PHYS40422: Applied Nuclear Physics Paul Campbell Room 4.11 Paul.Campbell-3@manchester.ac.uk

1. PHYS40422: Applied Nuclear PhysicsPaul CampbellRoom 4.11Paul.Campbell-3@manchester.ac.uk • Interaction of Radiation with Matter • Radiation Detection • Biological Effects of Radiation • Applications of Nuclear Techniques • Nuclear Fission • Nuclear Fusion http://personalpages.manchester.ac.uk/staff/Paul.Campbell-3/phys40422.htm

2. Chapter 1. The Interaction of Radiation with Matter:1.1 Charged particles. • For E< few 100 MeV the main process is collisions with atomic electrons. • Energetic particles such as protons, alphas will be stripped of atomic electrons. • Protons and alphas lose little energy in each collision and deviate little in direction.

3. Maximum energy loss in a collision assumes M >> m After Before v v 2v m m M M For a 4 MeV alpha particle colliding with an electron this is about 2 keV

4. For heavy fast charged particles there is a fairly well-defined range e.g. for a mono-energetic beam of alphas entering a material: Variation in range called “straggling” (a stochastic effect)

5. Electrons do not travel far in any material. They are historically known as “Delta Rays” Typically collisions with large changes in direction. Collisions may take away a large fraction of the electron energy Electrons may also lose energy through Bremsstrahlung radiation During an interaction with another electron or a nucleus.

6. -particle tracks in a cloud chamber Electron tracks in a cloud chamber

7. Bethe-Bloch Formula for Stopping Power S m = electron mass NA = Avogadro’s number Medium: A, Z, ρ I = ionization potential Ion: zv ( = v/c)

8. Energy dependence of S 103 Protons in aluminium 102 -dE/dx (MeV g-1 cm²) 101 100 10-1 100 101 102 103 104 Proton energy (MeV)

11. SversusE: main features • Fall-off for E < ~ 100 keV: • max. E transfer 2mv2~ I [ln(2mv2/I)  0] • and z(eff) < z  tendency to pick up electrons • Slow risefor E > ~1 GeV (v  c) • In the range: ~ 100 keV < E < 1 GeV: • -dE/dx ~ 1/Ekwith k  0.8

12. Projectile dependence of S: • S  (p transfer)2/m (impulse)2/m • Impulse = (force) x (collision time) • Force  ze2 • Collision time ~ 1/v Hence: S  z2/mv2

13. Medium dependence of S S  electron density = Z atom density = Z  NA/A

14. ln(2mv2/I) term: • Arises from an integral over impact parameters corresponding to: • Max. energy transfer: 2mv2 • Min. energy transfer: I

15. Range Distance travelled before all energy is lost Note:R  1/ρ, since dE/dx  ρ, So range is often given as R = ρR in units of mass/unit area

16. Projectile dependence of R -dE/dx = S  z2f(v) KE E = ½ Mv2  dE = Mvdv giving, R =  dE/S  MF(v)/z2 So, for a given speed, S  z2and R  M/z2 E.g. 1 MeV proton and 4 MeV  particle (v same for both): S(p) = ¼ S(α) R(p) = R(α)

17. Medium dependence of R Both Z/Aand the log term vary slowly with A Bragg-Kleeman rule: An approximate relation for estimating relative ranges in different materials

18. Energy dependence of S: Calculating the Bragg Curve 103 Protons in aluminium 102 -dE/dx (MeV g-1 cm²) 101 Integrate to get E(x) 100 10-1 100 101 102 103 104 Proton energy (MeV)

19. Projectile ion loses energy along track S Distance of penetrationd Bragg curve – for particle energies above the maximum in S vs E Note that maximum ionization occurs at end of path.

20. Main features of Bragg curve: • Initially, E is maximum – then, decreases with d as particle loses energy • This means Sincreases with d because, (approximately) S  1/v2 • Near the end, S reaches a max. then falls, as 2mv2 ~ I [ln(2mv2/I)  0] • Also, at low v, electron pickup-and-loss reduces effective z

21. The Energy loss of electrons due to Bremsstrahlung Ignoring the slowly-varying log term this radiative effect gets large when the energy is much larger than the rest-mass energy, hence the relative importance for electrons.

23. Bremsstrahlung (dotted line) is more important in high-Z stoppers Solid lines are ionization stopping powers. Curves for electrons in Pb and Al.