physics-subatomic-particles

CHAPTER FIVE : REACTIONS .From the types of ageing that we are accustomed to, we might assume that, if therewere two unstable particles, then the one which had lived longer would be more likel yto decay than the other . However, this is not case, and, if the two particle smentioned were of the same typ e, then each would have an equal probability of decayin gfirst . All that it is possible to say is that, if we have a large number of a giventype of particle, then the average decay time will be the lifetime or mean life.,T ,Of that type of particle . We find that the probability, Ps, that a particle of mea nlife T decays in the next short interval of time s is given byPs . s/T ,so long as s«-r . Thus we may deduce that the number of particles remaining after atime t, N(t) is given byN(t) a ne tr1 rwhere n is the initial number of particles, T is their lifetime, and e is h'uler' sconstant . This exponential decay function has been amply tested by both practical an dtheoretical work . We must note that the lifetime of a given particle is measured whe nthe particle is at rest, and that when a group of particles travels at a relativisti cvelocity, as in a high-energy accelerator, the Fitzgerald-Lorentz time dilation equatio nt . - t- (V/c2 l xbecomes important .Let us now consider how we may represent pictorially the reactions between particles .The best method is to use Feynman diagrams, which were first suggested in 1949 byR .Feynman . These diagrams are graphs, where time is plotted along the x-axis, and on edimension of space is plotted along the y-axis . We will discuss the significance o fFeynman diagrams at a later stage . We will consider two basic types of reaction here .Let us have four particles, P, Q, Y, and Z, taking part in our reactions . In th efirst type of reaction, P and enter a 'black box' and Y and Z emerge from it, an dthere was no virtual emission of quanta involved . This type of reaction is known a sa single-vertex reaction . A reaction in which one virtual quantum is involved, such a sp+rr"yn ,is known as a two-vertex reaction, because the particles interact at two distinc tpoints in space : first, where the-I - is emitted, and second where it is absorbed . I tis often found that there are more virtual exchanges occurring in the 'black box 'than were initially thought . It is useful to use the rule that a particle enterin gthe black box is equivalent to its antiparticle leaving it . An example of a black boxreaction in experimental particle physics might b ep+v'--w prn - ,where an important particle in the reaction is uncharged and therefore difficult t odetect . rxamples of Feynman diagrams may be found in most text-books on particl ephysics .From our study of quantum numbers, we know that there are various conservatio nlaws which are never broken in particular types of interaction . A interesting consequenceof the conservation laws is the theory of decays known as the theory of'communicating channels' or states . A decay is considered to be complete when th eparticles produced in it have travelled out of the field of influence of the initialpaticle . The theory of communicating states, which we will meet again in chapter 6,