IoP Nuclear Physics Summer School Chester, September 2005 Andreas Görgen 1 Gamma-ray spectroscopy II Andreas Görgen DAPNIA/SPhN, CEA Saclay F-91191 Gif-sur-Yvette France [email protected]Lectures presented at the IoP Nuclear Physics Summer School September 4 – 17, 2005 Chester, UK
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Gamma-ray spectroscopy II - GSIweb-docs.gsi.de/~wolle/TELEKOLLEG/KERN/PDF/Goergen/Goergen-C… · Gamma-ray spectroscopy II Andreas Görgen DAPNIA/SPhN, CEA Saclay F-91191 Gif-sur-Yvette
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IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 1
Average of 8 stretched E2 transitions inTSD1 and TSD2
)2590(
)2525(
)90(
)25(
×
×
W
W
W
W
σ/I = 0.25 ± 0.02
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 7
Measuring the mixing parameter δδδδ
We know σ/I and have assigned Iπ
For wobbling bands, we expect
∆I=1 E2 inter-band transitions.⇒ L=1, L’=2, large δ
W(2
5×× ××9
0)
10% M190% E2
80% M120% E2
43/2+→ 41/2+
Angular distribution cannot distinguish between the two.
⇒ measure the linear polarization to establish electric or magnetic character.
49/2+
37/2+
41/2+
45/2+
47/2+
43/2+
39/2+
35/2+
697
639
579
659
643
626
655
596
534
TSD1 TSD2
Two possible solutions
wobbling
something else
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 8
Linear polarization
linear polarization: fixed direction ofelectric field vector E
E
B k
)0()90(
)0()90(1
°=+°=
°=−°===
ζζ
ζζ
NN
NN
QQ
AP
Clover detectors asCompton polarimeters(at 90°in Euroball)horizontal vs. verticalscattering
Compton scattering is sensitive to linear polarization:Klein-Nishina formula
E
k
θ
k’
ζ
−+=
Ωζθ
ω
ω
ω
ω
ω
ωσ 22
2
22
0 cossin2'
''
2
r
d
d
Effect is largest at θ=90°
N(9
0°)
-N(0
°)
electric transitions appear positive,magnetic transitions negative
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 9
Polarization measurement in 163Lu
0.10 ± 0.03579E2
0.13 ± 0.03697
0.06 ± 0.05386
0.05 ± 0.04534
-0.11 ± 0.05349M1
0.05 ± 0.05607inter-band
0.12 ± 0.05626
0.11 ± 0.05643
0.17 ± 0.09659
0.18 ± 0.09673
Eγ )0()90(
)0()90(
°+°
°−°=
NN
NNA
49/2+
37/2+
41/2+
45/2+
47/2+
43/2+
39/2+
35/2+
697
639
579
659
643
626
655
596
534
W(2
5×× ××90)
10% M190% E2
80% M120% E2
43/2+→ 41/2+
positive
positive
⇒ electric
negative
Confirmation of the wobbling modein 163Lu through combined angular distribution and linearpolarization measurement.
S.W. Ødegård et al., Phys. Rev. Lett. 86, 5866 (2001)
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 10
Jupiter: T = 9 h 50 min polar / equatorial
axis ~ 15/16
MacLaurin shapes
What happens if we spin a liquid drop ?
It becomes oblate !
MacLaurin shapeafter C. MacLaurin(1698-1746)
But what if we spin really fast ?
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 11
Jacobi shapes
piece of moon rock from Apollo mission
The equilibrium shape changes abruptly to a very elongated triaxial shape rotating about its shortest axis.
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 12
Carl Gustav Jacob Jacobi (1804 - 1851)discovered transition from oblate to triaxial shapesin the context of rotating, idealized, incompressiblegravitating masses in 1834.
In 1961 Beringer and Knox suggested a similartransition in the case of atomic nuclei, idealizedas incompressible, uniformly charged, liquid drops endowed with surface tension.
Liquid drop calculation
Jacobi transition for L > L1
Fission barrier vanishes for L > L2
The Jacobi shape transition in nuclei
W.D. Myers and W.J. SwiateckiActa Phys. Pol. B 32, 1033 (2001)
IoP Nuclear Physics Summer School Chester, September 2005Andreas Görgen 13
What is the signature of a Jacobi transition in nuclei ?
sharp decrease of frequency withincreasing angular momentum (giant backbend of the moment of inertia)
frequency of collective rotation is related to the E2 γ-ray energy:
many rotational bands at high spinquasi-continuous transitions
measure the energy of the quasi-continuous ‘E2 bump’as a function of angular momentum