WS09/10 Mahnke

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2 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 ))

3 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

4 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)

5 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)

6 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

7 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 )!!!

8 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).

9 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)

10 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

11 Range

12 Energy deposition (linear) Bragg-Peak de/dx x 1-MeV protons in silicon

13 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.

14 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

15 Ion beam analysis Rutherford-backscattering-technique RBS

16 Kinematic factor and energy loss determine the RBS-energy

17 Layered structures

18 2.3 Detectors Ionisation Ionisation chamber - semiconductor

19 Photo multiplier-sekundärelektronenvervielfacher continuous channelplate - Kanalplatten

20 Ge-Detector ball anti-compton-shield

21 Compton-suppression

22 2.4 Radiation effects biological effects modification Ionisation cell damage recovery direct collision genetic damage cell death organical malorganisation damage cancer

23 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 = 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)

24 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

25 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

26 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)

27 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

28 parameter set a V = MeV/c 2 a S = MeV/c 2 a C = 0.71 MeV/c 2 a A = MeV/c 2 a P = MeV/c 2 δ=0 for ug,gu-nuclei δ=1 for gg-nucei δ=-1 for uu-nuclei

29 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

30 it follows, for A= const, a mass valley with stable bottom. M(Z) = a + bz + cz 2 minimum: Z o = A/( A 2/3 ) prototype ß-decay: n p + e - + ν p n + e + + ν _

31 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 ν or 2p 2n + 2e + Lepton number conservation?

32 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

33 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

34 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

35 16 O on Au at 27 MeV α on 208 Pb at 60

36 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

37 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)

38 examples of electron scattering

39 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 = g/cm 3

40 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

41 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)]

42 Fine structure and hyperfine structure of the yellow Na-line

43 Laser spectroscopy

44 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

45 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 )

46 I π Hf E (MeV)