Decoherence in Nuclear Fusion

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Decoherence in Nuclear Fusion?

• M. Dasgupta
• Department of Nuclear Physics
• The Australian National University
• Canberra, AUSTRALIA

With D.J. Hinde, A. Diaz-Torres, B. Bouriquet,
C. Low, J.O. Newton
G. J. Milburn
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Fusion massive rearrangement of many body
quantum system
due to
Attractive nuclear interactions represented by
a short-range potential
3
r
Described by single potential model
(1) Is this description adequate?
4
Probing decoherence collisions with small
separation
Fusion at energies well above the barrier
significant overlap at the barrier radius
V
Fusion at energies well below the lowest barrier
increasing overlap between barrier radius and
inner turning point
total potential
r
nuclear potential
Butneed to know the nuclear potential!
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In the framework of the current model (coupled
channels)
Fusion at energies well below the lowest barrier
tunnelling dominated
(slope determined by
barrier width)
characterized by potential diffuseness
Fusion at energies around the barrier coupling
dominated
(barrier distribution)
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• Measurements of fusion of 16O with 208Pb and 204Pb

Magic nuclei theoretically easier
16O beam
208Pb target
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Fusion - evaporation
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Fusion - fission
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Fusion products
Alpha decay of residues
16O 208Pb 16O 204Pb
Direct detection
Fusion yield evaporation residues yield
fission yield
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Measuring fusion yields the challenges
Fusion cross-sections At best 10-9 of atomic
cross-sections
Large background of Coulomb scattered beam
particles (108 - 1015) fusion
cross-section ? exp k (E B)
Beam Energy needs to be very well defined
Target thin targets to minimize energy
integration, target impurity lt ppm
Separation and detection identify fusion
products amongst large background
Precision measurements require highly
efficient detection systems,
sophisticated
techniques
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Accelerator facility, Australian National
University
ions injected
Terminal voltage 15 Million Volts
experimental equipment
Beam 0.1c

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Fission Measurements

• Measure fission fragment positions
• Measure flight times
• Deduce velocity vectors

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Measured fusion cross-sections
Dasgupta et al, PRL 99 (2007) 192701
s (mb)
E. B (MeV)
One event per hour
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Fusion cross-section s R2 h? / (2E) ln 1
exp 2p/h? (E B)
E gt B
E lt B
p R2 E-B /E
? exp 2p/h? (E B)
s (mb)
E. B (MeV)
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Logarithmic slope

• cross-sections over several decades to be
  plotted on a
• linear scale
• comparison of tunnelling gradient independent of
  the
• weight of the lowest barrier

Hagino et al, PRC67(2003) 054603
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Logarithmic slope of the measured fusion
cross-sections
d(ln(E?)/dE
E B (MeV)
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Standard Woods-Saxon potential with and without
coupling
(E-shifted)
d ln(?E)/dE
Diffuseness Double folding model
E - B
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a 0.66 fm
d ln(?E)/dE
Factor of 1.5 of discrepancy in logarithmic
derivative
s (mb)
gt Factor of 20 discrepancy in measured and
predicted cross-sections
E B (MeV)
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larger diffuseness of Woods-Saxon potential
Below barrier slope not explained
Data well-above barrier well represented
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a 1.65 fm
Below barrier slope reproduced
d ln(?E)/dE
Data well-above barrier not reproduced
s (mb)
E B (MeV)
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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
Dasgupta et al, PRL 99 (2007) 192701
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Fusion well-below and well-above the barrier
For a given above barrier E cross-section
determined by the limiting l ? determined by
high-l barrier, R
r
Rl at smaller separations than R0
High l
V (MeV)
Inner turning point for a below barrier E appears
at same separation distance as the top of the
high l barrier
Low l
Two parts of fusion excitation function probe the
same separation
(True independent of the particular form of the
nuclear potential)
r (fm)
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Any physical mechanism invoked to explain below
barrier cross-sections should also reproduce
above barrier results

• 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

Is decoherence the answer to our woes?
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Will decoherence help?

• 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

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• Suppression of tunnelling system dependent

16O Pb
s (mb)
expectation
64Ni 64Ni
Jiang et al, PRL 93 (2004) 012701
E B (MeV)

• Ni Ni charge product is larger barrier at
  smaller
• separation than O Pb increased decoherence?

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V
Deviations observed at E 10 below B
r

• 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?

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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

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Summary and outlook

• Measurements of fusion cross-sections for
  well-below to well-above
• barrier for 16O 204,208Pb

• Cross-sections in tunnelling regime fall much
  faster than
• predicted (gtfactor of 20 disagreement in
  cross-sections)

• Commonly used coherent coupled channels model
  fails to provide a
• consistent description of fusion

• Need to go beyond this model consistent
  description with
• decoherence?

• Modelling an isolated system with couplings
  having a strong radial
• dependence - interesting area for new
  developments