I. N. Filikhin

Investigation of low-energy scattering in the nnpp system on the basis of differential equations for Yakubovsky components in configuration space

The s-wave differential equations for the Yakubovsky components characterizing the nnpp system have been solved by the method of cluster reduction. Two-cluster scattering at energies below the three-particle threshold in the singlet and triplet spin states has been considered. The MT I–III potential model has been used to simulate nucleon-nucleon interaction, and the Coulomb interaction between the protons has been taken into account. The singlet and triplet scattering lengths have been calculated for proton interaction with the triton (3H) and for neutron interaction with the 3He nucleus, and the deuteron-deuteron scattering length has also been determined. The low-energy behavior of the phase shifts and inelasticity factors in the corresponding scattering channels has been investigated. The features of the 0+ resonance in the 4He nucleus have been determined.

α8Be cluster model for the 0 2 + resonance in the 12C nucleus

The 02+ resonance in the 12C nucleus is treated on the basis of the α+8Be two-cluster model. An equation for the function describing the relative motion of the clusters is derived by using the s-wave differential Faddeev equations for the 3α system and by relying on the simplest version of the resonating-group method. A phenomenological potential is taken to simulate the pair αα interaction. A three-body potential binding three alpha particles together gives rise to a resonance in two-cluster α+8Be scattering. The calculated resonance features and the calculated parameters of the wave function of the system are compared with the results obtained by other authors.

Solving the differential Yakubovsky equations for p3He scattering by the cluster-reduction method

The cluster-reduction method has been used to solve numerically the differential equations for the s-wave Yakubovsky components in the nppp system. Proton scattering on a 3He nucleus has been considered for energies below the three-body threshold in the singlet and triplet spin states of the system. Nucleon-nucleon interaction has been simulated by the MT I–III potential, and the Coulomb interaction between the protons has been taken into account. Effective equations that describe the relative motion of clusters have been derived. The low-energy behavior of phase shifts has been analyzed. The values of 1A=8.2 fm and 3A=7.7 fm have been obtained for, respectively, the singlet and triplet scattering lengths. The calculated phase shifts agree well with experimental data.

Microscopic calculation of low-energy deuteron-deuteron scattering on the basis of the cluster-reduction method

The cluster-reduction method is used to solve numerically the differential equations for the s-wave Yakubovsky components characterizing the nnpp system in the S=2 spin state. Elastic deuteron-deuteron scattering is analyzed for the case where nucleon-nucleon interaction is simulated by the MT I–III potentials. Effective equations describing the relative motion of clusters is derived. The scattering length and phase shifts for low-energy deuteron-deuteron scattering are calculated.

ΛΛ 6 He and Λ 9 Be systems in the three-body cluster model treated on the basis of differential Faddeev equations

AbstractThe ΛΛ6He and Λ9Be hypernuclei are treated as the S=0, T=0 (for the former) and S=1/2, T=0 (for the latter) bound states of the three-cluster systems ΛΛα and Λαα, respectively. The cluster-reduction method is used to solve the s-wave differential Faddeev equations for these systems. On the basis of the MT I–III model, the ΛΛ interaction potential is specified in the form

Calculation of the binding energy and of the parameters of low-energy scattering in the Λnp system

V_{\Lambda \Lambda } = \frac{2}{3}V_{NN}

16O nucleus in the 4α cluster model

. Phenomenological potentials are used to describe Λα and αα interactions. The binding energies of the ΛΛ6He and Λ9Be hypernuclei and the parameters of low-energy Λ-hyperon and α-particle scattering on a Λ5He hypernucleus are calculated. It is shown that the proposed ΛΛ interaction potential makes it possible to reproduce faithfully the binding energy of the ΛΛ6He hypernucleus and that scattering in the ΛΛ5He system is similar to neutron scattering on a deuteron.

Ground state of the 4a + ? nucleus within the 4 a +? cluster model

The Λ13C hypernucleus is treated as a (1/2)+ bound state of the Λααα system. The s-wave model is used on the basis of differential equations for the corresponding Yakubovsky components. No account is taken of 2+2 clustering in the system. Phenomenological potentials are used to simulate the αα and αΛ interactions. The system as a whole is bound owing to the additional potential of three-body interaction between the alpha-particle clusters. The differential equations for the Yakubovsky components are solved numerically by the cluster-reduction method. The binding energies are calculated for the ground and the first excited state of the Λ13C hypernucleus. It is shown that the dominant type of clustering in the system is (Λαα)α.