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Multistep Multistep Coulomb & Nuclear Breakup Coulomb & Nuclear Breakup of Halo Nucleiof Halo Nuclei

Ian Thompson, Surrey University, United Kingdom;withSurrey: Jeff Tostevin, John Mortimer, Brian CrossPorto: Filomena Nunes

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Breakup DynamicsBreakup Dynamics

Recoil & Finite Range of projectile vertex.Final-state (partial wave) interference Nuclear and Coulomb mechanismsCore 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)

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Previous Reaction TheoriesPrevious 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.

solutionsAdiabatic (high energy)

e.g. Glauber (eikonal); Bremstrahlung.Coupled Channels

CRC: expand on bound states CDCC: expand on continuum bin states

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Adiabatic Few-body ModelAdiabatic 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

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Deuteron breakup via Coulomb Deuteron breakup via Coulomb BremstrahlungBremstrahlung

Forward-angle protonenergy distributions fromJ.A. Tostevin et al, Phys. Letts. B424 (1998) 219;Phys. Rev. C57 (1998) 3225.

Agreement is best for heaviertargets: dominated by Coulomb.

Now need to include nuclear breakup mechanisms equally well!

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Improving on BremstrahlungImproving on Bremstrahlung

Need: Nuclear mechanisms Non-adiabatic effects Proton halo breakup e.g. 8B

Try CDCC: Coupled Discretised Continuum Channels Proposed by Rawitscher, developed by Kamimura

group. Treat Coulomb and Nuclear mechanisms

Need 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

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Discretised Continuum binsDiscretised Continuum bins

The breakup continuum is integrated in `bins’, so the continuum is represented by an orthonormal basis set:

Continuum bins for 8B(`up arrows’ for DWBA are shown)

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Couplings between BinsCouplings 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 couplingshave yet longer range.

Not:

But:

Semiclassical methodsassume these Coulombform factors too.

Surface peaked.

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Testing CDCC ConvergenceTesting CDCC Convergence

Compare, in Adiabatic Few-Body Model, with Bremstrahlung integral

Compare, in first-order PWBA model, with semiclassical theory

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SubCoulomb SubCoulomb 88B + B + 5858Ni @ NDNi @ ND

Multistep Coulomb only

Multistep Nuclear Only

from F.M. Nunes and I.J. Thompson, Phys. Rev. C59 (1999) 2652

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Coulomb+Nuclear MultistepCoulomb+Nuclear Multistep

Coulomb+nuclear Effect of continuum-continuum couplings

Green lines: no continuum-continuum couplings

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Convergence: max bin EConvergence: max bin Erelrel

8B angular distribution

7Be angular distributions

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Breakup energy distributionsBreakup energy distributions

lab(7Be) = 20 + 21 deg

lab(7Be) = 30 deg

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ConclusionsConclusions

CDCC method is useful for two-cluster halo nuclei: Finite-range & recoil included Coulomb and nuclear both approach convergence

Large radii and partial-wave limits needed, but feasible nowNon-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)