Subatomic Physics

124 The Subatomic Zoo
Table 5.11: Nuclear Energy Level Characteristics for the Three
Regions Shown in Fig. 5.34. E is the excitation energy, Γ the average
level width, and D the average level spacing.
Typical Values
Region Characteristics E (MeV) Γ(eV) D (eV)
I. Bound states Γ ≪ D ≈ E 1 10 −3 10 5
II. Resonance region Γ < D ≪ E 8 1 10 2
III. Statistical region D ≪ Γ ≪ E 20 10 4 1
Nevertheless, the states are no longer bound but are now classed as resonances. In
the idealized cross-section curve in Fig. 5.34, the individual resonances are shown in
region II. As the energy is further increased, the resonances become more numerous
and their widths increase. They begin to overlap, and the individual structure averages
out. In region III, called the statistical region, the envelope of the overlapping
individual resonances is measured, and it displays a prominent feature, called the
giant resonance: At around 20 MeV excitation energy, the total cross section goes
through a pronounced maximum. At much higher energies, the continuum loses all
features.
The three regions shown in Fig. 5.34 are characterized by three numbers, the
average level width, Γ; the average distance between levels, D; and the excitation
energy, E. Typical values of these three quantities for the three regions are given
in Table 5.11. Details vary widely from nuclide to nuclide, but the gross features
remain. Exploration of the excited states of baryons with A = 1 is more difficult for
three reasons: (1) No bound states exist and resonances are harder to study than
bound states. (2) Most of the resonances decay by hadronic processes, their widths
are large, and it is difficult to separate individual levels. (3) The only stable baryon
that can be used as a target is the proton; liquid hydrogen targets are standard
equipment in all high-energy laboratories. No isolated neutron targets exist. All
other baryons (Table 5.6) have such a short lifetime that experiments of the type
shown in Fig. 5.32 are not possible, and indirect methods must be used.
The first excited proton state was discovered by Fermi and collaborators in 1951.
They measured the scattering of pions from protons and found that the cross section
increased rapidly with energy up to about 200 MeV pion kinetic energy and then
leveled off or decreased again. (46) Brueckner suggested that this behavior could
be interpreted as being due to a nucleon isobar (excited nucleon state) with spin
3/2. (47) It took some more time and many more experiments before it became clear
that the Fermi resonance is only the first of many excited states of the nucleon.
The investigation of excited proton states proceeds similarly to the study of
46 H. L. Anderson, E. Fermi, E. A. Long, and D. E. Nagle, Phys. Rev. 85, 936 (1952).
47 K. A. Brueckner, Phys. Rev. 86, 106 (1952).