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

PHYS40422: Applied Nuclear Physics Paul Campbell Room 4.11 Paul.Campbell-3@manchester.ac.uk. Classical Bethe Bloch formulation. We have already shown the maximum energy loss in a collision  assumes M >> m. After. Before.

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

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  1. PHYS40422: Applied Nuclear PhysicsPaul CampbellRoom 4.11Paul.Campbell-3@manchester.ac.uk Classical Bethe Bloch formulation

  2. We have already shown the 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

  3. Trying to derive this – the 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)

  4. Consider particle of charge ze, passing a stationary charge Ze ze • Assumptions • Target is non-relativistic • Target does not move b y r θ x Ze

  5. Force on in-coming projectile • Now need to calculate momentum transfer…i.e. the impulse, • We remember dt = dt/dy dy = (1/velocity) dy • And y = b tan q so dy = b sec2q dq, so, dt = (1/velocity) sec2q dq • Integral is easy!!!

  6. Non-relativistic energy transferred???

  7. Energy transfer via the atom to an individual electron is (Z = 1, M = me)

  8. So energy transfer depends on impact parameter b • Need to integrate over all impact parameters, correcting for the number of possible targets at distance b (i.e. multiply by target density) • So consider cylinders of constant b through the material… b db ze

  9. Try and justify a minimum and maximum b… • Calculate average energy loss... IMMEDIATELY a problem… The integral, bar constants is just 1/b. Again an easy integral but a major problem if we integrate from zero to infinity… • Easier to see if we express b in terms of E, so an Emin and Emax • Emax? Take this to be the head on collision. Emin? Take this to be the ionisation potential…

  10. This was just a simplified derivation (to say the least) • Far from complete • But gets you the key elements of.. • The (relativistic) correct answer, • Return to lecture notes 2…

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