1cea/dam/dif/dpta/spn workshop esnt, saclay, june 28- july 8 2005 giant resonances and inertia...
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1CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
Giant resonances and inertia parametersWithin the QRPA with the Gogny force
in axial symmetry.
Giant resonances and inertia parametersWithin the QRPA with the Gogny force
in axial symmetry.
S.PÉRU, J.F. Berger, M. Girod,H. Goutte,N. Pillet.
CEA Bruyères-le-Châtel, France
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2CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
HF+RPA calculations in spherical symmetry
for exotic nuclei :78Ni
100Sn132Sn
208Pb is taken as a reference
Previous work,
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3CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
ISGMR
Central
+densité
Central
+densité
+SO
Central
+densité
+Coulomb
Central
+densité
+Coulomb
+SO
78Ni 18.55 17.10 18.59 17.17
100Sn 18.19 16.81 18.54 17.22
132Sn 16.07 15.06 16.26 15.29
208Pb 13.73 13.05 14.10 13.46
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4CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
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5CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
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6CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
The Coulomb term is important for the dipole response.But it is time computer consuming.
The Spin-Orbit term can not be neglected.The calculation is relatively fast.
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7CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
HFB+QRPA in axial Symmetry
Spherical nuclei:2+
1 in O isotopes
GMR in 90Zr
Deformed nuclei :24Mg 22Mg28 Si
Inertia parameters :Quadrupole “mass”
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8CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
FormalismFormalism
1°HF+RPA
2°HFB+QRPA
,**
YX
Y
X
AB
BA
are quasi-particules states (qp).
In our approach The effective interaction D1S is used both in the mean field and in the QRPA matrix.As the axial symmetry is imposed, QRPA state are obtained by K blocs.
.0~
aaYaaX ph
ph
hph
p
ph
ij
ij
jij
i
ij
YX
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9CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
Axial QRPA
Spherical RPA
16O
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10CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
Skyrme results from E.Kahn and Nguyen Van Giai, Phys. Lett.B 472 (2000)253.
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11CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
10 15 20 25
M1 / M0 = 17.65 MeV
M1 / M0 = 17.89 ± 0.20 MeV
D.H.Younblood,H.L.Clark, and Y.-W.Lui,Phys. Rev. Lett.82 ,4 (1999)
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12CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
2,221,120,2020
ˆ05
1ˆ05
1ˆ05
1ˆ0~
KKKKKK QQQKJMQ
Restoration of rotational symmetry for deformed states
KJ
KM
KJ
KJMK DDd
JKJM
RR
4
12
We want to calculate : KJMQˆ0
~for all QRPA states (K ≤ J)
202
20ˆ YrQ
For example : Jπ = 2+
In intrinsic frame
YrDYr 22
Using rotational approximation and relation for 3j symbol
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13CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
24Mg β=.51
Jπ=2+
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14CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
[9-41MeV] HFB+QRPA %EWSR=76.6 ; M1 / M0 = 17.64 MeV
Exp. %EWSR= 72 ± 10; M1 / M0=16.9 ± 0.6 MeV
Exp. : D.H. Youngblood, Y.-W. Lui, and H.L. Clark, Phys.Rev.C 60 (1999)014304
Quadrupole
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15CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
D.H. Youngblood, Y.-W. Lui, and H.L. Clark, Phys.Rev.C 60 (1999) 014304
24Mg ISGMR
%EWSR=72 ± 10M1 / M0=21.0 ± 0.6 MeV
%EWSR = 94M1 / M0= 20.47 MeV
[9-41 Mev]
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16CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
[13-30meV] : 82%EWSR, M1 / M0 = 18.72 MeV
Quadrupole
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17CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
Monopole
[13-40 MeV] : 92%EWSR, M1 / M0=20.86 MeV
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18CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
28Si Monopole
D.H. Younboold, Y.-W. Lui, and H.L.Clark,Phys. Rev. C, 65,(2002) 034302
[10-35 MeV] 92% EWSR, M1 / M0 = 21.11 MeV
81 ± 10 % EWSR, M1 / M0 = 21.25 ± 0.38 MeV
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19CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
28Si Quadrupole
D.H. Younboold, Y.-W. Lui, and H.L.Clark,Phys. Rev. C, 65, (2002) 034302
[13-35 MeV] 70% EWSR, M1 / M0 = 21.27 MeV [7-35 MeV] 71.5% EWSR, M1 / M0 = 20.49 MeV
M1 /M0 =18.54 ± 0.25 MeV68 ± 9 % EWSR
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20CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
n
iE
QM i
n
nQ
0,0 202
20
Q
QM 21201
Consistent calculations CHFB and QRPA (a)=(c).
Inertia parameters
(c) Constraint HFB
(a) QRPA
i
HFBHFB
i
QQM
220 00
20(b) Inglis-Belayev
21
320
M
MQMATDHF "Mass":
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21CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
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22CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
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23CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
Summary
Coulomb and spin-orbit terms have to be taken into account,
Effect of the pairing treatment in 2+1 states in QRPA?
Relatively good agreement with experimental data for giant resonnances.
Fragmented strength for monopole and quadrupole response in deformed nuclei.
Inertia parameters are very different from the Inglis-Belayev ones.
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24CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005
Gogny forceGogny force
21
2
21
211221.12
212103
jjjj
2
1
2
2112
2121
.
1
PPM- PH-PBW r-r
-exp
rr
ett
rriW
rrrrPxt
pv
zz
ls
s
j j
=
P is isospin exchange operatorP is spin exchange operator
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25CEA/DAM/DIF/DPTA/SPN Workshop ESNT, Saclay, june 28- july 8 2005