rising confining potential and the kinetic energy is taken in a relativistic form. We solve the integral equations in Coulomb-Sturmian basis. This basis facilitate an exact treatment of the confining potentials.
Microstructure changes during annealing of nano-crystalline silver and amorphous silicon multilayers (Ag/a-Si) have been studied by X-ray diffraction and transmission electron microscopy. The dc-magnetron sputtered Ag/a-Si multilayers remained stable even after annealing at 523K for 10h, and microstructural changes occurred only above 600K. The degradation of Ag/a-Si multilayers can be described by the increase of size of Ag grains, formation of grooves and pinholes at Ag grain boundaries and by the diffusion of silicon atoms through the silver grain boundaries and along the Ag/a-Si interfaces. This results in thinning of a-Si layers, and in formation of Ag granulates after longer annealing times.
Two body data alone cannot determine the potential uniquely, one needs three-body data as well. A method is presented here which simultaneously fits local or nonlocal potentials to two-body and three-body observables. The interaction of composite particles, due to the Pauli effect and the indistinguishability of the constituent particles, is genuinely nonlocal. As an example, we use a Pauli-correct nonlocal fish-bone type optical model for the $α-α$ potential and derive the fitting parameters such that it reproduces the two-$α$ and three-$α$ experimental data.
In quantum mechanics with minimal length uncertainty relations the Heisenberg-Weyl algebra of the one-dimensional harmonic oscillator is a deformed SU(1,1) algebra. The eigenvalues and eigenstates are constructed algebraically and they form the infinite-dimensional representation of the deformed SU(1,1) algebra. Our construction is independent of prior knowledge of the exact solution of the Schrödinger equation of the model. The approach can be generalized to the $D$-dimensional oscillator with non-commuting coordinates.
The Hamiltonian of a Coulomb plus polynomial potential on the Coulomb-Sturmian basis has an infinite symmetric band-matrix structure. A band matrix can always be considered as a block-tridiagonal matrix. So, the corresponding Green's operator can be given as a matrix-valued continued fraction. As examples, we calculate the Green's operator for the Coulomb plus linear and quadratic potential problems and determine the energy levels.
The two-body Coulomb Hamiltonian, when calculated in Coulomb-Sturmian basis, has an infinite symmetric tridiagonal form, also known as Jacobi matrix form. This Jacobi matrix structure involves a continued fraction representation for the inverse of the Green's matrix. The continued fraction can be transformed to a ratio of two $_{2}F_{1}$ hypergeometric functions. From this result we find an exact analytic formula for the matrix elements of the Green's operator of the Coulomb Hamiltonian.