two-quasineutron configuration has the lowest calculated

1 78

energy for Hf with N = 106, so that strong mixing with the two-

level being about one-third two-quasiproton and two-thirds two-quasi­

neutron [He 68], In 17 6Hf the two-quasineutron energy is higher and

the mixing is much less (there is about 2% of the two-quasineutron

configuration in the band head [Kh 72]). Thus the 8 state in Hf,

for which the two-quasineutron energy is even higher, is expected to be effectively pure two-quasiproton.

A positive identification of the configuration of the 1857 keV

level in Hf is not possible because there are spin 4, 5 and 7 two-

quasiproton configurations all at low energy and, as discussed in section 3.2, the experimental information is insufficient to distinguish between these alternatives.

The low-lying two-quasineutron configurations for ?2Hf eit^ier

have low spin and are not expected to be populated in the (160,4n) reaction, or involve the 7/2+ [633] state from the i^^/2 orkital. This high-j particle is expected to be strongly influenced by the Coriolis

force and will be discussed in the next section, in connection with the rotation-aligned bands.

The systematic observation of isomeric quasiparticle levels in the even-even hafnium isotopes is itself a point of interest. These levels are populated following heavy-ion,xn reactions because they have high K, while being sufficiently low in energy. The trends in population intensity following a,xn reactions are described in [Re 73]. In the heavier hafnium isotopes, there is the unusual combination of low-lying high-ß orbitals for both protons and neutrons, and in particular there are both proton and neutron 6+ and 8 two-quasi­

particle configurations at low energy. The mixing of proton and

neutron configurations results in these high-K levels having unusually low energy, and these levels are favourably populated following heavy- ion,xn reactions. As discussed, in the neutron-deficient hafnium

172

isotope Hf, the neutron-proton configuration mixing is no longer a

dominant factor: the observed isomeric levels are at higher energy

and are only weakly populated. Isomeric levels may well be weakly

populated (following heavy-ion,xn reactions) in the majority of even- even rare-earth nuclei, but coincidence experiments of high

Figure 5.5: The moment-of-inertia parameter, calculated from the Al =1 energy level differences, as a function of spin for the

172 174

deformation-coupled two-quasiparticle bands in Hf and W.

Finally, the more-or-less regular behaviour of the presently observed deformation-coupled rotational bands is illustrated in figure 5.5, where the moment-of-inertia parameter A = fi2/2j is calculated from the Al = 1 energy level differences (cf. figure 4.5) and shown as a

2

function of I . A gradual increase in moment of inertia (decrease in

A) with spin is evident, except in the band based on the spin (5) 1857

keV level; in this band the moment of inertia is already high and has

significant oscillations, indicating Coriolis coupling effects. The

generally smooth behaviour of these bands is to be contrasted with the

irregularities of the rotation-aligned bands. Further, the moment of

inertia of the 6 + and 8 bands is similar to that .of the gsb at low spin, and this is also in contrast to the rotation-aligned bands,

which have high moments of inertia. These features of the aligned

5.5 TWO-QUASIPARTICLE ROTATION-ALIGNED BANDS

5.5.1 Systematics of the Negative-Parity Yrast States

Although the proposed negative-parity decoupled bands, observed in each of the even-even nuclei studied, have only had their parity measured in 174W, and the even-spin assignments are not conclusively

established, these assignments will be tacitly assumed. In the

following comparison it will become clear that the interpretation is supported by the smoothly varying features through the range of

tungsten isotopes. The comparison with W is particularly useful

because levels in this neighbouring nucleus have been populated using

several techniques: e.g. radioactive decay [Go 70]; the (p,4n)

reaction [Ca 76] with low angular momentum transfer; and the (a,3n)

reaction [Do 76] extending the knowledge to higher spin.

First of all, the excitation energies of the negative-parity yrast states are compared for the even-even tungsten isotopes 172_>180w

in figure 5.6. A similar, though more limited, comparison could be

made for the hafnium isotopes. (Where known, 2 octupole states for

these nuclei have been included in figure 5.4.) All the tungsten

isotopes represented in figure 5.6 are well deformed, with similar moments of inertia in their gsb's, so that a meaningful comparison may

be made. Apart from the similarities in excitation energy, the most

obvious feature in the negative-parity yrast states (figure 5.6) is the smooth transition from the octupole bands of the heavier isotopes

to the decoupled bands of the neutron-deficient isotopes. The

octupole character of the bands in the heavier isotopes has been established, for example, from the decay of the 2 band heads, which is by El transitions with significant M2 and E3 admixtures [Ko 71,

He 72], as well as from the strong excitation of the 3 states by both

inelastic scattering [Gu 71] and Coulomb excitation [Me 77]; the

latter finds B(E3,0~> 3) strengths of about six times the approximate single-particle value.

The increasing Coriolis coupling strength with decreasing neutron number in the tungsten isotopes with N >104 has recently been

negative parity yrast states

NEUTRON NUMBER (l

80

Figure 5.6: The energy levels of the negative-parity yrast states in

the tungsten isotopes with 98 < N <106.

172 174 176

from W, W and W follows this trend, and is vividly portrayed

in a plot of the moment-of-inertia parameter, A

(E ! " E i - i)/21