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.

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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

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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.

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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
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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
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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).

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DWBA to 3-body continuum

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

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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
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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.

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0, 1- three-body resonances?
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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).