# Integrated asymmetry calculation

where

   total number of neutrons detected, k = [Up,Side], m = [D2O, H2O]
weighted (NaI, Ref) coefficient, k = [Up,Side], m = [D2O, H2O]

• For detector A summation is over [1000:1600] bin numbers
• For detector C summation is over [900:1600] bin numbers

# Error calculation

what is $\sqrt{up}$ ?
Does $\sqrt{up}$ = number of counts in in the detector
up spectrum as suggested above?  Why not use $N_{up}$ as variable.
If distribution is Binomial (detector yes/no) then width of distribution is
$1.265\sqrt{N}$ = 2 times e error.
Relative error = $\frac{error}{Ave} = \frac{0.6325 \sqrt{N}}{N/2}$

If you are measuring total number of neutrons detected then you will have binomial if you
break up the time spectrum into bins and don't integrate then probability distribution
is combination of detection probability and time measurement probability.


If we take:

then

where

# Cases was analysed

Det A (was analized all possible combination):

D2O Up,   files# [40,56,102,108,205,210,230];
H2O Up,   files# ;
D2O Side, files# [48,74,78,82,86,90,94,146,190,225,235];
H2O Side, files# ;


Det C (was analized all possible combination):

D2O Up,   files# [49,75,79,83,87,91,95,147,191,226,236];
H2O Up,   files# ;
D2O Side, files# [41,57,103,107,206,211,231];
H2O Side, files# ;


# Results

Table 1: Det A, weighted with
Table 2: Det C, weighted with
Table 3: Det A, weighted with
Table 4: Det C, weighted with


# Example of bin by bin asymmetry

Change the X-axis to nanosecond or neutron energy (TF). A:Have done.