31 March 04 MSU 1

Resonant and Non-resonant Continuum Structures

Ian ThompsonUniversity of Surrey,Guildford, EnglandwithJ. Tostevin, T. Tarutina (Surrey),B. Danilin (Surrey, Kurchatov), S. Ershov (Surrey, DUBNA)

31 March 04 MSU 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!

31 March 04 MSU 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!!

31 March 04 MSU 4

Direct & resonant 14N(p,)

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 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!

31 March 04 MSU 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.

31 March 04 MSU 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.

31 March 04 MSU 8

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 9

19F

16O

14N

12C

11B

N=8

N=14

Momentum content: p-shell

E.Sauvan et al., Phys Lett B 491 (2000) 1

distributions narrow (weak binding) or s-states as one crosses shell or sub-shell closures

No gammadetection

31 March 04 MSU 10

SM calculation predict no 16C(0+) in the 17C(g.s.). Experiment measured a 20% branch into 16C(0+) .Higher order processes?

9Be(17C, 16C )X(Ebeam=60 MeV/A)

Maddalena et al., PRC63(01)024613

(a) 8% s + 92% d (b) 26% s + 74% d(c) 100% d

Knockout reactions

31 March 04 MSU 11

Ground state structure of 8B

from D.Cortina-Gil et al., Phys Lett B 529 (2002) 36, NPA 720 (2003) 3

Proton removal from 8Bmeasured at the GSI withgamma coincidences, sees a (15%) branch from an excited 7Be(1/2-) core component in the 8B wave function.

p3/2

137 keV

p3/2

566 keV

31 March 04 MSU 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.

Just as these three Borromean rings are

linked together…

...so too are the pieces that make up the halo nucleus 6He

31 March 04 MSU 13

Three-body coordinatesRelative coordinates:

‘Collective’ coordinates: the hyper-radius and hyperangle.(up to mass-related scaling constants)

31 March 04 MSU 14

Three-body Wave functions

Angular-dependence

Hyper-radial dependence

Coupled equations

31 March 04 MSU 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.

31 March 04 MSU 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

31 March 04 MSU 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, etcCan 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 18

1N stripping from 6He g.s.

Calculate overlaps: <5He(Eα-n) | 6He(gs)> for a range of 5He(Eα-n) bin states,

smooth histogram of Glauber bin cross sections.

GSI data (H.Simon) Theory: σstr=137 mb, σdiff=38 mbExpt: σstr=127±14 mb, σdiff=30±5 mbfrom T. Tarutina thesis (Surrey)Promising technique!

31 March 04 MSU 19

1N stripping from 14Be g.s.

Calculate overlaps: <13Be(Eα-n)|14Be(gs)>

Inert-core 13,14Be wfs.

GSI data (H.Simon)

Theory: σstr=109 mb, σdiff=109 mbExpt: σstr=125±19 mb, σdiff=55±19 mb

See softer data, and not pronounced virtual-s and resonant-d peaks.

New theory needed?

31 March 04 MSU 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.

31 March 04 MSU 21

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 22

Continuum Spatial Correlations

Now average scattering wave functions over angles of kx and ky, to see spatial correlations in continuum states in 6He:

from B. Danilin, I. Thompson, PRC 69, 024609 (2004)

31 March 04 MSU 23

‘True’ 3-body resonances?

Expect continuum wave functions like:

31 March 04 MSU 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)

31 March 04 MSU 25

Virtual states & Resonances

Virtual n-n pole Effect of n-n ‘resonance’ in E(c-n), E(cn-n) coordinates

from B. Danilin, I. Thompson et al, (in preparation)

31 March 04 MSU 26

6He excitations & resonances

Pronounced 2+ resonance No pronounced 1- resonance

31 March 04 MSU 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).

31 March 04 MSU 28

DWBA to 3-body continuum

Exact T-matrix:

DWBA T-matrix:

Distorted waves:

3-body final states:

31 March 04 MSU 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

31 March 04 MSU 30

() 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 31

0+, 1- three-body resonances?

From DWBA cross sections:

Pure resonance:

31 March 04 MSU 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).