Pairing and twonucleon correlations

1
Pairing and two-nucleon correlations

• Herbert Müther
• Universität Tübingen
• with T. Frick, A. Rios, W.H. Dickhoff, A. Polls
• and A. Sedrakian

• Pairing of dressed nucleons
• Self-consistent Greens functions (dressed
  nucleons)
• SCGF plus BCS
• Pairing of fermions with different abundancies
• Blocking effect
• Pairing and symmetry breaking (LOFF, DFS)

2
Mean field BCS in Infinite Nuclear Matter
1S0 neutron-neutron pairing in nuclear matter at
half saturation density

• momentum depend. D(k)
• diff. NN interaction
• diff. Single-particle spectra
• very similar to pairing gaps in finite nuclei.

3
Proton Neutron Pairing in symmetric nuclear
matter at saturation density

• 3S1 and 3D1 contr.

pn pairing gap much larger than nn Obvious
pn interaction more attractive But
finite nuclei?
4
Greens function and T-matrix approach

• Single-particle Greens function
• Dyson equation
• Self-energy , T-matrix

S


g(w) g0(w) g0(w) S(w) g(w)

• Pairing instability
• Finite temperature

5
Self-energy and spectral function

• Strength above and below the Fermi energy as in
  BCS
• gapless superfluidity ?

• Real and imaginary part of the retarded
  self-energy
• kF 1.35 fm-1 ,T 5 MeV, k 1.14 fm-1

6
BCS in the framework of SCGF

• Generalized Greens function Extend

Generalized Dyson equation Gorkov equation
Leads to e.g.

-
D
gpair g - g D f

7
Pairing Self-energy D, generalized Gap equation

• F(w) Fermi function
• If we replace S(k,w) by HF approx. and Spair(k,w)
  by BCS Usual Gap equation
• If we take Spair(k,w) S(k,w) Corresponds to
  the homgenous solution of T-matrix eq.

8
Proton neutron pairing in nuclear matter

Using CDBonn Dashed lines quasiparticle
poles Solid lines dressed nucleons No pairing
at saturation density
9
Pairing and spectral function
Spectral functions S(k,w) dashed Spair(k,w)
solid r 0.08 fm-3 T 0.5 MeV k 193 MeV/c
0.9 kF
10
Pairing in neutron matter
Dressing effects weaker, but non-negligible
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Blocking Effect in asymmetric matter
protons
neutrons

• the DFS phase is favored as compared to LOFF.

Pairing suppressed
Loophole Pair with finite momenta
LOFF Larkin, Ovchinnikov, Fulde, Ferell
12
Pairing Gap in the LOFF phase

• For small asymmetries
• Maximal gap at P0
• For large asymmetries
• Maximal gap at finite P
• There is a region of
• asymmetries, in which
• pairing at finite P only

13
Deformed Fermi Surfaces

• Blocking effects in
• asymmetric nuclear matter

Alternative Loophole Deformed Fermi Surfaces (we
consider quadrupole deformation only)

• Gain in Energy Pairing
• Loss in Energy kinetic energy

14
Gap parameter in DFS
proton
neutron
Prolate neutron and oblate proton Fermi surface
DFS yields breaking of rotational symmetry
only Neutrons with highest momenta along one
axes Protons with highest momenta in a
plane perpendicular to axes
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DFS versus LOFF

• General case where finite momentum and
  deformations are allowed
• Starting from the DFS phase ground state and
  adding finite momentum always increases the
  energy! DFS is the minimum
• Starting from the LOFF phase small perturbations
  reduce the energy LOFF phase is unstable!

Free energy of the combined LOFF DFS phases at
fixed asymmetry
r0.17 fm-3, a0.35, T3 MeV
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Conclusions

• Consistent treatment of short-range and pairing
  correlations
• Short-range correlations quench pairing
  significantly
• No proton-neutron pairing at normal density
• Correlation effects are weaker in neutron matter
• Pairing correlations lead to breaking of
  symmetries
• The DFS phase is favored as compared to LOFF
  (Nuclear Matter, Atom Gas, Quark Matter)