the Wigner energy and the generalized. blocking phenomenon. cranking in isospace - response of t=0 pairing. against rotations in isospace. reality or fiction ?. n-p pairing in N=Z nuclei. Motivation & fingerprints ( basic concepts ): . W. Satuła University of Warsaw. - PowerPoint PPT Presentation
30
n-p pairing in N=Z nuclei W. Satuła University of Warsaw reality or fiction? Motivation & fingerprints (basic concepts): cranking in isospace - response of t=0 pairing against rotations in isospace elementary isobaric exciatations in N~Z nuclei – a need for isosopin symmetry restoration the Wigner energy and the generalized blocking phenomenon symmetric nuclear matter calculations binding energies - mean-field crisis around N~Z line high-spin signatures of pn-pairing
Transcript
n-p pairing in N=Z nuclei
W. SatułaUniversity of Warsaw
reality or fiction?
Motivation & fingerprints (basic concepts):
cranking in isospace - response of t=0 pairing against rotations in isospace
elementary isobaric exciatations in N~Z nuclei – a need for isosopin symmetry restoration
the Wigner energy and the generalizedblocking phenomenon
symmetric nuclear matter calculations binding energies - mean-field crisis around N~Z line
high-spin signatures of pn-pairing
Structure of nucleonic pairs N=Z nucleons start to occupy „identical” spatial
orbitals Nuclear interaction favoures L=0 coupling Pair-structure is governed by the Pauli principle:
– Isovector (or 1S0) pairs T=1, S=0
- Isoscalar (deuteron-like or 3S1) pairs T=0, S=1
Tz +1 0 -1
Sz +1 0 -1
Neutron
+
-
Proton
From M. Baldo et al. Phys. Rev. C52, 975 (1995)
free-space sp spectrum
BHF sp spectrum
(in-mediumcorrections)
3S1-3D1 (coupled) pairing gap in symmetric Nuclear Matter from Paris VNN
tensor-forceenhancement
Gaps from local effective pairing interaction
E. Garrido et al. PRC60, 064312 (1999)PRC63, 037304 (2001)
DDDI:
DDDI used in Skyrme-HFB calculations by Terasaki et al. NPA621 (1997) 706.
Cut-off!!!(otherwise divergent!)
Isoscalar pairingTensor forceenhancement
ro
3S1-3D1 (coupled) pairing gap in symmetric Nuclear Matter including relativistic corrections
Includes relativistic in-medium corrections(sp levels from Dirac-Brueckner-HF)
Saturationdensity
O. Elgaroy, L.Engvik, M.Hjorth-Jensen, E.Osnes, Phys.Rev.C. 57 (1998) R1069
Empirical NN interaction in N~Z
T=1 channel: J=0 coupling
dominates T=0 channel:
J=1 and J=2j are similar
T=0 is, on the average, stronger than T=1 by a factor of ~1.3
The lowest: T=0, T=1 & T=2 in e-e nuclei T=0 & T=1 states in o-o nuclei The model needs to be extended to include isospin projection isospin cranking
A. Macchiavelli et al. Phys. Rev. C61 (2000) 041303(R) J.Janecke, Nucl. Phys. A73 (1965) 73
strong T=0 pairing limit!
Energy:
The extreme s.p.model:
4-fold degenerated equidistant
s.p. spectrum
Eigen-states (routhians) are 2-fold (Kramers) degene-rated „stright lines”:
Crossings form simple arithmetic serie:
„inertia” defined throughmean level spacing !!!
0
5
10
15
20
20 30 40 50 A
DET
=2 [M
eV]
hWS+HT=1 -wtx
2028
14
T=2
iso -crank ing
vacuum
T=2 states in e-e nuclei
hWS+HT=1+HT=0-wtx
DE= deT212
Iso-cranking gives excitation energy which goes like:
mean level spaceing at the Fermi energy
+ Epair
D [M
eV]
0
1
2
3
0 1 2 3hw [MeV]
DT=0
DT=1
48Cr
0
1
2
3 6
Tx
(iso)Coriolis antipairing effect
D/e = 0.5;1.0;1.50
0.5
1.0
1.5
iso-
mom
ent o
f ine
rtia D/e = 0.001
0.3
0.4
0.5
0.6
0.7
0 1 2 3
Tz01234is
o-m
omen
t of i
nerti
a
hw
e=1
iso-MoI
T=1 states in e-e N=Z nuclei T=1 states: 2qp + isocranking
Isocranking N=Z odd-odd nuclei
3de
T
4
2
5
3
10iso-signatureselection rule
de
de
2de 4de 6de
hw
de
de
de
de 5de hw
de
odd-T sequence
even-T sequence
Eeven-T = 1/2deTx2
Eodd-T = 1/2deTx2 - 1/2de
DET=
1 - D
E T=0
[MeV
]
-0.5
0.0
0.5
1.0
20 30 40 50 60 70A
crank
ing2qp
vacuum
T=1T=0
expth
T=0 vs T=1 states in o-o N=Z nuclei
Neutron-proton pairing collectivity(a fit plus three easy steps)
Fit of GT=0 /GT=1ET=2 - ET=0 (even-even)
(I)
ET=1 - ET=0 (even-even)(II)
ET=1 - ET=0 (odd-odd)(III)
W. Satuła & R. Wyss Phys. Rev. Lett., 86, 4488 (2001);
Phys. Rev. Lett., 87, 052504 (2001)
Wigner energy linked to the n-p pairing collectivityT=2 states in even-even nuclei obtained from isocrankingT=1 states in even-even nuclei obtained as 2qp excitationsT=1 states in odd-odd nuclei obtained from isocrankingT=0 states in odd-odd nuclei obtained as 2qp excitations
E= (de+k)T212
mean -- field
(Hartree)HMF =hsp- (w - k T )T
iso-cranking with isospin-dependent frequency!!!
1H=hsp- wT+ kTT2
extreme sp model
12E= (de+k)T2+ kT1
2
HartreeHartree- -Fock
Schematic isospin-isospin interaction:
de 3de
de
de
de
hw de+k 3(de+k)
l
even-even vacuum
see e.g. Bohr & Mottelson „Nuclear Structure” vol. INeergard PLB572 (2003) 159
Resistance of nucleonic paires against fast rotation:
Pairing in fast rotating nucleiMuller et al., Nucl. Phys. A383 (1982) 233
J. Terasaki, R. Wyss, and P.H. Heenen PLB437, 1 (1998)
[nf7/2 pf7/2]4 4
16+
Collective (prolate)rotation
Non-collective (oblate) rotation
isoscalarpairing
d3/2 g9/2-1
T=1 collapses
Skyrme interaction in p-h DDDI in p-p channel fully self-consistent theory no spherical symmetry two-classes of solutions:
no T=0 atlow spins
(termination)
48Cr ; HFB calculations including T=0 & T=1 pairing
exp
- T=0 dominated at I=0- T=1 dominated at I=0
Conventional TRS calculations involving only T=1 pairing:
R.Wyss, P.J. Davis, WS, R. Wadsworth(1) 73Kr – manifestation of (dynamical) T=0 pairing?
Scattering of a T=0 np pair
n(fp)ng9/2n(fp)ng9/2
n(fp)ng9/2n(fp)ng9/2
p(fp)pg9/2p(fp)pg9/2
p(fp)pg9/2p(fp)pg9/2
1qp configurationn(fp)(-) vacuum
ng9/2(+) pg9/2 p(fp)(-)
3qp configuration
in 73Kr
What makes the 1qp and 3qp configurations alike?
051015202530
0.4 0.8 1.2 1.60.2 0.6 1.0 1.4hw [MeV]
I x
73Kr
theoryexp
DT=0
Dp
Dn
00.51.0
D [M
eV]
TRS involving T=0 and T=1pairing
(2) 73Kr – manifestation of (dynamical) T=0 pairing?
-0.5
0.0
0.5
1.0
1.5
2.0
0.5 1.0 1.5hw [MeV]
Ew [M
eV]
75Rb 3qp
1qp
5
10
15
20
25
30(+,+)
(-,+)75RbIx
0.5 1.0 1.5hw [MeV]
0.5 1.0 1.5
1qp
3qp
positive parity negative parityall bands
Excellent agreement was obtained in: Tz=1 : 74Kr,76Rb, D. Rudolph et al. Phys. Rev. C56, 98 (1997) Tz=1/2: 75Rb, C. Gross et al. Phys. Rev. C56, R591 (1997) Tz=1/2: 79Y, S.D. Paul et al. Phys. Rev. C58, R3037 (1998)
Conventional TRS calculations involving only T=1 pairingin neighbouring nuclei:
(3) 73Kr – manifestation of (dynamical) T=0 pairing?
SUMMARYPart of T=0 correlations in N~Z nuclei is definitelybeyond standard formulation of mean-field(Wigner energy)
Adding T=0 pairing helps but cannot solve the problem of the Wigner energy (symmetry energy) in N~Z nuclei which seems to be beyond mean-field There is no convincing arguments for coherency of the T=0 phaseTheoretical treatment of T=1 states in e-e nuclei and T=0 states o-o nuclei requires angular momentum and isospin projections
Independent least-square fits of: the Wigner energy strength: aw|N-Z|/Aa
the symmetry energy strength: as(N-Z)2/Aa
4asT(T+x); x=aw/2as
Fit includes N~Z nuclei with:very consistent with: Janecke, Nucl. Phys. (1965) 97
![Experimental Program on Halo Nuclei€¦ · According to the ‘‘pairing-plus-quadrupole’’ model [25], ... Woods-Saxon potential for a given value of S 2n=2, with a diffuseness](https://static.documents.pub/doc/80x56/5e9b37f3a20f8314114bd3e7/experimental-program-on-halo-according-to-the-aapairing-plus-quadrupoleaa.jpg)
