Decoherence in Nuclear Fusion?
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Transcript of Decoherence in Nuclear Fusion?
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Decoherence in Nuclear
Fusion?
With:
D.J. Hinde, A. Diaz-Torres,
B. Bouriquet, C. Low, J.O. Newton
G. J. Milburn
M. Dasgupta
Department of Nuclear Physics
The Australian National University
Canberra, AUSTRALIA
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Attractive nuclear interactions – represented by a short-range potential
Fusion – massive rearrangement of many body quantum system
due to
Potential energy
attractive nuclear
Repulsive electrostatic
r
Barrier against fusion
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V
r
r
Described by single potential model
Inclusion of coherent superposition of distinct physical states of the separated nuclei
Multitude of excitations
complete dissipation of the K.E. into internal excitations
Coupled-channels modelBlack hole
(1) Is this description adequate?
Decoherence?
(2) Are effects of decoherence observed?
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Probing decoherence – collisions with small separation
Fusion at energies well below the lowest barrier –
increasing overlap between barrier radius and inner turning point
V
r
Fusion at energies well above the barrier –
significant overlap at the barrier radius
But…need to know the nuclear potential!
nuclear potential
total potential
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Fusion at energies well below the lowest barrier – tunnelling dominated
(slope determined by barrier width)
Fusion at energies around the barrier – coupling dominated
(barrier distribution)
In the framework of the current model (coupled channels):
Fusion at energies well above the barrier – potential dominated
(determined by nuclear potential shape)
characterized by diffuseness
characterized by potential diffuseness
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Measurements of fusion of 16O with 208Pb and 204Pb
16O beam 208Pb target
Magic nuclei – theoretically easier
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Fusion - evaporation
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Fusion - fission
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16O + 208Pb
16O + 204Pb
fission
nevaporation residue
Alpha decay of residues
Direct detection
Fusion products
Fusion yield = evaporation residues yield + fission yield
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Beam – Energy needs to be very well defined
Target – thin targets to minimize energy integration, target impurity < ppm
Precision measurements require – highly efficient detection systems,
– sophisticated techniques
Separation and detection – identify fusion products amongst large background
– Large background of Coulomb scattered beam
particles (108 - 1015)
– fusion cross-section exp { k (E – B) }
Measuring fusion yields – the challenges
Fusion cross-sections – At best 10-9 of atomic cross-sections
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Terminal voltage:
15 Million Volts
experimental equipment
Beam 0.1c
ions injected
Accelerator facility, Australian National University
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Fission fragmentdetector 1
Fission fragmentdetector 2
Beam
Monitor detectors(out of plane)
Target
Fissionfragment 1
Fission fragment 2
Fission Measurements
• Measure fission fragment positions• Measure flight times• Deduce velocity vectors
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0.00001
0.0001
0.001
0.01
0.1
1
10
100
1000
-12 -8 -4 0 4 8 12 16 20E - B (MeV)
s (
mb)
16O+208Pb Fusion this work
16O+204Pb Fusion this work
16O+208Pb Fusion PRC60
s (m
b)
16O + 208Pb this work
16O + 208Pb Morton et al (1997)
16O + 204Pb this work
E. – B (MeV)One event per hour
Measured fusion cross-sections
Dasgupta et al, PRL 99 (2007) 192701
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0.00001
0.0001
0.001
0.01
0.1
1
10
100
1000
-12 -8 -4 0 4 8 12 16 20E - B (MeV)
s (
mb)
16O+208Pb Fusion this work
16O+204Pb Fusion this work
16O+208Pb Fusion PRC60
s (m
b)
16O + 208Pb this work
16O + 208Pb Morton et al (1997)
16O + 204Pb this work
E. – B (MeV)
Fusion cross-section: σ = R2 ħω / (2E) ln [ 1 + exp { 2π/ħω (E – B) } ]
E > B
π R2 [ E-B ] /E
E < B
exp { 2π/ħω (E – B) }
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Logarithmic slope
d [ln(sE)]
dE
cross-sections over several decades to be plotted on a linear scale
comparison of tunnelling gradient independent of the weight of the lowest barrier
Below barrier shape deviates from parabolic d ln(sE) /dE increases
Parabolic barrier: sE exp[(2/ћ )(E – B)]
= 2ћd [ln(sE)]
dE Value independent of B
Hagino et al, PRC67(2003) 054603
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d(ln
(Es)
/dE
E – B (MeV)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-12 -10 -8 -6 -4 -2 0 2 4 6 8
16O+208Pb 2004 (2 MeV)
16O+204Pb 2004 (2 MeV)
16O+208Pb 1997 (2 Mev)
16O + 208Pb this work
16O + 208Pb Morton et al (1997)
16O + 204Pb this work
Logarithmic slope of the measured fusion cross-sections
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Standard Woods-Saxon potential with and without coupling
d [ln(sE)]/dE
0
500
1000
1500
-10 0 10 20 30 40
E – B (MeV)
s (mb)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-12 -10 -8 -6 -4 -2 0 2 4 6 8
16O+208Pb 2004 (2 MeV)
16O+204Pb 2004 (2 MeV)
16O+208Pb 1997 (2 Mev)
a=0.66 fm, no coupling, iwbc
a=0.66, coupled, IWBC
a = 0.66 fm, coupled
a = 0.66 fm no coupling
E - B
(E-shifted)
Diffuseness: Double folding model
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0.000001
0.00001
0.0001
0.001
0.01
0.1
1
10
-12 -10 -8 -6 -4 -2 0E - B (MeV)
s (
mb
)
0.0
1.0
2.0
3.0
-12 -8 -4 0 4 8
a = 0.66 fm
Factor of 1.5 of discrepancy in logarithmic derivative
> Factor of 20 discrepancy in measured and predicted cross-sections
E – B (MeV)
d [l
n(sE
)]/d
Es
(mb)
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larger diffuseness of Woods-Saxon potential
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-12 -10 -8 -6 -4 -2 0 2 4 6 8
16O+208Pb 2004 (2 MeV)
16O+204Pb 2004 (2 MeV)
16O+208Pb 1997 (2 Mev)
a=1.18 fm, no coupling, iwbc
a=1.18, coupled, IWBC
0
500
1000
1500
-10 0 10 20 30 40
16O+208Pb Fusion
a=1.18, no coupling, IW BC
a=1.18 fm, coupled, IW BC
E – B (MeV)
s (mb)
d [ln(sE)]/dE
a = 1.18 fm, coupled
a = 1.18 fm no coupling
Data well-above barrier well represented
Below barrier slope not explained
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0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
-12 -10 -8 -6 -4 -2 0 2 4 6 8
16O+208Pb 2004 (2 MeV)
16O+204Pb 2004 (2 MeV)
16O+208Pb 1997 (2 Mev)
a=1.65 fm, no coupling, iwbc
0
500
1000
1500
-10 0 10 20 30 40
16O+208Pb Fusion
a=1.65, no coupling
E – B (MeV)
s (mb)
a = 1.65 fm
d [ln(sE)]/dE
Below barrier slope reproduced
Data well-above barrier not reproduced
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0.000001
0.00001
0.0001
0.001
0.01
0.1
1
10
-12 -10 -8 -6 -4 -2 0E - B (MeV)
s (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. – B (MeV)
simultaneous description of fusion well-above
and well-below the barrier is not obtained
Some physical effect not being included → affects fusion in both energy
regimes
0
500
1000
1500
-10 0 10 20 30 40
E - B (MeV)
s(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. – B (MeV)
s(mb)
Dasgupta et al, PRL 99 (2007) 192701
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0
50
100
150
5 10 15 20
Inner turning point for a below
barrier E appears at same
separation distance as the top of
the high l –barrier
Fusion well-below and well-above the barrier
Two parts of fusion excitation function probe the same separation
For a given above barrier E –
cross-section determined by the
limiting l → determined by high-l barrier, R
Rl at smaller separations than R0
Low l
High l
r (fm)
V (
MeV
)
r
(True independent of the particular form of the nuclear potential)
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Not true for explanations so far:
Shallow nuclear potential (~ 10 MeV) → leads to no trapping
potential pocket for higher l –value
Large diffuseness used for above barrier results → fail to describe
below barrier cross-sections
Any physical mechanism invoked to explain below barrier cross-sections
– should also reproduce above barrier results
Is decoherence the answer to our woes?
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A gradual onset of decoherence – with increasing overlap → system
becomes more classical → tunnelling increasingly suppressed as E is
reduced
It can result in energy dissipation – giving angular momentum and energy
loss → changes the above barrier cross-section
Will decoherence help?
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0.000001
0.00001
0.0001
0.001
0.01
0.1
1
10
-12 -10 -8 -6 -4 -2 0E - B (MeV)
s (m
b)
E – B (MeV)
expectation
Suppression of tunnelling – system dependent
64Ni + 64Ni
s (m
b)
Ni + Ni – charge product is larger – barrier at smaller
separation than O +Pb – increased decoherence?
16O + Pb
Jiang et al, PRL 93 (2004) 012701
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Ni + Ni results extrapolated (by others) to reactions of
astrophysical interest e.g. C + C
O + Pb data do not support such extrapolation
Need to have an understanding of the correct physics
Is there another probe?
V
r
Deviations observed at E ~ 10% below B
Astrophysical interest
E << B
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Reflected flux complementary to tunnelling
Deep inelastic events (events with large energy loss) even at deep-sub-barrier energies
Experiments done and more planned
Log
(pro
babi
lity)
Measured energy (MeV)50 100
Giant resonances
elastic
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Summary and outlook
Cross-sections in tunnelling regime fall much faster than
predicted (>factor of 20 disagreement in cross-sections)
Measurements of fusion cross-sections for well-below to well-above
barrier for 16O + 204,208Pb
Need to go beyond this model – consistent description with
decoherence?
Commonly used coherent coupled channels model fails to provide a
consistent description of fusion
Modelling an isolated system with couplings having a strong radial
dependence - interesting area for new developments