Subatomic Physics

568 Collective Model
nucleons outside a closed shell exert on those inside the shell. For a single nucleon
outside a closed shell the polarizing effect is too small to deform the core. When
two nucleons are present outside the closed shell, two competing effects occur: The
pairing force tends to keep the nucleus spherical, whereas the polarizing force tries
to deform the nucleus. When only a few nucleons are present outside a closed shell,
the pairing force wins out, but the polarizing effects become dominant as more and
more nucleons are added. This feature is shown schematically in Fig. 18.16.
Figure 18.16: Potential energy surfaces
as a function of deformation (see Section
18.1). The three curves are (a) for
a closed shell nucleus, (b) for a nucleus
near a closed shell and (c) for a nucleus
far from a closed shell. A permanent
deformation occurs in the last case.
The deformed shell or Nilsson model, Section
18.4, combines essential aspects of the
two extremes. The Nilsson model shows that
especially stable structures should occur for
very anisotropic orbitals or large deformations.
Nilsson energy levels, Fig. 18.17, show energy
gaps when the ratio of major to minor axes
are integers, such as 2:1, 3:1, and somewhat
smaller gaps when the ratio is 3:2. These
“superdeformed” shapes have been found at
high angular momenta in heavy ion reactions
through gamma-ray deexcitation studies in
152 Dy and 149 Gd; they correspond to yrast levels
of 50–60�. (48) Although the shell model and
its extensions have given us considerable insights,
what really is needed is a microscopic
theory in which the features of the unified
model are explained by the known properties
of nuclear forces.
The nucleon density and the effective single particle potential that acts on a baryon
can be investigated with hypernuclei. (49) In order to understand that we should first
note that the time scale for nucleons to move accross the nucleus is ∼ 10 −22 sec,
which one gets by assuming nucleons are moving at ∼ 10% of the speed of light
and covering distances of ∼ 10 −14 m. In hypernuclei nuclei, one or sometimes two
neutrons are replaced by hyperons, mostly lambdas. The lambda is unaffected by
the Pauli exclusion principle and can only decay weakly when bound in the nucleus
so that it lives a long time (∼ 10 −10 sec) compared to the sampling time mentioned
above. The potential that acts on the Λ 0 in a nucleus is related to that which acts
48 R.V.F. Janssens and T.L. Khoo, Annu. Rev. Nucl. Part. Sci. 41, 321 (1991); P.J. Nolan
and P.J. Twin, Annu. Rev. Nucl. Part. Sci. 38, 533 (1988).
49 O. Hashimoto and H. Tamura, Prog. Part. Nucl. Phys. 57, 564 (2006); A. Gal, Adv. Nucl.
Phys., (J.W. Negele and E. Vogt, eds.) 8, 1 (1975); R.E. Chrien, Annu. Rev. Nucl. Part. Sci.
39, 113 (1989).
50 B. Holzenkamp, K. Holinde, and J. Speth, Nucl. Phys. A500, 485 (1989).