1. 1 Multistep Coulomb & Nuclear Breakup of Halo Nuclei Ian Thompson, Surrey University, United Kingdom; with Surrey: Jeff Tostevin, John Mortimer, Brian Cross Porto: Filomena Nunes

2. 2 Breakup Dynamics  Recoil & Finite Range of projectile vertex.  Final-state (partial wave) interference  Nuclear and Coulomb mechanisms  Core excitation (initial and/or dynamic)  Final-state interactions:  between halo fragments (needed if resonances)  between fragments and target (needed if close in)  Multistep Processes (higher order effects)

3. 3 Previous Reaction Theories  Semiclassical Theory (1st order eikonal)  DWBA:  Prior DWBA, DWIA (FSI between fragments to all orders)  Post DWBA (FSI fragment-target to all orders)  Time-dependent Schrödinger Eqn. solutions  Adiabatic (high energy)  e.g. Glauber (eikonal); Bremstrahlung.  Coupled Channels  CRC: expand on bound states  CDCC: expand on continuum bin states

4. 4 Adiabatic Few-body Model  Projectile excitation energy << beam energy  so scattering parametric for projectile inner coordinates [with eikonal dynamics, this gives Few- Body Glauber]  Neglect halo-nucleon target interaction  eg for neutron halo in Coulomb breakup  Gives soluble 3-body  (RC Johnson et al, PRL 79 (1997) 2771)  Use adiabatic  in post T-matrix integral  Gives Bremstrahlung integral for Coulomb breakup

5. 5 Deuteron breakup via Coulomb Bremstrahlung Forward-angle proton energy distributions from J.A. Tostevin et al, Phys. Letts. B424 (1998) 219; Phys. Rev. C57 (1998) 3225. Agreement is best for heavier targets: dominated by Coulomb. Now need to include nuclear breakup mechanisms equally well!

6. 6 Improving on Bremstrahlung  Need:  Nuclear mechanisms  Non-adiabatic effects  Proton halo breakup e.g. 8 B  Try CDCC: Coupled Discretised Continuum Channels  Proposed by Rawitscher, developed by Kamimura group.  Treat Coulomb and Nuclear mechanisms xNeed to check convergence of long-range Coulomb process!  All higher-order effects with a (r,R,L) reaction volume  Can calculate fragment coincident angular distributions

7. 7 Discretised Continuum bins  The breakup continuum is integrated in `bins’, so the continuum is represented by an orthonormal basis set: Continuum bins for 8 B (`up arrows’ for DWBA are shown)

8. 8 Couplings between Bins The Nuclear couplings extend as far as the ground state  0 (r), as do the deviations of the Coulomb couplings from 1/R +1. Continuum-continuum couplings have yet longer range. Not: But: Semiclassical methods assume these Coulomb form factors too. Surface peaked.

9. 9 Testing CDCC Convergence  Compare, in Adiabatic Few-Body Model, with Bremstrahlung integral  Compare, in first-order PWBA model, with semiclassical theory

10. 10 SubCoulomb 8 B + 58 Ni @ ND  Multistep Coulomb only  Multistep Nuclear Only from F.M. Nunes and I.J. Thompson, Phys. Rev. C59 (1999) 2652

11. 11 Coulomb+Nuclear Multistep  Coulomb+nuclear  Effect of continuum- continuum couplings Green lines: no continuum-continuum couplings

12. 12 Convergence: max bin E rel  8 B angular distribution  7 Be angular distributions

13. 13 Breakup energy distributions   lab ( 7 Be) = 20 + 21 deg   lab ( 7 Be) = 30 deg

14. 14 Conclusions  CDCC method is useful for two-cluster halo nuclei:  Finite-range & recoil included  Coulomb and nuclear both approach convergence xLarge radii and partial-wave limits needed, but feasible now xNon-adiabatic treatment of Coulomb breakup  Multistep effects manifest from all final-state interactions  Still need equivalent method for three- cluster projectiles (e.g. two neutron halo nuclei)