Faddeev calculations are reported for 5 ΛΛ H, 5 ΛΛ He and 6 ΛΛ He in terms of two Λ hyperons plus 3 H, 3 He, 4 He nuclear clusters respectively, using ΛΛ central potentials considered in past non-Faddeev calculations of 6 ΛΛ He. The convergence with respect to the partial-wave expansion is studied, and comparison is made with some of these ΛΛ hypernuclear calculations. The ΛΛ − ΞN mixing effect is briefly discussed.

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A three-dimensional model of InAs/ GaAs quantum rings based on a single sub-band approach with an energy dependence of the electron effective mass is used to describe the capacitance-voltage spectroscopy by Lorke et al. ͓Phys. Rev. Lett. 84, 2223 ͑2000͔͒. The confinement states energy problem is solved numerically using the finite elements method. Observed deviation of an electron effective mass from the bulk value is explained by the nonparabolic effect. Additional energy of the election ground state due to an external magnetic field is estimated and compared with the capacitance-voltage data. The model is also applied to describe the far-infrared measurements.

The Faddeev-Yakubovsky equations in configuration space are applied to the study of the four-body system α comprising three distinct particles. We use the OBE-simulating potential of the NSC97 model for the and interactions. For the α and α interactions we use phenomenological potentials. The Faddeev-Yakubovsky equations for the system and its subsystems are numerically solved in s-wave approach by the cluster reduction method. We evaluate the binding energy of the hypothetical multi-strangeness nucleus 7 0 He. We find that the existence of the ground state of this nucleus depends strongly on the behavior of the α potential at small distances. In particular, for a Woods-Saxon type potential having no repulsive core, the system can be bound.

The Faddeev equations in configuration space are used to study the 12C nucleus considered as the 3α cluster system. The model includes a phenomenological (Ali–Bodmer) pair potential having s, d and g partial wave components, a three-body potential and takes into account the Coulomb interaction. The range parameter of the three-body potential is fixed by adjusting the position of the diffraction minimum of the 12C elastic form factor. To choose this parameter, we apply an s-wave model that allows us to reproduce well observed characteristics of the 0+1 and 0+2 states. The model must be supplemented by the assumption of a distortion in the charge density of an α cluster inside the 12C nucleus. The calculations of the energies of several low-lying levels of 12C reveal unnaturally large contributions from the higher partial waves of the αα potential. We did not find the additional broad 0+ resonance which was recently reported (Kurokawa C and Kato K 2005 Phys. Rev. C 76 021301-1). The calculated resonance energies for the 0+3 and 0+4 states are in satisfactory agreement with the experimental data.

A new computational method for solving the configuration-space Faddeev equations for three-nucleon systems has been developed. This method is based on the spline decomposition in the angular variable and a generalization of the Numerov method for the hyperradius. The s-wave calculations of the inelasticity and phase shift as well as breakup amplitudes for n-d and p-d breakup scatterings for lab energies 14.1 and 42.0 MeV were performed with the Malfliet-Tjon I-III potential. In the case of n-d breakup scattering the results are in good agreement with those of the benchmark solution [J. L. Friar, B.

Configuration space Faddeev equations are applied for studying the 9ΛBe hypernucleus in the ααΛ cluster model. To describe αα and αΛ interactions, various phenomenological potentials are used. Contributions to the binding energy of the ground state coming from higher partial waves of the nuclear interactions are studied. The core effect of the nuclear αα potential is also considered.

We evaluate the mass polarization term of the kinetic-energy operator for different three-body nuclear AAB systems by employing the method of Faddeev equations in configuration space. For a three-boson system this term is determined by the difference of the doubled binding energy of the AB subsystem 2E 2 and the three-body binding energy E 3 (V AA = 0) when the interaction between the identical particles is omitted. In this case: |E 3 (V AA = 0)| > 2 |E 2 |. In the case of a system complicated by isospins(spins), such as the kaonic clusters K − K − p and ppK − , the similar evaluation is impossible. For these systems it is found thatA model with an AB potential averaged over spin(isospin) variables transforms the later case to the first one. The mass polarization effect calculated within this model is essential for the kaonic clusters. Besides we have obtained the relation |E 3 | ≤ |2E 2 | for the binding energy of the kaonic clusters.Keywords Mesic nuclei · Mass polarization · Faddeev equation · Nucleon-kaon interactions 1 IntroductionThe mass polarization effect of the kinetic-energy operator is well known in atomic physics [1,2]. The kinetic energy operator in the Schrödinger equation for an Nelectron atomic system with a finite nuclear mass M in the centre-of-mass coordinate system is comprised of two parts: the kinetic energy term related to the introduction of the reduced mass and the mass polarization term (MPT) −h 2 M i