Download Short-Lived Resonance States

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 (10-15
m) while an atomic diameter is about 0·1
nanometer (10-10 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 10-10
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 10 -15m or 1 fm corresponds to about
10 -23 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 10 - 3 of the strong field so
that the associated time will be correspondingly
greater, viz. 103x 10-23 = 10-20 s. Most
electromagnetic interactions have lifetimes of the
order of 10-15 10 -20s, which corresponds roughly to
the time taken for a photon to pass across an atom,
i.e., 1/3x 10 - 18 s.
• Table 27.1 also shows that the strength of the
weak interaction as 10 -13 times that of the
strong interaction, so that the corresponding
weak interaction time will be 10 13x 10-23
s=10-10. Most weak decay processes have a
mean lifetime 10 -8 _ 10 -13s, 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 10 -10 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 p 0 - the lightest of all the strongly
interacting particles with a mean lifetime of about 10 16 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
10 -23 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 + + 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 10 - 7 times the previous shortest
lived particle, namely the p o -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 10-23 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 10 -23 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 10 -23 s, showing strong
nuclear decay. Originally called a N*
resonance, indicating a nucleon excited state,
it is now designated as D 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. 27.3.
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 b - 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.