Probing nuclear potential with reactions Krzysztof Rusek Heavy Ion Laboratory, University of Warsaw, The Andrzej Soltan Institute for Nuclear Studies,

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

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

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

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

Complete fusion R V

Supression above the Coulomb barrier L.R. Gasques et al. PRC79 (2009)

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

The method (continuum-discretized coupled-channels) [T + ε g.s. – E + ] χ el (R) = χ inel (R) Φ(r,R) = ψ g.s. (r)χ el (R) + ψ 1exc (r)χ inel (R) +..

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

The concept of DPP (dynamic polarization potential) local, L-dependent DPPs, many methods to derive L-independent DPP. If the method is working well, results (σ el ) should be close to CDCC 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] χ el (R) = E χ el (R) χ el (R) from CDCC calculations

Case 1 – 4 He U Solid, dashed – CDCC, Dotted – OM+DPP Strong repulsion at the surface is due to nuclear interactions (absorption) 238 U Level Scheme < E(level) <Gamma Energy Level Energy Level T1/2 Level Spin-parity Final Level Highlight: Image Height: Level Width: Band Spacing: List of levels Bands: Non-band levels

Case 1 – 4 He U Solid, dashed – CC, Dotted – OM+DPP Strong repulsion at the surface is due to nuclear interactions (absorption) 238 U Level Scheme < E(level) <Gamma Energy Level Energy Level T1/2 Level Spin-parity Final Level Highlight: Image Height: Level Width: Band Spacing: List of levels Bands: Non-band levels Exp. data of Budzanowski et al., PL 11 (1964) 74

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

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

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

DPP real = V 1 df/dR + V 2 g(R) DPP imag = W 1 df/dR + W 2 g(R) f(R) = [1+exp(R-R 0,i )/a 1 ] g(R) = [1+exp(R-R 0,i )/a 2 ] Parametrization V 1 /W 1 V 2 /W 2 R o,i a1a1 a2a2 real imag

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

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

Recipe V = Vo + iW + DPP Vo – from densities W – a half of V 0 DPP – coupling with direct reaction channels

Parametrization V 1 /W 1 V 2 /W 2 R o,i a1a1 a2a2 real imag V 1 /W 1 V 2 /W 2 R o,i a1a1 a2a2 real imag V 1 /W 1 V 2 /W 2 R o,i a1a1 a2a2 real imag α U 7 Li Pb 6 He Pb

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

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

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

The method (continuum-discretized coupled-channels) [T + ε i – E + ] χ i (R) = χ k (R) Φ(r,R) = ψ 1 (r)χ 1 (R) + ψ 2 (r)χ 2 (R) + ….. prof. G. Rawitscher

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