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IoP Nuclear Physics Summer School Chester, September 2005Andreas 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


Outline

First lecture

Properties of γ-ray transitions

Fusion-evaporation reactions

Germanium detector arrays

Coincidence technique

Nuclear deformations

Rotation of deformed nuclei

Pair alignment

Superdeformed nuclei

Hyperdeformed nuclei

Triaxiality and wobbling

Second lecture

Angular distribution

Linear polarization

Jacobi shape transition

Charged-particle detectors

Neutron detectors

Prompt proton decay

Recoil-decay tagging

Rotation and deformation alignment

Third lecture

Spectroscopy of transfermium nuclei

Conversion-electron spectroscopy

Quadrupole moments and transition rates

Recoil-distance method

Doppler shift attenuation method

Fractional Doppler shift method

Magnetic moments

Perturbed angular distribution

Magnetic Rotation

Shears Effect

Fourth lecture Fast fragmentation beams Isomer spectroscopy after fragmentation E0 transitions Shape coexistence Two-level mixing Coulomb excitation Reorientation effect ISOL technique Low-energy Coulomb excitation of 74Kr Relativistic Coulomb excitation of 58Cr Gamma-ray tracking AGATA


Summary (I) veto

nw=0

nw=1

nw=2

0.015

0.25

0.45I-2

I

I-3I-2

I-4

1

1

1


Angular correlation

Iiπ

Ifπ Ef

Ei

Eγ ,L,L’,δ

∑+=k

kk PAW )(cos1)( ϑϑ

Ylm(θ,ϕ)

m=+1m=0m=-1

simple example:

0+

0+

1+

30o

30o

90o

30o

90o

90o

30o

),;,(

),;,(

1221

2211

θγθγ

θγθγ

I

IRDCO =

Directional correlation from oriented states

Most transitions following fusion-evaporation reactions have stretched dipole or quadrupolecharacter.

⇒ compare experimental RDCO with values fordipole-dipole, dipole-quadrupole, quadrupole-quadrupole cascades

⇒ often sufficient for spin assignments

∆ l=1

∆ m=0

∆ l=1

∆ m=±1

∆ l=2

∆ m=±2

∆ l=2

∆ m=±1

∆ l=2

∆ m=0


Angular distribution

∑+

−=

−

−

=I

Im

m

m

mP

'2

2

2

2

2

'exp

2exp

)(

σ

σAlignment of angular momentum after fusion-evaporation reaction:

[ ]),,','(2),,',(2),,,(1

1)(),,',( 2

2 ifkifkifkikifk IILLFIILLFIILLFIIILLA δδδ

ρ +++

=

)(0)1(12)( mPkmImIIII

Im

ii

mI

iiki∑

+

−=

− −−+=ρ

The coefficients Ak depend on the multipolarity L

the mixing parameter δ the population width σ

Iiπ

Ifπ Ef

Ei

Eγ ,L,L’,δ

∑+=k

kk PAW )(cos1)( ϑϑ

σ/I is approximately constant (for a given reaction).Normalize to transition with known multipolarity, e.g. 2+→0+

−++++−=

−+

fii

i

II

ifk III

kLLkLLkILLIILLF if

'

011

')12)(12)(1'2)(12()1(),,',(

1

Ferentz-Rosenzweig coefficients

Clebsch-Gordan

Racah

P(m)


Example: Angular distribution with EUROBALL

25o angle: ring1 + ring2 (tapered)ring 7 (clusters)

90o angle: ring4 + ring5 (clovers)

25o

All θθθθ

90o

All θθθθ

25o

90o

90o

25o

25o

25o

90o

90o

139La(

29Si,5n)

163Lu with Ebeam= 153 MeV

Average of 8 stretched E2 transitions inTSD1 and TSD2

)2590(

)2525(

)90(

)25(

×

×

W

W

W

W

σ/I = 0.25 ± 0.02


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


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


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)


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 ?


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.


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)


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

γω E21=h

48Ca + 50Ti @ 200 MeV48Ca + 64Ni @ 207 MeV48Ca + 96Zr @ 207 MeV48Ca + 124Sn @ 215 MeV

series of experiments with Gammasphere

as neutron rich as possible:⇒ higher fission barrier


108 Compton-suppressedHPGe detectors

Measuring angular momentum with Gammasphere

108 Ge detectors6 x 108 = 648 BGO detectors

increase in false veto signalsreduced Ge efficiency but very high granularity

K M J

K = number of hits = fold

M = γ rays emitted = multiplicity (from response function)J = initial angular momentum (from angular distribution)


Incremental spectra:

Multiplicity (Kav-1) gated spectrum

subtracted from (Kav+1) spectrum

The E2 bump

K measures the angular momentumE2 bump measures rotational frequency


two modifications:

lower effective moment of inertia at low spin due to pairing

no collective rotation about axially symmetric (MacLaurin) shapes in nuclei,

instead, collective rotations are associated with (mostly) prolate shapes

→ no sharp transition caused by breaking of axial symmetry, but smooth transition

Comparison to liquid drop calculations

D. Ward et al., Phys. Rev. C 66, 024317 (2002)


Charged-particle evaporation 40Ca+40Ca @ 167 MeV

80Zr79Zr1n

78Zr2n

79Y1p

77Yp2n0.18

78Ypn

78Sr2p

76Sr2p2n4.06

77Sr2pn2.95

75Srαn

77Rb3p

2.31

75Rbαp

5.35

76Rb3pn101

74Rbαpn2.49

73Rbαp2n0.01

72Rbαp3n

76Kr4p

74.2

74Krα2p20.3

75Kr4pn132

73Krα2pn

52

72Kr2α

0.37

71Kr2αn0.18

75Br5p

68.2

73Brα3p128

74Br5pn3.23

72Brα3pn38.2

71Br2αp11.4

70Br2αpn6.82

74Se6p

1.57

72Seα4p102

73Se6pn

71Seα4pn0.46

70Se2α2p

94

69Se2α2pn1.57

68Se3α

5.07

73As7p

71Asα5p2.03

72As7pn

70Asα5pn

69As2α3p35.6

68As2α3pn

67As3αp15

76Yp3n

66Ge3α2p8.3

69Geα6pn

68Ge2α4p0.37

67Ge2α4pn

64Ge4α

1.48

65Ge3α2pn

70Kr2α2n

69Br2αp2n

67Se3αn

66As3αpn

cross sections in mb

The nucleus of interest is often only weakly populatedcompared to a large background of other nuclei.

Additional sensitivity from: charged-particle detectors neutron detectors recoil detectors tagging techniques

neutrons are deeply bound, charged-particle evaporationfavored despite Coulomb barrier


Charged particle detection

∆E E

100µm 1mm

p, α

Si telescope

E

mZ

dx

dE2

∝

stopping power

∆E

E

beam

Italian Silicon Sphere ISISLaboratori Nazionali di Legnaro

30 hexagons12 pentagons

used with GASP and Euroball

Microball, Washington University St. Louis

95 CsI(Tl) Scintillatorsin 9 rings

used with Gammasphere


Neutron detection

Gammasphere with Microball and Neutron shell(Washington University, St. Louis)

Euroball with Neutron wall (Uppsala University)

can be used to select or veto neutron evaporation most powerful together with charged-particle detection used to study nuclei near N=Z line

isospin symmetry proton-neutron pairing shape coexistence astrophysical rapid-proton capture process

neutrons are separated from γ rays by time of flightand pulse shapes (zero-crossing time)

difficult to distinguish two-neutron hit from scattering


Prompt proton decay in 58Cu

D. Rudolph et al., Phys. Rev. Lett. 80, 3018 (1998)Eur. Phys. J. A 14, 137 (2002)

28Si(36Ar,αpn)58Cu gate on 1α + 1p +1n σrel = 0.3 % Gammasphere, Microball, Neutron Shell


Ionisationchamber

Recoil decay tagging

Beam

Filter

γ detectors

Recoils

Identification :

ToF, recoil energy,

characteristic decay

SiliconDSSD

∆E, T E, T

Eγ, T

ToF, ∆E-E

recoil identified

associate

with γ

α decay: Eα, T

same pixel

T ≈ T½

isotope identified

Pin diodes:electrons Planar Ge


JUROGAM – RITU – GREAT at Jyväskylä

tim

e o

f flig

ht

[a.u

.]

energy in Si detector [a.u.]

fusion-evaporationresidues

scatteredbeam

109Ag(83Kr,3n)189Bi ; 12µb

α energy [keV]

counts

ground state

excited states

α spectrumat focal plane


Recoil-decay tagging: 189Bi spectra

α energy [keV]

counts

1/2+

9/2-

9/2-

1/2+

3/2+

189Bi

185Tl

6672

6831

71067286

185

284

454

total γ

recoilgate

α gate6672

prompt γ rays at target

13/2+357

Eγ [keV]

cou

nts

α and γ tagging:

α gate: 6672 keV; γ gate: 357 keV

T1/2=667 ms

Trecoil - Tα [s]

T1/2=880 ns

Tγ - Tα [µs]

recoil gated

α gated6672 keV

γ rays at focal plane

A. Hürstel et al.,Eur. Phys. J. A 15, 329 (2002)


189Bi level schemes

1/2+

9/2-

9/2-

1/2+

3/2+

189Bi

185Tl

6672

6831

71067286

185

284

454

Eγ [keV]

cou

nts

α and γ tagging: α gate: 6672 keV; γ gate: 357 keV

9/2-

357880 ms

α gate 7266 keV

A. Hürstel et al., Eur. Phys. J. A 21, 365 (2004)


Systematics of the neutron-deficient Bi isotopes

P. Nieminen et al

Phys. Rev. C 69, 064326 (2004)

9/2-

13/2+

17/2+

21/2+

25/2+

29/2+

357

420

313

375

446

189Bi

9/2-

13/2+

17/2+

21/2+

25/2+

252

198

270

343

187Bi

626

9/2-

13/2+

15/2+

17/2+

19/2+

21/2+

605

323

299

327

320

622

647

193Bi

429

318

279

325

248

597

572

9/2-

13/2+

15/2+

17/2+

19/2+

21/2+

604

191Bi

M1E2M2

A. Hürstel et al.

Eur. Phys. J. A21, 365 (2004)

strongly coupled bands deformation aligned

decoupled bands rotation aligned

large Ω small Ω

Ω Ω

Ω=3/2Ω

=13/

2Ω

=9/2 Ω

=1/2

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