Electromagnetic logitidinal shower development

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# Electromagnetic logitidinal shower development - PowerPoint PPT Presentation

Electromagnetic logitidinal shower development. Depth (in X o )at which the shower has the maximum number of particles: (e.g.: http://rkb.home.cern.ch/rkb/PH14pp/node58.html )

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Electromagnetic logitidinal shower development

Depth (in Xo)at which the shower has the maximum number of particles:

(e.g.: http://rkb.home.cern.ch/rkb/PH14pp/node58.html )

tmax≈ ln ( E /  ) - c (with:   550 MeV/Z c  1 for electrons (ZPb = 82) )

Shower depth for 95% lognitudinal containment:

T95[Xo]≈ tmax+ 0.08·Z + 9.6

Parametrization for average differential longitudinal energy deposit:

DE = k · t(a-1) · e-bt · dt ( with: k= E ba / (a) )

Integrate this up to some depth t’ :

Et’ = E = E· GAMDIS ( ’ , a) (with:  = bt )

Differentiate DE and set to zero (for shower maximum):

 tmax = (a-1) / b

CERN Library function

Fit for a and b and see whether they follow a logarithmic energy dependence

Compare : tmax = (a-1)/b with tmax theory : tmax ≈ ln ( E /  ) - c

Fit for a,b : All energies, all X0,

for 5 possibilities of x0junk: (1.8, 1.9, 2.0, 2.1, 2.2)

and then form the average over the results for a and b.

a vs E

a

a = a1 + a2 lnE

a1 = 1.68 0.36

a2 = 1.02 0.08

E[GeV]

b vs E

b

b = b1 + b2 lnE

b1 = 0.397 0.46

b2 = 0.002 0.05

E[GeV]

Depth of shower maximum

Data : tmax = (a-1)/b with a and b from fits as a function of energy

Theory : tmax ≈ ln ( E /  ) - c

theory

data

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