Coherence and Decoherence in Collisions of Complex Nuclei

1
Coherence and Decoherence in Collisions of
Complex Nuclei
Quantum Information and Many-body Physics, PITP
(UBC), Vancouver, Dec07

• D.J. Hinde, M. Dasgupta, A. Diaz-Torres
• Department of Nuclear Physics
• Research School of Physical Sciences and
  Engineering
• Australian National University
• G.J. Milburn
• Department of Physics
• University of Queensland

2
Atomic nucleus a complex many-body system

• 6 to 250 constituent nucleons
• Protons, neutrons - Fermions
• Well-defined internal excitations
• Single-particle excitations (one n or p to new
  orbital)
• Coherent collective excitations many nucleons
• Many collective modes (0.06 -20 MeV)
• Vibrational excitations surface or volume modes
• Rotational excitations nuclear deformation
  (shapes)
• Vary systematically nuclear structure
• Shells gaps play crucial role magic
  (extra-stable) nuclei
• Nuclear structure, interactions from first
  principles? - NO

3
Nucleus-nucleus collisions

• Long-range Coulomb repulsion
• Short-range nuclear attraction
• Potential barrier capture or fusion barrier

Fusion Barrier (typically 100 MeV)
VB
Coulomb repulsion
rB
Nuclear attraction
VC a Z1Z2/R
Potential Energy
Z1
Z2
R
R
4
Inter-nuclear potential

• Coulomb potential exactly calculable
• Nuclear potential is not so easy
• Options
• Double folding model (also for Coulomb
  interaction)
• Fold matter densities with phenomenological
  n-n interaction
• Exponential at and outside barrier radius
  (not closed expression)
• Simple, convenient expression
• VN(r)V0/(1exp(r-R0)/a) Woods-Saxon
  potential
• Exponential at and outside barrier radius
• Find parameters by fitting experimental data
• Fit peripheral part of double-folding potential
  with Woods-Saxon form
• Problem in region inside barrier radius
• Re-organization of nuclear matter to find lowest
  energy configuration
• Does system have time to find this
  configuration adiabatic?

5
Nucleus-nucleus collisions

• Currently two theoretical approaches
• Classical or semi-classical trajectory
  (Sommerfeld parameter)
• Coherent time-independent quantum description
  (1980s-1990s)
• Classical trajectory model
• Distance of closest approach defines minimum
  surface separation
• Kinetic energy loss macroscopic friction -
  irreversible
• No quantum tunnelling
• Coupled-channels model
• Time-independent Schrodinger eqn
• Radial separation r is key variable
• Coupling of relative motion to specific internal
  excitations
• No energy loss reversible
• Trapping inside barrier by playing a trick

..
6
6037
Coupled-channels model
Etc.
keV
Many excited states
279
269
77
ground state
0
197Au
197Au
16O
16O
Interacting nuclei are in a linear superposition
of various states
Effectively changes the interaction potential
C.H. Dasso et al., Nucl. Phys. A405 (1982) 381
7
Coupled-channels model


h2 d2
?
Vnm (r) ym(r) 0
VJ(r) en E yn(r)
2? dr2
mn
/

• Each combination of energy levels (m) is a
  channel
• Collective, strongly-coupled channels should be
  included (Vnm Vmn)
• Isocentrifugal approximation
• The centrifugal energy is independent of the
  channel
• It is incorporated in the inter-nuclear potential
  (up to J100, E100
  MeV)
• Boundary conditions at two positions
• Distant boundary
• Incoming Coulomb wave in channel 0 (nuclei in
  ground states)
• Outgoing Coulomb waves in all channels
• Inside the barrier only an incoming wave (or
  imaginary potential)

8
Coupled-channels model

• Simplifying approximations for illustration
• Two channels
• en ltlt Vnm (e.g rotational nuclei)
• Solve coupled equations at each value of r
• Then VJ(r) VJ(r) VCoupling(r) and
  VJ(r) VCoupling(r)
• The potential barrier is split into two
  barriers
• (eigenchannel picture)
• More channels, more barriers
• Coupling matrix elements proportional to Z1Z2
• like the uncoupled barrier energy itself
• Width of barrier distributions 0.1 VB large
  effect!

9
Fusion barrier distribution
1
Single-barrier
Probability
E
nuclei in a superposition of states
VB0
Probability
Distribution of barrier energies - eigenchannels
E
VB2
VB3
VB1
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Coupled-channels model

• Energy E below VJ(rB)
• Incoming wave b.c. inside rB plays no role
• Reaction processes are elastic and inelastic
  scattering
• Observables are the populations and energies of
  physical channels m
• Shows the strongly coupled channels
• Energy E above VJ(rB)
• Incoming wave b.c. inside rB acts like a black
  hole calculate fusion
• Irreversibility inside rB - BUT - no effect on
  coherence!
• Always assumed irreversibility does not reach out
  to rB invisible
• Potential (fusion) barrier acts as a filter at rB
• Measuring the distribution of barrier energies
  and probabilities allows us to see the
  eigenchannels of the system at the barrier radius

11
Z1Z2 496
3-
12
10
8
6
4
2
0
0
Wei et al., Phys. Rev. Lett.
(1991)
Morton et al., Phys. Rev. Lett.
(1994)
12
Fusion barrier distribution
58Ni 60Ni Z1Z2 784
2
2
0
0
13
Fusion barrier distribution
58Ni 60Ni Z1Z2 784
2
0
14
Fusion barrier distribution
58Ni 60Ni Z1Z2 784
2
0
Looks pretty good! Whats the problem? why
should we treat decoherence explicitly? Doesnt
it seem to be invisible inside the barrier?
15
Problem area 1

• Breakup of weakly-bound nuclei
• Excited to energy above breakup threshold outside
  rB
• Coupling to continuum - and back again! (Vnm
  Vmn)
• No irreversibility in CC model
• wavefunction exists in linear superposition
  of fragmented and not fragmented at all distances

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Radioactive neutron-halo nucleus 6He (E lt VB)
Scattering
Breakup, no capture - Irreversible ?
Slow neutrons
Breakupcapture - irreversible
Hot target nucleus - irreversible
Excitation of low-E state - reversible
Stable target nucleus
Classical trajectory model with stochastically
sampled breakup function A. Diaz-Torres et al.,
Phys. Rev. Lett. (2007)
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Problem area 2

• Probing inside the fusion barrier
• High J values (larger Vn to counter centrifugal
  pot)
• High Z1Z2 (larger Vn to counter Coulomb pot)
• Deep sub-barrier tunnelling

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Probing larger nuclear density overlap
J100
J100
Large Z1Z2
E
J70
J0
J0
r
large matter overlap small
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High E,J, large Z1Z2

• High E,J and large Z1Z2 (Classical limit)
• No potential pocket
• Large overlap of matter distributions
• Dominant process is KE loss, J-loss, no capture
• Deep-inelastic scattering up to hundreds of MeV
  E loss
• Energy dissipated into heat irreversible!
• Modelled classically trajectory, friction
  (1970s)
• High E,J or large Z1Z2 at low E,J
• Less matter overlap
• Dominant process is capture (fusion)
• Still see deep-inelastic products with finite
  probability

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A new model is needed

• Treat irreversibility in a consistent way
• Include effect of irreversibility on coherent
  superpositions
• Decoherence
• Need to identify mechanism(s) for decoherence
• Must be internal to colliding nuclear system
  (mini universe)
• Associated with density of levels of system (size
  of environment)
• i.e. lowest energy excited states will not lead
  to decoherence
• Fermi gas level density r exp2(AU/k)1/2
  Uthermal energy
• A200, k8 MeV, U20 MeV 1015
  levels/MeV !
• U E - V
• At inner turning point U 0, at top of barrier
  U0
• Coupling to high energy collective vibrations can
  result in decoherence even when U0 how?

21
Coupling to Giant Resonances

• Giant Resonances volume oscillations dipole,
  quadrupole.
• Highly collective (large coupling strength 80
  of sum-rule)
• High energy (10-20 MeV)
• Identified as likely doorways for energy loss
  already in 1976
• (semi-classical picture) R.A. Broglia, C.H.
  Dasso, Aa. Winther, Phys Lett 61B(1976)113
• Giant resonance states have 10 MeV width
• Rapidly decay to 1015 non-collective states in
  same energy range!
• Environment even when classically U0!

• Lindblad equation, wave packet (A. Diaz-Torres,
  ANU)
• Quantitative coupling to environment
• Energy loss
• Trapping inside fusion barrier
• Wave packet is currently wide (8 energy spread
  want lt1)
• Need additional decoherence where Ugt0 inside
  fusion barrier

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Measurements sensitive to decoherence?

• Fusion barrier distributions for larger Z1Z2
• Lose sharp structures in barrier distributions
  decoherence?

32S208Pb Z1Z21312
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Measurements sensitive to decoherence?

• Deep-sub-barrier tunnelling probability (next
  talk)
• Reduced tunnelling probability decoherence?

• Deep-inelastic probabilities and energy spectra
• Evidence for role of giant resonances in
  decoherence
• Measure properties of reflected flux (next talk)

24
Measurements sensitive to decoherence?

• Mott scattering of identical nuclei
• Loss of amplitude of interference fringes
  decoherence?

Rmin
Probability of excitation depends exponentially
on Rmin Weak measurement distinguishing paths
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Mott scattering
36S 36S Z1Z2 256
208Pb 208Pb Z1Z2 6724
Below fusion barrier
Above fusion barrier
Need to account for flux loss to fusion
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Conclusions

• Irreversibility needs to be correctly
  incorporated into quantum mechanical picture of
  nuclear collisions
• Decoherence through couplings with giant
  resonance
• Quantitative couplings to resonances and
  environment
• Breakup of weakly-bound nuclei
• Irreversibility is clearly necessary
• Decoherence in fusion
• Next talk
• Deep-inelastic reactions irreversible energy
  loss
• Complementary to fusion (scattered back from
  barrier)
• Decoherence in Mott scattering
• May be a sensitive probe?

27
Wrong Way Go Back
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Breakup probabilities vs. Rmin
Extrapolated prompt breakup probability at fusion
barrier radii PBU 0.36 to 0.58 (Depends on L)
Incomplete fusion probability PICF
0.32 (Average over L)
(Hinde et al., Phys. Rev. Lett. 89 (2002) 272701)