Physics 736. Experimental Methods in Nuclear-, Particle-, and Astrophysics. Lecture 4

Transcription

1 Physics 736 Experimental Methods in Nuclear-, Particle-, and Astrophysics Lecture 4 Karsten Heeger heeger@wisc.edu

2 Homework Homework is posted on course website I will always give you at least one week to complete homework Solutions will be posted after homework is due You can provide feedback on difficulty and usefulness of homework.

3 Rescheduling of Lectures We need to reschedule a few lectures. no lectures on Feb 8, 10, 15 I will make it up to you by providing pizza or cookies. We will have a doodle poll to identify days and times for make-up lectures

4 Rescheduling of Lectures no lectures on Feb 8, 10, 15

5 Review of Last Lecture stopping power (MeV/(g/cm 2 ))

6 Review of Last Lecture What is stopping power? S(E) = de dx

7 Review of Last Lecture Which region is described by the Bethe-Bloch formula? stopping power (MeV/(g/cm 2 )) I II III

8 Review of Last Lecture What describes the functional form of the Bethe-Bloch formula? stopping power (MeV/(g/cm 2 )) II

9 Interaction of Photons photons photoelectric effect Compton scattering pair production nuclear photo dissociation (γ,n)

10 Interaction of Photons Compton scattering Inverse Compton scattering - in Compton scattering the incoming photon scatters off an electron that is initially at rest. - electron gains energy and the scattered photon has a frequency less than that of the incoming photon. - inverse Compton scattering takes place when the electron is moving, and has sufficient kinetic energy compared to the photon. In this case net energy may be transferred from the electron to the photon. - inverse Compton effect is seen in astrophysics when a low energy photon (e.g. of the cosmic microwave background) bounces off a high energy (relativistic) electron. Such electrons are produced in supernovae and active galactic nuclei

11 Interaction of Charged Particles characteristic features energy loss deflection of particles from incident direction classes of particles e +,e - heavy particles: μ, π, p, α primary processes inelastic collisions elastic scattering

12 Interaction of Charged Particles charged particles inelastic collisions w/ atomic e- elastic scattering stopping power Cherenkov radiation energy loss of electrons and positrons collisions radiation (Bremsstrahlung) Coulomb scattering energy loss distributions nuclear reactions

13 Stopping Power stopping power for muons in copper stopping power (MeV/(g/cm 2 )) stopping power less because ions attach electrons - nuclear inelastic collisions if you consider nuclei instead of muons - bremsstrahlung important for electrons and muons minimum ionizing particles S(E) = de dx

14 Stopping Power stopping power for muons in copper

15 Stopping Power Bohr (classical treatment) de dx = 4πz2 e 4 m e v 2 N eln γ2 mv 3 ze 2 ν Bethe-Bloch (QM) - # = 2 n N^ r! ^, " p + il^ (ry^) -' P I = mean excitation potential

16 Stopping Power Bethe-Bloch - # = 2 n N^ r! ^, " p + il^ (ry^) -' P with density and shell corrections G de dx typically de/dx depends only on β (given a particle and medium)

17 Stopping Power Bethe-Bloch t -wrth correctrons --.wilhout cortections >t0 D :, d tot to3 Energy [Mev] los

18 Stopping Power Energy Dependence of Bethe-Bloch t -wrth correctrons --.wilhout cortections non-relativistic E de dx 1 β 2 >t0 D :, each particle has different de/ dx can be used for PID d minimum ionizing tot to3 Energy [Mev] los v =0.96c same point for all particles of same charge high E most relativistic particles have energy loss rates close to the minimum + radiation losses for e +/-

19 Stopping Power Bethe-Bloch At low β -de/dx 1/β 2 decreases rapidly as β increases. reaches a min at βγ 3 (a particle at the energy loss min is called mip). typically de/dx depends only on β (given a particle and medium)

20 Stopping Power Bethe-Bloch de/dx lor l03 Energy ['lev] ro5 low momentum region where -de/dx 1/β 2 and the relativistic rise depend on m so can be used for particle identification (PID)

21 Stopping Power Bethe-Bloch For a given particle (z) and target (I,N,Z,A), the energy loss depends only on the velocity of the particle! Most relativistic particles have energy loss rates close to the minimum (mip = minimum ionizing particles)~ 2 MeV/g/cm2

22 Example: cosmic muons and plastic scintillator

23 Stopping Power Bragg Curve de/dx depends on kinetic energy charged particle is more ionizing towards the end of its path

24 Stopping Power electronic and nuclear stopping electronic stopping = - slowing down due to the inelastic collisions between bound electrons in the medium and the ion moving through it - collisions may result in excitations nuclear stopping = - elastic collisions between the ion and atoms in the sample Resources The stopping and range of ions in matter Stopping Power for light ions

25 Stopping Power electronic and nuclear stopping

26 Stopping Power scaling laws if we know de/dx for one particle we can scale to another one de 2 dx (T 2)= Z2 2 Z 2 1 de 1 dx ( T 2 M 1 M 2 ) mass thickness de/dx varies little when expressed in terms of mass thickness

27 Channeling ooooo ooooo oooo ooooo critical angle for channeling φ c = zza0 Ad 1670β γ

28 Range range depends on - material - particle type - energy Ftj.2.1 distrib form Transmission A!ao.b.r thiclnaa3

29 Range Pb Fe C R/M (g cm 2 GeV 1 ) H 2 liquid He gas βγ = p/mc Muon momentum (GeV/c) Pion momentum (GeV/c) Proton momentum (GeV/c) Figure 27.4: Range of heavy charged particles in liquid (bubble chamber)

30 Cherenkov Radiation v particle > c n cos θc = 1 βn(w)

31 Cherenkov Radiation

32 Cherenkov Radiation Sudbury Neutrino Observatory

33 Cherenkov Counters

34 Bremsstrahlung

35 Collision vs Radiation Loss collision loss radiation loss de dx Z A 1 β 2 [ln(energy)] de dx EZ2

36 Collision vs Radiation Loss? ql o a x l0' tt UJ o Bremsstrohlung loss :.:.:.:.:.:.;.:.;.;. lo3 Energy [Mev] critical energy (de dx ) rad = ( de dx ) coll E c 800 MeV Z +1.2

37 Collision vs Radiation Loss stopping power for muons in copper? ql o a x l0' tt UJ o Bremsstrohlung loss :.:.:.:.:.:.;.:.;.;. lo3 Energy [Mev]

38 Radiation Length radiation length - mean distance over which a high-energy electron loses all but 1/e of its energy by bremsstrahlung - 7/9 of the mean free path for pair production by a high-energy photon L rad = 716.4A Z(Z +1)ln(287/ Z) g/cm 2

39 Range and Absorption of Electrons straggling range for electrons < range number-distance curves for electrons absorption of beta electrons gtcmz I = I 0 e µx

40 Karsten Heeger, Univ. of Wisconsin NUSS, July 13, 2009