Gamma-ray spectroscopy II

Transcription

1 Gamma-ray spectroscopy II Andreas Görgen DAPNIA/SPhN, CEA Saclay F Gif-sur-Yvette France Lectures presented at the IoP Nuclear Physics Summer School September 4 17, 2005 Chester, UK 1

2 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 74 Kr Relativistic Coulomb excitation of 58 Cr Gamma-ray tracking AGATA 2

3 Summary (I) veto I-2 1 I-4 n w = n w =2 I-3 n w =1 I I-2 3

4 Angular correlation I i π E i E γ,l,l,δ Y lm (θ,ϕ) l=1 m=0 l=1 m=±1 I f π E f + W ( ϑ) = 1 A k P k (cosϑ) k l=2 m=0 l=2 m=±1 l=2 m=±2 simple example: o 30 o 90 o 1 + m=+1 m=0 m=-1 30 o 90 o 90 o 30 o 0 + Directional correlation from oriented states R DCO = I( γ 1, θ1; γ 2, θ2) I( γ, θ ; γ, θ ) Most transitions following fusion-evaporation reactions have stretched dipole or quadrupole character. compare experimental R DCO with values for dipole-dipole, dipole-quadrupole, quadrupole-quadrupole cascades often sufficient for spin assignments 4

5 Angular distribution I i π I f π E i E γ,l,l,δ E f P(m) Alignment of angular momentum after fusion-evaporation reaction: + W ( ϑ) = 1 A k P k (cosϑ) k P( m) = 2 m exp 2 2σ I m' exp 2 2σ + m' = I 2 The coefficients A k depend on A ( L, L', I k f, I i 2 [ F ( L, L, I, I ) + 2δ F ( L, L', I, I ) 2δ F ( L', L', I, I )] 1 ) = ρ k ( Ii ) k f i k f i + 1+ δ I + m= I Ii m ρ ( I ) = 2I + 1 ( 1) I m I m k 0 P( m) k i i 2 k f i i the multipolarity L the mixing parameter δ the population width σ i Ferentz-Rosenzweig coefficients F k ( L, L', I f, I ) = ( 1) i I f + I i 1 (2L + 1)(2L' + 1)(2I + 1)(2k + 1) σ/i is approximately constant (for a given reaction). Normalize to transition with known multipolarity, e.g i L 1 L' 1 Clebsch- Gordan k 0 L Ii L' I i Racah I k f 5

6 Example: Angular distribution with EUROBALL 25 o angle: ring1 + ring2 (tapered) ring 7 (clusters) 90 o angle: ring4 + ring5 (clovers) W (25) W (90) W (25 25) W (90 25) 139 La( 29 Si,5n) 163 Lu with E beam = 153 MeV Average of 8 stretched E2 transitions in TSD1 and TSD2 90 o 25 o σ/i = 0.25 ± o 90 o 25 o 90 o 25 o 90 o All θ All θ 25 o 90 o 6

7 Measuring the mixing parameter δ TSD1 TSD2 49/2 + 45/ /2 + 43/2 + W(25 90) 41/2 + 37/ /2 + 35/2 + We know σ/i and have assigned I π For wobbling bands, we expect I=1 E2 inter-band transitions. L=1, L =2, large δ 43/2 + 41/2 + 80% M1 20% E2 Two possible solutions 10% M1 90% E2 wobbling something else Angular distribution cannot distinguish between the two. measure the linear polarization to establish electric or magnetic character. 7

8 Linear polarization B E k Clover detectors as Compton polarimeters (at 90 in Euroball) horizontal vs. vertical scattering linear polarization: fixed direction of electric field vector E k E θ k ζ P = A Q = 1 Q N( ζ = 90 ) N( ζ = 0 ) N( ζ = 90 ) + N( ζ = 0 ) Compton scattering is sensitive to linear polarization: Klein-Nishina formula 2 2 dσ r0 ω' ω' ω 2 2 = + 2sin θ cos ζ 2 dω 2 ω ω ω' Effect is largest at θ=90 electric transitions appear positive, magnetic transitions negative N(90 )-N(0 ) 8

9 Polarization measurement in 163 Lu 49/2 + 47/ /2 + 43/ /2 + 39/ /2 + 35/2 + E2 M1 inter-band N(90 ) N(0 ) A = Eγ N(90 ) + N(0 ) ± ± ± ± ± ± 0.05 positive negative W(25 90) ± ± ± ± 0.09 positive electric 43/2 + 41/2 + 10% M1 90% E2 80% M1 20% E2 S.W. Ødegård et al., Phys. Rev. Lett. 86, 5866 (2001) Confirmation of the wobbling mode in 163 Lu through combined angular distribution and linear polarization measurement. 9

10 MacLaurin shapes What happens if we spin a liquid drop? It becomes oblate! Jupiter: T = 9 h 50 min polar / equatorial axis ~ 15/16 MacLaurin shape after C. MacLaurin ( ) But what if we spin really fast? 10

11 Jacobi shapes The equilibrium shape changes abruptly to a very elongated triaxial shape rotating about its shortest axis. piece of moon rock from Apollo mission Andreas Görgen IoP Nuclear Physics Summer School Chester, September

12 The Jacobi shape transition in nuclei Carl Gustav Jacob Jacobi ( ) discovered transition from oblate to triaxial shapes in the context of rotating, idealized, incompressible gravitating masses in In 1961 Beringer and Knox suggested a similar transition in the case of atomic nuclei, idealized as incompressible, uniformly charged, liquid drops endowed with surface tension. Liquid drop calculation Jacobi transition for L > L 1 Fission barrier vanishes for L > L 2 W.D. Myers and W.J. Swiatecki Acta Phys. Pol. B 32, 1033 (2001) 12

13 What is the signature of a Jacobi transition in nuclei? sharp decrease of frequency with increasing angular momentum (giant backbend of the moment of inertia) frequency of collective rotation is related to the E2 γ-ray energy: hω = E γ many rotational bands at high spin quasi-continuous transitions measure the energy of the quasi-continuous E2 bump as a function of angular momentum series of experiments with Gammasphere Ca MeV 48 Ca MeV 48 Ca MeV 48 Ca MeV as neutron rich as possible: higher fission barrier 13

14 Measuring angular momentum with Gammasphere 108 Compton-suppressed HPGe detectors K M J 108 Ge detectors 6 x 108 = 648 BGO detectors K = number of hits = fold M = γ rays emitted = multiplicity (from response function) J = initial angular momentum (from angular distribution) increase in false veto signals reduced Ge efficiency but very high granularity 14

15 The E2 bump Incremental spectra: Multiplicity (K av -1) gated spectrum subtracted from (K av +1) spectrum K measures the angular momentum E2 bump measures rotational frequency 15

16 Comparison to liquid drop calculations D. Ward et al., Phys. Rev. C 66, (2002) 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 16

17 Charged-particle evaporation 40 Ca MeV The nucleus of interest is often only weakly populated compared to a large background of other nuclei. neutrons are deeply bound, chargedparticle evaporation favored despite Coulomb barrier 76 Y p3n 75 Sr αn 78 Zr 2n 77 Y p2n Sr 2p2n Zr 1n 78 Y pn 77 Sr 2pn Zr 79 Y 1p 78 Sr 2p Additional sensitivity from: charged-particle detectors neutron detectors recoil detectors tagging techniques 70 Kr 2α2n 69 Br 2αp2n 72 Rb αp3n 71 Kr 2αn Br 2αpn Rb αp2n Kr 2α Br 2αp Rb αpn Kr α2pn Br α3pn Rb αp Kr α2p Br α3p Rb 3pn Kr 4pn Br 5pn Rb 3p Kr 4p Br 5p Se 3αn 68 Se 3α Se 2α2pn Se 2α2p Se α4pn Se α4p Se 6pn 74 Se 6p As 3αpn 67 As 3αp As 2α3pn 69 As 2α3p As α5pn 71 As α5p As 7pn 73 As 7p 64 Ge 4α Ge 3α2pn 66 Ge 3α2p Ge 2α4pn 68 Ge 2α4p Ge α6pn cross sections in mb 17

18 Charged particle detection Si telescope E E p, α beam Italian Silicon Sphere ISIS Laboratori Nazionali di Legnaro 30 hexagons 12 pentagons used with GASP and Euroball 100µm 1mm stopping power de dx mz E 2 E E Microball, Washington University St. Louis 95 CsI(Tl) Scintillators in 9 rings used with Gammasphere 18

19 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 flight and pulse shapes (zero-crossing time) difficult to distinguish two-neutron hit from scattering 19

20 Prompt proton decay in 58 Cu 28 Si( 36 Ar,αpn) 58 Cu gate on 1α + 1p +1n σ rel = 0.3 % Gammasphere, Microball, Neutron Shell D. Rudolph et al., Phys. Rev. Lett. 80, 3018 (1998) Eur. Phys. J. A 14, 137 (2002) 20

21 Recoil decay tagging γ detectors Filter Identification : ToF, recoil energy, characteristic decay Beam Recoils Ionisation chamber Eγ, T associate with γ Pin diodes: electrons Silicon DSSD Planar Ge α decay: E α, T E, T recoil identified ToF, E-E same pixel T T ½ isotope identified E, T 21

22 JUROGAM RITU GREAT at Jyväskylä 109 Ag( 83 Kr,3n) 189 Bi ; 12µb scattered beam α spectrum at focal plane ground state time of flight [a.u.] fusion-evaporation residues counts excited states energy in Si detector [a.u.] α energy [kev] 22

23 Recoil-decay tagging: 189 Bi spectra 357 T 1/2 =880 ns 13/ /2 + counts /2-189 Bi 9/2 - T 1/2 =667 ms T recoil - Tα [s] γ rays at focal plane Tγ - Tα [µs] 284 3/2 + recoil gated α energy [kev] prompt γ rays at target 185 Tl 1/2 + total γ α gated 6672 kev recoil gate α and γ tagging: α gate: 6672 kev; γ gate: 357 kev A. Hürstel et al., Eur. Phys. J. A 15, 329 (2002) α gate 6672 counts 23 E γ [kev]

24 189 Bi level schemes Bi 1/2 + 9/2 - A. Hürstel et al., Eur. Phys. J. A 21, 365 (2004) /2-3/2 + α gate 7266 kev 185 Tl 1/2 + 9/ ms α and γ tagging: α gate: 6672 kev; γ gate: 357 kev counts E γ [kev] 24

25 Systematics of the neutron-deficient Bi isotopes M1 E2 M2 19/2 + 15/ Bi /2 + 17/2 + 13/2 + 9/2 - P. Nieminen et al Phys. Rev. C 69, (2004) 19/2 + 15/ Bi /2 + 17/2 + 13/2 + 9/ Bi 29/2 + 25/2 + 21/2 + 17/2 + 13/2 + 9/2 - A. Hürstel et al. Eur. Phys. J. A21, 365 (2004) Bi 25/2 + 21/2 + 17/2 + 13/2 + 9/2 - strongly coupled bands deformation aligned decoupled bands rotation aligned Ω=13/2 Ω=9/2 Ω=1/2 Ω=3/2 Ω Ω large Ω small Ω 25