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III. Results


          A. Muon’s mean lifetime
          A1. PMT operating voltage of 2.00kV


          The  raw  data  (spectrum)  obtained  from  the  USX
          MCA software is shown in fig. (11). The scale of the
          bins  in  the  horizontal  axis  was  converted  to  time
          units with the help of the calibration: every channel
          (bin)  represents  1/363.8      (see  fig.  (7)).  The
          standard deviation of this data group is    = 9.385
          counts.

                                                                  Figure 12. First curve fit.

                                                                   Additionally, when taking precise measurements
                                                                  over  small  intervals,  the  results  may  end  up
                                                                  depending  on  the  election  of  those  ranges.  In
                                                                  these cases, is better to group several of those small
                                                                  intervals, and work with less, but more populated
                                                                  ones.

                                                                   With this in mind, a redefinition of the bin size was
                                                                  made, grouping the counts of every 12 channels.
                                                                  The resulting histogram is shown in fig. (13). Each bin
                                                                  in the new spectrum spans over 12/363.8    , and
                                                                  the standard deviation of then new set of counts is
                                                                  σ = 92.7499 counts.
          Figure  11.  Original  spectrum  obtained  from  the  USX
          software.

          A curve fit was carried out for the distribution based
          on eq. (6), where in this case,   (  )represents the
          amount of muons that decayed in a time   , while
              and     are the parameters to be adjusted. The
                    
           0
          curve  fit  process  was  made  with  the  curve_fit
          function  from  the  optimize  package  in  the  SciPy
          library of the Python programming language; this
          function  uses  non-linear  least  squares  to  fit  a
          function to data.

          The  adjusted  curved  along  with  the  obtained
          parameters is shown in fig.12. The obtained value
          for  the  muon's  mean  lifetime  is     = (10.281 ±
                                             
          3.328)    .  When  this  value  was  obtained,  the     Figure 13. Spectrum with redefined bin.
          possibility that the distribution might be mounted on    To  identify  the  background,  a  new  model  was
          top of a background was considered.
                                                                  considered for the curve fit,

                                                                          (  ) =       −  /       +    .  (13)
                                                                                  0
                                                                                              0


              15
                            Tlahuizcalli ISSN: 2448-7260                    Año 10 Núm. 30 septiembre-diciembre 2024
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