keV for the present nuclei, thus e^ ftH )) « A.

Since the VMI is formally equivalent to the Harris parameterisation, the values

eqp(w=:0) can be determined from excitation energy o f the s-bandhead Eq(s) above the g - bandhead ^ ( g ) , in the three-band model, if the aligned angular momentum o f the s-band

is fixed. In the previous analysis, the value o f i was taken from either the CSM calculations

or the experimental Routhians and the value o f the pairing gap parameter Aflt is given by

2 6^ (01=0) should equal

(9.4)

The values

be = eqp(w =0)-A (9.5)

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The analysis of Garrett et al [GA80a] was largely confined to nuclei in the range 88<=N<=101 and showed that the values of ACSM (a) displayed an odd-even staggering which they attributed to blocking in the odd nuclei; (b) were generally higher (by « 10%) than the values of the pairing gap parameter deduced from the odd-even mass differences A ^ ; and (c) that the deduced pairing smoothly decreased with increasing N after N«92 and minimized near N=98.

Although Acsm is model dependent, and also depends on the other parameters employed in the CSM calculations, such as 7 (sections 6.1,6.2), the values of A ^ displayed a similar behaviour as a function of N, to those of ACSM, by gradually decreasing as N=98 is approached [GA80a].

9.4.2 A as a function o f neutron number

In Figure 9.13 the values of Afll obtained by fitting the even osmium isotopes, are plotted as a function of neutron number and compared with A ^. For 170- 174Os, the fitted values are in good agreement with the values ACSM required by the CSM to match the bandcrossing frequencies (see eg Table 6.1), supporting the fitting procedure. In the odd nuclei, due to blocking, the pairing is reduced.

The behaviour of Aflt and A ^, as a function of N, shows a clear minimum at N = 98, agreeing with the findings of [GA80a] and the conjecture that the increased moment of inertia in N=98 nuclei is due to a weaker pair field.

This contrasts with the behaviour of A ^ which for values of N>100 and N<98, are lower than those required to fit the s-band. A similar effect was found by Garrett et al [GA80a], using the CSM in a study of lighter isotopes. This implies that the A ^ obtained from systematics, while useful, are not an accurate guide to the value required to reproduce bandcrossings.

9.4.3

A

The value of Afil deduced for the 5/2+[402] band of 171 Re, is 899 keV, even lower than in 174Os, while that of the 9/2"[514] band, from a two-band fit, is higher (1298 keV), very near the value found for the isotone 172Os (1320 keV). The values of the pairing

174

deduced for both of these bands axe consistent with those required by the CSM to match crossing frequencies and alignments. Thus it is concluded that a reduced pairing in the 5/2 +[402] band is responsible for the AB neutron alignment and crossing frequency differences with the 9/2“[514] band, particularly, since these bands are expected to have similar deformation.

This effect is not confined to 171 Re. In 177Re, the AB crossing in the 5/2 +[402] band again precedes that in the 9/2~[514] band, although the total gain in aligned angular momentum has not been determined. Presumably the origin of this reduced pairing could lie in a proton-neutron interaction.

9.5 Complex neutron alignment interpretations

In Figure 9.13, the behaviour of the bandhead energies for N > 98 follows that of the deduced neutron pairing. The lower the value of the pairing, the greater the effect on the yrast sequence. This is also demonstrated in Table 9.2, where the ratio of d-bandhead energies to Aflt is listed.

The constancy o f this ratio for N > 98 suggests that the behaviour of the yrast band below the backbend in these nuclei is related to the neutron pairing. The bandhead energy of the (7zh9/2)o configuration depends on the p-n interaction, which presumably could influence neutron pairing, however, the mechanism is unclear. Perhaps the band fitted in the nuclei 174_182Os is unrelated to .any proton intruder configuration. Since the d-band tracks the behaviour of the S* to 12+ states, as this is the spin interval of the g-d crossing in these nuclei, the bandhead energy may simply reflect the influence of some other perturbation, in this spin region, on the g-band.

Either of the complex neutron alignment mechanisms are qualitatively consistent with this behaviour, as the bandhead energy of any band composed of aligned neutrons, must depend on the neutron pairing.

Table 9.2

Ratio, of pairing gap parameter to intruder bandhead energies. Neutron Number 94 0.97 96 0.46 98 0.17 100 0.21 102 0.23 104 0.28

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In Table 9.3, the results of Wyss et T ab le9.3

Deformation as a function o f frequency.

al’s [WY90] calculations of deformation as ^ ^ _ _ = = = = = = = = ,

a function of frequency, for l78.180*182Os Nucleus io 7

are listed. They indicate that in 178Os, the _{1780 s}

gsb 0.13 0.24 -1

AB neutron alignment will decrease e and

s-band

0.21 0.27 -1

0.25 0.21 -11

may therefore give rise to the complex _180Os 0.33 0.20 -11

gsb 0.13 0.23 -1

alignment mechanism discussed in section 0.21 0.24 -2

s-band 0.25 0.21 -12

7.2, of a prolate to triaxial shape change

1820 s

0.33 0.20 -12

during the AB alignment. This is gsb 0.130.21 0.220.22 -2-5

s-band 0.25 0.21 -12

consistent with the upbend observed in 0.33 0.21 -14

l78Os. A strong interaction with the prolate AB configuration gives rise to the upbend, while a weak interaction gives rise to the backbend associated with the less deformed triaxial configuration. As more neutrons are added, the Fermi surface rises, moving away from low -0 components of the i 13/2 shell, so that by N=106, a neutron alignment is no longer able to drive the nucleus to lower values of &2- Thus only the strongly interacting ground-prolate AB crossing is visible in 182Os. A two band fit to this backbend requires an interaction strength of about 270 keV.

The alternative BCAD crossing mechanism cannot be distinguished from the proposal of Wyss et al, by the alignment curves alone. These two mechanisms might be distinguished experimentally by measuring B(E2) values in the region of the upbends, as the BCAD configuration must favour smaller values of and positive values of y.

However, below N=98, the ratio of d-bandhead energy to A, in Os isotopes, changes quickly, perhaps implying that the upbend in 172Os, at N=96, is no longer related to the neutron pairing. A low value for A was found for the 5/2+[402] band of 171 Re, but the yrast band of 1720s, which also has an anomalous upbend, has a large value of A.

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