,,Sakir Ayik

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• ?? ??,???,Sakir Ayik
• 1. Introduction
• 2. Formulation of quantum diffusion theory
• 3. Barrier crossing problem
• 4. Summary

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? Reaction
Formation process
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J formation process

• Conditional saddle is inside the Coulomb barrier.
• Nuclear intrinsic degrees of freedom are excited.
• ? Energy dissipation
• ? Quasi-fission process is dominant.
• Energy dissipation and diffusion process.

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Classical diffusion process
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?Classical diffusion theory (C.D.T.)
(b reduced friction coefficient)
Thermal fluctuation is considered.
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The problems of C.D.T.
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• The reaction must be occurred
• at low temperature (1 MeV) to get
• the evaporation residues.
• The fission barrier (which arise
• from shell correction energy)
• vanishes at high excitation energies.
• The curvature of
• the conditional saddle (1 MeV).

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Quantum effect is dominant for the case of low
temperature (1 MeV).
We apply quantum diffusion theory to formation
process and calculate the probability to
overcome the conditional saddle.
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• Formulation of QDT

(See nucl-th/0203043, PRC69(2004)054605 for
details.)

• von Neumann eq.

HA collective degrees of freedom to fuse HB
nuclear intrinsic degrees of freedom
(heat bath, environment) VC coupling A with B
Galilei trans.

• Classical trajectory

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• Fluctuation force

• We expand the von Neumann equation with respect
  to f (q(t), x).

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• Wigner transformation

c.f. Kramers equation
Classical fluctuation-dissipation theorem
? ?
? Friction coefficient
? Diffusion coefficient
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• Caldeira-Leggett model

?(), ?(-) by Caldeira-Leggett model
?Spectral function
Consistent with the linear response theory.
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?Caldeira-Leggett model
subspace B Environment
?Spectral densityOhmic dissipation
friction coefficient
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?Normalized ?(E)(t) (diffusion coef.)
? Temperature
non-Markovian effect
Horizontal line Temperature
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?1-dim. barrier crossing problem.
Conditional saddle parabola
P
erfc

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_at_ Note
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• We assume that DAW(p,q,t) is a Gaussian.

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Classical trajectory is given by
W is the barrier curv.(1MeV)
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?Barrier Crossing Probability
Quantum .D.T Classical .D.T const. Q.D.T
neglect the non -Markovian effect
non- Markovian effect
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Summary
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• We develop the quantum diffusion theory and apply
  it to the dynamical formation process.
• The formation probability of QDT is enhanced
  compare with that of classical diffusion theory.

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Future works

• Apply to super-Ohmic case.
• Multi-dimensional diffusion.
• Friction force.
• Initial channel energy dissipation
• Fission statistical and dynamical decay mode.