Redo problem 3 of homework 5 for extra credit. (Pair creation problem.)

Recall from last lecture:

Interactions of Particles with Bulk Matter



passing particle ionizes an atom, leaving behind an electron and positive ion.


passing particle excites (or ionizes) an atom which emits light (visible or u.v.) as it returns to an unexcited state

showers (electromagnetic and hadronic)

cascade of secondary particles created when particles that interact electromagnetically and strongly pass through high A/Z material.

Cerenkov radiation

emission of light (visible and u.v.) when the speed of a particle, βc, exceeds the speed (phase velocity) of light in a medium, c/n where n is the index of refraction (analogy of sonic boom for a vehicle exceeding the speed of sound)

transition radiation

emission of light (visible and u.v.) when a particle passes from one medium to another of differing EM properties
e+, e-infinite
p, pbarinfinite
μ+, μ-2.2×10-6 s
π+, π-2.6×10-8 s
K+, K-1.2×10-8 s
K0S0.89×10-10 s
K0L5.2×10-8 s
Λ, Λbar2.6×10-10 s

These are the particles we are concerned with measuring. Other particles that we may be interested in -- such as W±, Z0, t quark, D0, B0 -- eventually decay into the particles above, sometimes after several intermediate stages. We learn about the unstable particles by reconstructing them from their decay products.

Experimental Examples (continued)


Electromagnetic and hadronic showers.

Particle Identification

We'd like to know whether a charged track is due to a e+, μ+, π+, K+, or p. This is the task of particle identification. There are several ways to differentiate particle types:

The differences in the way particles interact show up in calorimetry. Let's consider how to "weigh" a particle to determine its mass. From the measurement of track curvature we determine p = βγm. If we can measure another quantity that depends differently on mass, then we should be able to determine the mass from these two measurements.

Kinematics of Scattering with Atomic Electrons

As a prelude to the calculations for a particle traversing bulk matter, let's consider the situation where a particle of mass m, four-momentum pi, scatters from atomic electrons which we'll treat as being at rest. After the collision, the particle has 4-momentum pf and the electron is ejected from the atom with 4-momentum pe. We can solve this situation in general, but we are specifically interested in the case of maximum momentum transfer. This occurs when the electron momentum is in the same direction as the momentum of the incoming particle. In this situation, conservation of energy/momentum gives:

|pi| = |pf| + |pe|
(pi2 + m2)½ = (pf2 + m2)½ + (pe2 + me2)½

Scattering Probabilities

Møller scattering

Φcol(Ei,Ef)dEf = 2Cmec2dEf[Ei/{Ef(Ei - Ef)} - 1/Ei]2

or by factoring out the first term in the square brackets:

Φcol(Ei,Ef)dEf = 2C {mec2Ei2 dEf/((Ei - Ef)2 Ef2)} [1 - Ef/Ei + (Ef/Ei)2]2

Bhabha scattering

Φcol(Ei,Ef)dEf = 2C (mec2dEf/Ef2) [1 - Ef/Ei + (Ef/Ei)2]2

Scattering of spin 0 particles of mass m

Φcol(Ei,Ef)dEf = (2Cmec22) (dEf/Ef2) [1 - β2 (Ef/Ef max)]

Scattering of spin ½ particles of mass m

Φcol(Ei,Ef)dEf = (2Cmec22) (dEf/Ef2) [1 - β2 (Ef/Em) + ½{Ef/(Ei + mc2)}2]

Scattering of spin 1 particles of mass m

Φcol(Ei,Ef)dEf = (2Cmec22) (dEf/Ef2) [(1 - β2 (Ef/Em))(1 + (1/3)(Ef/Ec)) + (1/3)(Ef/(Ei + mc2))2(1 + ½(Ef/Ec))]
where Ec = m2c2 / me.

Energy loss formula

The detection of particles relies on a transfer of energy from the incoming particle to the bulk medium of detection.

Copyright © Robert Harr 2003