Subatomic Physics

122 The Subatomic Zoo
5.13 Excited States of Baryons
The problem of finding all excited states of the baryons is probably hopeless. It is
crucial, however, to find enough states to be able to discover regularities, get clues
to the construction of theories, and test the theories. Even this more restricted
requirement is very difficult to fulfill in subatomic physics. A great deal of ingenuity
and effort has been expended on nuclear and particle spectroscopy, the study of
nuclear and particle states. In the present section we shall give some examples of
how excited states and resonances are found.
As a first example, we consider the nuclide 58 Fe, with a natural abundance of
0.31%. Two ways in which the energy levels of 58 Fe have been investigated are
sketched in Fig. 5.32. An accelerator, for instance, a Van de Graaff, produces a
proton beam of well-defined energy. The beam is momentum-analyzed and transported
to a scattering chamber where it hits a thin target. The target consists of an
iron foil that has been enriched in 58 Fe. The transmission through the foil can be
studied as a function of the energy of the incident proton, or the scattered protons
can be momentum-analyzed. Consider the second case, denoted by (p, p ′ ). The
notation (p, p ′ ) indicates that incoming and scattered particles are protons but that
the scattered particle has a different energy in the c.m. The momentum and hence
the energy of the scattered proton p ′ are determined in a magnetic spectrometer,
i.e., a combination of bending magnet, slits, and detectors. If the kinetic energy of
, the nucleus received an
the incident proton is Ep and that of the scattered one is E ′ p
energy Ep − E ′ p, and a level at this energy was excited. The experiment constitutes
a nuclear Franck–Hertz effect. (A correction has to be applied because the 58Fe ∗
nucleus recoils, and the recoil energy must be subtracted from Ep − E ′ p in order to
find the correct excitation energy.) A typical result of such an experiment is shown
in Fig. 5.33. The appearance of many excited levels is unmistakable. The reaction
(p, p ′ ) is only one of many that are used to excite and study nuclear levels. Other
possibilities are (e, e ′ ), (γ,γ ′ ), (γ,n), (p, n), (p, γ), (p, 2p), (d, p), (d, n), and so
forth. Decays are also sources of information, and Fig. 4.7 gives an example of a
partial gamma-ray spectrum. Data from a large variety of experiments are used to
piece together a level diagram of a particular nuclide. For 58Fe, the level diagram
is shown in Fig. 5.37.
As the excitation energy is increased, the situation becomes more complex. In
a simplified picture it can be discussed by referring to Fig. 5.30 with the essential
aspects shown in Fig. 5.34. At an excitation energy of about 8 MeV, the top of
the well is reached, and it becomes possible to eject a nucleon from the nucleus, for
instance, by a reaction (γ,n), (γ,p), (e, ep), or (e, en). Just above the well, such
processes are still not very likely, and most excited states will return to the nuclear
ground state by the emission of one or more photons, because particle emission is
inhibited by reflections from the nuclear surface (Fig. 5.30), angular momentum effects,
and the small number of states available per unit energy (small phase space).