RCNP.08 Breakup of halo nuclei with Coulomb-corrected eikonal method Y. Suzuki (Niigata) 1.Motivation for breakup reactions 2.Eikonal and adiabatic approximations 3.Coulomb-corrected eikonal model 4. Application to 2n halo nuclei Collaborators: B. Abu-Ibrahim (Cairo) P. Capel, D. Baye, P. Descouvemont (ULB) PTP112 (2004), PTP114(2005), PRC78(2008), PRC submitted

・ Breakup reactions are important to study halo nuclei which are characterized by weakly bound, short-lived, few-cluster structure ・ E1 strength, NN correlation are deduced from breakup cross sections FSI, breakup into continuum ・ Sound reaction theory is needed to extract structure information Perturbation expansion, Adiabatic approximation, Eikonal approximation, CDCC, … 1. Motivation Information on B(E1) distribution First-order perturbation theory for Coulomb breakup Contribution of other multipoles to breakup cross sections?

New 2n correlation experiment (Nakamura et al.) Taken from K. Hagino

Target C f Projectile Eikonal approximation 2. Eikonal and adiabatic approximations --- Case of one-neutron halo nucleus ---

DEA (Dynamical Eikonal Approximation) Adiabatic approx.

11 Be+ 208 Pb at 69 MeV/nucleon Angle-integrated cross sections as a function of the relative energy of n- 10 Be fragments Test of DEA G. Goldstein et al. PRC73 (2006) N. Fukuda et al. PRC70 (2004)

RCNP.08 Test of eikonal and adiabatic approximations α+ n + n three-body model for 6 He CDCC T. Matsumoto et al. PRC70 (2004) Glauber model: 3α microscopic cluster model w.f. for 12 C NN profile function Eikonal approx.: N- 12 C optical potential Folding Full 40 MeV/nucleon VMC w.f. for 6 He --- Breakup effect in elastic scattering of 6 He on 12 C --- B. Abu-Ibrahim & Y.S. NPA728 (2003) V. Lapoux et al. PRC66 (2002)

Logarithmic divergence Coulomb-corrected eikonal phase (CCE) 3. Coulomb-corrected eikonal Long-ranged breakup effect (adiabatic approx. breaks down) J. Margueron et al. NPA703 (2002) Rutherford scattering

Breakup of 11 Be (one-neutron halo nucleus) on Pb ＰＴＰ 112 (2004) Test of CCE

b-dep. of elastic breakup probability 11 Be on 208 Pb at 69 MeV/nucleon CCE vs DEA

4. Application to breakup of two-neutron halo nucleus Challenging four-body problem including continuum final states ・ Expensive computation time ・ Final-state interaction ・ Extraction of E1 strength function or effects of other multipoles Case study: 6 He breakup on 208 Pb at 70, 240 MeV/A ・ Reaction dynamics is fully taken into account in CCE model ・ 6 He is described with α+ n + n three-body model ・ Bound and continuum states of 6 He are described with HHE RCNP.08 PRC submitted

6 He breakup on 208 Pb at 70 MeV/A Dotted lines denote final plane waves Comparison with solid lines denotes the importance of FSI. --- Contribution of partial cross sections --- Cross sections are directly measurable. Determining E1 strengths relies on model assumptions (e.g. 1 - dominance, elimination of nuclear effects). J=0,2 contributions: 10% at low energies, 35% at E=5MeV

--- Double differential cross sections from 1 - component --- Core 1 2 information on correlations The peak corresponds to the broad 1 - resonance.

6 He breakup on 208 Pb at 240 MeV/A Dashed, dotted denote 1 - partial cross sections T. Aumann et al. PRC59 (1999) No convolution

E1 strength distribution of 6 He Myo et al. PRC63 (2001)

RCNP.08 Summary ・ A correction is introduced to avoid the divergence due to the Coulomb interaction in the eikonal model. ・ The CCE is accurate enough to take into account the reaction dynamics, making it possible to reconstruct the properties of two- and three-body projectile wave functions. ・ Bound and continuum states of three-body system are described in HH basis with full account of final state interactions. ・ Various cross sections, in particular including multi-differential cross sections can be calculated. ・ The contribution of various multipole transitions is quantified. ・ The CCE is applied to 6 He+ 208 Pb at 70 and 240 MeV/nucleon. The results disagree with the 240 MeV data. B(E1) strength? Further new data are desirable.