Integrated asymmetry

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Integrated asymmetry calculation

[math]Asymm = \frac{\sum \left[\left(\frac{up(ii)}{Wup}-\frac{upbg(ii)}{Wupbg}\right) - \left(\frac{sd(ii)}{Wsd}-\frac{sdbg(ii)}{Wsdbg}\right)\right]} {\sum \left[\left(\frac{up(ii)}{Wup}-\frac{upbg(ii)}{Wupbg}\right) + \left(\frac{sd(ii)}{Wsd}-\frac{sdbg(ii)}{Wsdbg}\right)\right]}[/math]

where

up(ii)   - D2O, detector Up,   Wup - weighted coefficient for up(ii)

upbg(ii) - H2O, detector Up,   Wup - weighted coefficient for upbg(ii)

sd(ii)   - D2O, detector Side, Wup - weighted coefficient for sd(ii)

sdbg(ii) - N2O, detector Side, Wup - weighted coefficient for sdbg(ii)

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

Error calculation

[math]Error = \sqrt{\left(\frac{\partial A}{\partial\ up}\right)^2(\delta\ up)^2 + \left(\frac{\partial A}{\partial\ Wup}\right)^2(\delta\ Wup)^2+...}[/math]
If assume:

• [math]\delta\ up = \sqrt{up},\ \delta\ Wup = \sqrt{Wup},[/math]
• [math]\delta\ upbg = \sqrt{upbg},\ \delta\ Wupbg = \sqrt{Wupbg},[/math]
• [math]\delta\ sd = \sqrt{sd},\ \delta\ Wsd = \sqrt{Wsd},[/math]
• [math]\delta\ sdbg = \sqrt{sdbg},\ \delta\ Wsdbg = \sqrt{Wsdbg},[/math]
  

Then [math]Error = \sqrt{...}[/math]

Cases was analysed

Det A:

D2O Up,   files# [40,56,102,108,134,205,210,230];

H2O Up,   files# [44];

D2O Side, files# [48,74,78,82,86,90,94,146,180,190,225,235];

H2O Side, files# [52];

Det C:

D2O Up,   files# [49,75,79,83,87,91,95,147,181,191,226,236];

H2O Up,   files# [53];

D2O Side, files# [41,57,103,107,135,206,211,231];

H2O Side, files# [45];

The results are (File:Asymm table .pdf):

Table 1: Det A, weighted with NaI detector

Table 2: Det C, weighted with NaI detector

Table 3: Det A, weighted with Ref detector

Table 4: Det C, weighted with Ref detector

Change the X-axis to nanosecond or neutron energy (TF)

Only one "s" in Asymmetry

Example of bin by bin asymmetry

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