physics-subatomic-particles

f+K +84Ptakes place, so that S=1 for the K , and hence I . -) This implies that the K+ is onemember of an isotopic doublet, whose other member is neutrally charged . We are forcedto conclude that this other member is the K° . But that, then, is the status of the K °?The only reasonable conclusion is that this has Se -1, and that it is the antiparticl eof the K } . But it too mist form a doublet, the other member of which must be the antiparticleof the K ' , the 7° particle . Thus we see that, unlike, for example, than. .. ,the K° is not its own antiparticle . As we shall see in chapter 7, this fact ha sprofound results on particle symmetries .Let us now consider the quantum number of parity . We first define an operator, P ,such that?1 .4f(x,y,z) _ y(-x,-y,-z) ,which corresponds to a rotation through 180 about the x-axis, followed by a reflectionin the plane x= O . From our studies of angular momentum, we know that all wave function sare invariant under the transformation of rotation, and so the only real significanc eof the operator P is in its space reflection component . It is a fact of wave mechanic sthat for all physically meaningful waves 'f , l(r ~' must be invariant under the Por fl operation . Hut, taking a snuare root, we find thatP'1(f(x,y,z) _ +1 14r ( x ,y, z ) or -l`}r(x,y,z) •In the first case we say that the wave function Nr has even parity, and in the second ,that it has odd parity . Hence, by knowing the wave function of a given particle, w emay assign to that particle an intrinsic parity, P, which can take the values of eithe rt 1 or -1 . There can be no absolute measure of parity, and so we measure all paritie srelative to that of the proton, which we cal lIn particle physics, however, we are often concerned with systems containing mor ethan one particle, and thus we need to know what the parity of a system of two particles ,A and B, which are rotating around each other with a an angular momentum of L ;'(, is .We know that the wave function of the complete system i slir ( A )• ( B )•1f ( L ) ,and that thereforeP(A+B) e P(A) .P(B) .P(L) .We find that P(L) is given by the formul aP(1, ) ' (- I ) L ,by studying the spherical harmonics . Let us now attempt to deduce theoretically th eintrinsic parities of the charged pions . We know that the reaction-,f - d-wn n ,where d is the deuteron, takes place . It has been shown that nearly all-n - particlesare captured and cascade into the lowest energy level orbit in about . 1C" °s . Thus ,since the angular momentum in this orbit is zero, the parity of the d-r system wil lbe the same as the parity of the ir - particle on its own . Now let us consider the totalparity of the n-n system . The bxclusion Principle (see chapter 3) forbids L= 0 fo rthis system, and therefore the lowest possible value is L= 1 . Since the neutron ha seven parity, we see that the n-n system must therfore have odd parity, so that th eparity of the charged pions is odd, because parity is conserved in a strong interactio nof this type .The assumption that parity is conserved in strong interactions brings about som einteresting comments . It implies that the laws of nature are the same on both side sof a mirror . In a comparatively macrocosmic sense, this is not true, since comple xorganic molecules are more often right- than left-handed . However, if we have a beamof, for example, polarised - ° particles, then we find that the direction in r ;hich