Gamma-ray spectroscopy of excited states in exotic nuclei Lecture III

1. Gamma-ray spectroscopy of excited states in exotic nucleiLecture III STFC Postgraduate Nuclear Physics Summer School Newcastle-Upon-Tyne, 2007

2. Why study gamma-ray emissions? • Strong force constrains the distribution and motion of the nucleons within the nucleus. • Nuclear charges and currents generate (time-varying) EM potentials/fields. These reflect the underlying structure. • Gamma rays arise from EM interactions and allow a probe of structure without large perturbations of the nucleus. • EM interaction is well understood.

3. Ii Ei i E , L f If Ef YESE1M2E3M4 NOM1E2M3E4 Gamma-ray transitions Reduced transition probability B()

4. Deformation can be dynamic Octupole (Y31) Vibration Nuclear Deformation

5. Noncollective Level Scheme • 148Gd is an example of a nucleus showing single-particle behaviour • Complicated set of energy levels • No regular features e.g. band structures • Some states are isomeric

6. Collective Level Scheme This nucleus has 347 known levels and 516 gamma rays !

7. Gamma ray interactions in matter

9. HP Germanium detector with Compton suppression shield. Average separation of consecutive  rays in a cascade. Peak-to-Total ratio FWHM of detector resolution for  rays in spectrum Resolving power

10. Escape suppression increases the peak-to-total (PT) from ~20% to ~60%.

11. Gammasphere

12. High-fold Data & Multidimensional Analysis EUROGAM II Unpacked Quadruples Unpacked Triples Unpacked Quintuples Probability of detecting high-fold events increases with increased photopeak detection efficiency. Raw fold

13. A superdeformed band in 149Gd. Spectra showing the effect of ‘gating’ on coincident transitions. For a review of spectrometer arrays and their properties see C.W. Beausang & J.Simpson, J. Phys. G22 (1996) 527.

14. Generating spectra from high-fold coincidence data. Event 3 (100,200)(200,100) (100,500)(500,100) (100,250)(250,100) (200,500) (500,200) (200,250) (250,200) (250,500) (500,250) Raw Event 1: 100, 200. Raw Event 2: 100, 200, 300. Raw Event 3: 100, 200, 500, 250. E2 Event 1 (100, 200)(200,100) Event 2 (100,200)(200,100) (100,300)(300,100) (200,300)(300,200) 1 1 1 500 400 1 1 300 1 1 1 1 1 1 2 3 1 200 1 2 3 1 1 1 100 100 200 300 400 500 E1

15. 100 200 300 400 500 E2 1 1 1 500 400 1 1 300 1 1 1 1 1 1 200 3 3 1 1 1 100 3 E1 100 200 300 400 500 Counts 2 1 E1

16. A. Goergen

17. Superdeformed Band in 192Hg (Cascade of E2 transitions) M1 cascade in 198Pb Can you tell the difference between these bands? Differences revealed by angular distributions

18. Angular Distributions • The general form for the angular distribution function of radiation emitted following a heavy-ion fusion-evaporation reaction is: W(θ) = A0 [ 1 + Q2{A2/A0}P2(cosθ) + Q4{A4/A0}P4(cosθ) ] where Qk are geometrical attenuation coefficients which account for the finite size of the detectors and Pk(cosθ) are Legendre polynomials • The measured Ak/A0 coefficients are compared to theory for different types of radiation

19. Angular Distributions in 109Te • Typically A4/A0 is close to zero • A2/A0 ~ +0.3 for a pure quadrupole (ΔI = 2) transition • A2/A0 ~ -0.3 • for a pure dipole • (ΔI = 1) transition A J Boston et al., PRC 61 (1999) 064305.

20. Multipole Mixing Ratio • Because of the relative multipole transition probabilities, we only need to consider M1/E2 mixing • For a ΔI = 1 transition, M1 radiation accounts for 1 /[1+δ2] (typically 95%) of the intensity, while E2 radiation accounts for δ2 / [1+δ2] (typically 5%) of the intensity • The mixing ratio can be positive or negative and perturbs the angular distribution

21. Theoretical Ak/A0 Values If the two lowest multipoles of the radiation are L and L’= L+1, the Ak/A0 coefficients may be written as: Ak/A0 = αkBk(Ji) [1/(1+δ2)] [ Fk(Jf L L Ji) + 2δ Fk(Jf L L’ Ji) + δ2 Fk(Jf L’ L’ Ji) ] where αk are attenuation coefficients, Bk(Ji) are statistical tensors for complete alignment, and δis the multipole mixing ratio:

22. Linear Polarisations • Compton scattering can be used to measure the gamma ray linear polarisation – the direction of the electric vector with respect to the beam-detector plane • The linear polarisation distinguishes between magnetic (M) and electric (E) character of radiation of the same multipolarity • The scattering cross section is larger in the direction perpendicular to the electric field vector of the radiation

23. Experimental Asymmetry • The experimental asymmetry is defined as: A = { N90- N0 } / {N90+ N0 } where N90and N0are the intensities of scattered photons perpendicular and parallel to the reaction plane • The experimental linear polarisation is then: P = A / Q where Q is the polarisation sensitivity of the detector (a function of gamma ray energy) • For a stretched E2: P > 0 For a stretched M1: P < 0

24. Spins and Parities • Combining linear polarisation and angular correlation measurements uniquely defines the multipolarity of gamma rays • Data from Eurogam

26. Destruction of Pairing • Strong external influences may destroy the superfluid nature of the nucleus • In the case of a superconductor, a strong magnetic field can destroy the superconductivity: the ‘Meissner Effect’ • For the nucleus, the analogous role of the magnetic field is played by the Coriolis force, which at high spin, tends to decouple pairs from spin zero and thus destroy the superfluid pairing correlations

28. Return of Collectivity in 158Er

29. Band Termination in 158Er

30. Large Deformations • Deformed shell gaps (new ‘magic numbers’) emerge when the ratio of the major andminor nuclear axes are equal to the ratio of small integers • A superdeformed shape has a major to minor axis ratio of2:1 • A hyperdeformed shape hasa major to minor axis ratio of3:1

31. Superdeformed 152Dy • The SD band in 152Dy is a very regular structure with equally spaced gamma-ray transitions • The spacing is relatively small, i.e. the band has a large moment of inertia (close to the rigid body value) Original SD γ-ray spectrum from 1986 (Daresbury)

32. Lifetimes and Quadrupole Moments Units: T(E2) in s-1, B(E2) in (eb)2, E in MeV.

33. Doppler Shift Attenuation Method (DSAM) • Measure lifetimes in the range 10-15 <  < 10-12 s. • Stopping time in metal foil is comparable to lifetimes of excited states.   v/c v0/c  

34. Centroid shift method 17 90 If  = forward = 180 - backward 163

35. Calculate F() for different quadrupole Moments and find best fit. (a) 131Ce SD1 Q = 7.3(3) (b) 131Ce SD2 Q = 8.2(4) (c) 132Ce SD 1 Q = 7.4(3) (d) 132Ce SD 2 Q = 7.2(4) (e) 132Ce SD 3 Q = 7.0(4) Excited SD band in 131Ce has a larger Q due to a configuration Involving a hole in neutron d3/2 orbital. Specific orbitals have different core polarising properties. RM Clark et al., PRL 76 (1996) 3510.

36. Shape coexistence

37. Pb Prolate 4p-4h Even-mass Pb excitation level systematics Oblate 2p-2h 186Pb Spherical 0p-0h

38. Tagged Recoil Distance Method

39. The Koln Plunger Device

40. PROLATE OCTUPOLE OBLATE GAMMA 186Pb

41. The Concept Compton continuum. => Large peak to total ratio Without Compton suppression shields Less solid angle coverage => Big drop in efficiency With BGO shielding Path of -ray reconstructed to form full energy event => Compton continuum reduced => Excellent efficiency ~50% @1MeV => Greatly improved angular resolution (~10) to reduce Doppler effects With highly segmented detectors

42. The Concept Compton continuum. => Large peak to total ratio Without Compton suppression shields Less solid angle coverage => Big drop in efficiency With BGO shielding Path of -ray reconstructed to form full energy event => Compton continuum reduced => Excellent efficiency ~50% @1MeV => Greatly improved angular resolution (~10) to reduce Doppler effects With highly segmented detectors

43. AGATA Ge crystals size: length 90 mm diameter 80 mm 180 hexagonal crystals 3 shapes 60 triple-clusters all equal Inner radius (Ge) 22 cm Amount of germanium 310 kg Solid angle coverage 80 % Singles rate ~50 kHz 6480 segments Efficiency: 40% (Mg=1) 25% (Mg=30) Peak/Total: 65% (Mg=1) 50% (Mg=30)