T=0 Pairing in Coordinate space

1
T0 Pairing in Coordinate space
Workshop ESNT, Paris
Shufang Ban
Royal Institute of Technology (KTH) Stockholm,
Sweden
2
Outline

• 1. Introduction delta force in HFB
• 2. Symmetry of the s.p. wave function
• 3. Delta matrix can be real
• 4. If real kappa is possible?
• 5. Summary and further work

3
1. Introduction
1.1 Algorithm for using delta force in HFB
calculations
4
T1 pairing (nn, pp)
Local Delta potential
5
All the possible pairing correlations
Alan L. Goodman, Phys. Rev. C 58(1998)R3051
6
1.2 using delta force in generalized HFB
calculations including np-pairing
Local in Coordinate space
7
2. Symmetries of the s.p. wave function
Four real components
8
2. Symmetries of the s.p. wave function
x y z
1 p
2 _ _ p
3 _ -p
4 _ -p
1 P. Bonche, H. Flocard, and P. H. Heenen,
Nucl. Phys. A 443 (1985) 39
9
2. Symmetries of the s.p. wave function
10
2. Symmetries of the s.p. wave function
Static Triaxial-de Cranking np paring Cranking np paring
Parity Yes Yes Yes Yes
Time-reversal Yes No Yes No
Signature Yes Yes No No
Phase convention Yes Yes Yes Yes
Calculated Coor-space 1/8 1 1/8 2 1/4 1/4
1 P. Bonche, H. Flocard, and P. H. Heenen,
Nucl. Phys. A 443 (1985) 39 2 P. Bonche, H.
Flocard, and P. H. Heenen, Nucl. Phys. A 467
(1987) 475
11
3. Pairing matrix can be real
12
Paring matrix can be real
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
the np pairing can be described in general.
17
5. Summary and further work

• Using delta force, we can get the local pairing
  matrix,
• for both with or without np pairing cases.

2. The np pairing breaks axial and signature
symmetries, we must calculate it in ¼ space when
parity and phase convention are required.

• Chose complex wave function, assume real kappa,
• the pairing matrix can be real.

4. Using complex wave function and real kappa,
the np pairing can be described without lose
generality. There are still remained questions.
18
Thank you !
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
2. Symmetries of the s.p. wave function
x y z
1 p
2 - - p
3 - -p
4 - -p
23
1.2 using delta force in generalized HFB
calculations including np-pairing
Wave function
Delta force
24
5. Summary and further work
Cranking triaxial-deformed wave function as input
Construct density matrix and T1 pairing matrix
in ¼ space
Assure starting values for the delta potential,
T0 paring
Get the H for HFB equation, solve it and get
first U, V
Mixing neutron proton in quasi-particle basis
Calculate new density matrix and pairing matrix
Calculate new density matrix and diagonalizes in
canonical basis