Title: Resonant and Nonresonant Continuum Structures
1Resonant 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)
2Which 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!
3Role 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!!
4Direct 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?
5Reactions 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!
6Elastic 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.
7Stripping 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.
8StrippingDiffraction 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)
9Momentum 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
10Knockout 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
11Ground 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
12Two-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
13Three-body coordinates
Relative coordinates
Collective coordinates the hyper-radius and
hyperangle.
(up to mass-related scaling constants)
14Three-body Wave functions
- Angular-dependence
- Hyper-radial dependence
-
- Coupled equations
15Three-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.
16Wave 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
171 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?
181N 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!
191N 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
20Elastic 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.
21Continuum three-body wave functions
- Three-body scattering at energy E
-
- Plane wave 3-3 scattering states
- Dynamical solutions for scattering states
22Continuum 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
23True 3-body resonances?
- Expect continuum wave functions like
24Continuum 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)
25Virtual states Resonances
from B. Danilin, I. Thompson et al, (in
preparation)
266He excitations resonances
273-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).
28DWBA to 3-body continuum
- Exact T-matrix
- DWBA T-matrix
-
- Distorted waves
- 3-body final states
2911Li(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
30s(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.
310, 1- three-body resonances?
32Conclusions
- 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).