Short-Lived Resonance States

Forces and Fields Since 1932, the number of fundamental particles has increased enormously, and the description of these new particles and their interactions was soon found to be inadequate in terms of the two fields. Since the diameter of a nucleus is measured in femtometres ( m) while an atomic diameter is about 0·1 nanometer ( m) the repulsive force between two nuclear protons will be times larger than the electrostatic force between a nuclear proton and an orbital electron in an atom.

But nuclear protons do not repel each other and so we conclude that there must be an even stronger attractive force within the nucleus, between protons, which overcomes the strong Coulomb repulsive force. This force, which is associated with the production of mesons, is the third field of force and is involved in the so-called strong interactions.

It occurs between nucleons and is a short-range force acting at distances appreciably less than a nuclear diameter. Theory shows that the strong interaction is about 137 times as great as the electromagnetic interaction within the nucleus. It is the interaction considered by Yukawa in his original theory of meson production. The fourth and last type of force, known as the weak interaction, is also a nuclear force which governs the radioactive meson decay processes. It is involved in lepton changes and is only about times the strength of the electromagnetic field.

Thus there are four basic force fields in physics, each of which has a 'source', such as charge for the electromagnetic field or mass for the gravitational field, and a field particle associated with the energy changes of the system. These are shown in Table 27.1, which includes a rough guide to the relative interaction strengths. Just as the photon is the quantum of the electromagnetic field the meson is the quantum of the nuclear field. The 'graviton' and the 'intermediate boson'.

Associated with each of these fields is a characteristic time. The range of the strong interactions m or 1 fm corresponds to about s, which is the minimum time for a signal to travel across a nucleus of diameter 3 fm. This is the basic nuclear time for comparison purposes, so that an event taking place in a shorter time interval than this has no meaning. The strength of the electromagnetic field is of the strong field so that the associated time will be correspondingly greater, viz x = s. Most electromagnetic interactions have lifetimes of the order of s, which corresponds roughly to the time taken for a photon to pass across an atom, i.e., 1/3x s.

Table 27.1 also shows that the strength of the weak interaction as times that of the strong interaction, so that the corresponding weak interaction time will be x s= Most weak decay processes have a mean lifetime _ s, which is very long compared with the time associated with strong interactions. The word 'stable' is used to describe all particles except the strong interaction particles, i.e. all particles immune to strong decay.

Physical phenomena are ultimately measured in terms of energy changes arising from four basic types of physical force. All atomic and nuclear interactions can be described in terms of electromagnetic, strong and weak interactions or forces. Strong interactions involve particles of high energy whereas lepton decay processes are the result of weak interactions. The electromagnetic interaction is proportional to the charges involved. The name 'hadron' is used for particles that interact with each other through the strong interaction.

What is an Elementary Particle? Fifty years ago it was easy to build a system of atoms and nuclei using only Protons and electrons and even with the advent of the neutron there was little difficulty in setting up models in terms of three elementary particles as units. With the discovery of the first antiparticle, the positron, and the emergence of the neutrinos and mesons; it became clear that use of the word elementary as referring to the permanent units of an atom was obsolete.

The words 'elementary' and 'fundamental’, became meaningless. Of these particles only the electrons, proton and neutrinos are infinitely stable. The others have comparatively short lifetimes, so that it is impossible to recognize them all as fundamental or elementary. However, as these particles have discrete masses it is not impossible to regard them as higher quantum states of a basic state or states.

We shall return to this point in our discussion of resonance particles and quarks. Thus the lifetime of S may be regarded as long compared with the strong interaction characteristic time, and in this chapter all particles with this lifetime are regarded as stable.

Short-Lived or Resonance Particles The neutral pion   - the lightest of all the strongly interacting particles with a mean lifetime of about s characteristic of electromagnetic decay is the one of the shortest-lived of pions. During the last few years there has been a profusion of new particles which have increased the number already known to more than 100. These are the new resonance particles which are extremely unstable with lifetimes of about s showing that they are strongly interacting particles. They are called resonance particles because they are recognized by the resonance peaks in a normal energy spectrum of an event.

Thus if protons were collected at various energies in a   + P + collision, the energy distribution curve Could be as shown in Fig. 27.1, which is purely schematic. Peak I is the main peak of the proton beam and peaks II, III and IV are inelastic (high-absorption) scattering peaks coinciding with resonance states between the two particles. This curve shows that the system, can exist in a set of intermediate short-lived excited states.

These new enhanced probability, Or resonant states, can be assigned mass, charge and spin consistent with the conservation laws. Their independence is momentary, as decay times are only times the previous shortest lived particle, namely the   -meson. Although too short to measure, this time is sufficient for the excess energy to reassemble in the form of mesons and other particles. Resonances can therefore only be inferred by their decay products and this is how such particles have been found.

The first resonant particle to be discovered was the N* particle, in 1951, by Fermi, but it remained unnamed. In 1960 the reaction was being studied by Alvarez and his group at the Lawrence Radiation Laboratory and many hundreds of plates were analyzed by a computer. Some of the results suggested that the conservation of linear momentum law was being violated and two resulting particles were indicated rather than three. Possibilities were

where y* is a suggested new resonance particle (or an excited baryon state) showing strong nuclear decay in S into The analysis of a large number K - + p + events gave a most probable y* mass of 1385 MeV and a decay time of s, showing the y* particle to be a strong interaction particle. This is now designated as an excited L state. (See Table 27.2C.) The Fermi particle of 1951 was eventually named the N* particle.

The scattering cross-section in pion-proton collisions gave a resonance peak at about 200 MeV corresponding to a rest mass of the 'particle' of 1236 MeV. Again the estimated lifetime was about s, showing strong nuclear decay. Originally called a N* resonance, indicating a nucleon excited state, it is now designated as  baryon resonance.

Other resonances have since been discovered, and although the recognition of such states is difficult their masses and spin characteristics have been measured. They all show strong nuclear decay yielding baryons (often nucleons) and mesons which are easily observed. Including these resonances there are now nearly a hundred 'particles' which are listed as in Tables 27.2 A, Band C. These show the long-lived 'stable' particles together with the mass spectrum of leptons, mesons and baryons without their antiparticles. The resonant particles can be looked Upon as the excited states of some of the stable particles with correspondingly greater masses and higher (real) spins J.

Mesons are then regarded as mass energy emission when transitions take place between the resonant particles, and to the (relatively) stable ground states corresponding to the old particles. The production of mesons therefore follows the transitions permitted by the appropriate conservation laws. A simple example is the production of excited Pions of spin one from the transitions shown in Fig This is only part of many quantum exchange possibilities between resonance and long-lived states.

Conservation Laws: Baryon and Lepton Conservation We are already familiar with many conservation laws in atomic and nuclear systems, such as the conservation of 1. charge, 2. mass/energy, 3. linear momentum 4. and angular momentum. In atomic physics we know that the application of these laws leads to selection rules for allowed spectra and in nuclear physics to the prediction of new particles, e.g. neutrinos. In the field of sub nuclear physics we are now presented with a whole new list of particles which are observed in collision Experiments and in different modes of decay. Some modes of decay are never observed, and it is natural to suppose that these are prevented by some unknown law of conservation. Thus new laws of conservation have been deduced from a study of all possible types of particle reaction and decay, as well as mathematically.

One of the great mysteries of nuclear physics is the stability of the proton. We know that the free neutron is unstable to    decay by, “ so why not since spins would still be conserved? Some laws must prevent this. This is the law of conservation of baryon number in which all baryons are assigned a baryon number B= 1, all anti baryons have B= -1, and all mesons and leptons have B = O. Thus for we have so that this reaction 'goes'; but for we have. This decay does not occur as the baryon number is not conserved. 4

similarly it can be shown that lepton numbers must also be conserved if we assign a lepton number l = 1 or -1 as follows to the leptons, remembering that l = 0 for mesons and baryons, and treating muons and electrons differently, The equation then has

Proton decay is really forbidden because it is the lightest baryon in the mass spectrum. See Table 27.2C. The muon decays we discussed in the last chapter, viz

are seen also to conserve the lepton numbers and therefore 'go'. Since muon and electron decays are all weak interactions, i.e. strong interactions do not produce leptons, it follows that lepton conservation does not apply to decay by strong interactions.