Relative kinetic energy correction to fission barriers

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Relative kinetic energy correction to fission
barriers

• 1. Motivation
• 2. Results for A70-100 systems
• 3. A cluster model perspective
• 4. Prescription based on w.f. localization
• some results
• 5. Conclusions

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A
A relative kinetic energy problem
Nucleus A100, ET intrV,
T intr T- T cm
100 nucleons, T intr 0
2 nuclei A50, T intr(5050) T intr (100) T
rel T rel T cm1 T cm2 T cm(12)
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Within HF
Asymptotically
The last term is T rel and should be subtracted
to have a correct barrier for fusion, J.F.
Berger and D. Gogny, N.P. A 333 (1980) 302
Fission barriers In macro-micro mathods, a
deformation dependent Wigner term was
introduced to improve agreement with the data for
lighter systems, W.D. Myers and W.J. Swiatecki,
N.P. A 612, 249 (1997) Problems with a
transition from one- to two-piece systems are
spelled out in P. Moller, A.J. Sierk and A.
Iwamoto, P.R.L. 92, 072501 (2004)
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Our code assumes two symmetry planes, so we can
study tip- and side collisions. The HF (BCS)
problem is solved on a spatial mesh.
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Various forces have specific prescriptions to
correct for the c.m. motion of the
system -one-body part of P2/2Am amounts to
16.5-18.5 MeV (like SkM) -total P2/2Am (with
two body part) amounts to 5-8 MeV (like SLy6)
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P.R. C 74, 051601(R) (2006)
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16 T.S.Fan et al.., N.P.A 679, 121 (2000) 8
K.X. Jing et al., N.P. A 645, 203 (2000)
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48 Ca 208 Pb
48 Ca 48 Ca
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Dispersion of particle number in the k-th
orbital
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Gradual subtraction of E kin rel no exact
prescription available
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48 Ca 244 Pu Z114, A292
Q 225 b, For SkM E constr E neck 25.7
MeV vs 15 MeV
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Can one learn anything from the theory of light
nuclei? R.G. Lovas et al., Phys. Rep. 294, 265
(1998)
Overcomplete basis
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No prescription for T rel.
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B corr 4.2 MeV
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Q300 b
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At Q200 b, T rel 1.9 MeV
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Q125 b
Q200 b
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