Interaction of gamma-rays with matter Photo effect Compton - PowerPoint PPT Presentation

Nuclear Spectroscopy II Augusto O. Macchiavelli Nuclear Science Division Lawrence Berkeley National Laboratory Many thanks to Dirk Weisshaar Work supported under contract number DE-AC02-05CH11231.

Outline γ -ray Spectroscopy Interactions of gamma-rays with matter Scintillators Ge –detectors Compton-suppression Resolving power Some examples of quadrupole collectivity Cranking analysis Superdeformation Wobbling Tidal waves

Gamma-ray Spectroscopy and Nuclear Physics Gamma-ray spectroscopy has played a major role in the study of the atomic nucleus. • à Coincidence relations Level/decay scheme • Angular distributions à /correlations Multipolarity, spins • à Linear polarization E/M, parity • à Doppler shifts Lifetimes, B(E/M λ ) “Effective” Energy resolution ( δ E), Efficiency ( ε ), Peak-to-Background (P/T) Resolving Power

Interaction of gamma-rays with matter Photo effect Compton scattering A photoelectron is ejected Elastic scattering of a carrying the complete gamma ray off a free electron. gamma-ray energy (- binding) A fraction of the gamma-ray energy is transferred to the Compton electron Pair production If gamma-ray energy is >> 2 m o c 2 (electron rest mass 511 keV), a positron-electron can be formed in the strong Coulomb field of a nucleus. This pair carries the gamma-ray energy minus 2 m o c 2 .

tric: ¡ Pho Photoelec electri ~ ¡Z 4-­‑5 , ¡E g -­‑3.5 mpton: ¡ Comp ~ ¡Z, ¡E g -­‑1 ¡ Pa Pair ¡ ¡produc>on: ¡ ~ ¡Z 2 , ¡increase ¡with ¡E g

Scintillators Scintillators are materials that produce ‘ small flashes of light ’ when struck by ionizing radiation (e.g. particle, gamma, neutron). This process is called ‘ Scintillation ’ . Scintillators may appear as solids, liquids, or gases. Major properties for different scintillating materials are: • Light yield and linearity (energy resolution) • How fast the light is produced (timing) • Detection efficiency Organic Scintillators ( “ plastics ” ): Light is generated by fluorescence of molecules; usually fast, but low light yield Inorganic Scintillators : Light generated by electron transitions within the crystalline structure of detector; usually good light yield, but slow

Scintillator spectrum (here CsI(Na)) Compton edge Backscatter peak

CAESAR at NSCL DALI2 at RIKEN RIBF

Germanium Semi-conductor Detectors Energy resolution ! conduction band p n ε =3 eV 0.7 eV signal valence band - HV Intrinsic energy resolution determined by statistics of charge carriers ~ N → FWHM = 2.35 F E γ / ε

Compton Suppression Improve peak-to-total ratio Peak/Total = 20% ε =20% P/T=55% ε =20% Veto Compton suppressor CAESAR, EUROBALL, GAMMASPHERE

Effective Resolution: Doppler Broadening V ± Δ V Doppler shift Moving nucleus Δθ Ν θ 1 − V 2 Δθ D c 2 0 E γ = E γ 1 − V γ -ray detector cos θ c Broadening of detected gamma ray energy due to: � Spread in speed Δ V � Distribution in the direction of velocity Δθ Ν � Detector opening angle Δθ D è è Need accurate determination of V and θ . è è Minimize opening angle and particle detector

Doppler Broadening

Resolving Power… A figure of merit (resolving power) could be measured by the ability to observe weak branches from rare and exotic nuclear states.

Improving Peak-to-Background… …using F-fold coincidences (here ‘ matrix ’ : F=2) δ E: ‘ effective ’ E-resolution ( Δ E det and Δ E Doppler ) SE: average energy spacing à E x -E y coincidences go into peak (blue) à “ everything else ” spread over red area, as it isn ’ t coincident with any E x

Improving Peak-to-Background… …using F-fold coincidences (here ‘ matrix ’ : F=2) Projection

Cut along δ E Improvement of P/BG by factor SE/ δ E !!!

Note: r >1, ε <1 δ E )( P r ≈ ( SE T ) With α = 1/ r f The counts in the peak of interest N = α N o ε f The resolving power is RP = 1 α * = r f *

Evolution of Gamma-ray Spectroscopy Resolving Power Development of new detectors and techniques have always led to discoveries of new and unexpected phenomena.

“ Spectroscopic history ” of 156 Dy

Number of modules 110 Peak efficiency 9% (1.33 MeV) Ge Size 7cm (D) × 7.5cm (L) Peak/Total 55% (1.33 MeV) Distance to Ge 25 cm Resolving power 10,000

Courtesy of Robert Janssens

150 Nd( 48 Ca,4 n ) at 201 MeV

Auxiliary Devices

� Channel selection - lower background � Recoil correction - better Resolution 28 Si+ 58 Ni = => 80 Sr + α 2 p Yrast SD band No Background subtraction GS alone γγ γγ MB + GS γγ γγ , no Recoil C. MB + GS γγ γγ + RC (const β ) MB+GS γγ γγ + RC- β ( Ε π )

132 Xe + 208 Pb @ 650MeV e c n e r e f f i D F O T Scattering Angle

SOME EXAMPLES

Cranking analysis: Angular momentum and moments of inertia as functions of the rotational frequency ω = ∂ E ∂ I rotational frequency I ( ω ) angular momentum ℑ (1) ( ω ) = I ω kinematical moment of inertia ℑ (2) ( ω ) = dI d ω dynamical moment of inertia p = m (1) v f = m (2) a f = dp / dt = ( dp / dv ) a

Cranking ¡analysis: ¡ Experimental ¡formulae ¡ Δ I = 1 -transitions:  ω ( I ) = E ( I ) − E ( I − 1) E '( I ) = 1 ) −  ω ( I ) I ( 2 E ( I ) + E ( I − 1) Δ I = 2 -transitions:  ω ( I ) = E ( I ) − E ( I − 2) 2 E '( I ) = 1 ) −  ω ( I ) I ( 2 E ( I ) + E ( I − 2)

40 J [ � ] 35 163 Er band A 30 25 20 J 15 J = ℑ ω 10 ( 2 ) slope ℑ 5 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 � [ MeV ] ω ω 1 2 63 . 4 MeV � − ℑ =

Coriolis effects Problem #5 j Ι / J ∼ 2 2 Δ ~ ( I − 2 j ) 2 + 2 Δ 2 ℑ E(MeV) I ~ I 2 I 2 ℑ Stephens and Simon

2 nd Backbending (alignment) ….

ℑ Δ v ≈ 0.75 Δ v − 2 rigid

Coexistence of Excitations Normal-Deformed Super-Deformed Rotational Bands Rotational Bands ( β ~0.3) ( β ~0.6)

Superdeformation shell ¡structure ¡ Harmonic oscillator Wood Saxon potential

80 Se + 76 Ge @ 311MeV and 108 Pd + 48 Ca @ 191MeV

Extend our microscopic understanding of collective rotations in a “ complex rotor ”

8p-8h • 28 Si( 20 Ne,2 α ) 40 Ca • 24 Mg( 24 Mg,2 α ) 40 Ca 4p-4h • 8p-8h structure identified as π 3 4 , ν 3 4 known β 2 (high) ~ 0.59 β 2 ( ( low) ~ 0.4

36 Ar ¡: ¡Comparison ¡with ¡Theory ¡ ~ Const. Occupancy Band Termination β 2 ~ 0.46 • Configurations dominated by core excitations from sd to pf shell ( π 3 2 , ν 3 2 )

Normalized Quadrupole Moment 236 U 2:1 152 Dy (Deformation) 108 Cd 192 Hg 60 Zn 36 Ar 82 Sr 132 Ce 3:2 208 Pb ground states 1:1 Mass A