A) Interaction of electromagnetic radiation with matter B) Interaction of charged particles with matter C) Interaction of neutral particles with matter σ th = 8π/3 r e 2 the most relevant processes for gamma radiation (or x-rays): - photo effect (absorption) - Compton effect -Pair production Pair production σ pair ~Z 2 ln (2(E/mc 2 ))
Inverse Compton scattering Colliding beams: Laser e-beam energy increase of backscattered photons E x 2 γ 2 E photon (1 cos Θ photon ) / (1 + γ 2 Θ x2 ) Electron bunch: one pass in a linear machine High energy beam dump
H.E.S.S.-telescope for high-energ gamma radiation High-Energy Stereoscopic System (High energy gamma astronomy in Namibia) Electromagnetic shower (Physik-Journal, Jan. 2008)
I (d) = I 0 exp{-l(σ ph + σ com + σ pair )ρd/a} = I 0 exp{-(µ/ρ)(ρd)} (L Avogadro number, L=6 x 10 23, ρ density)
A) Interaction of electromagnetic radiation with matter B) Interaction of charged particles with matter C) Interaction of neutral particles with matter A) electromagn. radiation B) charged particles N 0 N(x) E 0 E(x)= E 0 (de/dx) dx 0 x 0 x N(x) = N 0 exp(-µx) N(x) = N 0 für (x<r) = 0 for x>r Θ charged particles: Coulomb-interaction Rutherford-scattering bremsstrahlung (for light particles) Cerenkov-radiation
Collisions with 1. electrons (of the atom) a) elastic b) inelastic 2. nucleus (of the atom) a) elastic b) inelastic energy transfer leads to stopping T = 4 m 1 m 2 /(m 1 +m 2 ) 2 E 1 sinθ/2 (cms) heavy on light: little energy is transfered ionisation (20 30 ev for molecules, 2-3 ev in semiconductor) potential is the Coulomb potential, i.e. Rutherford scattering many collisions: statistical process, small scattering angles, straight path ( track )!!!
Bethe-Bloch-formula -de/dx = 4π Z 12 e 4 /m e v 12 n 2 Z 2 [ln(2m e v 12 /I) ln(1-ß 2 ) - ß 2 ] I average ionisation energy I=11.5 Z 2 ev. valid for: v 1 >> Z 1 v 0 (velocity in 1. Bohr orbit) Characteristics of electronic stopping: smallv: -de/dx~v 1 ~E 1/2 1 mediumv: -de/dx~1/e 1 ~MZ 12 /E 1 particle identification high v: -de/dx slow increase with E 1 minimum in ionisation at around 2M 1 c 2 total stopping: nuclear collisions have to be included (relevant at low energies).
Bethe-Bloch-formula -de/dx 1/ρ ~ const (absorbing material) (Z/A ~ ½) Z effective nuclear collisions Addendum for light particles: collisions and radiation (bremsstrahlung)
range R = E 0 de/(de/dx) Tables e.g. Northcliffe and Schilling Nucl. Data Tables A7 (1970) 233 Computer programs TRIM and more recent versions SRIM etc. relevant and useful for: - detectors - ion implantation - modification (incl. medical-therapeutical applications) - analysis - slowing down
Range
Energy deposition (linear) Bragg-Peak de/dx x 1-MeV protons in silicon
C) Interaction of neutral particles with matter most important example: neutrons when captured, results in γ-radiation, s.a., in collisions, leads to energy transfered to charged particles, s.a.
Application of stopping of charged particles Coulomb scattering (Rutherford) Coulomb force F = zze 2 /r 2 Polar coordinates r= l 2 /mzze 2 1/(1- ε cosφ) with l 2 = b 2 2mE and ε 2 = 1 + 2El 2 /m(zze 2 ) 2 r i.e. (1- ε cosφ) 0, then cosφ = sin Θ/2 then b = zze 2 /2E cotθ/2 finally dσ/dω = (zze 2 /4E) 2 1/sin 4 Θ/2
Ion beam analysis Rutherford-backscattering-technique RBS
Kinematic factor and energy loss determine the RBS-energy
Layered structures
2.3 Detectors Ionisation Ionisation chamber - semiconductor
Photo multiplier-sekundärelektronenvervielfacher continuous channelplate - Kanalplatten
Ge-Detector ball anti-compton-shield
Compton-suppression
2.4 Radiation effects biological effects modification Ionisation cell damage recovery direct collision genetic damage cell death organical malorganisation damage cancer
Some units used in radiation safety activity (source strenght) 1 decay/sec = 1 Bequerel (Bq) (ancient unit 1 Curie = 37 GBq) radiation dosis (energy dosis, absorbed energy) 1 J/kg = 1 Gray (Gy) (old unit 1 rad = 0.01 Gy) ionisation dosis (ion pairs) 1 Röntgen = 1.61 10 12 ion pairs in 1 g air (for tissue 1 Röntgen 1 rad = 0.01 Gy = 0.01 Sv) biological dosis 1 Sievert = RBW x 1 Gy RBW relative biological effectiveness x-ray (gamma) 1 beta 1 n, p 10 alpha 20 fission fragments >100 dose rate (radiation dosis per time) 1 Sievert/h = 1 Sv/h (old unit 1 Rem = 10 msv/h)
natural radiation ca. 2 msv/a (cosmic radiation (f(h) and geographical position), Environment (inside, outside), medical diagnostics) limits given by safety regulations (law) oriented at natural radiation exposure level 20 msv/a for persons professionally working with or exposed to radiation 1 msv/a for non-professionally exposed persons
Tumor therapy with ions especially with protons at HZB (ISL (Homeyer, Kluge, Heufelder et al.), now PT (Denker et al.) jointly with Charité-UKBF (Foerster)) since 1998 more than 1000 patients
3. Nuclear properties charge Z: Moseley-law 3.1 Nuclear mass Experimental measurement mass spectrograph after Thomson und Aston essential q/m mass spectrum A=20 (resolution ca. 1:100000)
Binding energy mass formula (liquid drop model v. Weizsäcker) B = a V A a S A 2/3 a C Z 2 /A 1/3 a A (N-Z) 2 /A + a P δ/a 1/2 volume surface Coulomb asymmetry pairing
parameter set a V = 15.85 MeV/c 2 a S = 18.34 MeV/c 2 a C = 0.71 MeV/c 2 a A = 23.22 MeV/c 2 a P = 11.46 MeV/c 2 δ=0 for ug,gu-nuclei δ=1 for gg-nucei δ=-1 for uu-nuclei
volume term: B/A = const, A ~ V ~ R 3 surface term: O ~ R 2 ~A 2/3 Coulomb term: homogeneously charged sphere 3/5 q 2 /R empirically from quantum mechanics: asymmetry term: (N-Z) Pairing: separation energy of a neutron
it follows, for A= const, a mass valley with stable bottom. M(Z) = a + bz + cz 2 minimum: Z o = A/(1.98 + 0.015A 2/3 ) prototype ß-decay: n p + e - + ν p n + e + + ν _
2 parabola for uu- and gg-nuclei separated by 2δ Double beta-decay: 2 possibilities (resp.): _ 2n 2p + 2e + 2 ν or 2n 2p + 2e 2p 2n + 2e + + 2 ν or 2p 2n + 2e + Lepton number conservation?
3.2 Nuclear radius Experimental determination depends on type of interaction: charge radius, mass radius Definition of cross section: each scattering center is associated with a scattering area σ, called cross section. Simple definition: let k be the number of centers per area, F the total area, then the probability for a hit is W = kf σ/f = k σ and with the density of incoming particles j, the rate of events (for scattering, reaction, ) is R = k σ j F or σ = R /(j kf) σ = number of events/time/center/current density of incoming particles
Definition of the differential cross section: solid angle: surface fraction dω=dφ sinθ dθ / total surface of the unit sphere dω = 4π dσ/dω (Θ) = number of particles scattered into the solid angle / time / current density dσ/dω (Θ) = db/dθ b/sinθ
a) Radius as determined by Coulomb scattering (Rutherford) Coulomb force F = zze 2 /r 2 Polar coordinates r= l 2 /mzze 2 1/(1- ε cosφ) with l 2 = b 2 2mE and ε 2 = 1 + 2El 2 /m(zze 2 ) 2 r i.e. (1- ε cosφ) 0, then cosφ = sin Θ/2 then b = zze 2 /2E cotθ/2 finally dσ/dω = (zze 2 /4E) 2 1/sin 4 Θ/2
16 O on Au at 27 MeV α on 208 Pb at 60
b) Radius from scattering of high-energetic particles (p, n, e,..) wavelength smaller than the object : => diffraction patterns wavelength according to de Broglie: λ =h/p 1.minimum at sinθ = 0.61 λ/r neutron scattering with 14 MeV-neutrons result: R=r 0 A 1/3
Electron scattering (Hofstatter, Stanford) charge distribution, no point charge dσ/dω = dσ/dω point F(q) 2 with form factor F(q) = ρ(r)exp(-iqr) d 3 r (q = k k ) (Fourier-transformed charge density)
examples of electron scattering
Wood-Saxon (Fermi-) distribution ρ(r) = ρ 0 / (1 + exp{(r-r)/a}) approximately: a = 0.54 fm R = r 0 A 1/3 r 0 = 1.25 fm t = 4.4 a ρ 0 = 10 14 g/cm 3
c) myonic atoms m µ = 207 m e - Bohr radius 1/207 compared to an electronic atom - 1s orbit plunges into the nucleus - ev-binding energies become kev-binding energies ( E(Fe) Α=2 2.5 kev) d) isotopic shift x-ray transitions E ~ A 2/3 ( E(Hg) Α=2 0.15eV) Laser spectroscopy ( Hyperfine interaction ) e) isomeric shift Mössbauer spectroscopy different radii within the same nucleus f) Coulomb energy of mirror nuclei e + - decay: end point energy versus A 2/3
3.3 Nuclear states: nuclear spin, parity and excitation energy Nuclear spin I: Nucleons (proton, neutron) are Fermions with s=1/2 Total angular momentum of the nucleon j = l + s (vector sum) Total angular momentum of the nucleus I I = i j i = i (l i + s i ) gg-nucleus I=0 uu-nucleus I 0, but also I=0 ug-,gu-nuclei I half integer Total angular momentum of the atom ( hyperfine structure ): nuclear spin I + electronic shell J = atomic spin F splitting of atomic J leads to 2I+1 (I J) or 2J+1 (J I) sublevels H Hfs = A I J with E Hfs = A/2 [F(F+1) I(I+1) J(J+1)]
Fine structure and hyperfine structure of the yellow Na-line
Laser spectroscopy
Parity π (I π ): symmetry behavior of the wave function under reflection (in space) Π op Ψ(r) = Ψ(-r) = πψ(r) if Π op H Π -1 op = H with HΨ=EΨ 2-fold application = identity operation therefore: eigenvalues for parity operation +1 or -1. Parity is a multiplicative quantum number Parity even (+1): Parity odd (-1): with even orbital angular momentum with odd orbital angular momentum characterizing energy levels E 3 I π 3 E 2 E 1 0 A Z X I π 2 I π 1 I π 0
Isospin-concept Isospin-operator analogous to spin τ, τ z : proton τ z π=+1/2 π T z = i τ zi = 1/2 (Z-N) neutron τ z ν=-1/2 ν Q = (1/2 +T z ) e generalized Q=[(B+S+C)/2 + T z ] e (Baryon number, S Strangeness, C Charm) Dinucleon T=1 T=0 generalized Pauli principle Total wave function must be totally antisymmetric when interchanging 2 particles Ψ(r 1,r 2 )Χ(s 1,s 2 )Φ(t 1,t 2 )
I π 20+ 18+ 16+ 14+ 12+ 10+ 8+ 6+ 4+ 2+ 0+ 170 72 Hf E (MeV) 4.417 3.764 3.150 2.565 2.014 1.504 1.042 0.641 0.321 0.100 0