The nuclear structure of 178Hf studied by the 181Ta(p, α)178Hf reaction

NUCLEAR PHYSICS A

Nuclear Physics A569 (1994) 523-546 North-Holland

The nuclear structure of 178Hfstudied by the “‘Ta(p, a) 178Hfreaction D.G. Burke Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, L8S 4Ml Canada

0. Straume

‘, G. LBvhgiden,

T.F. Thorsteinsen,

A. Graue

Institute of Physics, University of Bergen, Allkgaten 55, N-5007, Bergen, Norway

Received (Revised

1 July 1993 14 September

1993)

Abstract The microscopic structures of levels in 178Hf have been studied by the ‘s’Ta(p, (u) reaction using 17 MeV protons. The reaction products were analyzed with a magnetic spectrograph and detected with photographic emulsions, yielding an overall resolution of Q 20 keV (FWHM). Levels with significant populations must involve a proton in the ~‘[404] Nilsson orbital, which of various two-quasiproton forms the ground state of the *‘ITa target nucleus. The admixtures configurations were extracted from the observed cross sections. The ground-state band is populated unusually weakly, while a large $‘[404];‘[404] strength is observed for the K” = O+ band at 1199 keV. This is attributed to the irregular filling of Nilsson proton states in this region, whereby the ;‘[404] orbital appears as the ground state for tantalum as well as lutetium nuclei. For the well-known K” = 8- bands at 1147 and 1479 keV the present results confirm in a direct manner the 4 -[514], + 3 +[404], admixtures proposed earlier on the basis of gamma-ray mixing ratios and log ft values. An upper limit of - 5% for the 4 -[514], - s +[404], configuration in the K” = l- band at 1310 keV is consistent with earlier proposals that this is predominantly a 4’[624], - i-[514], two-quasineutron band. A new K” = l- band has been assigned at 1513 keV, which has the main q-[514], - ;‘[404], strength. Levels previously assigned as a K’ = 2- band at 1566 keV are shown to be rotational excitations based on this new K”=lband. The K”=3+ band at 1758 keV is found to be predominantly the ;‘[404], - 1/2+[411], configuration, while the strength for the K” = 4+ parallel coupling of the same two protons is spread over more than one band.

Key words: NUCLEAR REACTIONS 18tTa(p, o), E = 17 MeV; measured a&,0). deduced levels, J,z-, Nilsson configurations. Natural Ta target,magnetic spectrograph.

r Present

Address:

STATOIL,

Sandslihaugen

03759474/94/$07.00 0 1994 - Elsevier SSDI 0375-9474(93)E0502-Y

30, 5020 Bergen,

Science

Norway.

B.V. All rights reserved

“sHt

524

D. G. Burke et al. / 178Hf

1. Introduction

In spite of the fact that 178Hf has been the subject of many studies, and that several interesting phenomena were discovered for the first time in this nuclide, there are still many open questions concerning its nuclear structure. Among the features discovered in early works were the AK = 0 mixings in low-lying high-K bands [l], such as the K = 8 bands at 1147 and 1479 keV. These were interpreted as having admixtures of the K” = 8-, i-[.514] + :‘[624] two-quasineutron state and the K” = 8-, :‘[404] + i-[-514] two-quasiproton state, and for the lower band the magnitude of the two-quasiproton component was inferred to be N 36% from observed limits on the E2/Ml mixing ratios of intraband gamma transitions [2]. Log ft values for the feeding of these levels confirmed this interpretation [3]. Massmann et al. [4] described such mixing in terms of the residual neutron-proton interaction. Later, Soloviev and Sushkov [5] were able to explain these and other such mixed states in terms of high multipolarity phonons. This description extends the picture of well-known quadrupole 0 = 2) and octupole (A = 3) phonons, and shows that many mixed bands in deformed rare-earth nuclei can be explained as phonons with A values of 5, 6,7, and 9. The K” = 8- bands in 178Hf involve A = 9, and the degree of mixing is reproduced quite well by the calculation [5]. There are, however, other two-quasiparticle states expected at relatively low excitations, which have not been located experimentally, and some of these might also be subject to AK = 0 mixing. In fact, it has recently been pointed out [6] that “*Hf is a very special case in that the expected set of low-lying two-quasineutron Gallagher-Moszkowski pairs has K” values which match very closely those of the low-lying two-quasiproton configurations. This can be seen in Fig. 1, where the upper matrix for two-quasineutron states shows the same K” values for the Gallagher-Moszkowski pairs as the lower matrix for two-quasiproton states. Even the ordering of the expected bands is very similar. Unfortunately, only a few of these bands have been identified thus far. The many studies of 178Hf levels following beta decays of “‘Lu and i’*Ta, and from reaction studies such as (n,r), (a,Xn), etc., have been summarized in the Nuclear Data Sheets [7]. A fairly detailed discussion of the microscopic structures of levels was given by Fogelberg and Backlin [8]. Hague et al. [9] performed “‘Hf(n 7y) experiments and measured gamma rays with curved-crystal spectrometers, as well as conversion electrons and average resonance capture (ARC) spectra. This work established a large number of multipolarities and precise transition energies, resulting in a level scheme with a much more detailed set of spin-parity values than was available earlier. However, many of the expected bands indicated in Fig. 1 were still not located. For example, although two K” = 1- bands are predicted at low energies, only one had been reported up to N 2 MeV excitation energy. In the present work the structure of 178Hf has been studied by the 181Ta(p, a)178Hf reaction. It has been

D.G. Burke et al. / 178Hf

525

;;+

-l---l-i---k I1 +- [5211

[510]

4”

4"

1514

5-

f

I6331

608

560

3”

$-

4-

4-

[6511

A

g

El21

746

3’

806

f

o-

3-

4-

i

5”

I+

8”

5+

4”

6-

3-

1662

5-

1637

15 141 ++ I4021 I

$-

Tc-Ti

150

$+ 14041

8-

0

1479 tnx

g

[5141

57 0

458

i-

6”

1+

3”

$-

[5231

>800

+- [54 11 $+ t4021 795

4"

7-

o-

3-

4-

i

5”

4-

1+

8”

5”

4”

6-

3-

1756

15141554 rmx

1

++,+4111

7-

5-

150

Fig. 1. Expected low-lying Gallagher-Moszkowski pairs of bands in r’*Hf. The matrix of expected two-quasineutron pairs in the top half of the figure is seen to have counterparts with the same K” values, and even the same ordering, in the lower half which shows two-quasiproton pairs. The axes of each matrix are labelled with the Nilsson orbitals, and the energies (in keV) at which these states are observed in the A = 177 isotone (isotope). For each two-quasiparticle entry in the matrices the K” value for the “singlet” band expected at the lowest energy is given on the left and that for the higher energy “triplet” band is on the right. The known band-head energies are given, and cases of mixed or vibrational character are indicated.

found [lo] that the cross sections for this reaction correlate well with those from (t,cu) studies to the same final states, and thus the (p, (~1 reaction can give useful information on proton hole states in cases for which the target nuclides needed for Cd, 3He) or (t, (Y>studies are unstable. This approach has been used previously in this laboratory for studies [ll-131 of 17*Yb, ls9Ho, and 15’Tb. Since the tslTa target ground state has a proton in the 3’[404] orbital, the ‘81Ta(p,a)‘78Hf reaction should populate selectively the two-quasiproton states that have one proton in this orbital. Hence, it should be possible to make rather direct measurements of the 5’[404] + z-[514] two-quasiproton admixtures in the two K” = 8bands. The experimental procedures and results are presented in sect. 2, and the new configuration assignments deduced from these data are discussed in sect. 3.

526

D.G. Burke et al. / ‘78Hf

2. Experimental

details and results

The measurements were performed using beams of 17 MeV protons from the McMaster University tandem Van de Graaff accelerator. The target was prepared EXCITATION

0

10000,

1

,

,

,

,

1000 ,

ENERGY

(KEV)

,

,

,

,

2000 ,

181

ci a

L?

1000

5

6

7

a

9

10

EXCITATION ,

,

,

7/2+[404]

I

,

178

Hf

8=10”

PLATE

10000

,

Ta(pd

Ground state band

4

,

1500 j

11

12

13

DISTANCE

(CM)

ENERGY

(KEV)

I

I

I

7/2+[404]+5/2+[4021

7/2+[404]-

14

I

15

I

16

2000

I

I 1/2+[4

17

1 1I

1000

100

10

i 9

10

11

PLATE

12 DISTANCE

13

14

(CM)

Fig. 2. (a) Spectrum of alpha particles from the 181Ta(p, (Y)‘78Hf reaction at 0 = 10”. The configuration assignments indicated are discussed in detail in the text. (b) An expanded view of the complex portion of the spectrum of (a) between 1 and 2 MeV of excitation energy.

by vacuum eva~ratio~ of natural tantalum metal (w&b is almost 100% “‘Ta) to a thickness of * 90 yg/cm2 on a 20 p.g/cm’ carbon foil. The aIpba-pa~ticIe reaction products were analyzed with the Enge split-pole mag~ctic spectrograph and detected with Iiford K-minus-l photographic emulsions. Spectra were recorded at 8 = 6” and at 5” intervals from 8 = 10” to 30”. The spectrum obtained at B = 10” to 1

1

1

0.2

a.1 0

$0

20

to

46

0.6

0

10

20

do

40

0

10

20

a0

40

0

10

20

a0

40

0

?O

20

OQ

40

1276 krV

i 0.2

0

10

to

20

*o

40

0.6

10

REACTION

0.1

lo

ANGLE,

(degrees)

Pig. 3. Angular d~st~~but~~usfor strongly ~~~~ated teveis in the ““Tat& (ul’78Hf reaction, The curves shown with the data points are calculated arrgufar dis~~buti~ns for the assigned co~igura~~ns, obtained from DWBA predictians and the program EVE as described in sect. 3.1. For cases af daubiets the dashed curves show the predicted cross sections for each of the assigned components, and a solid curve indicates the sum of the dashed curves. As usual, the calculated curves have been shifted verticaiiy to provide the best fit to the data points, and the resulting absolute values give an indication of the spectroscopic strengths as discussed in the text.

D. G. Burke et al. / i78Hf

IT*? en6 1768

4,11697

6,6+

10

keV

keV

8,f..

keV

4,s’

1868 ul6 1866

keV keV

9,8-

10

0

20

20

40

10

0

20

a0

40

b

10 2004

k.V

2023

I

keV

2224

keV

2285

keV

(6,l’1

f6.S+1

+-f-J& 1

f-yyj

I_,

f.

.

1

0.4

2610

0.6

keV

2064

keV

10

‘Or

TLy

4,4+

i

lo

f f

* 10

f

1

1

0

3 3

20

20

40

10

REACTION

10

1 20

SO

ANGLE.

40

0

10

20

20

40

(degrees)

Fig. 3 - continued.

is shown in Fig. 2. The overall resolution was G 20 keV full width at half m~imum for all the measurements. The intensities of peaks in the spectra were converted to absolute cross sections by recording short exposures of elastically scattered protons at 8 = 30” on several occasions just after one of the main (p, cy) exposures. For this purpose the cross section for elastic scattering at 8 = 30” was assumed to be 4870 mb/sr (- 90% of the Rutherford cross section), as predicted by an optical model calculation with parameters as described below. The integrated beam current passing through the target was also known for each exposure, and used in this procedure. Angular distributions of (p, a> cross sections for the strongly populated

D.G. Burke et al. / 178Hf

529

levels in 17*Hf are shown in Fig. 3. Measured excitation energies and the cross sections at 0 = 10” are presented in Table 1. In order to improve the accuracy of the excitation energies, all the photographic plates were scanned with a microscope equipped with a stage for which the position measurements were determined by a precision threaded rod. This yielded results in which the excitation energy values from spectra at different angles were much more consistent than previously experienced using microscopes equipped with spring-loaded dial gauges for the position measurements. The spectrograph calibration was performed using 8.78 MeV alpha particles from the 212Po decay in a radioactive source of 10.6 h 212Pb placed at the target location. A nuclear emulsion was exposed to these alpha particles for a series of magnetic field settings, and scanned with the same microscope and stage mentioned above. It was found that for each large well-resolved peak the excitation energy values in the spectra from different angles were usually within f 1 keV of the value obtained by averaging results from all angles. Furthermore, it was found that the averaged excitation energies for such cases agreed within - 1 keV with the more precise results from gamma-ray measurements, where these were known up to about 2 MeV excitation. This can be seen from a comparison of columns 1 and 2 in Table 1. The nuclear structure assignments indicated in Figs. 2 and 3 and Table 1 are discussed in the following section.

3. Interpretation

and discussion

3.1. General comments In the present work the Nilsson model is used as a basis for discussing the microscopic structure of 178Hf levels. The theoretical cross section for a singlenucleon transfer reaction leading to a rotational band member of spin If in an even-even deformed nucleus can be written [14,15]

Cai(Cj,),Pi(ZoK,jAK

I ZfK,) DW

(1)

where N is a normalization factor for the distorted-wave Born approximation (DWBA) cross sections, (da/dR>,,, and the first summation extends over all possible j, 1 values leading to the final state. The factor g2 has a value of 1 for the usual two-quasiparticle states, but has a value of 2 for K = 0 states formed by coupling two nucleons in time-reversed orbitals (e.g., as in ground-state bands). The Cjl values are expansion coefficients describing the Nilsson orbital of the transferred nucleon in terms of spherical states. The Clebsch-Gordan coefficient

530

D. G. Burke et al. / ‘78Hf

couples the odd target nucleon I,, K, with the transferred j, AK to form the final state If, K,.The quantity Piis a pairing factor, and for a pickup reaction in which the transferred nucleon is not the odd nucleon of the target, Pi2 = y2,the fullness probability in the target for the orbital from which the nucleon was picked up. If the reaction picks up the unpaired nucleon in the odd target and populates the ground-state band of the final nucleus, Pi2 = Q2,the emptiness factor in the final nucleus ground state for the orbital of the transferred nucleon. In Eq. (1) the final state is assumed to be a Coriolis-mixed configuration, with amplitudes a, for the various two-quasiparticle configurations. Although the (p, a> reaction is not a single-nucleon transfer process, it is found that for beam energies comparable to the value used here the reaction can be described as pickup of a triton, and the dominant transition amplitude has the two transferred neutrons coupled to L = 0 and J = 0. For example, the angular distributions of cross sections and analyzing powers, and relative spectroscopic strengths, for the 208Pb(ij, a)205T1 reaction have been explained rather well with this description [16]. Thus it would be expected that Eq. (1) should give a first approximation for the cross sections in the (p, (~1 reactions of the present case. Previous studies [lo,121 in this mass region indicated that it was difficult to obtain reliable absolute values for spectroscopic strengths with the (p, (Y) reaction, and the value of the normalization factor, N, needed to reproduce known spectroscopic strengths varied with j and 1. Even in the case of the doubly-magic 208Pb target, only the relative (p, a> strengths were considered [161. However, since many of the Nilsson proton orbitals in the deformed rare-earth region have their wavefunction dominated by a single j, 1 component, the relative cross sections for various couplings resulting when a proton is picked up from a particular orbital are approximated quite well by Eq. (1). Even these relative values can be very helpful in arriving at an interpretation of the nuclear structure. Since it is not possible in this work to extract spectroscopic strengths from the data for each j value which can contribute to the population of any final state, the approach used was to compare the experimental cross sections with predicted values. The latter were calculated with the computer program EVE, which was written for the case of Coriolis-mixed states in even-even residual nuclides [17l. The Nilsson wavefunctions used in this program were calculated for a deformation 6 = 0.3, and for potential well parameters K = 0.0637 and p = 0.600. The singleparticle cross sections were obtained from a DWBA calculation using the program [18] DWUCK4, with optical-model parameter sets Pl, Al, and B2 of ref. 1101.The value of the normalization factor used was N = 60, as determined for the analysis of 175Lu(p7 a)‘72Yb results [ll] with the same optical model parameters. This value was established from (p, a) pickup of a ;+[4111 proton, for which the dominant transfer has I= 2. From the results of refs. [lo-121 it would be expected that this value of N should yield absolute cross sections with an accuracy of 30-50% for relatively strong transitions involving +‘[4111 proton pickup. However, for pickup

D.G. Burke et al. /

17’Hf

531

of protons from other orbitals, the absolute values may be incorrect by a factor of 3 or more 111,121. The calculated curves shown with the experimental angular distributions in Fig. 3 are the results of the EVE calculation for the assigned configurations of the various levels. These curves do not exhibit very much diffraction structure, reflecting the nature of the DWBA predictions for these experimental conditions. Furthermore, even for transitions dominated by a single Z-value it is not easy to determine the I-value from the angular distributions. For example, DWBA curves for 1 = 4 and I= 5 are rather similar and there is little hope of distinguishing them from each other. However, in this mass region the shell model states available have I-values of 2, 4, and 5, so the only strong transitions observed are dominated by one of these values. The DWBA angular distribution for an 2 = 2 transition decreases more rapidly with angle than those for E= 4 and 5 transfers, which tend to be flatter. For some of the strong peaks (e.g., between 1758 keV and 2383 keV1 that can be attributed to pickup of a f +[411] proton, the angular distributions have the slope predicted for E= 2 transitions. In the following subsections, the properties of various bands populated in this study are discussed. 3.2. The ground-state band and the K” = 0 + band at I199 keV In order to populate the ground-state band of *‘sHf with the (p, CY)reaction, the unpaired proton in the “iTa target must be picked up. This proton is in the z +[404] Nilsson orbital [19] which originates from the g7,2 shell model state and has a dominant I = 4, j = 5 component in its wavefunction. Eq. (1) in subsect. 3.1 can be used to estimate the expected relative cross sections for the ground-state band, but more uncertainty arises in attempting to predict the absolute values. In addition to the uncertainty in the normalization factor, N, mentioned above, the value needed for the pairing factor in Eq. (1) may also be unusual because of the irregular filling of the proton orbitals in this region. For the odd lutetium (2 = 71) isotopes with 167 G A ==s179 the ;‘[404] orbital forms the ground state [19,20] so it might be expected that the fullness factor, Y2, for this orbital in the Z = 72 hafnium isotones would be somewhat greater than 50%. However, the i ‘[404] orbital is also found as the ground state of the Z = 73 tantalum isotopes with 175
D.G. Burke et al. / “‘Hf

532

Table 1 Levels populated in the ‘*lTa(p, a)“sHf Excitation energy (keV) previous a

present b

reaction

Cross section ’ (0 = IO”) (bb/sr)

[I, K”l d

Two-quasiproton configuration populated

0.46

0, Of

;+[4041-

+4041

93.18

93 (1)

0.94

2, o+

;+i4041-

$+[4041

306.62

305 (1)

0.61

4, o+

; + [4041 - ; + 14041

0

0

632.18

630 (2)

0.13

6, Of

; + [4041 - ;

1147.42

1148 (1)

2.36

8, 8-

; + [4041+ g ; [5 141

1199.40

1200 (2)

0.49

0, o+

; + 14041- ; + [404]

1276.70

1276 (1)

1.28

2, Of

; + 14041- ;

1364.09

1363 (1)

2.05

9, 8-

; + [4041+ f; [5141

1450.37

1447 (2)

0.54

4, Of

; + [4041- ;

1479.01 1496.45 1513.61 1513.83

1478 (1)

2.75

8, 8-

; + [4041+ ; - [514]

IO.7 e

2, o+ 2, o+ 4, 4+

1506 (2)

1513.89 I 1554.00 1561.54

(3.0 f 0.2) f 1559 (1)

1566.67 i 1601.47

1598 (2)

1639.76

1639 (1)

1697.50

1698 (1)

1747.10 1758.15 ) 1803.39 1808.27 1818.29 I 1862.21 1863.71 1869.84 1 1939.20 1942.01 >

1754 (1)

1812 (2)

i (1.3 f 0.2) f 0.3

[4041

14041 [404]

1, 1-

; + 14041 - 4 - [5 141

6, 6+

; + [404] + 2 + 14021

(2’) 2, 1-

; + 14041- ; - [5 141

10,8-

; + 14041+ f - [5141

3.34

3, 1-

; + [404]-

2.74

9, 8-

; + [4041+ ; - 15141

4 - [5141

(2.8 f 0.3) f

4, 1-

; + 14041- f J 15141

( (4.2 + 0.3) f

3,3+

; + [404] - f

0.34

[4111

i 3, 2, 3o+ ?+ 3, 3+

1868 (1)

5, 1-

; + [404] - 4; [514]

4, 3+

; + 14041 - + [4111

10,8-

; + [4041+ p - 15141

1941(l)

1.25

2004 ( 1)

1.4

(5,3+)

;+[404]-

2023 (1)

(6, 1-j

; + [404] - ; - [514]?

(4,4+)

; + [404] + + + [4111?

2116 2179 2204 2224 2255

(1) (1) (1) (1) (1)

1.6 2.1 1.4 1.1 2.8 1.2

2310 2354 2383 2463 2508 2537

(1) (1) (1) (1) (1) (2)

7.0 6.1 7.5 2.2 2.9 3.6

2, ?+ f+[4111?

D.G. Burke et al. /

i78Hf

533

Table 1 (~ntinued) Excitation energy (keV) previous a

Cross section c

present b

(e = loof fnb/sr)

2584 (3) 2604 (3) 2627 (1)

1.6 1.5 2.7

11, W

d

Two-quasiproton configuration populated

a Previous energy values are from Hague et al. [9], except for the level at 1513.89 keV assigned in the present work. b Uncertainties on the present values are shown in parentheses (in keV). These include the statistical uncertainties in the peak-fitting process and an estimated calibration uncertainty of 1 keV, added in quadrature. c Uncertainties on the absolute cross sections are believed to be within + 30%. For large well-resolved peaks the relative cross sections within each spectrum, or from one angle to another for a given peak, are within * 10%. d The I, lyq values in this column are from the Nuclear Data Sheets 171,except for the newly assigned XI” = l- band at 1513 keV, and for the 3,3+ band at 1862 keV discussed in ref. [251. For these cases the K-values differ from those adopted earlier in ref. [7]. e Obscured by an impurity peak at this angle. r These values were obtained by fitting the observed multiplet with two peaks, for which the positions were held at the energy values indicated, and finding the two intensities which resulted in the best fit to the experimental count rates.

excited bands in *‘*Hf, only the one at 1199 keV has a significant population. Since the only K” = f ’ proton orbital in this mass region is the g’f4041 one, this $7 = Of band most likely contains a large K” = O+, ~‘[4041- ~‘E4041 component, which would be responsible for the (p, ar) population. The observed relative cross sections within this band are similar to those of the ground-state band, consistent with this assumption. The cross sections expected for these K” = Of bands are given by Eq. (1) with the pairing factor, PF, being the emptiness factor, lJ2, of the 3 +[404] orbital in the 178Hf ground state, when calculating the ground-state band. For the excited band Pi2 = V2, the fullness factor for the $ +[404] orbita in the 178Hf ground state [21], assuming all such strength to excited configurations is in one band. Essentially, if a fraction U2 of the strength goes to the ground-state band the remaining fraction 1 - U2 = 1/* must go elsewhere that is, to excited states. It can be seen from Table 1 that the summed cross section for the excited I(” = O+ band is slightly larger than that for the corresponding members of the ground-state band. Due to Q-value dependence, the DWBA cross sections for the excited band are N 11% smaller than those for the ground band, and when this correction is included the excited band has _ 25% more strength than the ground band. Thus the fullness factor, V 2, discussed above is larger than U2 by at least _ 25%. If there were any undetected weak populations of similar components in other excited K” = O+ states the ratio of V2/U2 would be slightly

534

D.G. Burke et al. / ‘78Hf

larger. Since U2 + v2 = 1, these results suggest U2 - 0.44 and V2 - 0.56. These values are consistent with the value of vz = 0.55 used in a recent analysis of ‘78Hf(t,a)177Lu data [20]. Using U2 = 0.44 from above, Eq. (1) gives predicted cross sections at 8 = lo” for the O+, 2+, 4+, and 6+ members of the ground-state band to be 1.5, 3.4, 1.0 and 0.04 kb/sr, respectively. Comparison with the corresponding experimental values of 0.5, 0.9, 0.6, and 0.1 ub/sr from Table 1 shows that the relative intensities within the band are predicted approximately (especially when considering the very small values of these cross sections). The summed cross section is smaller than predicted by a factor of - 2.8. This is similar to the situation observed for the 175Lu(p, c~)‘~~Yb reaction performed with the same experimental conditions and analyzed with the same DWBA parameters [ll]. In that case the population of the ground-state band also involved pickup of the i +[404] proton, and the observed cross section summed over the ground-state band was smaller than the predicted value by a factor of - 2.2. This was attributed to the uncertainty in the value of N mentioned in subsect. 3.1 above, and the rather similar factor needed for the present 178Hf results therefore follows a consistent pattern. It is also noted that (P,(Y) results on even-even erbium nuclei [12] required a smaller value of N for the +‘[404] orbital than for the ++[411] one. The observation of a large g +[4041- g +[4041 component in the 1199 keV K” = O+ band is consistent with predictions of the quasiparticle-phonon model of Soloviev. In this model it is calculated that this K” = O+ state would have a 59% admixture of the G+[404] - g +[404] two-quasiproton configuration [22]. Although the normalization problems described above make it difficult to extract a reliable numerical value for the admixture from the present data, it is evident that the i +[4041- $ +I4041 two-quasiproton component is the dominant one in this band. The excited K” = O+ band discussed above is a rare case in the sense that such bands usually do not have such large strengths in single-nucleon transfer reactions. This is because the pairing factor in Eq. (1) is usually appreciably less than 0.5. However, in the present case this factor is larger because of the irregular filling of proton states in which the $‘[404] orbital appears as the ground state of tantalum as well as lutetium nuclides. 3.3. The K” = 8 - bands at 1147 keV and 1479 keV These well-known bands are both populated in the (p, (Y) experiment through their ;‘[404] + z-[514] components. The q-[514] orbital for the picked-up proton originates in the h11,2 shell and has a large wavefunction amplitude only for I = 5, j = y. The spin 8 and 9 band members are strongly populated, as expected, and the angular distributions shown in Fig. 3 have shapes which are consistent with the predicted curves, which are dominated by 1 = 5. There is also evidence for weak population of the Z = 10 member (at least for the lower band) and this is probably

D.G. Burke et al. / ‘78Hf

535

due to a redistribution of the strength due to multi-step processes in the reaction. The sum of cross sections at 8 = lo” for the I” = 8- and 9- members of the 1147 keV band is 4.4 pb/sr and that for the 1479 keV band is 5.5 pb/sr. Considering the small Q-value dependence of the DWBA cross sections, the strength to the upper band is 130% of that to the lower band. Assuming the full K” = 8-, $‘[404] + ;-[514] strength is in these two bands, these observed relative strengths imply admixtures of N 43% of the ;‘[404] + :-[514] two-quasiproton configuration for the 114’7keV band, and N 57% for the 1479 keV band. Since these values are obtained from measurements of relative intensities within each spectrum, it would be expected that the uncertainty on the relative admixtures should be no more than lo-20%. This direct method of obtaining the two-quasiproton admixtures is consistent with the value of (36 k 51% for the i +[4041+ g -[514] admixture in the 1147 keV band, which was obtained by Helmer and Reich [2] from limits on the E2/Ml mixing of the intraband gamma transitions, and the value of (34 f 4)% obtained from ratios of ft values by Ward and Chu [3]. Although the I = 9 member of the band is predicted from Eq. (1) to have a cross section N 40% larger than that for the I = 8 band head, the observed values are roughly comparable to each other. The predicted ratio does not change significantly when K” = 7-I;+[4041 + g-152311, K” = 6-{;+[404] + $-[532]], etc., states are included in the model and Coriolis mixing is taken into account. As expected, this mixing increases appreciably the absolute cross sections predicted for the K” = 8- bands, as strength is brought down from levels at higher energies. Since the energies of these higher-lying configurations are not known, and their effect is found to be mainly a renormalization of the strengths, detailed fits have not been performed in the present study. The summed cross section predicted by Eq. (1) for the pure K” = 8- {:‘[404] + :-[514]] configuration is 12.6 pb/sr at 8 = lo”, which is fortuitously similar to the experimental value of 10.2 pb/sr summed over both bands and Q-value corrected to the energy of the 1147 keV one. The value of N = 60 thus already overestimates the cross sections, and if the effects of Coriolis mixing for the final states were included the predicted values would be still larger. 3.4. The K” = l-

band at 1310 keV

The existence of this K” = 1- band has been well established [71 but its microscopic structure has not been determined experimentally. As seen in Fig. 1, there are two K” = l- bands expected at low energies, the :‘[6241- g-[514] two-quasineutron and the z-[514] - $‘[404] two-quasiproton configurations. The latter of these can be populated in the (p, c-u>reaction by pickup of a z -[5141 proton, as for the K” = 8- bands discussed in the previous subsection. Often it is found to be rather difficult to identify such low-K bands formed by coupling two high-K Nilsson orbitals, because the available strength is distributed

536

LAG. Burke et al. / ‘78Hf

over many different band members according to the Clebsch-Jordan coefficients of Eq. (1). The high-K band formed by parallel coupling of the two orbitals usually has much larger cross sections because the strength tends to be concentrated in one or two states. However, in the present case the K= 8 strength was split between two bands and each band had two strongly-populated members. Thus the strength was distributed among four levels. To a first approximation, the total cross section for the K” = l- band should be the same as for the K” = 8- bands, and in subsect. 3.3 this was found to be 10.2 kb/sr at 19= 10”. From Eq. (1) and considering the small Q-value dependence of (da/dfi>,, it would thus be expected that the cross sections for various spin members I” of a pure K = 1 g-E5141 - ;‘[404] band would be l- :O.O p.b/sr, 2- : 1.6 pbfsr, 3- :2.9 ub/sr, 4- : 2.8 /Lb/St+, 5- : 1.7 ub/sr, 6 : 0.7 F/bsr, and 7- : 0.2 pb/sr. Thus, if almost all of the K” = l- strength were concentrated in one band there would be large cross sections for only about four or five states, and the largest observed cross sections should be comparable to those observed in the K” = 8- bands. The excitation energies for rotational members of the 1310 keV band are well known [7], and from the present experiment there is no clear evidence for any observable population of this band. In order to set an upper limit on the :-[514] - :‘[404] admixture it is most useful to consider the I = 4 rotational member at 1539 keV, which is in a clean region of the spectrum and would have one of the largest predicted cross sections. There is no peak observed at this energy, and at 6 = 10” an upper limit of N 0.15 pb/sr can be established for any possible cross section. This is only N 5% of the expected value listed above, and implies that the KT = l- band at 1310 keV has an admixture of G 5% of the q-[514] - 3’[404] two-quasiproton configuration. This is consistent with the predictions of Soloviev and Shirikova [23], in which this band is expected to have a dominant (96%) admixture of the $‘[624] - i-[514] two-quasineutron configuration, and only a 1% admixture of the two-quasiproton component discussed above. The two-quasineutron component could be tested experimentally, as it should be observable in both the (d, p) and (d, t) reactions, but careful experiments would be required because the dominant I-transfer values in these reactions would be I= 6 and 1 = 5, respectively. 3.5. The new KR = I- band at 1513 keV In the previous subsection it was found that very little, if any, of the K” = l-, 4 -[514] - $ +[404] strength was observed in the K” = 1- band at 1310 keV. Since the K” = 8- parallel coupling of the same two protons has its strength split between the 1147 and 1479 keV bands, it would be expected that the K” = ltwo-quasiproton state should be found well below 2 MeV excitation. However, there are no other previously assigned K” = 1- bands in this energy region [7]. As mentioned in subsect. 3.4 above, the expected K” = l- band should have some

LAG. Burke et al. / 17’Hf

537

members with (p, tu) cross sections comparable to the largest of those in the K” = 8- bands, and therefore they should be detectable in the experimental spectrum. There is, in fact, a set of peaks with reasonable energy spacings and cross sections for this K” = l- band. The spin 2 G I G 6 members, which are the ones expected to have observable cross sections, have all been detected, although in many cases the peaks are in partially-resolved doublets (see Fig. 2 and Table 1). This interpretation places the K” = l- band head, which should have very little cross section and was not observed with certainty, just above an excitation energy of 1.5 MeV. Such an interpretation must be considered cautiously and documented carefully, however, because the average resonance capture (ARC) measurements [9] claim to have located all the levels with 2 d Z & 5 in the region below 1.8 MeV excitation energy, and thus some explanation is needed if new assignments are made in this region. Since most of the levels in this band have other previously known levels nearby, it is necessary to establish that the observed intensity is not due to these other levels. A careful examination of the results shows that this can be done, because the other previously-assigned levels should have negligible cross sections. In some cases this is because the previously-assigned configurations have K” values that cannot be populated in the (p, a) reaction (see Fig. 1, and note that only the two-quasiproton configurations involving the $ +[404] ground-state proton of the lBITa target should be populated). In some other cases there are K” assignments for which the possibility of population cannot be ruled out by the above argument, but for which any two-quasiparticle state which could explain the observed intensity would also have other rotational-band members which should have large cross sections, contrary to the experimental results. Thus, after close examination it is concluded that the observed cross sections cannot be attributed to any pre~ously-mown configurations, and yet the completeness argument for the ARC data [91 does not allow the introduction of new levels with the proposed Z” values in this energy range. A hint leading to the solution of this dilemma is obtained by noticing that the spin 2, 3, 4, and 5 members of the new Krr = 1 - band proposed in Table 1 are at the same energies as the corresponding spin members of the previously assigned [7,9] K” = 2- band at 1566.67 keV. The (p, (~1cross section cannot be due to a K” = 2- band because there are no K” = 2- two-quasiproton states involving the :“[404] proton orbital (see Fig. 1). The I” values for the previously known levels are considered to be very reliable, as they are based on multipolarities of many gamma transitions obtained from conversion-electron measurements [9]. However, the K-value of 2 was probably chosen because the lowest member located for the band had I = 2. In order to explain the present (p, LY)results, it could be suggested that the pre~ously-assigned K” = 2-band is actually the set of rotational excited states of a K” = l-band, for which the f = 1 band head was not located in the ARC experiments. One way to test the above suggestion with the data that are available is to

D.G. Burke et al. / ‘78Hf

538 Table 2 Branching 1310 keV Gamma multipolarity

ratios for decay of previously-assigned

Initial state IW E(keV)

K” = 2- levels to members

Final state

Relative

In

Exp. =

E(keV)

of the K” = l-

22233344222333344-

1566.7 1566.7 1566.7 1639.8 1639.8 1639.8 1747.1 1747.1 1566.7 1566.7 1566.7 1639.8 1639.8 1639.8 1639.8 1747.1 1747.1

12323434123123434-

a From data of Hague et al. [9] (see text). A b From Alaga rules (see text). ’ Hague et al. [9] report this transition to obtained from the experimental conversion conversion coefficients. d Hague et al. [9] report this transition to obtained from the experimental conversion conversion coefficients.

1310.1 1362.6 1433.6 1362.6 1433.6 1538.8 1433.6 1538.8 1310.1 1362.6 1433.6 1310.1 1362.6 1433.6 1538.8 1433.6 1538.8 dash indicates

at

strengths calculated Ki = 2

Ml Ml Ml Ml Ml Ml Ml Ml E2 E2 E2 E2 E2 E2 E2 E2 E2

band

100 85 112 100 $13 c < 134 100 Q 37 100 < 73 d 1520 _ 49 100 100 Q 226 the component

b K, = 1

100 55 11 100 140 180 100 108 100 214 150 114 0 100 140 100 568

100 55 178 100 22 141 100 12 100 24 67 114 95 100 71 100 225

was not observed.

be E2, but the upper limit for Ml presented here was coefficient given [9] (with its uncertainty) and theoretical be Ml, but the upper limit for E2 presented here was coefficient given [9] (with its uncertainty) and theoretical

consider the gamma decays from these levels and compare the branching ratios to different members of lower-lying bands with Alaga-rule predictions made for initial K-values of 1 and 2. It is seen from Table 4 of Hague et al. [9] that the strongest decays from the levels in question feed various members of the K” = lband at 1310 keV, and the comparisons of relative strengths to members of this band are shown in Table 2. Individual Ml and E2 strengths were obtained from the measured intensities and Ml/E2 mixing results given in Table 4 of Hague et al. [9], corrected for the E: (or E:) factor appropriate for Ml (or E2) transitions. The relative values predicted are ratios of squared Clebsch-Gordan coefficients 1(I&&AK I I&,) 1’ calculated for initial K-values of Ki = 1 and Ki = 2. It can be seen from Table 2 that this comparison shows a preference for a K-value of 1 for the initial states rather than K = 2. The branching ratios for Ml transitions agree better with Ki = 1 predictions for all three initial states for which data are available. The results for E2 transitions from the I” = 2- and 3- states are

D.G. Burke et al. / 178Hf

2-

539

1857.144 1639.753

1566.665 1513.894 _

2-

1362.546

1-

1310.063

:

:

:

:

:

V-

Fig 4 Partial level scheme of level at 1513 keV. Transitions placed in their level scheme. discussed in the text. For each

and

1513.612

i

8 0

scattered

2+

3

..

2-

1260.243

. 3

3

17sHf showing transitions relevant to the newly-assigned I, K” = 1, lshown as solid heavy lines were observed by Hague et al. [9], but not Those shown as dashed lines are probable gamma-ray doublets as transition shown, the energy (in keV), intensity (in the units of Hague et al. [9]), and the multipolarity [93 are given.

do not favor either

K,-value,

while those from the I” = 4- state are

more consistent with Ki = 1. The assignment of K” = 1- to these levels would be much more convincing if the Z = 1 band head could be located. Its expected energy can be estimated as - 1513 keV, by extrapolating the band to lower spin using the Z(Z + 1) rule and noticing that there is a small odd-even staggering in the known band members. This energy region is already complicated as there are previously-known levels [7] with Z,K” = 5,2- at 1512.596 keV,2,0+ at 1513.612 keV, and 4,4+ at 1513.835 keV. However, a search of the gamma ray list in Table 1 of Hague et al. [9] shows several unassigned transitions which can be used to support the existence of a new Z,K” = l,llevel at 1513.894 keV. These are shown in the partial level scheme of Fig. 4, and include the 52.774 keV Ml + E2 intraband transition populating the band head, as well as several others. The decay pattern of the proposed l- level at 1513.894 keV is consistent with those for the higher-spin band members, as the strongest transition is to the K” = l- band based at 1310 keV. Also, as for the higher-spin band members, this level does not decay to the gamma-band at 1174 keV, but does decay to the K” = 2- band at 1260 keV and probably also to the ground-state band. The ground-state transition is shown as a dashed line in Fig. 4 because its existence is less clear. The observed transition with energy 1513.725 + 0.066 keV was assigned as the ground-state decay from the level at 1513.612 k 0.016 keV by Hague et al. [9]. The discrepancy in energy could be explained if the

D.G. Burke et al. /

540

"8Hf

observed transition were an unresolved doublet including the 1513.894 keV decay to the ground state. The latter transition would be El, whereas the one from the previousiy-assigned 1” = 2+ 1eveI at 1513.612 keV would have to be E2. Although the measured internal conversion coefficient (Ye= 0.0017 rrt:0.0005 agrees with the theoreticai value of 0.00154 for E2 rather than with 0.00067 for El, the experimental uncertainty is Iarge enough to be consistent with an unresolved doublet in which up to N 40% of the gamma intensity is in the El component. The 151.343 keV transition to the 1, K” = 2, l- level at 1362.546 keV is also shown as a dashed line because the observed gamma ray with this energy has already been assigned elsewhere in the decay scheme [9]. Thus it may be a doublet also. With the interpretation outlined above the population extracted for the I” = llevel at 1513.894 keV in the (n,r) experiment would have a value between 0.8 and 1.2, in the units used by Hague et al. [91, and from their Fig. 18 it is seen that this intensity is consistent with the systematics shown for the popuIations of the higher band members, which were labelled as the K” = 2- band. The combination of the (p, a) data, the branching ratio comparisons, and the information in Fig. 4 supposing a new 1” = i-level at 1513.895 keV constitutes ove~helming evidence in favor of re-assigning the previous IL” = 2- band at 1566.67 keV as rotationa excited members of the new K” = l- band. In order to compare the observed distribution of (p, a) strength among the various band members with predictions of Eq. (11, the values are summarized in Table 3. Since the spin 2, 4, and 5 members have other populated states between 6 and 12 keV from their known energies, and the experimental resolution was N 20 keV, the peak-fitting program used to analyse the spectra usually found these peaks to be doublets, but did not reliably or consistently determine the proper positions for the

Table 3 Cross sections for the K” = l-

$-[514] - z +[404] two-quasiproton

band at 1513 keV

Spin I

Energy (keV)

Cross section @ = 10’) (ub/sr) calculated a

experimental b

1

1513.89 1566.67 1639.76 1747.10 1863.71 2023

-0

< 0.7 c 1.3 & 0.2 3.3 2.8 t 0.3 1.7 rl: 0.7 1.6

2 3 4 5 6

1.5 2.8 2.7 1.7 0.6

a Assuming the pure two-quasiproton configuration and using the total strength of the K” = 8- bands at 1147 keV and 1479 keV to obtain the empirical transfer cross section for pickup of a $- [5X4] proton. b From Table 1. The uncertainties given for several values arise from the deconvolution of partially resolved peaks. See text. ’ Peak obscured by impurity at this angle.

D.G. Burke et al. / “‘Hf

541

individual peaks in the doublets. Thus, once the assignments were established as above, the peak-fitting program was used in a mode whereby each of the doublets was fitted with two peaks for which the positions were held fixed at values corresponding to the precisely-known energy values, as indicated in Table 1. The peak intensities which then gave the best fit to the data are shown in Table 1, with the uncertainty obtained from the deconvolution procedure. It is seen from the comparison in Table 3 that the observed cross sections are in very good agreement with predicted values, and are consistent with essentially all of the z-[514] - $‘[404] strength being located in this K” = l- band. In fact, the cross section for the I = 4 member is - 19 times larger than the upper limit set for the I, K” = 4, l- level at 1539 keV in subsect. 3.4, consistent with the conclusion drawn there that the lower K” = l- band contained G 5% of this two-quasiproton configuration. It IS likely, however, that a very small amount of mixing between the two K” = l- bands exists, because the strongest gamma decays from the upper band are Ml transitions to the lower one, even though higher energy El transitions are allowed by angular momentum and K-selection rules. Any such mixing of the K” = l- bands would increase the overlap of the wavefunctions and lead to an enhancement of the Ml transitions, which could explain why this is the dominant decay mode. 3.6. The I, K” = 6, 6 ’ level at 1554 keV

This level is well known, and Khoo and Lovhoiden [24] have suggested that it has a N 69% admixture of the $ ‘[404] + 5 +[402] two-quasiproton state and - 31% of the $-[514] + $-15121 ho-quasineutron state. Thus, it is believed to be the counterpart of one of the K” = 6+ band heads in r“jHf which have been well studied and can be described by the calculations of Soloviev and Sushkov [51. The two-quasiproton admixture in “sHf should be populated in the (p, ar) reaction, although the spectroscopic strength should be small because the 2’[402] orbital is above the Fermi surface in the rslTa target. However, almost all the cross section to this K” = 6+ band will be in the band head, since the $‘[402] orbital originates from the ds,z shell and has a large Cj, value for j = G only. From studies of the 18’Hf(t cu) reaction [20] it was found that a reasonable empirical value for the factor iT”‘C2+,2] of the $‘[402] orbital was - 0.2, and a slightly larger value may be appropriate for the “‘Ta target. Using this value in Eq. (11, and assuming the final state is a pure 3 ‘[4041+ 5 ‘[402] configuration, the cross section for the I = 6 band head is predicted to be - 3.8 bb/sr at 8 = 10”. The observed value of 3.0 kb/sr is therefore consistent with the presence of a dominant admixture of this two-quasiproton configuration in the band, as suggested earlier [24]. However, it is not possible to extract a reliable quantitative value for the admixture from the present data, because of the uncertainties in the values of N and of V2. It might be expected that since the K” = 6” ho-quasineutron state responsible for the

D.G. Burke et al. / “‘Hf

542

mixing in 176Hf would be at higher energy in 178Hf (as one of the neutron orbitals involved would be farther from the Fermi surface), the observed 6+ state in 178Hf may be predominantly the two-quasiproton configuration. The present results would also be consistent with this. 3.7. The K” = 3 + band at 1758 keV and the 2+[4041 k $ +[411l configurations The largest peaks below an excitation energy of 2 MeV in the (p, a) spectrum of Fig. 2 are for levels at 1758 keV and 1869 keV, which are the known [7] 3+ and 4+ members of a K” = 3+ band. It is expected that the strongest peaks would arise from pickup of a ++[411] proton, leading to bands with K” = 3+ and K” = 4+, and the Gallagher-Moszkowski splitting should give the K” = 3+ band the lower energy. Thus, the 1758 keV band can be confidently assigned as predominantly the configuration. The observed and K” = 3+, +‘[404] - ++[411] two-quasiproton predicted cross sections at 8 = lo” are compared in Table 4, where the agreement is seen to be fair. The summed cross section observed for this band is N 60% of the value predicted using a reasonable value of V2 = 0.9 for the ++[4111 orbital in 181Ta. Although a large part of this difference may be due to uncertainty in the absolute cross sections, it is also quite possible that the 5’[404] - ++[411] strength may be fragmented and might not all be located in this band. (The value of N = 60 was chosen to reproduce the cross sections for ++[4111 pickup 1111,so the absolute cross sections should be predicted better for this band than for any of the ones discussed previously).

Table 4 Cross sections Level I, K”

for the K”=

3+ and K’=

4+, i’

4,4+ 5,4+ 6, 4+

[411] bands

Energy

Cross section (0 = 10”) (pb/sr)

CkeV)

calculated unmixed

3,3+ 4,3+ 5,3+ 6, 3+

[404] T i’

1758.15 1869.84 2004 (2310)? (2383)?

experimental a

c

mixed b

8.1 5.6 2.2 0.5

8.1 6.2 2.4 0.5

10.4

9.8

5.5 1.2

5.3 1.2

4.2 + 0.3 4.4 + 0.7 1.4 (7.0) (7.5)

a These are predicted cross sections for the pure two-quasiparticle states indicated, before any Coriolis mixing has been considered. b These values are predicted cross sections for the states after Coriolis mixing of the wavefunctions has been included, as described in the text. ’ From Table 1.

L&G. Burke et al. / “‘Hf

543

From Table 4 it is seen that the cross section for the spin-3 member of this band is expected to be larger than that for spin 4, but the observed values appear to be rather similar. There are rather large uncertainties on the experimental values, arising from the process of deconvoluting the doublets, but probably not large enough to account for the discrepancy. The difference between the observed and predicted cross section ratios is likely due to a nuclear structure effect because when the same configuration was studied with the (p, a) reaction in 172Yh the 1 = 3 cross section was N 40% larger than the I = 4 one, as predicted [ll]. It is seen from Table 4 that Coriolis mixing with the K” = 4+ band above can explain part of the difference by transferring some J,K” = 4,4+ strength to the f,K” = 4,3+ member. This mixing is more effective in 178Hf because the two bands are much closer in energy than in 172Yb. One possibility which cannot be excluded is that a small part of the K” = 3+, :‘[404] - $[411] strength may have been transferred to the K” = 3+ band which is based at 1862.21 keV. The latter band was incorrectly assigned 17,9] as part of a K” = 2+ band based at 1808 keV, but has recently been shown [25] to have K” = 3+ and to be predominantly the $-[514] - i-[.510] two-quasineutron configuration. The location of the parallel-coupled K” = 4+, 5’[404] + $+[411] state is not clear. The predicted cross sections for this band are listed in Table 4, and those for the spin 4 and 5 members are very large. Experimentally, there are several strong peaks observed and the ones at 2310 and 2383 keV are possible candidates for the I = 4 band head, since they have the largest cross sections of all the peaks in the spectrum - almost as large as the expected value for the J = 4 band head, which is predicted to have the largest cross section in the spectrum. There are many levels in this region, such as those at 2116, 2224, 2310 and 2383 keV, which have angular distributions consistent with 1= 2 transfers (see Fig. 3). Thus, it is quite likely that there is mixing of levels which has caused a fragmentation of strength for both the K=3 and K=4bands.

Although the K”= 8- and K” = l- bands formed by the :+[624] + $-[514] two-quasineutron and the !-[514] of ;‘[4041 two-quasiproton states have been sought and studied in various even-even hafnium nuclei for many years, this is the first time that all four bands have been located in one such nuclide. If one uses the expressions given by Casten 1261for two-state mixing, with the band-head energies and two-quasiparticle admixtures given in subsects. 3.3 and 3.4 above, it is found that the unperturbed energies for the K” = S- and K” = 1- two-quasineutron band heads are 1265 keV and 1315 f 5 keV, respectively. The corresponding values for the ho-quasiproton bands are 1361 keV and 1509 f 5 keV, respectively. These results were obtained using the upper limit of 5% for the ~o”quasiproton

544

D.G. Burke et al. / “‘Hf

admixture in the K” = l- band at 1310 keV, and this causes the +5 keV spread for K” = l- values. The matrix elements for the interactions are found to be 159 keV for the 8- bands and < 43 keV for the l- bands. Massmann et al. [4] have been successful in calculating values of such matrix elements from the basic np interaction and obtained values of 133 keV to 158 keV for the 8- case, depending on the np force used. They did not publish a value for the l- bands, but it is common for the parallel-coupled bands to have significantly different matrix elements than the antiparallel-coupled ones [4,27]. It should be pointed out that before the unperturbed energies obtained from this analysis are used for the determination of Gallagher-Moszkowski splittings, it may be necessary to consider the effects of other interactions. For example, the K” = l- level at 1310 keV is assigned [6,23] as an octupole vibration, so its nature is probably more complex than assumed above and an energy shift may result from the octupole properties. Also, shifts due to Coriolis mixing with higher-lying configurations have not been considered here because the energies of the relevant higher-lying states are not known. By using an analysis similar to that of Helmer and Reich [2], it is found that the Al = 1 intraband transitions in the K” = 1- bands are expected to be almost pure Ml, and this is seen to be the case from the data of Hague et al. [9]. The 52.774 keV gamma ray assigned here as the I” = 2- to I” = l- transition of the new 1513 keV band is listed [9] as having Ml + E2 character. However, from the value of the internal conversion coefficient given [9] it can be concluded that the E2 component is at most a few percent.

4. Summary

The (p, cz) reaction has been used to study the nuclear structure of 178Hf, by observing two-quasiproton admixtures in which one proton is in the ;‘[404] orbital. The ground-state band of 178Hf was populated rather weakly as more than half of the K” = Of, 3’[404] - $‘[4041 strength went to the Of band at 1199 keV. This unusual occurrence could be attributed to the irregular filling of proton orbitals in this region, whereby the :‘[404] orbital appears as the ground states of lutetium (2 = 71) and tantalum (2 = 73) nuclides. The i-[514] + ;‘[404] two-quasiproton admixtures in the K” = 8- bands were observed directly, confirming earlier conclusions concerning their strong mixing. An upper limit of N 5% of the K” = l-, z-[514] - $‘[404] strength was found in the previously-known K” = lband at 1310 keV, but essentially its full strength was observed in a newly-assigned K” = 1- band at 1513 keV. A set of levels which had previously been assigned as a K” = 2- band starting 1566 keV was shown to be instead the rotational excitations based on the new K” = l- band. The main part of the K” = 3+, ;‘[404] - ++[411] strength was located in the 1758 keV band.

D.G. Burke et al. /

178Hf

545

The analysis of the (p, cu) data was aided ~nsiderably by the availability of I” values for a large number of levels. In particular, the high resolution gamma-ray and conversion electron measurements [91 following the (n, -y> reaction provided much useful information without which the present data would have been difficult to interpret. In turn, the (p, (~1 results have made it possible to extend the interpretation of the (n, y) data by showing how some of the unplaced transitions should be fitted into an enlarged level scheme. Once again, the advantage of applying complementary spectroscopic techniques to study the structure of a specific nucleus has been demonstrated. One great advantage of the direct stripping or pickup reactions is that they are very selective and populate only a specific subset of the many levels in a particular nuclide. In order to locate some of the many other expected “*Hf configurations shown in Fig. 1 it could be useful to perform high-resolution studies of (d, p), (d, t>, t3He, a) and (a, 3He) reactions. For these studies it would be very important to use targets with especially high enrichments (preferably z+ 99%) or the intrinsically larger cross sections from even-even isotopic impurities would obscure much useful information.

The authors gratefully acknowledge useful discussions with Prof. PC. Sood, and thank him for reading the manuscript and making several useful comments. He also provided a diagram which has been adapted slightly to form figure 1 of the present work. Thanks are also due to the Natural Sciences and Engineering Research Council of Canada, and the Norges ~menvitenskapelige Forskningsr%d, for financial support for this project.

References [l] [2] [3] [4] [S] [6] [7] [8] [9]

[lo] (111 (121 1131 f14]

C.J. Gallagher and H.L. Nielsen, Phys. Rev. 126 (1962) 1520 R.G. Helmer and C.W. Reich, Nucl. Phys. All4 (1968) 649 T.E. Ward and Y.Y. Chu, Phys. Rev. Cl2 (1975) 1632 H. Massmann, J.O. Rasmussen, T.E. Ward, P.E. Haustein and F.M. Bernthal, Phys. Rev. C9 (1974) 2312 V.G. Soloviev and A.V. Sushkov, J. Phys. G16 (1990) L57 R.K. Sheline, M.M. Minor, PC. Sood and D.G. Burke, Pramana J. Phys., 41 (1993) 151 E. Browne, Nucl. Data Sheets 54 (1988) 199 B. Fogelberg and A. Backlin, Nucl. Phys. A171 (1971) 353 A.M.I. Hague, R.F. Casten, I. Forster, A. Gelberg, R. Rascher, R. Richter, P. van Brentano, G. Berreau, H.G. Borner, S.A. Kerr, K. Schreckenbach and D.D. Warner, Nucf. Phys. A455 (1986) 231 M.A.M. Shahabuddin, J.C. Waddington, D.G. Burke, 0. Straume and G. bvhoiden, Nucl. Phys. A307 (1978) 239 D.G. Burke and J.W. Blezius, Can. J. Phys. 60 (1982) 1751 E. Hammaren and D.G. Burke, 2. Phys. A305 (1982) 143 D.G. Burke, G. Kajrys and D. Beachey, Nuct. Phys. A492 (1989) 68 B. Elbek and P.O. Tjom, Adv. Nuci. Phys. 3 (1969) 259

546

D. G. Burke et al. / ‘78Hf

(151 R.C. Thompson, A. Ikeda, P. Kleinheinz, R.K. Sheline and P.J. Daly, Phys. Lett. 355 (1975) 447 [16] E. Gadioh, P. Guazzoni, S. Mattioli, L. Zetta, G. Graw, R. Hertenberger, D. Hofer, H. Kader, P. Schiemenz, R. Neu, H. Abele and G. Staudt, Phys. Rev. C43 (1991) 2572 [17] CR. Hirning and D.G. Burke, Can. J. Phys. 55 (1977) 1137 [18] P.D. Kunz, Computer program DWUCM, University of Colorado, unpublished 1191A.K. Jain, R.K. Sheline, P.C. Sood and K. Jain, Rev. Mod. Phys. 62 (1990) 393 1201 D.G. Burke and P.E. Garrett, Nucl. Phys. A550 (1992) 179 1211D.G. Burke and B. Elbek, Mat. Fys. Medd. Dan. Vid. Selsk. 36, no. 6 (19671, see pages 6 and 31 [22] E.P. Grigoriev and V.G. Soloviev, The structure of even deformed nuclei (Nauka, Moscow, 1974) p. 237 [231 V.G. Soloviev and N.Yu. Shirikova, Z. Phys. A334 (1989) 149 [24] T.L. Khoo and G. Lovhoiden, Phys. Lett. B67 (1977) 271 1251 R.K. Sheline, D.G. Burke, M.M. Minor and PC. Sood, Phys. Rev. C48 (1993) 911 1261 R.F. Casten, Nuclear structure from a simple perspective (oxford Univ. Press, New York, 1990) p. f271 EG. Burke, W.F. Davidson, J.A. Cizewski, R.E. Brown and J.W. Sunier, Nucl. Phys. A445 (1985) 70