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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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slide1

PAIRING PROPERTIES

OF SUPERHEAVY NUCLEI

A. Staszczak, J. Dobaczewski and W. Nazarewicz

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

slide2

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

slide3

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”

slide4

Size of the basis

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

slide5

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.

slide11

Total Energy Etot [MeV]

Hexadecapole Moment Q40 [b2]

Quadrupole Moment Q20 [b]

MIX

SLy4

 Etot

Q40

slide12

Pairing Gap Dn/p [MeV]

Total Energy Etot [MeV]

Quadrupole Moment Q20 [b]

MIX

SLy4

 Etot

Dn

Dp

slide13

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.

slide16

Total Energy Etot [MeV]

Hexadecapole Moment Q40 [b2]

Quadrupole Moment Q20 [b]

G

SLy4

slide17

Pairing Gap [MeV]

Total Energy Etot [MeV]

Quadrupole Moment Q20 [b]

G

SLy4

 Etot

Dn

Dp

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