physics-subatomic-particles

Thus we may say tha tErr : P/n ,where P is the probability that the A particles from the beam react with the Bparticles in the target . We may think of cross-section using the following model :a circular disc, corresponding to its field of influence, of area d--units is assignedto each'B particle in the target . The discs are orientated perpendicularly to th eapproaching beam, and if an A particle hitsa disc, it undergoes change, whereas if i tdoes not, it proceeds unaffected . We have n B particles, each of area 6rmTPer uni tarea of our thin target . Thus the total area, T, covered by the B particles is n 6T.T .Thus an area T of the target is 'opaque', while the rest of the area, (1-T) is trans -parent to the approaching ,articles . Thus the probability of interaction, P, in thi sthin target, between the A and B particles is seen to be fl -a,-Let us now try and generalise our result ford-gar for thicker targets . Let P(n) b ethe probability that an A particle is removed from the beam by a thin layer of Bparticles of projected surface density n . G(n) is the probability of transmissionthrough this layer . ObviouslyG(n) c 1 - P(n) .Let us place two layers, one of projected surface density n„ and the other of projectedsurface density n , , on top of each other, so that their total surface density i s(n,- en,.) . Thus, the probability that a particle passes through both layers is given byG(n,+ n 2) G(ni) .G(n2) .This equation must be true for any positive real numbers n, and n, . . Thus the generalsolution i sG(n) exp(-Kn) ,where K is any real constant . Thus we hav eP(n) 1 - exp(-Kn) .As n tends to zero, P(n)/n tends to K, so that we may conclude that K 6,, . Thus w ehave the relationP(n) = 1 - exp(-n6ts. )for our probability of interaction . The cross-section of a collision process i susually computed using this formula . A common measurement of cross-section in subatomi cprocesses is the barn (b) or millibarn (mb) . 1 barn lO ~m2 , and 1 mb = 10 zl m 2 .Total cross-section, 6ror or 6, as defined as the cross-section of all the processe swhich scatter or otherwise remove particles from the primary beam . Elastic cross-section ,6E,, is the cross-section for elastic scattering, for exampl ep-f p —4 P~P •cross-section, or reaction cross-section is given byInelastic`6 ,Ne L - 6r - d E LWe can also define a differential cross-section, dd/dlt, by the equatio nhI/I = ((d6/dA)ASL)Pux ,where x is the target thickness, and LEI/I is the fraction of the total beam flu xscattered into a solid angle &a, and N is the number of particles in the target pe runit area . It is often useful to define this differential cross-section so that it i srelativistically invariant, but we will not do this here .Until now, we have concerned ourselves purely with those particles which decay vi athe weak or electromagnetic interaction in a comparatively long amount of time .Particles with weak decay modes are termed semi-stable, and those with electromagn eticones, meta-stable . But we might ask ourselves if there are also particles whic hdecay by the strong interaction, in a correspondingly short amount of time . The