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Lectures in Milano University Hiroyuki Sagawa, Univeristy of Aizu March, 2008

Lectures in Milano University Hiroyuki Sagawa, Univeristy of Aizu March, 2008. 1. Pairing correlations in Nuclei. General aspects of HFB HFB and Quadrupole Respons in weakly bound states. Stable Nuclei. Unstable Nuclei. Excitations to the continuum states in drip line nuclei.

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Lectures in Milano University Hiroyuki Sagawa, Univeristy of Aizu March, 2008

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  1. Lectures in Milano UniversityHiroyuki Sagawa, Univeristy of AizuMarch, 2008 • 1. Pairing correlations in Nuclei General aspects of HFB HFB and Quadrupole Respons in weakly bound states

  2. Stable Nuclei Unstable Nuclei Excitations to the continuum states in drip line nuclei Breakdown of BCS approximation

  3. Hartree-Fock Bogoliubov approximation Trial Wave Function Coordinate Space Representation

  4. New quasi-particle picture different to BCS quasi-particle!! wave function will be upper comp. non-local lower comp local Pair potential Pair potential goes beyond HF potential

  5. Hartree-Fock Bogoliubov Equations in the coordinate space Coupled differential HFB equations Mean Field Potential V(r) Pairing Potential

  6. Mean field and HFB single particle energy ei continuum HFB resonance 0 bound 2l l resonance

  7. Features of HFB solutions normalization occupation probability

  8. occupation probability/MeV normalization

  9. Quasi-particle wave functions of weakly bound states

  10. Model Mean field of cooper pairs Density dependent pairing interaction • l is fixed to be Deff =E qp(lj) 2. The depth of Woods-Saxon potential is changed to adjust the eigenenergy eWS . 3. Mass number is fixed to be A~84 . Pair potential 4.Average pairing strength D is given for a fixed l.

  11. Volume-type and Surface-type PairingCorrelations Volume-type Surface-type Average strength of pair field

  12. 3s1/2orbit

  13. 3s1/2orbit

  14. asymptotic behavior of j(r) or v(r) HF HFB Pairing correlation may give a quenching on the halo effect. On the contrary, more states around the Fermi sursface will be weakly-bound states due to the pairing.

  15. Effective Pair Gap of A=80

  16. Quasi-particle energy Quasi-particle energy of HFB is very different from BCS for weakly-bound low-l orbits.

  17. 2qp excitations ei continuum HFB resonance 0 bound 2l l resonance

  18. Multipole Response Function a) Ei, Ejboth discrete b) Ei discrete Ej continuum

  19. c) Ei ,Ej both continuum rmax =64fm w max=10MeV Sum Rule NEWSR EWSR

  20. Quadrupole Response Volume pairing

  21. Volume pairing

  22. Summary １．We solved a simplified HFB equations in the coordinate space with the correct asymptotic boundary conditions. 2. Quadrupole Response in the limit of eWS(d5/2) ->0 • The peak energy becomes lower and the widths gets broader while the total strength increases dramatically. (b)HFB continuum effect plays an important role in low-energy quadrupole excitations. (c) The continuum 2qp excitations involving weakly bound S½ neutrons enhances NEWSR value compared with the results of BCS. (d) HFB rms radius is slightly smaller than BCS one . (e) The 2qp excitations without S ½ neutrons show only enhancement.

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