An economical method to calculate eigenvalues of the Schroedinger Equation

The method is an extension to negative energies of a spectral integral equation method to solve the Schroedinger equation, developed previously for scattering applications. One important innovation is a re-scaling procedure in order to compensate for the exponential behaviour of the negative energy Green's function. Another is the need to find approximate energy eigenvalues, to serve as starting values for a subsequent iteration procedure. In order to illustrate the new method, the binding energy of the He-He dimer is calculated, using the He-He TTY potential. In view of the small value of the binding energy, the wave function has to be calculated out to a distance of 3000 a.u. Two hundred mesh points were sufficient to obtain an accuracy of three significant figures for the binding energy, and with 320 mesh points the accuracy increased to six significant figures. An application to a potential with two wells separated by a barrier, is also made.Comment: 19 pages, 3 figures, submitted to Eur. J. Phy

Two-proton correlation function: a gentle introduction

The recent COSY-11 collaboration measurement of the two-proton correlation function in the pp -> ppeta reaction, reported at this meeting [1], arouse some interest in a simple theoretical description of the correlation function. In these notes we present a pedagogical introduction to the practical methods that can be used for calculating the correlation function.Comment: Prepared for the proceedings of the Symposium on Meson Physics at COSY-11 and WASA-at-COSY, Krakow, Poland, 17-22 June 200

Experimental proton-proton correlation function derived for the pp -> ppeta reaction

Based on the high statistics data from the pp -> ppX reaction measured by the COSY-11 collaboration [1] we have derived a two-proton correlation function for the production of the ppeta and pp+pions systems. The measured correlation function normalized to the value simulated for a point-like source was compared with a theoretical prediction in order to estimate the size of the reaction volume.Comment: Talk given at the Symposium on Meson Physics at COSY-11 and WASA-at-COSY Krakow, Poland, 17-22 June 200

Energy level displacement of the excited nl state of pionic hydrogen

The energy level displacements of the excited nl states of pionic hydrogen and the contribution of the ns -> 1s transitions and the (pi^-p)_Coul -> 1s transitions of the pi^-p pair, coupled by the attractive Coulomb field in the S-wave state with a continuous energy spectrum, to the shift of the energy level of the ground state of pionic hydrogen, caused by strong low-energy interactions, are calculated within a quantum field theoretic, relativistic covariant and model-independent approach developed in nucl-th/0306047.Comment: 18 pages, no figures, latex, text is revised, references are adde

Phenomenology of pp->pp eta reaction close to threshold

The recent high statistics measurement of the pp -> pp eta reaction at an excess energy Q=15.5 MeV has been analysed by means of partial wave decomposition of the cross section. Guided by the dominance of the final state 1S0 pp interaction (FSI), we keep only terms involving the FSI enhancement factor. The measured p-p and p-eta effective mass spectra can be well reproduced by lifting the standard on-shell approximation in the enhancement factor and by allowing for a linear energy dependence in the leading 3P0->1S0,s partial wave amplitude. Higher partial waves seem to play only a marginal role

On kaonic hydrogen. Quantum field theoretic and relativistic covariant approach

We study kaonic hydrogen, the bound K^-p state A_(Kp). Within a quantum field theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic hydrogen in terms of the amplitude of K^-p scattering for arbitrary relative momenta. The amplitude of low-energy K^-p scattering near threshold is defined by the contributions of three resonances Lambda(1405), Lambda(1800) and Sigma^0(1750) and a smooth elastic background. The amplitudes of inelastic channels of low-energy K^-p scattering fit experimental data on near threshold behaviour of the cross sections and the experimental data by the DEAR Collaboration. We use the soft-pion technique (leading order in Chiral Perturbation Theory) for the calculation of the partial width of the radiative decay of pionic hydrogen A_(pi p) -> n + gamma and the Panofsky ratio. The theoretical prediction for the Panofsky ratio agrees well with experimental data. We apply the soft-kaon technique (leading order in Chiral Perturbation Theory) to the calculation of the partial widths of radiative decays of kaonic hydrogen A_(Kp) -> Lambda^0 + gamma and A_(Kp) -> Sigma^0 + gamma. We show that the contribution of these decays to the width of the energy level of the ground state of kaonic hydrogen is less than 1%.Comment: 33 pages, 1 figure, latex, References are adde

Effective range function below threshold

We demonstrate that the kernel of the Lippmann-Schwinger equation, associated with interactions consisting of a sum of the Coulomb plus a short range nuclear potential, below threshold becomes degenerate. Taking advantage of this fact, we present a simple method of calculating the effective range function for negative energies. This may be useful in practice since the effective range expansion extrapolated to threshold allows to extract low-energy scattering parameters: the Coulomb-modified scattering length and the effective range.Comment: 14 pages, 1 figur

Do we understand the ηN\eta N interaction from the near threshold η\eta photoproduction on the deuteron?

The effects of final state interaction in incoherent $\eta$ photoproduction on deuteron are studied within a three-body approach including a realistic $NN$ potential. The results are compared with available data, and differences with other theoretical predictions are analyzed. The role of the $\eta N$ interaction and the possibility of extracting the $\eta N$ scattering parameters from this reaction are discussed.Comment: 9 pages revtex including 6 ps-figure