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PAIRING PROPERTIES OF SUPERHEAVY NUCLEI A. Staszczak, J. Dobaczewski and W. Nazarewicz (KFT UMCS) (IFT UW) (ORNL & UT). The constrained HF procedure The constraints act as the external fields capable to deform the nucleus in different ways

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PAIRING PROPERTIES

OF SUPERHEAVY NUCLEI

A. Staszczak, J. Dobaczewski and W. Nazarewicz

(KFT UMCS) (IFT UW) (ORNL & UT)


  • The constrained HF procedure

  • The constraints act as the external fields capable to deform the nucleus

    in different ways

  • The collective coordinates can be defined in a natural way by measuring

  • the deformations generated by the various constraints

The constrained mean field theory defines the deformed states

(BCS- or HFB-type) that solve the variational equation:

quadratic multipole constraints

with the constraint conditions

The multipole constraints prescribe different kinds of deformation characterized by the set of parameters


is the many-body nuclear (non-relativistic) Hamiltonian

center-of-mass “projection” term

(in the VAP technique),

to eliminate spurious mode associated

with the broken translational symmetry

nuclear effective interaction term

(Skyrme, Gogne type forces)

To describe the fission process most “important” are the low-multipolarity

mass moments, i.e.,

“nuclear stretching”

“reflection-asymmetry”

“necking”


Size of the basis

1140 s. p. states of deformed 3D h. o.


Zero-range pairing force:

R. R. Chasman, Phys. Rev. C 14 (1976)1935.

G. F. Bertsch and H. Esbensen, Ann. Phys. (N.Y.) 209 (1991)327.

In the paring (BCS) window Wn/pN (or Z) s. p. states are taken,

parameters are chosen to reproduce Dn/pfor 252Fm.

and

Seniority pairing:

J. Dudek, et al., J. Phys. G6 (1980)447.







Total Energy E tot [MeV]

Hexadecapole Moment Q40 [b2]

Quadrupole Moment Q20 [b]

MIX

SLy4

 Etot

Q40


Pairing Gap Dn/p [MeV]

Total Energy Etot [MeV]

Quadrupole Moment Q20 [b]

MIX

SLy4

 Etot

Dn

Dp


Summary

We compared “volume”, “surface” and “mixed” zero-range nuclear pairing forces with monopole pairing.

Applying “mixed” -interaction we have investigated total binding energies (barriers) and spectral pairing gaps along fission paths of even-even superheavy nuclei with N = 184.




Total Energy E tot [MeV]

Hexadecapole Moment Q40 [b2]

Quadrupole Moment Q20 [b]

G

SLy4


Pairing Gap [MeV]

Total Energy Etot [MeV]

Quadrupole Moment Q20 [b]

G

SLy4

 Etot

Dn

Dp


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