26. passage of particles through matter - Particle Data Group
26. passage of particles through matter - Particle Data Group
26. passage of particles through matter - Particle Data Group
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>26.</strong> Passage <strong>of</strong> <strong>particles</strong> <strong>through</strong> <strong>matter</strong> 19<br />
1.00<br />
Pair production<br />
(X 0 N A /A) dσ LPM /dx<br />
0.75<br />
0.50<br />
0.25<br />
1 TeV<br />
10 TeV<br />
100 TeV<br />
1 EeV<br />
1 PeV<br />
100 PeV<br />
10 PeV<br />
0<br />
0 0.25 0.5 0.75 1<br />
x = E/k<br />
Figure <strong>26.</strong>14: The normalized pair production cross section dσ LP M /dy, versus<br />
fractional electron energy x = E/k.<br />
formula for the differential cross section [37] reduces to<br />
dσ<br />
dE = A [<br />
1 −<br />
4<br />
X 0 N 3<br />
x(1 − x) ] (<strong>26.</strong>25)<br />
A<br />
in the complete-screening limit valid at high energies. Here x = E/k is the fractional<br />
energy transfer to the pair-produced electron (or positron), and k is the incident photon<br />
energy. The cross section is very closely related to that for bremsstrahlung, since the<br />
Feynman diagrams are variants <strong>of</strong> one another. The cross section is <strong>of</strong> necessity symmetric<br />
between x and 1 − x, as can be seen by the solid curve in Fig. <strong>26.</strong>14. See the review by<br />
Motz, Olsen, & Koch for a more detailed treatment [47].<br />
Eq. (<strong>26.</strong>25) may be integrated to find the high-energy limit for the total e + e −<br />
pair-production cross section:<br />
σ = 7 9 (A/X 0N A ) . (<strong>26.</strong>26)<br />
Equation Eq. (<strong>26.</strong>26) is accurate to within a few percent down to energies as low as<br />
1 GeV, particularly for high-Z materials.<br />
June 18, 2002 13:57
Change language