S. L. Yakovlev

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.

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 n

Ground state of the 4α + Λ nucleus within the 4α+Λ cluster model

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

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

n. 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.

Solving the differential Yakubovsky equations for p 3 He scattering by the cluster-r

The cluster-reduction method is used to solve the differential Faddeev equations for S=1/2, T=0 and S=3/2, T=0 spin-isospin states of the Λnp system in the s-wave approximation. The NN interaction is simulated on the basis of the MT I–III potential model, and the ΛN potential is set to VΛN=VNN/2. This simple option makes it possible to reproduce faithfully the binding energy of the hypertriton Λ3H. The doublet and quadruplet Λd scattering lengths and the low-energy phase shifts are calculated. It is shown that the effective-range approximation is applicable to the cases of doublet and quadruplet scattering.

16 O nucleus in the 4a cluster model

The s-wave bound state of the 4α+Λ system is investigated. The relevant solution to the Schrödinger equation is expanded in the basis formed by the eigenfunctions of Hamiltonian for the 4α subsystem. Differential equations for Yakubovsky components are employed to calculate basis functions. Phenomenological potentials for αα and αΛ interactions are used. In the 4α system, additional three-particle potentials for the interaction between α clusters are introduced in such a way as to reproduce the experimental data on the binding energies, the root-mean-square radii, and the charge form factors for the 12C and the 16O nucleus. The binding energy, the root-mean-square radius, and the hyperon distribution in the ground state of the Λ17O nucleus are calculated. The results of the calculations are in good agreement with those obtained on the basis of the 16O+Λ two-particle model with the phenomenological Woods-Saxon potential.