Page 8 - Tlahuizcalli CB-30_Neat
P. 8

I. Introduction                                          These decay processes are described by transition
                                                                  probabilities per unit time    characteristic of each
          Muons  are  some  of  the  most  useful  types  of      type of muon. In a sample of    muons, the mean
          particles in modern experimental physics. Evidence      number of particles decaying in a time      will be
          of that can be found in the recent growth of fields     given by
          like  muon  radiography,  or  muon  imaging,  where
          detectors  are  placed  inside  or  nearby  big                          = −        ,     (3)
          constructions  like  pyramids,  to  capture  muons
          passing through them in order to create an image
          of their structure (O’Keefe, 2021).                     where we have assumed that    is large enough so
                                                                  that it can be considered continuous. Integrating
           Since the number of applications of muon physics       this expression leads to the usual exponential law
          depends in great part of the development of new         for  the  remaining  amount    (  )  of  a  sample  of
          techniques for their detection, measuring some of       particles at a time t (Oda, 2005),
          its properties like the mean lifetime and speed, can
          have  a  great  pedagogical  value  for  graduate                    (  ) =       −     ,  (4)
                                                                                      0
          students.
                                                                  Where       corresponds  to  the  initial  number  of
                                                                           0
           Many  previous  projects  (Liu,  2007)  (Barnet  et  al,   particles  at     = 0.  It  is  more  common  to  use  the
          2012)  have  determined  both,  the  mean  lifetime     inverse of   
          and the speed of muons originated by cosmic rays.
          The  main  goal  of  this  work  is  to  confirm  previous                  1
          experimental results. This should be reproducible in                      = ,          (5)
                                                                                    
          any   laboratory   with   scintillators   with   the                          
          characteristics  specified  in  this  report,  by  anyone
          with a basic graduate level knowledge of Physics.       which is known as the mean lifetime, i.e., the time it
                                                                                                     ⁄
          We also intend to determine how the results can be      takes for the sample to decay to 1    of its  initial
          affected by the conditions of the experiment like       concentration.  In  terms  of  the  mean  lifetime,  the
          the place where the detectors are located.              power law can be expressed as

          I. Theoretical Foundation                                           (  ) =        −  /      .  (6)
                                                                                     0
          A. The muon                                             On the other hand, the half-life    ⁄  is defined as
                                                                                                   1 2
                                                                  the time it takes for the sample to decay to one-
          Cosmic  rays  are  a  form  of  high-energy  radiation   half  of  its  initial  concentration;  that  is,     =    ⁄
          that originate from outside the solar system. When                    1                               1 2
          they reach Earth, the rays collide with particles in    when   (  ) =    ; from equation (4) we can write
                                                                                   0
                                                                                2
          the  upper  atmosphere  to  produce  a  "shower"  of
          particles, including muons.                                          1
                                                                                 =    −     1 2 ,  (7)
                                                                                        ⁄
                                                                               2
           Muons  are  the  most  numerous  cosmic  charged
          particles at sea level. Most of them are produced       calculating  the  logarithm  of  both  sides,  and
          high in the atmosphere (typically 15km). Muons are      dividing by −  , we obtain
          very similar to electrons, with an electric charge of
          −   and spin 1 2, but with a much higher mass and                      1
                       ⁄
          they are unstable. The decay of muons and their                   ⁄ =     2 =        2.       (8)
                                                                           1 2
                                                                                            
                                                                                   
          antiparticles, is mediated by the weak interaction,
          and can be summarized as follows:                       B. Muon detection
                    −
                          −
                      →    +    +             (1)                 All detectors are based on the transference of part
                                  
                                                                  or  all  of  the  kinetic  energy  to  the  detector  mass,
                          +
                    +
                      →    +    +    .        (2)                 where  it  is  converted  into  some  other  form  of
                                 
                                       
                                                                  radiation to be analyzed. All modern detectors are
              7
                            Tlahuizcalli ISSN: 2448-7260                    Año 10 Núm. 30 septiembre-diciembre 2024
   3   4   5   6   7   8   9   10   11   12   13