Motivation Spins and excited states of double-magic nucleus 16 O Decay spectra are caused by electro-magnetic transitions. g-spectroscopy deals with g-ray detection and is one of the most relevant methods to investigate excited states in nuclei.
Reminder transition probability of g-decays Results of multipole expansion for single proton transitions: E 14 2/3 3 M 13 3 1 1.010 A E 1 5.610 E E 7 4/3 5 M 7 2/3 2 7.310 A E 2 3.510 A E E 2 7 M 4/3 7 3 34A E 3 16A E E -5 8/3 9 M -6 2 9 4 1.110 A E 4 4.510 A E Important ratios: E, M E, M 1-5 10 E M 10 2 Multipole radiation contains angular momentum l and parity: 5 l l l -1 Elektrische Multipolstrahlung l 1 electric multipole radiation magnetic multipole radiation -1 Magnetische Multipolstrahlung
Selection rules for g-transitions For EM interaction the following quantities are conserved: - energy - momentum - angular momentum - parity Consider transition: i f Selection rules Angular momentum: Parity: i f g I I Lg I - I Lg I I m m - m i f i f i f example: I 3 I 2 - Ii 0 If 0 Lg i f
g-spectroscopy Example: spins and excitation energies of 152 Dy Superdeformed states at spin >24 hbar
Charmonium and Positronium Different quantum numbers: Charmonium: n = N + 1 Positronium: n = N + L + 1 For n = 1 and n = 2 similarity of spectra At small distances q-antiq potential is Coulomb like, at larger distances linear increase ( quark confinement )
Quark-Antiquark-Potential r 4 s c V - k r 3 r s : Coupling constant of Strong interaction Coupling constant is getting smaller at increasing smaller distances At small distances quarks are quasi-free particles asymptotic freedom
photon counts g-spectroscopy of ψ -decays g-zerfall der 3 2 S 1 Resonanz L = 0 L = 0 L = 1 photon enenergy [MeV] S = 0 S = 1 S = 1 Direct production of charmonium via virtual photon P produces states with quantum number J - 1 Other intermediate states are populated via g-transitions. For ψ exist eight allowed transitions which are detected via g-spectroscopy of decay photons. Selection rules for electric dipol transition: ΔL = 1 ΔS = 0 Selection rules for magnetic dipol transition: ΔL = 0 ΔS = 1
Detection of Higgs Boson
Detection of g-radiation g-ray Absorber Detector x Intensity of incoming g-rays: I 0 Absorber of thickness dx reduces I 0 by di: di = -Idx is absorption coefficient After thickness x intensity is reduced: I = I 0 exp(-x) (Beer s law) Thickness which reduces the intensity by factor 1/e is: 1/. absorption coefficient = PE + CS + PP
Detection of g-radiation is linear attenuation coefficient [cm -1 ] relationship between cross section s and : n s r N A A s n particle density cm -3 N A Avogadro constant A atom weight r density s cross section
Interaction of g-rays with matter photo-electric effect PE Compton scattering CS pair production PP
Photo-effect Full g-energy is absorbed by electron. Electron ionizes atom and carries kinetic energy: T = h - E B E B binding energy of electron h - photon energy Absorption has largest c.s. if h is slightly above E B means electron frequency is close by radiation frequency. Absorption peaks correspond to binding of M (n=3), L (n=2) and K (n=1) shell electrons. Absorptions coefficient PE decreases strongly with energy. For energies comparable K-shell: Z 4 /E 3 Photo-effect dominates for heavy material and high Z and at low g-energies.
Absorption coefficient for tungsten M edge L edge K edge Z= 74 10 kev 100 kev 1000 kev
Compton scattering Einlaufendes Photon E, Rückstoß Recoil Elektron Gestreutes Photon E S, S
Compton scattering Photon-electron scattering kinematic incoming photon E g, recoil electron scattered photon E Sg, S CS Z f(eg) energy and momentum conservation: photon energy changes from to S (scattered) S - h mc 1- cos
Compton scattering g-energy after scattering: hc Eg 1 1 - E E g, S g 1- cos 2 mc Eg, Eg 1 cos 1 2 mc Eg S -
Compton scattering backscatter peak ~ 200 300 kev
Compton scattering Differential cross section Klein-Nishina Formula ds d Zr 2 0 1 1(1 - cos ) with hν m c e 2 2 1 cos 2 2 1 2 2 (1 - cos ) 2 (1 cos )(1 (1 - cos )) and class. electron radius r 0
Klein-Nishina cross section
Pair creation Positron - Electron pair Requires g - energy > 1022 kev, min g (1 third particle (nucleus of atom) for momentum conservation PP Z 2 mean free path length: PP 9/7 L rad E 2m c e 2 me ) M
More about e + in solids Positron is slowed down and thermalized in solid state in less than 10-12 s = 1ps to thermal energies of E=0,04eV at T=300K. Typical e + -lifetime in solids in range of 100-300ps. Positron range in matter to thermalize depends on its kinetic energy and the matter density. Finally positron diffuses a small path length of a few 0,1m at thermal energies.
e + in solids Positron is captured along its diffusion path at trapping centers. Positron traps are: lattice vacancies, micro cavities, dislocations, grain- and phase boundaries, in amorphous matter: voids, cavities. Positron feels an attractive potential at lattice vacancies which is around 1eV deeper than in undisturbed crystal lattice. The positron can not escape the lattice trap due to its low thermal energy, it annihilates there with an electron into two 511 kev quanta. Direct radiation from annihilation into two 511keV- g-quanta with exact 180 directional correlation in CM system. Small differences from 180 in laboratory system occur.
Positronium: e + e - In vacuum, in gas and in some isolators one positron forms with one electron a hydrogen like bound state: positronium, Ps Positronium was first discovered in 1951, shortly after 3g-decay was found. In matter positronium transforms from ortho- into parapositronium. Interaction with electrons in surrounding causes: pick-off process. Due to the high efficiency of pick-off process in matter, the 3g- decay of the triplett state is strongly suppressed. -> Dominating radiation into two g-quanta. positronium, Ps states symbol decay vacuum lifetime Parapositronium, p- Ps Orthopositronium, o-ps Singulett Triplett 1S 0 2g 123 ps 3S 1 3g 140 ns
Summary: absorption of g-rays PE Z 4 /E 3 CS Z/E PP Z 2
Dependence of interaction from energy and absorber charge number Z
Electro-magnetic shower combination of pair creation and Bremsstrahlung cause an interaction of high energetic e -, e + and g s which constitute an electro-magnetic shower. -principal: photon converts into one e + e - - pair, e - and e + lose energy via Bremsstrahlung, photon converts again into e + e - - pair,... cascade stops around critical energy, rest is dominated by collisional energy loss -Simplified model: x=0 1 g E 0 0<x< 1L e + e - 0.5 x E 0 1L<x< 2L 2g e + e - 0.25 x E 0 2L<x< 3L 4g 2e + 2e - 0.125 x E 0 After t radiation length N~2 t E(t)~ E 0 /2 t
(1/E 0 ) de/dt Electro-magnetic shower Monte-Carlo simulation of 30 GeV electrons in iron: critical energy: E c =27.4 MeV radiation length: X 0 =13.84 g/cm 2 or d 0 =1.76 cm
Interaction of g-rays with matter Summary photo-electric effect Compton scattering pair production All interactions cause finally electrons sharing the initial g-ray energy!