Types Particle shower
the start of electromagnetic shower.
there 2 basic types of showers. electromagnetic showers produced particle interacts or exclusively via electromagnetic force, photon or electron. hadronic showers produced hadrons (i.e. nucleons , other particles made of quarks), , proceed via strong nuclear force.
electromagnetic showers
an electromagnetic shower begins when high-energy electron, positron or photon enters material. @ high energies (above few mev, below photoelectric effect , compton scattering dominant), photons interact matter via pair production — is, convert electron-positron pair, interacting atomic nucleus or electron in order conserve momentum. high-energy electrons , positrons emit photons, process called bremsstrahlung. these 2 processes (pair production , bremsstrahlung) continues until photons fall below pair production threshold, , energy losses of electrons other bremsstrahlung start dominate. characteristic amount of matter traversed these related interactions called radiation length
x
0
{\displaystyle x_{0}}
. both mean distance on high-energy electron loses 1/e of energy bremsstrahlung , 7/9 of mean free path pair production high energy photon. length of cascade scales
x
0
{\displaystyle x_{0}}
; shower depth approximately determined relation
x
=
x
0
ln
(
e
0
/
e
c
)
ln
2
,
{\displaystyle x=x_{0}{\frac {\ln(e_{0}/e_{\mathrm {c} })}{\ln 2}},}
where
x
0
{\displaystyle x_{0}}
radiation length of matter, ,
e
c
{\displaystyle e_{\mathrm {c} }}
critical energy (the critical energy can defined energy in bremsstrahlung , ionization rates equal. rough estimate
e
c
=
800
m
e
v
/
(
z
+
1.2
)
{\displaystyle e_{\mathrm {c} }=800\,\mathrm {mev} /(z+1.2)}
). shower depth increases logarithmically energy. while lateral spread of shower due multiple scattering of electrons. shower maximum shower contained in cylinder radius < 1 radiation length. beyond point electrons increasingly affected multiple scattering, , lateral sized scales molière radius
r
m
{\displaystyle r_{\mathrm {m} }}
. propagation of photons in shower causes deviations molière radius scaling. however, 95% of shower contained laterally in cylinder radius
2
r
m
{\displaystyle 2r_{\mathrm {m} }}
.
the mean longitudinal profile of energy deposition in electromagnetic cascades reasonably described gamma distribution:
d
e
d
t
=
e
0
b
(
b
t
)
a
−
1
e
−
b
t
Γ
(
a
)
{\displaystyle {\frac {de}{dt}}=e_{0}b{\frac {(bt)^{a-1}e^{-bt}}{\gamma (a)}}}
where
t
=
x
/
x
0
{\displaystyle t=x/x_{0}}
,
e
0
{\displaystyle e_{0}}
initial energy ,
a
{\displaystyle a}
,
b
{\displaystyle b}
parameters fitted monte carlo or experimental data.
hadronic showers
the physical process cause propagation of hadron shower considerably different processes in electromagnetic showers. half of incident hadron energy passed on additional secondaries. remainder consumed in multiparticle production of slow pions , in other processes. phenomena determine development of hadronic showers are: hadron production, nuclear deexcitation , pion , muon decays. neutral pions amount, on average 1/3 of produced pions , energy dissipated in form of electromagnetic showers. important characteristic of hadronic shower takes longer develop electromagnetic one. can seen comparing number of particles present versus depth pion , electron initiated showers. longitudinal development of hadronic showers scales nuclear absorption (or interaction length)
λ
=
a
n
a
σ
a
b
s
{\displaystyle \lambda ={\frac {a}{n_{a}\sigma _{\mathrm {abs} }}}}
the lateral shower development not scale λ.
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