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Resonant and Nonresonant Continuum Structures

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Title: Resonant and Nonresonant Continuum Structures


1
Resonant and Non-resonant Continuum Structures
  • Ian Thompson
  • University of Surrey,
  • Guildford, England
  • with
  • J. Tostevin, T. Tarutina (Surrey),
  • B. Danilin (Surrey, Kurchatov),
  • S. Ershov (Surrey, DUBNA)

2
Which Continuum?
  • Nuclei typically show few-body behaviour just
    near and above the cluster separation thresholds.
  • Many exotic nuclei have just one or a few bound
    states, hence
  • show pronounced cluster dynamics even in their
    ground states,
  • (nearly) excitations are in the continuum!

3
Role of the Continuum?
  • The continuum appears in several ways
  • Part of expansion of bound states
  • eg needed in RPA for weakly bound states
  • Dominated by resonances
  • These unbound states identified eg with shell
    model eigenstates above threshold
  • In non-resonant continuum
  • eg in breakup reactions, or low-energy capture.
  • ALL important parts of nuclear structure!!

4
Direct resonant 14N(p,g)
  • Fit R-matrix poles on top of potential
    contribution.
  • (rather than use background poles)
  • Sample question Is it a pole or direct part to
    the g.s. that is missing in range 1-2 MeV?

5
Reactions to probe structure
  • Near-threshold structure may be probed by elastic
    scattering or cluster transfers. But
  • Breakup is typically the largest.
  • Capture reactions probe similar structure.
  • Need resonant non-resonant structure!

6
Elastic Breakup
  • Elastic Breakup Diffraction Dissociation
  • all nuclear fragments survive along with the
    target in its ground state,
  • probes continuum excited states of nucleus.
  • For dripline nuclei , with few discrete states,
    these breakup reactions are the main probe of
    excited states.

7
Stripping Reactions
  • Stripping inelastic breakup,
  • removes a surface nucleon by a high-energy
    interaction with a target, which ends up not in
    its ground state.
  • Projectile residue core detected.
  • The final states of residue may be distinguished
    by coincident ?-rays.

8
StrippingDiffraction Expts.
  • Many measurements now, of spin, parity, and
    absolute spectroscopic factors.
  • Compare data with sum of diffraction stripping.
  • Probes spectroscopic factors L values for a
    wide range of final states.
  • High-energy reactions analysed using ablation or
    eikonal models
  • See review by Hansen and Tostevin, ARNPS 2003.
  • (Still need for low-energy quantum theory)

9
Momentum content p-shell
19F
No gamma detection
16O
14N
12C
11B
N14
N8
distributions narrow (weak binding) or s-states
as one crosses shell or
sub-shell closures
E.Sauvan et al., Phys Lett B 491 (2000) 1
10
Knockout reactions
9Be(17C, 16C g)X (Ebeam60 MeV/A)
(a) 8 s 92 d (b) 26 s 74 d (c) 100 d
SM calculation predict no 16C(0) in the
17C(g.s.). Experiment measured a 20 branch into
16C(0) . Higher order processes?
Maddalena et al., PRC63(01)024613
11
Ground state structure of 8B
p3/2 137 keV
p3/2 566 keV
Proton removal from 8B measured at the GSI
with gamma coincidences, sees a (15) branch from
an excited 7Be(1/2-) core component in the 8B
wave function.
from D.Cortina-Gil et al., Phys Lett B 529 (2002)
36, NPA 720 (2003) 3
12
Two-neutron Borromean halos
  • Such nuclei can be treated as 3-body systems.
  • Ground state properties of 6He, 11Li and 14Be
    can be treated as inert or rotational core two
    valence neutrons.
  • Interesting new physics
  • In each case, core neutron sub-system are
    unbound.
  • Extra neutron provides additional binding.

...so too are the pieces that make up the halo
nucleus 6He
Just as these three Borromean rings are linked
together
13
Three-body coordinates
Relative coordinates
Collective coordinates the hyper-radius and
hyperangle.
(up to mass-related scaling constants)
14
Three-body Wave functions
  • Angular-dependence
  • Hyper-radial dependence
  • Coupled equations

15
Three-body Hamiltonian H
  • Masses, spins and charges of three bodies
  • Potentials between each pair
  • List of occupied states that should be blocked by
    the Pauli Principle.
  • With H calculate potential couplings,
  • and solve the coupled equations.

16
Wave functions of 6He
  • Ground state wave function
  • Solution of coupled equations for E 0.97
    MeV.

Nuclei such as 6He have highly correlated cluster
structures
17
1 Neutron stripping from three-body Borromean
Nuclei
  • Removal of a neutron from 6He, 11Li, 14Be,
  • populates states of 5He, 10Li or 13Be.
  • Experiments measure decay spectrum of 5He 4He
    n, 13Be 12Be n, etc
  • Can we predict any energy and angular
    correlations by Glauber model?
  • Can we relate these correlations to the structure
    of the A1 or the A2 nucleus?

18
1N stripping from 6He g.s.
  • Calculate overlaps lt5He(Ea-n) 6He(gs)gt
    for a range of 5He(Ea-n) bin states,
  • smooth histogram of Glauber bin cross sections.
  • GSI data (H.Simon)

Theory sstr137 mb, sdiff38 mb Expt
sstr12714 mb, sdiff305 mb from T. Tarutina
thesis (Surrey)
Promising technique!
19
1N stripping from 14Be g.s.
  • Calculate overlaps lt13Be(Ea-n)14Be(gs)gt
  • Inert-core 13,14Be wfs.
  • GSI data (H.Simon)
  • See softer data, and not pronounced virtual-s and
    resonant-d peaks.
  • New theory needed?

Theory sstr109 mb, sdiff109 mb Expt
sstr12519 mb, sdiff5519 mb
20
Elastic Breakup of 2N halo
  • Elastic Breakup Diffraction Dissociation
  • all nuclear fragments survive along with the
    target in its ground state,
  • probes continuum excited states of nucleus.
  • Need correlations in the three-body continuum of
    Borromean nuclei.

21
Continuum three-body wave functions
  • Three-body scattering at energy E
  • Plane wave 3-3 scattering states
  • Dynamical solutions for scattering states

22
Continuum Spatial Correlations
from B. Danilin, I. Thompson, PRC 69, 024609
(2004)
  • Now average scattering wave functions over angles
    of kx and ky, to see spatial correlations in
    continuum states in 6He

23
True 3-body resonances?
  • Expect continuum wave functions like

24
Continuum Energy Correlations
  • Now average scattering wave functions over angles
    of kx and ky, for fixed three-body energy E.
  • Obtain similar plots for continuum energies.
  • (Continuum momentum and angular correlations for
    later)

25
Virtual states Resonances
from B. Danilin, I. Thompson et al, (in
preparation)
26
6He excitations resonances
27
3-body breakup final states
  • The three-body Borromean continum can be used as
    the final states in breakup reactions.
  • Available methods
  • DWBA, or
  • Eikonal (Glauber) models
  • 4-body CDCC (Kamimura et al) still difficult!
  • Show DWBA results from S.Ershov et al (submitted).

28
DWBA to 3-body continuum
  • Exact T-matrix
  • DWBA T-matrix
  • Distorted waves
  • 3-body final states

29
11Li(p,p) at 68 MeV/u (RIKEN)
  • DWBA spectrum (a).
  • Comparison (b) of the theoretical spectrum,
    corrected for experimental conditions, with data
    measured in experiment (Korsheninnikov, 97).
  • Solid, dashed and dotted lines show the total,
    dipole and monopole cross sections, respectively.
  • In (b), the thin solid line indicates the
    experimental background from materials other then
    protons in the target.

Similar results to Crespo, Thompson
Korsheninnikov, PRC 66 (2002) 021002
30
s(q) for 11Li(p,p) at 68 MeV/u
  • (a) Comparison of the theoretical calculations
    with experimental data
  • Solid, dashed and dotted lines show the total,
    monopole and dipole angular distributions,
    respectively.
  • In (b) and (c), solid lines show angular
    distributions for the monopole and dipole
    excitations, respectively.
  • Dashed and dotted lines are contributions from
    the halo neutrons and the core nucleons.

31
0, 1- three-body resonances?
32
Conclusions
  • Near-threshold states give rise to cluster
    dynamics and breakup
  • Continuum states necessary for spectroscopic
    probes.
  • Continuum structure includes correlations.
  • Spectroscopy of states in the continuum is just
    as important as spectroscopy of discrete states
    (bound states or discrete resonances).
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