V. M. Suslov

0+ states of the 12C nucleus : the Faddeev calculation in configuration space

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 prediction for the binding energy of the 7ΛHe hypernucleus

P-shell A = 7 hypernuclei are considered in the cluster 5ΛHe + N + N model. The folding procedure using the OBE simulating (NSC97f) model for ΛN potential and various αΛ potentials are applied to construct the 5ΛHe–N interaction. Configuration space Faddeev calculations are performed for the hyperon binding energy of the and hypernuclei. The new predicted value for BΛ(7ΛHe) is 5.35 MeV. This value was obtained with the 6ΛHe(2−) excitation energy equal to 0.26 MeV. Since the 2− state of 6ΛHe has not yet been observed, the 6ΛHe(2−) excitation energy was chosen to reproduce the experimental value of the excitation energy by the adjustment of the 5ΛHe–N effective potential. Our results are compared with those of Hiyama et al (1996 Phys. Rev. C 53 2075; 1999 Phys. Rev. C 59 2351).

Cluster calculation for 9ΛBe hypernucleus

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.

Three-body calculations for the K − pp system within potential models

We present three-body nonrelativistic calculations within the framework of a potential model for the kaonic cluster K − pp using two methods: the method of hyperspherical harmonics in the momentum representation and the method of Faddeev equations in configuration space. To perform numerical calculations, different NN and antikaon–nucleon interactions are applied. The results of the calculations for the ground-state energy for the K − pp system obtained by both methods are in reasonable agreement. Although the ground-state energy is not sensitive to the pp interaction, it shows very strong dependence on the K − p potential. We show that the dominant clustering of the system in the configuration Λ (1405) + p allows us to calculate the binding energy to good accuracy within a simple cluster approach for the differential Faddeev equations. The theoretical discrepancies in the binding energy and width for the K − pp system related to the different pp and K − p interactions are addressed.

Spectroscopy of the Λ7He nucleus in a three-cluster model

The Λ7He hypernucleus is considered within the Λ5He + n + n cluster model. The hyperon—nucleon interaction is described by a one-boson-exchange potential that is constructed on the basis of the NSC97f model. Phenomenological potentials are used to describe the αΛ and αN interactions. For the Λ5Hen interaction, use is made of the folding-model potential. The calculations of the hyperon binding energy in the ground state of the Λ7He hypernucleus on the basis of Faddeev equations in configuration space yield a result (5.35 MeV) that agrees well with preliminary experimental data (5.4 MeV). The problem of calculating the hyperon binding energy within the three-body approach is discussed. In calculating the energy spectrum of Λ7He, use is made of a version of the method of analytic continuation in the coupling constant. Low-lying excited states of this nucleus can be classified as an analog of the corresponding states of the 6He nucleus with allowance for the clustering of the Λ5He+n+n system in the 6He(Jπ)+Λ(s) form.

Low-lying resonances of 9ΛBe: Faddeev calculation with Padé-approximants

Configuration space Faddeev equations are applied to describe the 9 Λ Be hypernucleus in the αα Λ cluster model. For calculation of resonance state energies a variant of the method of analytical continuation in coupling constant is used. To realize this method, an auxiliary three-body potential is added to the Hamiltonian of the equations. A proper choice of strength parameter of the potential converts a resonance state into a bound state and an energy trajectory is obtained by variations of this parameter. To fulfill analytical continuation of this trajectory as a function of the strength parameter onto the complex plane, the Pade approximation is used. Spectrum of low-lying resonances is calculated with two α Λ phenomenological potentials. We predict existence of the 0 + 2 and 4 + 1 virtual states as well as the 2 + 2 resonance state near by the αα Λ threshold. The Be 8 ( L + ) + Λ ( s -wave ) configuration for description of the 9 Λ Be ground band is discussed.

An α-cluster model for Λ 9 Be spectroscopy

An α-cluster model is applied to study low-lying spectrum of the Λ9Be hypernucleus. The three-body ααΛ problem is numerically solved by the Faddeev equations in configuration space using phenomenological pair potentials. We found a set of the potentials that reproduces experimental data for the ground state (1/2+) binding energy and excitation energy of the 5/2+ and 3/2+ states, simultaneously. This set includes the Ali-Bodmer potential of the version “e” for αα and modified Tang-Herndon potential for αΛ interactions. The spin-orbit αΛ interaction is given by modified Scheerbaum potential. Low-lying energy levels are evaluated applying a variant of the analytical continuation method in the coupling constant. It is shown that the spectral properties of Λ9Be can be classified as an analog of 9Be spectrum with the exception of several “genuine hypernuclear states”. This agrees qualitatively with previous studies. The results are compared with experimental data and new interpretation of the spectral structure is discussed.

Bound state of the αΛΛΞ0 system

The Faddeev–Yakubovsky equations in configuration space are applied to the study of the four-body system αΛΛΞ comprising three distinct particles. We use the OBE-simulating potential of the NSC97 model for the ΛΞ and ΛΛ interactions. For the Ξα and Λα 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 . We find that the existence of the ground state of this nucleus depends strongly on the behavior of the Ξα potential at small distances. In particular, for a Woods–Saxon type potential having no repulsive core, the system can be bound.

On Mass Polarization Effect in Three-Body Nuclear Systems

The mass polarization effect is considered for different three-body nuclear AAB systems having a strongly bound AB and unbound AA subsystems. We employ the Faddeev equations for calculations and the Schrödinger equation for analysis of the contribution of the mass polarization term of the kinetic-energy operator. For a three-boson system the mass polarization effect is determined by the difference of the doubled binding energy of the AB subsystem