Multichannel nuclear reactions involving light neutron-rich nuclei: Microscopic approach
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NUCLEI Theory
Multichannel Nuclear Reactions Involving Light Neutron-Rich Nuclei: Microscopic Approach* Yu. A. Lashko** and G. F. Filippov*** Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine Received October 31, 2006
Abstract—The influence of the Pauli exclusion principle on the relative motion of light neutron-rich nuclei in their collision is investigated within the microscopic method using as an example 11 Be + n and 10 Be + 2 n nuclear reactions, as well as 3 n + n and 2 n + 2 n reactions. Antisymmetrization effects related to the kinetic and potential energy of the relative motion of colliding nuclei are analyzed. The influence of the Pauli exclusion principle on the kinetic energy of the relative motion of the 11 Be nucleus and a neutron is shown to result in their attraction. The same phenomenon is observed for the case of the 3 n + n cluster system. The strength of such attraction is high enough to ensure the existence of a bound state in the 12 Be nucleus and a low-energy resonance in the tetraneutron. The conclusion is drawn that, for a resonance state in the 4 n system to exist, the value of the oscillator length must be large enough. It is shown also that increasing the oscillator length results in depression of the cluster–cluster potential. PACS numbers: 21.60.Gx DOI: 10.1134/S1063778807080194
The influence of the Pauli exclusion principle on the relative motion of two nuclei (clusters) in their collision is not limited to damping of the wave function in the interior region of internuclear distances due to the elimination of the Pauli-forbidden states, but also significantly affects the interaction of colliding nuclei. An exact treatment of the antisymmetrization effects related to the kinetic energy of their relative motion results in either an effective repulsion or attraction of the clusters. Whereas the exchange terms are known to behave repulsively or attractively depending on the choice of the nucleon–nucleon interaction, the possibility for the kinetic exchange terms to contribute attractively has been discovered for the first time in [1]. In [1], we have performed the coupledchannel calculation of the 12 Be nucleus, provided that 6 He + 6 He and 8 He + 4 He clusterings are taken into account. In the latter case, an effective attraction arising from a kinetic-energy operator appears to be strong enough to ensure an existence of both a bound state and a resonance in the 12 Be compound nucleus even without an interaction between the nucleons of different clusters. The nature of the effective internuclear potential derived from the kinetic-energy operator modified by ∗
The text was submitted by the authors in English. E-mail: [email protected] *** E-mail: [email protected] **
the Pauli exclusion principle is determined by the eigenvalues of the antisymmetrization operator. A repulsion arises in the states whose eigenvalues are less than unity, whereas an attraction appears in the states with the eigenvalues exceeding unity. Such an unusual appearance of exchange effects in the allowed state
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