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Quantum Coherence and Decoherence in Low Energy Nuclear Collisions:
from Superposition to Irreversible Outcomes
D.J. HindeDepartment of Nuclear Physics
Research School of Physics and EngineeringThe Australian National University
With M. Dasgupta, M. EversDepartment of Nuclear Physics
Research School of Physics and EngineeringThe Australian National University
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Collision of two nuclei – relative co-ordinate r Coulomb repulsion – long range Nuclear attraction – short range – nucleonic d.o.f. Inter-nuclear potential
Isolated from external environments Mini-Universe MeV, fm (10-15m), zs (10-21s) Describe all constituents, all interactions Fully coherent q.m. description of collision
Introduction
r
r
V
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Geiger, Marsden, Rutherford (1909) : +197Au Discovered atomic nucleus Low energy – Coulomb field only Elastic (Rutherford) Scattering
E. Schrödinger
The first experiment studying nuclear collisions
Higher energy, Z1Z2 – inelastic scattering (excited states) Describe pure elastic scattering: optical model
Schrödinger eqn. + phenomenological imaginary potential Detector makes measurement
K.E.
dd
r
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Irreversible nuclear collision (fusion)
Neutron interaction with nucleus Bohr’s compound nucleus model Energy spread amongst nucleons Capture – “compound nucleus” Thermalization – Heat Bath
Effectively irreversible “Measurement” on neutron performed by nucleus (nucleons)
Nature 1936 N. Bohr
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Characterizing a “hot” nucleus
Fermi Gas Permutations of nucleon excitations Level density exp(aEx)1/2
Low energy collective states Surface vibrational states Rotational states Volume vibrational states
Excita
tion E
nerg
y
Collective states
Ground state
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Including excitations of colliding nuclei
Fermi Gas Permutations of nucleonic excitations Level density Collective surface vibrations, rotations Collective volume vibrations Excited states of separated nuclei Coulomb field Nuclear interaction Relative motion Coupling to (collective) states Includes some nucleonic d.o.f.
Excita
tion E
nerg
y
Collective states
Ground state
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Coupled-channels equation: key variable separation (r)
Channels (n,m) : combination of Projectile,Target states Strongly-coupled (collective) channels Reversible couplings (Vnm= Vmn) Boundary conditions :
Below-barrier scattering: distant boundary: Incoming plane wave in channel “0” (both nuclei in ground states) Outgoing spherical waves in all channels
+ VJ(r) +n – E φn(r) +h2 d2
2 dr2 ][ Vnm (r) φm(r) = 0m=n/
VJ(r) = VN + VC +J(J+1)h2/2r2 (Superposition of all J)
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Coupled-channels equation: key variable separation (r)
+ VJ(r) +n – E φn(r) +h2 d2
2 dr2 ][ Vnm (r) φm(r) = 0m=n/
VJ(r) = VN + VC +J(J+1)h2/2r2
r
Coherent superposition
Below-barrier
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Coupled-channels equation: key variable separation (r)
Channels (n,m) : combination of Projectile,Target states Strongly-coupled (collective) channels Reversible couplings (Vnm= Vmn) Boundary conditions :
Below-barrier scattering: distant boundary: Incoming plane wave in channel “0” (both nuclei in ground states) Outgoing spherical waves in all channels
+ VJ(r) +n – E φn(r) +h2 d2
2 dr2 ][ Vnm (r) φm(r) = 0m=n/
VJ(r) = VN + VC +J(J+1)h2/2r2 (Superposition of all J)
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Coupled-channels equation: key variable separation (r)
+ VJ(r) +n – E φn(r) +h2 d2
2 dr2 ][ Vnm (r) φm(r) = 0m=n/
VJ(r) = VN + VC +J(J+1)h2/2r2
r
Coherent superposition
Above-barrier?
? = Excited “Molecular” (compound nucleus) states
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Irreversible nuclear collision (fusion)
Neutron interaction with nucleus Bohr’s compound nucleus model Energy spread amongst nucleons Capture – “compound nucleus” Thermalization – Heat Bath
Fusion is irreversible (no superposition of fusion, elastic scattering)
Energy dissipation to other d.o.f. – c.n. nucleonic “heat bath” CC model does include nucleonic degrees of freedom explicitly
Nature 1936 N. Bohr
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Coupled-channels model
Channels: combination of P,T states (n,m) Include strongly-coupled (collective) channels Reversible couplings (Vnm= Vmn)
How is this physics inside the barrier treated in CC model ? Ingoing wave in superposition of all channels – “black hole” – IWBC
Imaginary potential acting on wavefunction – attenuation, absorption
Flux remains in superposition (scattered) or is “lost without trace”
Lost flux identified with fusion – in barrier passing picture, loss should only be inside barrier!
+ VJ(r) +n – E φn(r) +h2 d2
2 dr2 ][ Vnm (r) φm(r) = 0m=n/
VJ(r) = VN + VC +J(J+1)h2/2r2
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Barrier-passing picture – inside barrier(i) imaginary potential(ii) incoming wave boundary
condition Lost probability fusion
K.E. lost to complex excitations
Colliding nuclei lose individual identities – merge together
Fusion - completely irreversible
Coupled channels equations
Fusion – physical picture: Fusion – as modelled:
Nuclei in superposition of states (Include limited number of low lying collective
states, Purely quantal – reversible dynamics)
Irreversible Coherent superposition - reversible
r
Above-barrier
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Elastic scattering
Superposition of states
Channel couplings: scattering
Nuclei in ground-states
208Pb 3-
Inelastic scattering
Nucleon transfer reactions
TKEL (MeV)
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Single-barrier
VB0
E
1
VB2
EVB1
VB3
Approximation:
3 eigen-channels
3 eigen-barriers
Probability
Probability
Superposition of 3 states
Channel couplings: barrier distribution
Nuclei in ground-states
Reflected flux - scattering
Transmitted flux - fusion
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X. Wei et al., Phys. Rev. Lett. (1991) C.R. Morton et al., Phys. Rev. Lett. (1994)
3-
0+2+4+6+8+
10+
12+
0+
Z1Z2 = 496
Superposition, barrier distribution essential to describe near-barrier fusion!
Concept: N. Rowley et al., Phys. Lett. B254 (1991) 25
Review: M. Dasgupta et al., Annu. Rev. Nucl. Part. Sci. 48 (1998) 401
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Near barrier energies - coherence and dissipation
• Quantum: Coherent superposition - scattering, fusion barrier distribution
• Dissipative (irreversible energy dissipation)
- deep inelastic collisions
- compound nucleus formation
Classical or Semiclassical
treatment
GRAZING
Coupled channels formalism
Imposed mathematical
conditions
• Strong divide between two classes of model
do not include KE-dissipation out of CC model space in
scattering
unable to include superposition in classical dissipative models
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r
Irreversible dissipation
Coherent superposition – reversible couplings
r
Where is the transition?It is gradual or sharp?
How does it affect fusion?
Smooth transition from superposition to dissipation
Low Z1Z2
High Z1Z2
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Information from energy dissipative reactions
Fusion – energy- damping “invisible” inside barrier ? Deep inelastic events – energy damping mechanism?
Deep-inelastic measurements – systematics of E-dissipation
Fusion – above-barrier cross sections
– quantum tunnelling probability
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Mapping energy to radial separation
Radial dependence of probabilities
r
r
V
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Sub-barrier energy dissipation – nucleon transfer
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16O + 208Pb
Nucleon cluster transfer (2p,
208Pb 3-
n
p
2p
TKEL (MeV)
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32S + 208Pb E/VB = 0.96
Sub-barrier energy dissipation – nucleon transfer
g.s.
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Sub-barrier energy dissipation – nucleon transfer
Z=2: E* ~ 5-25 MeV, peak at 12 MeV
2p and -transfer (cluster transfer)
32S + 208Pb
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DIC Energy loss: (TKEL or E*)
40Ca + 208Pb E/VB = 1.05
S. Silzner et al., PRC 71(2005)044610
Eloss ~ 40 MeV
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10-6
10-5
10-4
10-3
10-2
10-1
100
101
103
102
55 65 75 85 95 105
EC.M. (MeV)
(m
b)
Transfer or Deep-Inelastic? Doesn’t matter what we call it Energy irreversibly lost
VB
19F + 232Th fission > 6 MeV (fission barrier)
Fusion-fission
Peripheral
Some flux in superposition Some flux with energy dissipation Lost to complex nucleonic degrees
of freedom – heat bath
Standard quantum models or classical models cannot simultaneously describe
Need to model “quantum to classical”
103
19F D.J. Hinde unpublished
E* in heavy nucleus – thermalized - fission
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From coherent superposition to irreversible outcome
W.H. Zurek, Rev. Mod. Phys. 75 (2003) 715; Phys. Today 44 (1991) 36 M. Schlosshauer, Decoherence and the quantum to classical transition, Springer (2007)
• Quantum decoherence – “dynamical dislocalization of Q.M.
superpositions”
(H.D. Zeh arXiv:quant-ph/0512078 v2) coherence shared with (lost in) environment
Idealized isolated system
Superposition of basis states
Described by coherent Q.M.Irreversible outcome (classical)
System “entangled” with environmentLoss of coherence in smaller
system
system
Complex environment
Sub-system
Larger system
Sub-system entangled with rest of system
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Example: Electron entanglement with a surface
Interference fringes
Heig
ht
ab
ove s
urf
ace
Splitter
Screen
Semiconductor
surface
Double-slit type experiment with single electrons
Electron passing above disturbs electrons in semiconductor
“which way” information destroys spatial coherence
Semi-conductor surface
RefocusSource
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Steep radial dependence Probability at RB ~ 0.1
Inside RB larger Nuclear interaction
Radial dependence of Z=2 probability
10-1
100
10-2
10-3
r
32S + 208Pb
RB
Pro
babili
ty
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Nuclei isolated – not external environment but internal
Nuclei overlap, interact strongly – nucleonic d.o.f. opened up
• Effectively irreversible Eloss from CC
space• Need to model dynamics outside CC space• Within Q.M. framework
P-space
Q-space
CC space
Nucleonic d.o.f.
relative motion + few channels
(collective, transfer?)
CC space
Scattering to discrete
states
– only need CC + Imaginary
potFeschbach formalism
Nucleonic d.o.f.
DIC – energy dissipation
in scattered flux
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Probing decoherence through fusion
E
large matter overlap small
J=0
J=70
r
Large Z1*Z2
J=0
J=100
Coherent superposition
Compound nucleus
Decoherence
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Reduction in fusion at above barrier energies
46 fusion excitation functions
Newton et al., PRC 70 (2004) 024605
increased reduction of fusion with Z1Z2
Fusion suppression above-barrier
Reported deep inelastic probability
close to VB
Wolfs, PRC 36 (1987) 1379Wolfs et al, NP 196 (1987) 113Keller et al, PRC36 (1987) 1364
Abov-b
arr
ier
suppre
ssio
n
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Fusion below and above the barrier inconsistent
– need to go beyond current models
– need to incorporate transition to irreversibility
explicitly
0.000001
0.00001
0.0001
0.001
0.01
0.1
1
10
-12 -10 -8 -6 -4 -2 0E - B (MeV)
(mb)
16O+208Pb
16O+204Pb
a = 0.66 fm
a = 1.65 fm
a = 1.18 fm
101
100
10-1
10-2
10-3
10-4
10-5
10-6
16O+208Pb
16O+204Pb
16O + 208Pb
16O + 204Pb
a = 0.66 fm
a = 1.18 fm
a = 1.65 fm
Ec.m. – VB (MeV)
0
500
1000
1500
-10 0 10 20 30 40
E - B (MeV)
(m
b)
a = 1.18 fm
a = 0.66 fm
a = 1.65 fm
a = 0.66 fm
a = 1.18 fm
a = 1.65 fm
Ec.m. – VB (MeV)
(mb)
M. Dasgupta et al., PRL 99 (2007) 192701Ni+Ni: C.L. Jiang et al., PRL 93 (2004) 012701
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Discussion points
• Extend coupled-channels model (or CRC)
• Nucleonic d.o.f. of separate nuclei vs. “molecular” nucleonic d.o.f. ?
• Links with decoherence in other quantum systems (here we are!)
- include many states at high Ex ?
- generic treatment or case-by-case (experiment) ?
- eliminate need for imaginary potential ?
- eliminate need for “friction” at high J (Bass model) ?
- describe DIC and coherent phenomena ?
• Feschbach model – P+Q vs. degrees of freedom
• Decoherence without dissipation ? (Mott scattering ?)
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Vtot
r (fm)
l =0
Woods-Saxon a = 0.66 fm
a = 1.18 fm
Qfus
Vtot
Elongation (fm)
Woods-Saxon a = 0.66 fm
adiabaticsudden
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Vtot
r (fm)
l =0
l =60
Woods-Saxon
a = 0.66 fm
a = 1.18 fm
Vtot
Qfus
Vtot
Elongation (fm)
Woods-Saxon a = 0.66 fm
adiabaticsudden
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Wolfs, PRC 36 (1987) 1379
Kinetic energy losses > 20 MeV
Deep inelastic reactions at E < VB
VB
Wolfs et al., PLB 196 (1987) 113
Keller et al., PRC 36 (1987) 1364
Near-barrier DIC: 58Ni+112Sn
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Recent density matrix model with coherence and
decoherence A. Diaz-Torres et al., Phys. Rev. C78(2008)064604
relative motion + few channels
(collective, transfer) Track energy dissipated through different
mechanisms
Suppresses quantum tunnelling (sub-barrier fusion)
Future applications: deep sub-barrier fusion –
astrophysics
GDRNucleonic d.o.f.
(ZP)(ZT)Nucleonic d.o.f.
(ZP-2)(ZT+2)
CC space
transfe
r
Doorway
states
(ZP+ZT)
Molecular C.N. d.o.f.
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Example: observation of collisional decoherence
Collision with a gas molecule localizes C70 destroys spatial
coherence
Independent point
source of
C70
diffraction
interference pattern measured
Single collision sufficient to destroy interference
Hornberger et al, PRL 90 (2003) 160401
Fringe visibility decreases with increasing pressure
System - environment interaction (measurement) - decoherence
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0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.80.2 0.4 0.6 0.80.2 0.4 0.6 0.80.2 0.4 0.6 0.8
E=143.2 MeV E=147.6 MeV E=152.0 MeV E=159.9 MeV E=168.2 MeV
[deg
] c
.m.
coun
ts
102
103
104
1
10
x 0.20 x 0.05 x 0.10
MR
x 0.15
50
100
150
180
45
135
90
0
0
32S + 232Th MAD vs. E/VB (Timescale ~10-20 s)E/VB =
0.93E/VB = 0.96
E/VB = 0.98
E/VB = 1.03
E/VB = 1.09
D.J. Hinde et al., PRL 101 (2008) 092702R. Bock et al., NP A388 (1982) 334 J. Toke et al., NP A440 (1985)
327
W.Q. Shen at al., PRC 36 (1987) 115 B.B. Back et al., PRC 53
(1996) 1734
(Shown effect of entrance channel dominant over EX)D.J. Hinde et al., PRL 100 (2008) 202701
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Mass-Angle Distributions for quasi-fission
235 MeV 48Ti
48Ti + 196Pt 48Ti + 186W 48Ti + 154Sm
MRMR MR
C.M.
Elastic, quasi-elastic and deep inelastic events
Detector acceptance
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0
45
90
135
180
0 0.5 1MR
(d
eg.)
(deg
.)
0
0.5
1
0 20 40 60 80Time
MR
04590
135180
0 20 40 60 80Time
(d
eg.)
MAD – mass-equilibration and rotation (GSI 1980’s)
Miminal mass-angle correlationStrong mass-angle correlation
160o
20o Scission
R. Bock et al., NP A388 (1982) 334
J. Toke et al., NP A440 (1985) 327
W.Q. Shen at al., PRC 36 (1987) 115
B.B. Back et al., PRC 53 (1996) 1734
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102
10
10.4 0.2 0.4 0.20.0 0.2 0.4 0.0 0.2 0.4
b)a)
0.2
0.4
0.0
0.4
0.2
v [
cm/n
s]
v - v [cm/ns]|| c.m.
232Th – fission after peripheral collision – Eloss – transfer/DIC
Energy dissipated → EX target → deformation energy → fissionE/VB = 0.96
E/VB = 1.03
16O D.J. Hinde et al., PRC 53 (1996) 1290
E* in heavy fragment - thermalized
32S D.J. Hinde et al., PRL 101 (2008) 092702
32S + 232Th fission: Velocity of fissioning nucleus w.r.t. C.M. velocity