Three-body calculation of the 1s1s level shift in kaonic deuterium

The first calculation of kaonic deuterium $1s$ level shift using Faddeev-type equations was performed. The obtained results were compared with commonly used approximate approaches.Comment: The version accepted in Phys. Lett.

Isospin mixing effects in low-energy KˉN−πΣ\bar{K}N - \pi \Sigma interaction

New strong coupled-channel $\bar{K}N - \pi \Sigma$ potential, reproducing all existing experimental data and suitable for using in an accurate few-body calculations, is constructed. Isospin breaking effects of direct inclusion of the Coulomb interaction and using of physical masses in calculations are investigated. The $1 s$ level shift and width of kaonic hydrogen, consistent with the scattering data, was obtained and the corresponding exact strong $K^- p$ scattering length was calculated. One- and two-pole form of $\Lambda(1405)$ resonance was considered.Comment: 24 pages, 5 tables, 4 figures; one sentence was changed and one reference adde

Search for long-lived states in antiprotonic lithium

The spectrum of the (L_i^3 + p-bar + 2e) four-body system was calculated in an adiabatic approach. The two-electron energies were approximated by a sum of two single-electron effective charge two-center energies as suggested in [6]. While the structure of the spectrum does not exclude the existence of long-lived states, their experimental observability is still to be clarified

KˉNN\bar{K}NN quasi-bound state and the KˉN\bar{K}N interaction: coupled-channel Faddeev calculations of the KˉNN−πΣN\bar{K}NN - \pi \Sigma N system

Coupled-channel three-body calculations of an $I=1/2$, $J^{\pi}=0^-$ $\bar{K}NN$ quasi-bound state in the $\bar{K}NN - \pi \Sigma N$ system were performed and the dependence of the resulting three-body energy on the two-body $\bar{K}N - \pi \Sigma$ interaction was investigated. Earlier results of binding energy $B_{K^-pp} \sim 50 -70$ MeV and width $\Gamma_{K^-pp} \sim 100$ MeV are confirmed [N.V. Shevchenko {\it et al.}, Phys. Rev. Lett. {\bf 98}, 082301 (2007)]. It is shown that a suitably constructed energy-independent complex $\bar{K}N$ potential gives a considerably shallower and narrower three-body quasi-bound state than the full coupled-channel calculation. Comparison with other calculations is made.Comment: 22 pages, 7 figures, 4 tables; minor corrections, accepted for publication in Phys. Rev.

NN potentials from inverse scattering in the J-matrix approach

An approximate inverse scattering method [7,8] has been used to construct separable potentials with the Laguerre form factors. As an application, we invert the phase shifts of proton-proton in the $^1S_0$ and $^3P_2-^3F_2$ channels and neutron-proton in the $^3S_1-^3D_1$ channel elastic scattering. In the latter case the deuteron wave function of a realistic $np$ potential was used as input.Comment: LaTex2e, 17 pages, 3 Postscript figures; corrected typo

Local realizations of contact interactions in two- and three-body problems

Mathematically rigorous theory of the two-body contact interaction in three dimension is reviewed. Local potential realizations of this proper contact interaction are given in terms of Poschl-Teller, exponential and square-well potentials. Three body calculation is carried out for the halo nucleus 11Li using adequately represented contact interaction.Comment: submitted to Phys. Rev.

Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states

If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Green's operator can be constructed in terms of a continued fraction. As an illustrative example we discuss the Coulomb Green's operator in Coulomb-Sturmian basis representation. Based on this representation, a quantum mechanical approximation method for solving Lippmann-Schwinger integral equations can be established, which is equally applicable for bound-, resonant- and scattering-state problems with free and Coulombic asymptotics as well. The performance of this technique is illustrated with a detailed investigation of a nuclear potential describing the interaction of two $\alpha$ particles.Comment: 7 pages, 4 ps figures, revised versio