V. I. Kukulin

Detailed study of the cluster structure of light nuclei in a three-body model

Abstract A model for three composite particles is used to study the ground state of the 6 Li nucleus making allowance for the Pauli principle. The relevant wave functions are found by solving a set of two-dimensional Hill-Wheeler integral equations on the quadrature Chebyshev grid. A nonorthogonal many-dimensional gaussian basis was taken to be the expansion basis, so that the wave functions obtained could be presented in the form of a superposition of gaussian functions convenient for applications. Six models (potentials) of the interaction in the NN and Nα subsystems including the central, spin-orbit, and tensor forces are studied. The Coulomb interaction is treated exactly (i.e. not in a perturbative manner). The wave functions obtained are used to analyze a broad spectrum of experimental data, including the 6 Li ground state. The applied model, which contains not a single free parameter, has been shown to permit a simultaneous description of the following principal parameters of the 6 Li ground state: the binding energy, the rms charge radius, the αd spectroscopic factor, the asymptotic constant of the αd channel, the charge form factor F ch ( q 2 ), the magnetic elastic form factor F M1 ( q 2 ) (up to q 2 ≲ 2.5 fm −2 ), the form factors of the quasielastic scattering reactions ( x , xα ) and ( x , x d), and the cross section for the diffractive scattering of protons from the 6 Li nucleus with E p = 600 MeV and E p = 1 GeV in a large range of scattering angles.

Detailed study of the cluster structure of light nuclei in a three-body model: (II). The spectrum of low-lying states of nuclei with A = 6

Abstract The three-body α + 2N model developed in our earlier works to describe the ground states of the A = 6 nuclei is generalized here to describe the spectrum of the low-lying states of these nuclei. The levels of the nuclei are shown to be differently sensitive to the various Nα interaction components, whence some conclusions concerning the true form of the Nα interaction are drawn. The geometric structure of the 6 Li and 6 He ground states is studied in detail. A significant contribution of the stretched cigar-shaped three-particle configuration NαN with an α-particle between two nucleons has been found. The wave functions of the ground and excited states of the A = 6 nuclei are tabulated. The wave functions found have been tested carefully using numerous experimental data.

A microscopically substantiated local optical potential for α-α- scattering

Abstract A deep l -independent local potential of the Woods-Saxon form for the description of the energy dependence of all α - α phase shifts measured is proposed. Wave functions in the α - α overlap region have the oscillator from 4S, 4D etc. The range of the S-phase shift variation equals 3 π . Application of the approach proposed to the 16 O - 16 O and NN-systems is discussed.

A stochastic variational method for few-body systems

A detailed description of the stochastic variational method (SVM) suggested recently for solving the few-body problem in quantum mechanics is given. Results obtained with the SVM in a randomized gaussian basis are compared with the analogous results of other authors. It is shown that the matrix elements of the Hamiltonian for all conventional forms of the N-N potentials (and for the Coulomb potential too) in the randomized gaussian basis are evaluated fully analytically. The asymptotic behaviour of the variational functions obtained is studied.

Detailed study of the cluster structure of light nuclei in a three-body model (IV). Large space calculation for A = 6 nuclei with realistic nuclear forces☆

Abstract The structure of all low-lying states for the A = 6 nuclei ( 6 He, 6 Li, 6 Be) is described in detail in terms of a realistic three-body α + 2N model using the full Reid soft-core NN potential (RSC), the accurate Nα interaction potential with odd-even splitting in central and spin-orbital components and the exact RGM Pauli projectors onto forbidden 0s-states in five-nucleon subsystems. The model thus includes all necessary types of forces: central, spin-orbital, tensor, Coulomb and partial exchange. The new refined version of the model gives a good agreement with experiment without any free parameters for all static characteristics of A = 6 nuclei (except for the 6 Li quadrupole moment), for the 6 Li electromagnetic form factors, for the Coulomb displacements of the 0 + 1 and 2 + 1 levels of three 6 He, 6 Li, 6 Be nuclei, for the 6 He β-decay probability and for the γ-widths of the 6 Li excited states. An analysis of the geometric shapes of low-lying states of 6 He, 6 Li, 6 Be nuclei is given.

The orthogonal projection method in scattering theory

Abstract This work gives a detailed account of the orthogonal projection method in the theory of two- and three-body scattering, which is based on the employment of orthogonal projecting pseudopotentials. The method is applied to a number of physical problems, of which the following the most important: the improvement of convergence and the rearragement of Born series to make them convergent at low energies in the presence of bound states in a system, as well as the consideration of the Pauli exclusion principle in the scattering of composite particles and in the integral theory of direct nuclear reactions. The properties of eigenvalues of kernels of the equations obtained are investigated and the conditions for the convergence of their iterations are derived. For the three-body problem, the general case of three different particles is considered, as well as two particular cases, namely, two particles in the field of a heavy core and three identical particles. The proven theorems are illustrated by numerical examples. Other useful applications of the proposed approach are listed and discussed, in particular, those in solid-state physics and in the theory of electromagnetic transitions. The approach suggested is compared with those of the other authors and the prospects of using the developed formalism are discussed.

Microscopically substantiated local optical potentials for scattering of light nuclei

Abstract A potential approach to the scattering of light nuclei is analysed in detail. It is shown that the deep optical potentials we introduced earlier, for the scattering of light clusters, are essentially phase-equivalent local potentials for the tedious exchange kernels of the resonating-group method and lead, practically, to the same wave functions. We demonstrate that these deep potentials involve the shell-model states of a system, forbidden by the Pauli principle, as their own bound states. Requirements for optical potentials and for optical wave functions of light nuclei following from the properties of these forbidden states have been formulated. The supermultiplet and even-odd l-splitting of optical potentials is investigated. The concrete systems α-α, α-t, t-3He and α-d (optical potentials, etc.) are investigated. We also briefly discuss the optical potentials for the scattering of heavy ions such as16O-16O and the relationship between our deep optical potentials and the commonly used shallow phenomenological potentials containing the repulsive core.

New mechanism for intermediate- and short-range nucleon-nucleon interaction

For the intermediate- and short-range part of the nucleon-nucleon interaction a new approach is suggested based on the formation of a symmetric six-quark bag in the state |(0s)6[6]X,L = 0 dressed due to strong coupling to π, σ and ρ fields (dressed bag). This new mechanism offers both a strong intermediate-range attraction which replaces the effective σ-exchange (or excitation of two isobars in the intermediate state) in traditional force models and also short-range repulsion. Part of the intermediate and the full long-range contribution to the nucleon-nucleon force is also in this approach described by the Yukawa meson-exchange mechanism. A simple illustrative model is developed which demonstrates clearly how well the suggested new mechanism can reproduce the NN data.

WAVE FUNCTIONS FOR MIXED CONFIGURATIONS AND THE RACAH ALGEBRA OF SU(4).

Abstract A new method of construction of many-nucleon wave functions with a given Young tableau for two unfilled shells is described. The Racah algebra of the group SU(4) is employed for obtaining the many-particle coefficients of fractional parentage as well as calculations of matrix elements of one- and two-particle operators.

Detailed study of the cluster structure of light nuclei in a three-body model: (III). Electromagnetic structure of 6Li

Abstract The multicluster dynamic model with the Pauli projection (MDMP) for treating light nuclei, developed earlier, is used to study in detail the 6 Li electromagnetic structure including all the measured elastic and inelastic, transverse and longitudinal, isoscalar and isovector electromagnetic form factors of the nucleus and to make some predictions concerning other, not yet measured, form factors. The model is also used to calculate all the measured radiation widths Γ γO of the excited 6 Li * states. A proper description has been obtained for most of the known electromagnetic form factors of the nucleus. The reasons for disagreement with experimental data in the case of large momentum transfers in the M1 form factors, both elastic and inelastic, are discussed. The elastic CO form factor of 6 Li and, probably, of other light nuclei in the region of the secondary maximum is shown to be defined, to a very great extent, by the behaviour of the α-particle charge form factor in the region of its secondary maximum. The radiation widths of the 3 + 0, 2 + 0, and 1 + 0 levels have been found to be highly sensitive to minor impurities of the wavefunction components with higher orbital moments for the excited states, as well as the ground state, of 6 Li. The Siegert theorem is shown to be of great importance when studying the probabilities of transverse electromagnetic transitions. The copious results obtained by the present authors, as well as elsewhere, concerning the diverse aspects of the behaviour of six-nucleon system in the strong, weak, and electromagnetic processes are used to formulate the concept of using the given system as an extremely convenient theoretical laboratory in nuclear physics. The relevant proposals concerning future experiments are formulated.