Subatomic Physics

564 Collective Model
nd d-bosons can be shown to correspond to a collective state expressed in terms
of the variables of the collective deformation. By minimizing the energy of the
state with respect to these variables, one obtains the equilibrium deformation of
a given nucleus and finds both spherical and deformed nuclei in the proper limits.
In addition, the low-lying levels are found to correspond to those of the collective
model. An example of some calculated low-lying rotational and vibrational spectra
are compared to experiment in Fig. 18.14.
18.7 Highly Excited States; Giant Resonances
The last several decades have seen considerable growth in the study of highly excited
states of nuclei, with particular attention focused on resonances and states of high
angular momentum. (35) These states can be excited with reactions initiated by
photons, electrons, pions, nucleons, and more massive projectiles.
To understand the nature of these states, residual forces between nucleons are
considered. Although nucleons can be represented reasonably well as moving in an
average (single particle) potential due to all other nucleons, there are important
residual forces. We have already mentioned the short-range pairing force that is
attractive and particularly strong for like nucleons in a relative s-state. The residual
forces tend to parallel the free nucleon–nucleon force, but there are also residual
effects due to long-range collective effects.
Resonances in the continuum can be studied with the help of high-resolution
detectors. Breathing mode oscillations of angular momentum L =0,dipoleresonances
(L = 1), quadrupole resonances (L = 2), octupole (L =3),andhigher
L resonances, as well as resonances built on excited states have all been observed.
Most of these resonances can occur with neutrons and protons oscillating together
(isospin I = 0) or against each other (I = 1). The first resonance found, the
electric dipole one, is an isovector mode with an energy of excitation given approximately
by E1 ∗ =77A −1/3 MeV, the energy at which the strength of the 1 −
excitation built on the ground state is concentrated. The resonance is observed in
photoreactions such as (γ,n), or its inverse, neutron capture. It is called a “giant
resonance,” because the strength is many times that of a single particle excitation.
The next resonance to be discovered was the giant quadrupole resonance of I =0
with E ∗ 2 =64A−1/3 MeV and a decay width that decreases with the mass number
A. (36) It may appear odd that the giant quadrupole resonance lies at an excitation
energy below that of the giant dipole, since the latter can be caused by moving
a nucleon to the next higher unfilled shell, whereas the quadrupole requires the
excitation through two major shells. Clearly, these are not simply single-nucleon
excitations; strong residual forces and cooperative phenomena are involved. We can
see the importance of residual forces and show the A −1/3 dependence by treating
35 G. F. Bertsch and R. A. Broglia, Phys. Today 39, 44 (August 1986).
36 M.B. Lewis and F.E. Bertrand, Nucl. Phys. A196, 337 (1972).