Subatomic Physics

558 Collective Model
Table 18.2: Deformed Nuclei Around A ≈ 23.
Ground-State Assignment
Shell Nilsson
Nuclide Z N Q δ ≈ ɛ Exp. Model Model
19 F 9 10 (1/2) + (5/2) + (1/2) +
21 Ne 10 11 9 fm 2 0.09 (3/2) + (5/2) + (3/2) +
21 Na 11 10 (3/2) + (5/2) + (3/2) +
23 Na 11 12 14 fm 2 0.11 (3/2) + (5/2) + (3/2) +
23 Mg 12 11 (3/2) + (5/2) + (3/2) +
So far we have studied the motion of a single particle in a stationary deformed
potential without regard to the motion of this well. The well is fixed in the nucleus.
If the nucleus rotates, the potential rotates with it. In the previous section we have
shown that the rotation of a deformed nucleus gives rise to a rotational band. Now
the question arises: Is it correct to treat rotation and intrinsic motion separately,
as was done in Eq. (18.21)? The separation is permissible if the motion of the
particle in the deformed well is fast compared to the rotation of the well so that
the particle traverses many orbits in one period of collective motion. In real nuclei,
the condition is reasonably well satisfied because the rotational motion involves A
nucleons and consequently is slower than the motion of the single valence nucleon.
Nevertheless, for a realistic treatment, the effect of the rotational motion on the
intrinsic level structure, given by the term Hp in Eq. (18.21), must be taken into
account. (18,19)
After asserting that intrinsic and rotational motion are indeed independent to a
good approximation, we can return to the interpretation of the spectra of deformed
nuclei. Since the nucleus can rotate in any state of the deformed nucleus, each
intrinsic level (Nilsson level) is the band head of a rotational band. In other words,
a rotational band is built onto each intrinsic level. Figure 18.7 gives an example of
three bands, built on three different Nilsson states.
18.5 Vibrational States in Spherical Nuclei
So far we have discussed two types of nuclear states, rotational and intrinsic. The
occurrence of different types of excitations is not peculiar to nuclei; diatomic
molecules were known long ago to display three different types of excitations,
18 O. Nathan and S.G. Nilsson, in Alpha-, Beta- and Gamma-Ray Spectroscopy, Vol. 1 (K.
Siegbahn, ed.), North-Holland, Amsterdam, 1965, p. 646.
19 A.K. Kerman, Kgl. Danske Videnskab. Selskab, Mat.-fys. Medd. 30, No. 15 (1956).