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🗀 Archive 2010-2015

Department of Structure of Atomic Nuclei

- We present a phase-space representation of quantum state vectors for two-cluster systems. Density distributions in the Fock-Bargmann space are constructed for bound and resonance states of
^{6;7}Li and^{7;8}Be, provided that all these nuclei are treated within a microscopic two-cluster model. The input parameters of the model and nucleon-nucleon potential were selected to optimize description of the internal structure of clusters and to reproduce position of the ground state with respect to the two-cluster threshold. The dominant two-cluster partition of each nucleus was taken into consideration. The density distribution in the phase space is compared with those in the coordinate and momentum representations. Bound states realize themselves in a compact area of the phase space, as also do narrow resonance states. We establish the quantitative boundaries of this region in the phase space for the nuclei under consideration. Quantum trajectories are demonstrated to approach their classical limit with increasing energy.*Yu.A. Lashko, G.F. Filippov, V.S. Vasilevsky* - General properties of resonance states of light nuclei that disintegrate into three cluster particles and do not disintegrate into two particles are studied in terms of a model that employs a basis of hyperspherical functions and thus provides implementing proper boundary conditions. It is established, that the increase of coupling between channels leads to the decrease of resonance energy. At certain values of the constant, responsible for coupling of channels, resonance states transform into bound states. It is shown, that narrow resonance states can exist with weak and strong coupling between channels. As a rule, energy and width of resonance states are decreasing when number of open channels is increased. There is large probability, as is established, to observe super narrow resonance state with large number of open channels. It is also demonstrated, that resonance states are formed and decay only in very restricted number of channels of three-cluster continuum. The simple model reproduces general properties of three-cluster systems, which were obtained in realistic three-cluster model.
*V.S. Vasilevsky*

- Influence of the Pauli principle on the relative motion of light neutron-rich nuclei in their collision is investigated within the microscopic method - an algebraic version of resonating-group-method - using as an example
^{6}He+^{4}He nuclear system. Antisymmetrization effects related to the kinetic energy of the relative motion of colliding nuclei are analyzed. The influence of the Pauli principle on the kinetic energy of the relative motion of the^{6}He nucleus and an alpha-particle is shown to result in their attraction for the L^{π}=0^{+}states. The strength of such attraction is high enough to ensure the existence of a bound state or a low-energy virtual state in the^{10}Be nucleus.*Yu.A. Lashko, G.F. Filippov* - Investigation of 6He resonance states was carried out by experimental and theoretical methods. Experiments were performed at the Kiev Institute of Nuclear Research of the National Academy of Sciences of Ukraine. Resonance states were detected from the coincidence spectrum of protons and alpha-particles, which are products of the four-particle reaction, initiated by interaction of alpha-particles with
^{3}H nuclei. For theoretical analysis of^{6}He continuous spectrum states, a microscopic three-cluster model was used. It was shown repeatedly, that this model is very suitable for investigation of the three-cluster continuum. New resonance states in^{6}He were found by experimental and theoretical methods. Total and partial widths were determined, and the dominant decay channels of the resonances were established. It was demonstrated that theoretical values of energy and width of resonance states in 6Не are in good agreement with experimental ones. By using the 1^{-}resonance state as an example, it was shown how resonances appear in the three-cluster continuum and how they can be observed by experimental and theoretical methods.*V.S. Vasilevsky*

- We formulated a general approach to construct phase portraits of a quantum system in the Fock-Bargmann space. The method was applied to the free motion of a 1D quantum particle, to the motion in the field of a Gaussian potential, and to the two-cluster system α+d. The phase portrait of the state of a quantum system characterized by the energy E is the density distribution over phase trajectories in this state. We have shown that the phase portraits provide an additional important information about quantum systems, as compared to the wave functions in the coordinate or momentum representation. The density distribution for a bound state is localized in a small area of the phase space, and all phase trajectories are finite. The phase portrait for the states of the continuum spectrum contains both infinite and finite trajectories. As the energy E increases, the contribution of the finite trajectories is reduced, and the infinite trajectories are condensed around the classical phase trajectories. Hence, the Fock-Bargmann space provides a natural description of the quantum-classical correspondence and allows us to establish, at which energy the quantum phase trajectories approach their classical limit.
*Yu.A. Lashko, G.F. Filippov, V.S. Vasilevsky, M. D. Soloha-Klymchak* - The structure of
^{10}В nucleus is investigated. For this aim, a microscopic three-cluster model is involved. The nucleus^{10}В is modeled as a three-cluster system, which consists from two alpha-particles and deuteron. This configuration has minimal threshold energy among other three-cluster channels, and allows one to take into account the dominant two-cluster channels of the^{10}В decay. Effects of the interacting cluster size and parameters of nucleon-nucleon interaction on the bound states are studied in detail. It is shown, that spin-orbital components of the potential have a large impact on the energy and relative position of the bound states. The spectroscopic factors for virtual decay of the^{10}В ground and excited states on three clusters α+α+d are calculated. They determine measure of clusterization and effects of the Pauli principle on the energy level. It is also demonstrated how shape and size of the nucleus depends on energy of the excited state.*V.S Vasilevsky, A.V. Nesterov, T.P. Kovalenko*

- Within the microscopic approach we have studied the structure of the wave functions of three-cluster atomic nuclei, belonging both to the discrete spectrum and to the continuous spectrum. We have shown that these wave functions are formed not only by the potential energy operator at small distance between clusters, but also by the antisymmetrization operator and kinetic-energy operator acting even at large intercluster distance. Asymptotic structure of the Pauli-allowed three-cluster basis states was shown to be reproduced by the Kravchuk polynomials, which become Hermitian polynomials at large number of oscillator quanta. An explicit form of the asymptotic three-cluster wave functions was determined and their continuum limit was established.
*G.F. Filippov, Yu.A. Lashko* - Spectrum of resonance states of three-cluster continuum in nuclei
^{9}Be and^{9}B is calculated with the Algebraic Version of the Resonating Group Method. The dominant three-cluster configurations α+α+n and α+α+p are involved to describe main properties of bound state in^{9}Be and resonance states in^{9}Be and^{9}B. Interaction between clusters is determined by the semi-realistic nucleon-nucleon potential containing the central and spin-orbital components. It is demonstrated that spin-orbital components play an important role in formation of bound and resonance states. With this potential our model yields set of resonance states which are in fairly good agreement with available experimental data. Analysis of scattering parameters and wave functions of continuous spectrum states indicates that resonance states in^{9}Be and^{9}B nuclei are formed in one channel of three-cluster continuum which is weakly coupled to other channels. This weak coupling of channels determines the existence of the very narrow resonance states with width less than 1 keV. The dominant channels of decay are determined for each resonance state in^{9}Be and^{9}B.*V.S. Vasilevsky, A.V. Nesterov, T.P. Kovalenko*