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Cluster structure of low-energy resonance in tetraneutron: microscopic approach

Cluster structure of low-energy resonance in tetraneutron: microscopic approach. Yuliya Lashko , G . F . Filippov. Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine. Erice. 2006.

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Cluster structure of low-energy resonance in tetraneutron: microscopic approach

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  1. Cluster structure of low-energy resonance in tetraneutron: microscopic approach YuliyaLashko, G.F. Filippov Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine Erice 2006

  2. The role of the Pauli principle in the formation of low-energy resonance in tetraneutron treated as a coupled-channel cluster system is studied Microscopic approach 1. Effective 2n-2n and 3n-n interactions 2.4nas a coupled-channel cluster system: 3n+n and2n+2n

  3. Approach:algebraic version of the Resonating Group Method (RGM) Main point: exact treatment of the Pauli principle in nucleus-nucleus collision problems RGM wave function φ(1), φ(2) areinternal cluster functions f(q) is a wave function of relative motion of clusters Transform to the Fock-Bargmann space− phase space ofcoordinatesξandmomentaη

  4. AVRGM wave function ψn− the Pauli-allowed harmonic-oscillator basis states A set of linear equations is solved to give wave functions and S-matrix elements

  5. Λn are the eigenvalues of the antisymmetrization operator is the number of oscillator quanta are the SU(3)-symmetry indices is an orbital angular momentum is a projection of the momentum is an additional quantum number Λn are proportional to the probability of thesystem being in the state determined by theeigenfunctionψn is the Pauli-forbidden state is the Pauli-allowed state is a“partly forbidden” state repulsion is a“super-allowed” state attraction

  6. 1. Effective 2n-2n and 3n-n interactions

  7. If r0 b,then the potential energy matrix in the h.o.representation is equivalent to the diagonal matrix which is a discrete analog of cluster-cluster potentialin the coordinate space

  8. The effective cluster-cluster potential decreases exponentially as oscillator length r0 increases

  9. There is no resonance in tetraneutron, provided that only 2n+2n cluster configuration is taken into account

  10. Effective attraction of3n andninduced by the exchange effects creates a bound state of4n with binding energyE0

  11. Strength of 3n-n interaction exceeds that of 2n-2n interaction by the difference Δ of intrinsic potential energy of 3n and two 2n

  12. 2.4nas a coupled-channel cluster system: 3n+n and2n+2n

  13. An effective attraction reveals itself in (2k,0)+-branch while in (2k,0)--branch an effective repulsion takes place

  14. Due to the difference in intrinsic potential energies of the clusters SU(3)-branches (2k,0)+ and (2k,0)- remain coupled at large k

  15. Effective attraction generated by the kinetic exchange terms creates a resonance in 4n

  16. Wave functions have a resonance behaviour at low energy. Configuration 3n+n is responsible for this resonance

  17. A resonance state in4n can be generated by kinetic energy exchange effects, if r0 is large Questions?

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