Transcript Resonant and Non-resonant Continuum Structures Ian Thompson University of Surrey, Guildford, England with J. Tostevin, T.

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)
31 March 04
MSU
1
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!
31 March 04
MSU
2
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!!
31 March 04
MSU
3
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?
31 March 04
MSU
4
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!
31 March 04
MSU
5
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.
31 March 04
MSU
6
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 g-rays.
31 March 04
MSU
7
Stripping+Diffraction 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)
31 March 04
MSU
8
Momentum content: p-shell
No gamma
detection
19F
16O
14N
12C
11B
N=14
N=8
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
31 March 04
MSU
9
Knockout reactions
g)X
(Ebeam=60 MeV/A)
9Be(17C, 16C
(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
31 March 04
MSU
10
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
31 March 04
MSU
11
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…
31 March 04
MSU
12
Three-body coordinates
Relative coordinates:
‘Collective’ coordinates: the hyper-radius and hyperangle.
(up to mass-related
scaling constants)
31 March 04
MSU
13
Three-body Wave functions
Angular-dependence
Hyper-radial dependence
Coupled equations
31 March 04
MSU
14
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.
31 March 04
MSU
15
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
31 March 04
MSU
16
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 A+1 or the A+2 nucleus?
31 March 04
MSU
17
1N stripping from 6He g.s.
Calculate overlaps:
<5He(Eα-n) | 6He(gs)>
for a range of
5He(E ) bin states,
α-n
smooth histogram of
Glauber bin cross
sections.
GSI data (H.Simon)
Promising technique!
31 March 04
Theory: σstr=137 mb, σdiff=38 mb
Expt: σstr=127±14 mb, σdiff=30±5 mb
from T. Tarutina thesis (Surrey)
MSU
18
1N stripping from
Calculate overlaps:
<13Be(Eα-n)|14Be(gs)>
Inert-core 13,14Be wfs.
GSI data (H.Simon)
See softer data, and
not pronounced
virtual-s and
resonant-d peaks.
New theory needed?
31 March 04
14Be
g.s.
Theory: σstr=109 mb, σdiff=109 mb
Expt: σstr=125±19 mb, σdiff=55±19 mb
MSU
19
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.
31 March 04
MSU
20
Continuum three-body
wave functions
Three-body scattering at energy E:
Plane wave 3-3 scattering states:
Dynamical solutions for scattering states:
31 March 04
MSU
21
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:
31 March 04
MSU
22
‘True’ 3-body resonances?
Expect continuum wave functions like:
31 March 04
MSU
23
Continuum Energy Correlations
Now average scattering wave functions
over angles of kx and ky, for fixed threebody energy E.
Obtain similar plots for continuum
energies.
(Continuum momentum and angular
correlations for later)
31 March 04
MSU
24
Virtual states & Resonances
from B. Danilin, I. Thompson et al, (in preparation)
Virtual n-n pole
31 March 04
Effect of n-n ‘resonance’ in
E(c-n), E(cn-n) coordinates
MSU
25
6He
excitations & resonances
Pronounced
31 March 04
2+
No pronounced 1resonance
resonance
MSU
26
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).
31 March 04
MSU
27
DWBA to 3-body continuum
Exact T-matrix:
DWBA T-matrix:
Distorted waves:
3-body final states:
31 March 04
MSU
28
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
31 March 04
MSU
29
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 March 04
MSU
30
0+, 1- three-body resonances?
Pure resonance:
31 March 04
From DWBA cross sections:
MSU
31
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).
31 March 04
MSU
32