Changes between Version 49 and Version 50 of DatabaseBasedAnalysis/Spectrum

Timestamp:

12/03/19 19:07:57 (5 years ago)

Author:

tbretz

Comment:

--

DatabaseBasedAnalysis/Spectrum

@@ -44 +44 @@
 As the simulated energy spectrum is independent of zenith angle, it can be expressed as
 
-\[dN_0(E,\theta) = N_0\cdot d\eta(E)\cdot d\eta(\theta)\]
+\[dN_0'(E,\theta) = N_0\cdot d\eta(E)\cdot d\eta(\theta)\]
 
 with the differential energy spectrum \(\eta(E)\) and the zenith angle distribution \(\eta(\theta)\), for the total production range \(E_\textrm{min}\)  to \(E_\textrm{max}\) and \(\theta_\textrm{min}\) to \(\theta_\textrm{max}\)
@@ -50 +50 @@
 
 
-\[N_0 = \int_{E_\textrm{min}}^{E_\textrm{max}}\int_{\theta_\textrm{min}}^{\theta_\textrm{max}} dN_0(E,\theta) = N_0\int_{E_\textrm{min}}^{E_\textrm{max}}\int_{\theta_\textrm{min}}^{\theta_\textrm{max}}\eta(E) dE \cdot \eta(\theta) d\theta= N_0\int_{E_\textrm{min}}^{E_\textrm{max}}\eta(E) dE\cdot \int_{\theta_\textrm{min}}^{\theta_\textrm{max}}\eta(\theta) d\theta\]
+\[N_0' = \int_{E_\textrm{min}}^{E_\textrm{max}}\int_{\theta_\textrm{min}}^{\theta_\textrm{max}} dN_0(E,\theta) = N_0\int_{E_\textrm{min}}^{E_\textrm{max}}\int_{\theta_\textrm{min}}^{\theta_\textrm{max}}\eta(E) dE \cdot \eta(\theta) d\theta= N_0\int_{E_\textrm{min}}^{E_\textrm{max}}\eta(E) dE\cdot \int_{\theta_\textrm{min}}^{\theta_\textrm{max}}\eta(\theta) d\theta\]
 
 consequently
@@ -58 +58 @@
 or
 
-\[N_0 = N_0\cdot \sum_{E_\textrm{min}}^{E_\textrm{max}}\omega_i(E) \cdot \sum_{\theta_\textrm{min}}^{\theta_\textrm{max}}\omega_i(\theta)\]
+\[N_0' = N_0\cdot \sum_{E_\textrm{min}}^{E_\textrm{max}}\omega_i(E) \cdot \sum_{\theta_\textrm{min}}^{\theta_\textrm{max}}\omega_i(\theta)\]
+
+with 
+
+\[\sum_{E_\textrm{min}}^{E_\textrm{max}}\omega_i(E) =\sum_{\theta_\textrm{min}}^{\theta_\textrm{max}}\omega_i(\theta) = 1\]