Probing nuclear potential with reactions

1. Probing nuclear potential with reactions Krzysztof Rusek Heavy Ion Laboratory, University of Warsaw, www.slcj.uw.edu.pl The Andrzej Soltan Institute for Nuclear Studies, www.ipj.gov.pl

2. Going out of the valley of stability Magic numbers are no longer magic Nuclear halos Importance of three-body forces Granulation of nuclear matter etc. Can we use the standard form of effective nucleus-nucleus potential?

3. Effective nucleus-nucleus potential G.R. Satchler, W.G. Love, Phys.Rep. 55 (1979)183 V = Vo + iW Vo : W = 0.5 Vo

4. Elastic scattering 6Li + 208Pb 6He + 208Pb Y. Kucuk, N. Keeley PRC 79 067601 (2009) Deviation from Rutherford c.s. at very forward angles

5. Elastic scattering ↓ ↑ L. Acosta et al. EPJ A in print Structure effects important!

6. Complete fusion V R

7. Complete fusion L.R. Gasques et al. PRC79 (2009) 034605 Supression above the Coulomb barrier

8. Complete fusion ↑ S.M. Lukyanov et al. PLB 670 (2009) 321 Enhancement below the Coulomb barrier

9. The method (continuum-discretized coupled-channels) Φ(r,R) = ψg.s.(r)χel(R) + ψ1exc(r)χinel(R) + .. [T + εg.s. – E + <ψg.s.(r)I V(r,R) Iψg.s.(r)>] χel(R) = <ψg.s.(r)IV(r,R)Iψinel.(r)> χinel(R) ... . . . . . . . . . . . . . . . . . . . . . .

10. The method at work ↓ K. R. PRC72, 037603 Structure of 6He is ”reflected” in elastic scattering close to the barrier

11. The concept of DPP(dynamic polarization potential) V = Vo + iW +DPP Method 1: inversion S→ V IP method of R.S. Mackintosh Review of IP method: V.I. Kukulin and R.S.Mackintosh, J. Phys. G: Nucl. Part. Phys. 30, R1 (2004) Method 2: „trivially equivalent potential” [T + Vo + i W +DPP]χel(R) = E χel(R) χel(R) from CDCC calculations local, L-dependent DPPs, many methods to derive L-independent DPP. If the method is working well, results (σel ) should be close to CDCC

12. 238U Level Scheme Case 1 – 4He + 238U Solid, dashed – CDCC, Dotted – OM+DPP Strong repulsion at the surface is due to nuclear interactions (absorption)

13. 238U Level Scheme Case 1 – 4He + 238U Exp. data of Budzanowski et al., PL 11 (1964) 74 Solid, dashed – CC, Dotted – OM+DPP Strong repulsion at the surface is due to nuclear interactions (absorption)

14. Case 2 – 7Li + 208Pb Exp. data Keeley et al., NPA 571 (1994) 326 Solid – CDCC, dashed – OM+DPP Coupling with unbound states generates similar DPP as with bound state

15. Case 3 – 6He + 208Pb Exp. data A. Sanchez-Benitez et al., NPA803 (2008) 30 Contiunnum dominated by L=1 states Long range attraction due to dipole polarizability

16. Conclusion Similar tendency – repulsion at the surface and long range attraction reflecting dipole couplings with the continuum

17. Parametrization DPPreal = V1 df/dR + V2 g(R) DPPimag = W1 df/dR + W2 g(R) f(R) = [1+exp(R-R0,i)/a1] g(R) = [1+exp(R-R0,i)/a2]

18. Consequences V = Vo + i W +DPP Explanation of all the effects observed for el. scatt. and fusion.

19. Consequences Prediction for fusion barrier distribution – shifts it to higher energies and make broader 6Li + 28Si K. Zerva et al., PRC80(2009)017601

20. Recipe V = Vo + iW + DPP Vo – from densities W – a half of V0 DPP – coupling with direct reaction channels

21. Parametrization α + 238U 7Li + 208Pb 6He + 208Pb

22. Energies 2 ÷10 MeV/A Ions 10B ÷40Ar

23. Potential from transfer reaction analysis B + b a + A Probability: potential a + A + structure + potential b + B

24. 10B + 7Li →8Be + 9Be A.T. Rudchik et al. PRC 79 054609 (2009)

25. The method (continuum-discretized coupled-channels) prof. G. Rawitscher Φ(r,R) = ψ1(r)χ1(R) + ψ2(r)χ2(R) + ….. [T + εi – E + <ψi(r)IV(r,R)Iψi(r)>] χi(R) = <ψi(r)IV(r,R)Iψk(r)> χk(R)

26. Input parameters • Structure of the projectile • (wave functions) • Fragment – target interactions • No free parameters