Coherence and Decoherence in Collisions of Complex Nuclei
D.J. Hinde, M. Dasgupta, A. Diaz-TorresDepartment of Nuclear PhysicsResearch School of Physical Sciences and EngineeringAustralian National University
G.J. MilburnDepartment of PhysicsUniversity of Queensland
Quantum Information and Many-body Physics, PITP (UBC), Vancouver, Dec’07
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
+++
+
++
Nucleus-nucleus collisions+
++
+++
++
++
Long-range Coulomb repulsion Short-range nuclear attraction Potential barrier – capture or fusion barrier
R
Potential Energy
R
VC Z1*Z2/RCoulomb repulsion
Nuclear attraction Z1 Z2
Fusion Barrier (typically 100 MeV)
rB
VB
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/(1+exp(r-R0)/a) [Woods-Saxon potential]
Exponential at and outside barrier radiusFind 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?
Inter-nuclear potential
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
Nucleus-nucleus collisions
..
ground state
Many excited states
Interacting nuclei are in a linear superposition of various states
197Au
0
77
269 279
keV
Effectively changes the interaction potential
C.H. Dasso et al., Nucl. Phys. A405 (1982) 381
Coupled-channels model
Etc.
197Au 16O 16O
6037
Coupled-channels model
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
J~100, E~100 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)
+ VJ(r) +n – E n(r) +h2 d2
2 dr2 ][ Vnm (r) m(r) = 0m=n/
VJ(r) = VN + VC +J(J+1)h2/2r2
Coupled-channels model
Simplifying approximations for illustration: Two channels n << 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 Z1*Z2
like the uncoupled barrier energy itself Width of barrier distributions ~ 0.1 VB – large effect!
Single-barrier
VB0
E
1
VB2
EVB1
VB3
Distribution of
barrier energies
- eigenchannels
Probability
Probability
nuclei in a superposition of states
Fusion barrier distribution
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
Wei et al., Phys. Rev. Lett. (1991)
Morton et al., Phys. Rev. Lett. (1994)
Concept:Review: Dasgupta et al., Annu. Rev. Nucl. Part. Sci 48 (1998) 401
Rowley et al., Phys. Lett. B254 (1991) 25
3-
0+
2+
4+
6+
8+
10+
12+
0+
Z1Z2 = 496
-200
0
200
400
600
90 95 100 105 110 115
Ec.m. (MeV)
d2 (E
s )/d
E2
ANU
1 ph in each nucleus
58Ni + 60Ni : Z1Z2 = 784Fusion barrier distribution
2+
2+
0+
0+
-200
0
200
400
600
90 95 100 105 110 115
Ec.m. (MeV)
d2 (E
s )/d
E2
ANU
2 ph in each nucleus
Fusion barrier distribution
0+
2+ 2+
2+
58Ni + 60Ni : Z1Z2 = 784
-200
0
200
400
600
90 95 100 105 110 115
Ec.m. (MeV)
d2 (E
s )/d
E2
ANU
3 ph in each nucleus
Looks pretty good!
What’s the problem? – why should we treat decoherence explicitly?
Doesn’t it seem to be “invisible” inside the barrier?
Fusion barrier distribution
2+ 2+ 2+
2+
0+
2+ 2+
58Ni + 60Ni : Z1Z2 = 784
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
ScatteringBreakup, no capture- Irreversible ?
Breakup+capture- irreversible
Radioactive neutron-halo nucleus 6He (E < VB)
Hot target nucleus- irreversible
Slow neutrons
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)
Problem area #2
Probing inside the fusion barrier High J values (larger Vn to counter centrifugal
pot) High Z1*Z2 (larger Vn to counter Coulomb pot) Deep sub-barrier tunnelling
Probing larger nuclear density overlap
E
large matter overlap small
J=0
J=100
J=70
r
Large Z1*Z2
J=0
J=100
High E,J, large Z1*Z2
High E,J and large Z1*Z2 (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 (1970’s)
High E,J or large Z1*Z2 at low E,J Less matter overlap Dominant process is capture (fusion) Still see deep-inelastic products with finite probability
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 : exp[2(AU/k)1/2] U=thermal energy A=200, k=8 MeV, U=20 MeV 1015 levels/MeV !
U = E - V At inner turning point U = 0, at top of barrier U=0 Coupling to high energy collective vibrations can result in
decoherence even when U=0 – how?
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” U=0! 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 <1%) Need additional decoherence where U>0 inside fusion barrier
Measurements sensitive to decoherence?
Fusion barrier distributions for larger Z1*Z2
Lose sharp structures in barrier distributions – decoherence?
-100
0
100
200
300
400
500
600
130 135 140 145 150 155 160
EC.M. (MeV)
d2E
/dE
2 (
mb
MeV
-1)
DE = 1.5-2.0 MeV
1 ph S,1 ph Pb
2 ph S, 2ph Pb
DE = 2.0-3.0 MeV
32S+208Pb: Z1Z2=1312
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)
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
Mott scattering
0
100
200
300
400
500
600
700
35 37 39 41 43 45
Theta lab (deg)
Co
un
ts
Experimental data Theoretical curve
0
100
200
300
400
500
600
700
35 36 37 38 39 40 41 42 43 44 45
Theta lab (deg)
Cou
nts
Experimental Data Theoretical Curve
Below fusion barrier
Above fusion barrier
36S + 36S : Z1Z2 = 256
Need to account for flux loss to fusion
208Pb +208Pb : Z1Z2 = 6724
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?
Wrong Way Go Back
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)
Fusion barrier radius(absorption)
