6/26/06David Gerstle1 Photon and Electron Cosmic Ray Flux Study David Gerstle LArTPC – Yale University Undergraduate

6/26/06David Gerstle2 Contents Photon and Electron flux data. Photon and Electron length in argon data. Conclusions

6/26/06David Gerstle3 Electron and Photon Flux Data Photons: Beuermann and Wibberenz, “Secondary spectra of electrons and photons in the atmosphere,” Can. J. Phys., 46, S1034, –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 –Electrons: from 0.03 GeV to 1 GeV dN/dE goes as ~E -1.7 ; from 1 GeV to 25 GeV as ~E 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.

6/26/06David Gerstle4 e - Depth Correction and Photon Factor Correction is proposed only for electrons. Exponential attenuation correction: I(E,d)=I 0 (E)*exp[-(d- d 0 )/Λ] where Λ is the attenuation length and d 0 is the original depth. There are two components of the electron flux though, π 0 and  decay. Thus the total adjusted flux is a weighted average of the two: –I(E,d)=I 0 (E)*(0.55*exp[-(d-d 0 )/Λ pi ]+0.45*exp[-(d-d 0 )/Λ mu ) –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.

6/26/06David Gerstle5 Electrons E -2.6 E -1.7 Yellow is original depth differential flux

6/26/06David Gerstle6 Blue are original Differential Flux Photons E -2.7 E -2.0

6/26/06David Gerstle7 Photons are Blue Electrons are Pink Emax ∫ (dN/dE)*dE E

6/26/06David Gerstle8 Interaction Length Data from NIST 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 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 g/cm^3 for the density of LAr.

6/26/06David Gerstle9 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

6/26/06David Gerstle10 Electrons These values are calculated from a density-dependent -dE/dx by integrating (by trapezoidal approximation). Electrons

6/26/06David Gerstle11 THE (sort of) BOTTOM LINE Energy Range (GeV) Integral Flux (m^2 s sr)^-1Range of lower Energy (m) ElectronsPhotonsElectronsPhotons