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Photon and Electron Cosmic Ray Flux Study

David Gerstle

LArTPC – Yale University Undergraduate

 

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Contents

• Photon and Electron flux data.

• Photon and Electron length in argon data.

• Conclusions

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Electron and Photon Flux Data• Photons: Beuermann and Wibberenz, “Secondary spectra of electrons

and photons in the atmosphere,” Can. J. Phys., 46, S1034, 1968.– Apparatus was a ‘lead scintillator sandwich’ with Cherenkov detector.

• Insisted on only single passing electrons (this excluded 10% of events).– Geomagnetic cutoff: 4.5 GV– Atmospheric depth: 750 g/cm^2

• Data were taken from a log/log dN/dE as a function of E plot; I only trusted myself to two significant figures.– Photons: from 0.03 GeV to 1 GeV dN/dE goes as ~E-2; from 1 GeV to 25

GeV as ~E-2.8. – Electrons: from 0.03 GeV to 1 GeV dN/dE goes as ~E-1.7; from 1 GeV to 25

GeV as ~E-2.6. • I calculated the integral flux [integral (dN/dE)*dE)] of each particle type

by a trapezoidal integral approximation from the highest energy to E.• Data have been adjusted to 990 g/cm^2 by the method Beuer…&W…

(sort of) suggest, as outlined on the following slide.

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e- Depth Correction and Photon Factor

• Correction is proposed only for electrons.• Exponential attenuation correction: I(E,d)=I0(E)*exp[-(d-

d0)/Λ] where Λ is the attenuation length and d0 is the original depth.

• There are two components of the electron flux though, π0

and decay. Thus the total adjusted flux is a weighted average of the two:– I(E,d)=I0(E)*(0.55*exp[-(d-d0)/Λpi]+0.45*exp[-(d-d0)/Λmu)– The relative weights were reported in the paper.

• Calculation shows that photon flux is ~1.7 times electron flux for all energies and ~1.3 times over 1 GeV [Richards and Nordheim, 1948].

• I multiplied the electron flux by 1.5 to get the photon flux.

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Electron Differential Intensity as a function of Energy

0.001

0.01

0.1

1

10

100

1000

0.1 1 10

E; (GeV)

dN

/dE

; (m

^2

s sr

GeV

)^-1

Electrons

E-2.6

E-1.7 Yellow is original depth differential flux

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Photon original depth Differential Flux as a function of Energy

0.001

0.01

0.1

1

10

100

1000

10000

100000

0.01 0.1 1 10 100

E; (GeV)

dN

/dE

; (m

^2

s sr

GeV

)^-1

Blue are original Differential Flux

PhotonsE-2.7

E-2.0

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Photons are Blue

Electrons are Pink

Emax

∫ (dN/dE)*dE

E

Electron and Photon Depth-Adjusted Integral from E to 60 GeV Fluxes as a function of Energy

0.01

0.1

1

10

100

0.01 0.1 1 10 100

E; (GeV)

N;

(m s

sr)

^-1

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Interaction Length Data from NIST

• http://physics.nist.gov/PhysRefData/Xcom/Text/XCOM.html • http://physics.nist.gov/PhysRefData/Star/Text/contents.html• Photons done by NIST XCOM: Photon Cross Sect. Database.

– I entered my own E and it calculated (among other things) pair production in the nuclear field and electron field (dn/dx in cm^2/g).

– Used 1.396 g/cm^3 for the density of LAr.• Electrons done by ESTAR: Stopping Powers and Range

Tables for Electrons– Only went up to 10 GeV → last e point omitted.– I could enter my own E values and it calculated collision, radiative and

total -dE/dx (in MeV cm^2/g).– Used 1.396 g/cm^3 for the density of LAr.

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Length in LAr (per photon) for Pair Production as a function of Energy

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.01 0.1 1 10 100

E; (GeV)

x(E

); (

m)

This is the distance a photon will likely travel in liquid argon before it produces an electron-positron pair; note that logarithmic x-axis.

Photons

~0.18 m

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Electrons

These values are calculated from a density-dependent -dE/dx by integrating (by trapezoidal approximation).

Electrons

Total distance traveled by an incident Electron as a function of Energy

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.00E-02 1.00E-01 1.00E+00 1.00E+01

E; (GeV)

x (m

)

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THE (sort of) BOTTOM LINE

Energy Range (GeV)

Integral Flux (m^2 s sr)^-1 Range of lower Energy (m)

Electrons Photons Electrons Photons

7 - 60 0.0417 0.0625 0.81 0.18

2.5 - 60 0.21 0.32 0.66 0.19

1.2 - 60 0.62 0.93 0.56 0.19

0.3 - 60 1.6 2.4 0.46 0.20

0.6 - 60 3.2 4.9 0.37 0.21

0.17 - 60 5.4 8.1 0.30 0.23

0.09 - 60 12 23 0.22 0.26

0.02 - 60 35 53 0.10 0.44