Rotational bands in 170Yb observed following (α,xn) reactions

Nuclear Physics A365 (1981) 61-92 0 North-Holland Publishing Company

ROTATIONAL BANDS IN “‘Yb OBSERVED FOLLOWING (a, xn) REACTIONS P. M. WALKER Science Research Council, Daresbury Laboratory, Daresbury, Warrington WA4 IAD, UK* and Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA

W. H. BENTLEY, S. R. FABER +, R. M. RONNINGEN

and R. B. FIRESTONE

*

Departments of Physics & Chemistry and Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA

F. M. BERNTHAL Departments of Chemistry and Physics and Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA* and Niels Bohr Institute, Risd, DK-4000 Roskilde, Denmark

and J. BORGGREEN,

J. PEDERSEN

and G. SLETTEN

Niels Bohr Institute, Risd, DK-4000 Roskilde, Denmark

Received 11 November 1980 (Revised 11 March 1981) At least seven side bands, with K” = (O+), (1 -), (27, (3-), 4-, 6-, and 7-, have been identified in ““Yb up to high spin, using y-ray techniques following (GL, 2n) and (a, 4n) reactions. Backbending in the positive-parity yrast band is confirmed, and candidates for low-spin members of the S-band are found. The negative-parity yrast band has behaviour characteristic of both strong coupling and decoupling. These properties, together with those in the other negative-parity side bands, are interpreted as arising from Coriolis effects on the quasiparticle configurations, and the experimental results are compared with a two-quasiparticle-plus-rotor calculation. Evidence of AK = 2 mixing is found in the K = (3) side band. The relationship between the moments of inertia of the positiveparity and negativeparity yrast bands in the N = 100 isotones is discussed in the framework of a simple empirical model, giving insight into the presence or absence of backbending. The negativeparity yrast bands in the N = 100 isotones are compared. Their significant differences are qualitatively reprodued in two-qnasiparticle-plus-rotor calculations.

Abstract:

E

NUCLEAR REACTIONS ‘@Er(C(,2n), E = 27 MeV ; i7”Er(a, 4n), E = 50 MeV; measured E,. I,, yy-coin, a-y(t), y@),ICC. “‘Ybdeduced levels, K, J, II, Tl12. Ge, Ge(Li), Si(Li)detectors, enriched targets.

* Present address. + Present address : Argonne National Laboratory, Argonne, Illinois 60439, USA. * Present address : Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720, USA. 61

62

P. M. Walker et al. / Rotational

bands

1. Introduction The study of side bands in well deformed nuclei leads to an understanding of the competition between rotational and quasiparticle degrees of freedom, and the Coriolis coupling between these excitation modes. In even-even nuclei the lowestlying negative-parity band (the negative-parity yrust band) usually shows the effects of Coriolis coupling, due to the necessary involvement of a unique-parity high-j nucleon. Further, the yrast bands may be observed experimentally up to high spin in a wide variety of nuclei, due to their favourable population following (heavy-ion, xn) reactions. Therefore, the opportunity exists to identify systematic features in such bands, and hence to distinguish between the competing dynamical influences. The N = 100 isotones display a range of properties. The positive-parity yrast bands of 174W and 17’Yb [refs. ‘,‘)I backbend, while that of r7’Hf [ref. “‘“)] does not. The negative-parity yrast bands are decoupled into odd and even spin sequences in 174W and 17’Hf [ref. 1,3-5)], while in 168Er [ref. 6)] the behaviour is much closer to the strongly coupled limit. However, the negative-parity yrast band of the intermediate isotone, 17’Yb , was not known, and the present experiments were carried out in order to locate this band, as well as to search for other side bands. As a result, conflicting properties were found 7, in the negative-parity yrast band of 17’Yb which could, at least qualitatively, be understood from the Coriolis effects on the quasiparticle structure. The present paper considers this and other side bands, and compares their structure with that calculated in a two-quasiparticleplus-rotor Coriolis coupling representation. Possible dK = 2 mixing between two side bands, with K = (1) and K = (3), is discussed. The relevance of the negativeparity yrast band to backbending in the positive-parity yrast band is considered, and the negative-parity yrast bands in the N = 100 isotones are compared.

2. Experimental techniques and results The experimental techniques are essentially the same as those used in a parallel study of 17’Yb which has recently been published *). Therefore, only a brief outline will be given here. After an initial study using the 16’Er(a, 2n)170Yb reaction at the Niels Bohr Institute, Ris$, more detailed measurements were made with beams provided by the MSU Cyclotron, using both the above reaction at 27 MeV, and the 17’Er(~ 4n)17’Yb reaction at 50 MeV. The latter favoured the population of high-spin states. Both oxide and metallic targets were used, all isotopically enriched.

63

P. M. Walker et al. / Rotational bands TABLE 1

Energies, intensities, angular-distribution coefficients and assignments for transitions placed in l”Yb following the 16*Er(u, 2n) reaction at 27 MeV and the 17’Er(a, 4n) reaction at 50 MeV

84.3 86.8 102.3 105.1 113.6 122.4 133.0 134.0 140.9 141.6 143.1 152.0 154.9 156.4 175.5 176.2 177.9 183.8 184.7 185.3 191.8 193.3 205.4 207.5 212.2 227.2 227.6 232.0 234.4 234.5 242.8 243.4 265.6 282.0 295.9 299.4 317.7 320.8 330.5 332.2 335.3 338.5 340.0 341.0 352.9 354.0 370.1 382.7

‘)

‘)

r) f) ‘)

‘)

‘)

‘) ‘) ‘)

‘) 9

180* 10 14_lr 1 3f 1 23k 2 6k 1 6k 1 2* 1 6k 1 2+ I 3* 1 13* 1 9* 1 7* 1 4* 1 3* 1 2+ 1 > 35 1 7+ 2 7* 2 3+ 1 I 24+ 4 1000+ 50 3* 1 4* 1 21: 1 3_+ 1 14+ 2 2-& 1 2* 1 2+ 1 2+ 1 2+ 1 46k 3 lo* 2 720+40 16k 2 3* 1 3* 1 4* 1 4* 1 > 2* 1 17* 2 5* 2 39* 4 3* 1 9+ 2 16+ 2 3* 1

0.136+0.007 -0.69OiO.029 -0.36 iO.10 -0.759_+0.017 -0.621 kO.055 -0.768kO.058

-0.017+0.010 -0.031+0.040 0.21 kO.13 0.043 f 0.024 0.031 kO.074 0.016kO.077

-0.61 50.08 -0.07 20.11 -0.59 +0.11 -0.921 kO.026 0.257 k 0.027 -0.385 + 0.040 -0.53OkO.060

-0.03 +0.11 0.09 +0.14 0.34 kO.15 0.105~0.035 0.055 f 0.038 -0.049kO.062 0.032 f 0.080

-0.64

kO.08

-0.09

kO.11

-0.68

+0.14

-0.11

kO.16

-0.149f0.022

- 0.037 + 0.030

0.287+0.030 0.289+0.007 0.04 ,0.07 0.23 kO.10

-0.064~0.040 -0.039~0.010 -0.12 kO.10 0.06 +0.13

0.44 *0.12 0.414+0.042

-0.03 kO.18 - 0.041 f 0.064

0.375 f 0.030 0.36 kO.08 0.342+0.007 0.31 kO.07

- 0.065 + 0.040 -0.06 kO.10 -0.059~0.010 0.01 kO.10

0.208 f 0.052 -0.181 kO.042

-0.046+0.050

0.401 kO.025

-0.102kO.032

0.376 f 0.062 0.380 + 0.046

- 0.054+ 0.083 -0.104+0.062

2+0 5-4 6-(3) 6-4 7-6 7-4 (1794 8-6 7-(3) 8-(3) 8-4 8-7 9-6 9-4 10-6 g-(3) 10_(3) 9-7 10-4 11-4 6-4 4+0 11_(3) 10-7 12-(3) 11-7 7-4 12-4 (1904 l3-(3) (12-7) 7_(3) 8-4 S-(3) 6+0 9-4 g-(3) (7+2) 10-6 (lo+0 9-7 7-7 2010 10-4 S+(2) 10_(3) 11-4 11_(3)

+ -+ + + -+ -+

o+o 4-4 5-(3) 5-4 6-6 6-4

-+ -+ + -+ -+ + + + + -+ -+ + + + -+ -+ + + -+ -+ -+ -+ + + + + -i -+ + + --) + + -+ + + + + + + + -+

5_(3)) 7-6 6-(3) 7-(3) 7-4 7-7 8-6 8-4 9-6 S_(3) g-(3) 8-7 9-4 10-4 4-4 2+0 10_(3) 9-‘7 11-(3) 10-7 5-4 11-4 1669) 12-(3) 11-7 5_(3) 6-4 6-(3) 4+0 7-4 7_(3) (5+2) S-6 8+0) 7-7 6-15 1669 8-4 6+(2) S_(3) 9-4 g-(3)

P. M. Walker ct al. / Rotaf~~na~ban&

64

TABLE:

1 (continued) A&A,

390. I 401.0 403.2 417.2 417.7 418.7 434.2 434.2 434.5 439.5 ') 446.7 453.9 474.3 480.2 492.8 505.1 506.2 514.3 3 540.7 543.1 545.8 565.1 570.3 597.1 h) 609.3 611.9 615.4 630.8 698.0 698.1 739.2 771.X 804.3 817.1 840.0 844.3 ') 870.6 872.3 887.0 908.8 935.9 939.6 948.0 950.5 955.4 974.7 981.1 991.0 999.5 1016.7 'f 1028.4

440,30 IO& 1 3) 1 20+ 2' 4+ I, i 8& 2 3+ I \ 5* 2 ) t;k 2 ! 101 2 3If:I 4+ 1 16O&lO 6+ 2 8, I <4 49J)rt 4 II) 3 7+ 1 42 2 742 5 <3 <3 202 2 12& 2 <3 <3 <3 6i: 2 ; 62 2 / 41 I 251 3 15) 2 6+ 2 if): 2 fs* 2 61t 2 f?+ I 5+ 2 37& 4 lo+ 2 5_c I 85 2 12+ 2 7rt:2 5+ 2 150~10 142 2 59+ 5 8& 2 165 2

“)

0.361f-o.009 0.281~0.03.5 0.345rto.043

-0.061 +o.oti5

0.423rtO.058

-0.077+0.080

0.316rfrfJ.040

-0.095-fO.053 -0.032+0.057

0.379+0.014 (0.341_+0.036)

(-0.008~0.052) - 0.021* 0.023

0.07 50.10 0.36Oj;O.OII (0.16 f0.08) (0.223ItO.043) (0.268+0.039) -0.155+O.OS6 (0.357-tO.043) (0.366+0.032) (0.29 t0.12) 0.317+0.052 -0.115~0.034 -0.263fO.057 0.44 -to.09

0.11 +a13 -0.090+0.019 t-U.26 +O.ll) (-0.168+0.066) (-0.051~0.059) -0.0I8~0.076 (-0.050+0.066) (-0.06Of0.049) (-0.10 sO.18) 0.119+0.066 -0.03h~0.047 0.035~0.076 -0.02 40.11

-0.288&0.027

-0.0X0+0.036

0.23 kO.15 -0.395f:o.oa -0.14 _to.ox

0.01 *0.20 -0.05 *0.09 -0.11 +0.11

0.063~0.011 -0.210_c0.065 -0.203_t0.018

0.01340.015 -0.25540.088 -0.009~0.025

-0.2O4~0.056

-0.138&0.075

X+0 6’0 6-6 + 6-4 2413 * 2010 12-4 --t10-4 12 ..(3) + lo-(31 N'(2)-+ x+(2) (9.4 + 10'0) (9+2 -a 7+2) Il.7 --t 9-7 13 4 + 11-4 13"(3)--tll_(3) (12+2) -+ 10+(2) 10+0 + 8+0 (14+2 + 12'2) 14-4 + 12..4 (IS 4) -+ 13-4 6.6 3 5-4 7-6 --t 6-4 (l2+0) + 12+0 (15-I -+I3 I) 12+0 + 10'0 (16-4) - 14 4 (17-4 + 15-4) 14'0 -12-o 7-4 + 8'0 18'0 + 16'0 16'0 + 14'0 (20.0 -a 18'0) (lOTO) 4 10'0 13-4 + 12'0 77 + 6-4 5 -4 + 6+0 II--4 - 10+0 (7"2) --)r8+0 S'(O)+ 8"O 7-7 + 5-4 1835 + 8+0 (13-l -+12+0) (5+2 + 6'0) 94 + 8'0 IOC(2)-L 10-o 7 '(3)-+ 8.-O 6'(O) + 6‘0 (II-I) + 10'0 1529 -a 6'0 2413 + lo+0 4-4 + 4+0 S-(2)+ 8+0 7-4 -+ 6'0 (4fO) + 4+0 6+(2)-r fs+o

P. M. Walker et al. / ~otationul

bands

65

TABLE1 (continued)

E, “1OW

I:“’ “)

1042.5 1046.2 1052.1 1067.8

15& lo+ lo+ 754

2 2 2 6

-0.33 kO.13 -0.29 +0.08 -0.33 +0.10 -0.226kO.024

0.13 +0.18 -0.18 +O.ll -0.01 go.13 -0.005f0.032

1087.0

15+ 2

0.000+0.056

-0.157+0.077

1095.8 1131.2 1139.1 1172.2 ‘) 1182.4 1207.7 ‘) 1230.4 1232.8 1244.0 1251.6 1257.7 1261.3 1330.0 1383.0

17+ 3 124 2 171_ 2 75 2 16+ 2 29+ 4 lo& 2 7+ 2 13+ 2 15+ 3 19+_ 3 17+ 3 14+ 2 18& 2

- 0.223 f 0.052 -0.30 50.08 -0.16 kO.10

-0.2I51tO.069 -0.14 +0.10 0.12 50.13

-0.092*0.044

-0.015~0.~0 0.26 +0.09

4/A, ‘f

-&IA, ‘>

-0.25 f 0.07 0.44 10.11 0.35 -0.23 -0.46 -0.38 -0.25 -0.22

kO.08 +0.07 +O.ll +0.09 + 0.07 + 0.07

-0.22 0.21 0.00 0.12 0.12 -0.10

kO.10 50.09 +0.15 +0.12 20.09 +0.09

I:K, -+ I;Kt ‘)

(9-l) -+ 2010 -+ (4+2) -+ 5-4 -+ (12+0) + i 5-(3) -+ 1669 -+ 1409 -+ (7-l) -+ (10’0) -+ (5+2) --f (7+2 -+ 8+(O) -+ (5-l) -+ 6’(O) -+ 1529 -+ g-(3) i) 1835 -+ 7-(3) -+ 5_(3) -+

8+0 s+o 4’0 4,+0 10’0 6+0 6+0 4+0 6+0 8’+0 4+0 6’0) 6”O 4+0 4+0 4’0 s+o 6“O 6”O 4+0

*) Energy uncertainties are 0.1 keV for most transitions, rising to 0.5 keV for weak transitions at high energy. 4 Intensities are given relative to the 4 -+ 2, 193 keV transition in the (a, 2n) reaction. ‘) Coeflicients in parentheses are from the (a, 4n) data. d, Where no K-assignment is possible, level energies are given. Assignments in parentheses are tentative. The significance of the K-assignment is discussed in the text. 7 Poorly resolved, or unresolved from transition in ’ bYYb; angular distribution coefficients (if given) are liable to systematic error. ‘) As ‘) but contaminant is unidentified. “) As ‘) but annihilation radiation. “) As ‘) but 74Ge(n, n’) edge. ‘) As ‘) but “Al(n, n’).

2.1. SINGLES y-RAY MEASUREMENTS

Three sets of six-point y-ray angular distributions were measured; one for each of the (01,2n) and (a, 4n) reactions with a 7 yO effkient coaxial Ge(Li) detector, and one for the (a, 2n) reaction with a high-resolution planar Ge detector. A spectrum for the latter is shown in fig. 1. Gamma-ray energies, relative intensities and angular distribution coefficients are given in table I. 2.2. GAMMA-GAMMA

COINCIDENCE

MEASUREMENTS

Three sets of y-y coincidence measurements were made; one for each of the (a, 2n> and (a, 4n) reactions with two coaxial Ge(Li) detectors, and one for the (M,2n) reaction with a planar Ge detector and a coaxial Ge(Li) detector. For each

I

‘000 CHANNEL

NUMBER

I

2000

3000

I

90”

27 MeV

Fig. f . Singles y-ray spectrum at PO’ to the beam direction, using a planar Ge detector, taken during bombardment afa 2 mg cm -’ 16%r target with 27 MeV cl-particles. Transitions (with energies in keV) are assigned to “OYb unless otherwise indicated. “c” indicates unassigned transition.

1

singles

‘68Er(a.2n)‘70Yb

P. M. Walker et al. i Rotational

6-l

band.7

measurement, between 20 and 60 million coincident events were written event by event on magnetic tape in three parameter y-y time format, for subsequent off-line analysis. Examples of analysed spectra are given in figs. 2 and 3, for the Ge-Ge(Li) coincidence measurement, with each of the detectors represented. These results are discussed in greater detail in sect. 3. The y-y-time data were also used to search for half-lives in the range of about 5 ns to 5 ps. In this way the 1259 keV level was found to have a half-life of 370 _t 15 ns (from the time spectrum for the 981 keV depopulating transition). No other isomers in this time range could be assigned to ““Yb. 2.3. TIMING

MEASLKEMENTS

In order to search for half-lives of 5 5 ns, an additional timing experiment was performed using the (x, 2n) reaction, with the planar Ge detector and the r.f. signal from the cyclotron to reference the natural beam bursts. Only a limited range of y-ray energies (28&600 keV) was investigated, since this represented the most interesting region of the spectrum, and the data were recorded event by event on magnetic tape in two parameter y-time format. An experimental timing resolution of 3.5 ns FWHM was obtained. Examples of time spectra are given in fig. 4. Only one level could be assigned a half-life in the range 0.5 5 T+ 2 5 ns; that is the 2190 keV level with Tt = 2.820.3 ns, from the time spectrum for the 338 keV depopulating transition, illustrated in fig. 4. (Both the slope method and the time centroid shift method yield consistent values.) 7

zoo-

i? ,l

1000

:

: 7

I

0

liuJJ

I

I

E

; m

i

\

I

200

keV GATE

Id,; +

2000 CHANNEL

!Y 0

._-_

I

.-

NUMBER

Fig. 2. Background-subtracted coincidence *pray spectra, illustrating events in a planar Ge detector in coincidence with events in a coaxial Ge(Li) detector at 266 keV and 1000 keV, following the 16sEr(z, 2n)““Yb reaction at 27 MeV.

P. M. Walker et al. / Rotational

bands

L80i

&.I ; 3 i? L N > -

(trL*)

-

8ltr IO+-

____--_

@JGE)

SE -

31t10 6EE----+

-_______fwg XV9

282==

-

-

LZZ--;

802”

*81----7

502-

:61

______SL,-

29 d

i ICI-

UV~paO’~-+

33NNYH3

M3d

SJ.Nn03

P. M. Walker et al. / Rotational

341 keV

TAC

15

69

(prompt)

IO -TIME

bands

5

0

hs)

Fig. 4. Examples of time spectra for y-ray tansitions in 17”Yb, relative to cyclotron beam pulses, following the 16’Er(c(, 2n) reaction.

2.4. CONVERSION

ELECTRON

MEASUREMENTS

Conversion electron intensities were measured at the NBI in singles using the (c(, 2n) reaction with a Si(Li) detector at 120” to the beam direction. A mini-orange magnet assembly with a lead/gold plug was used to filter out other reaction products. With a metal target of 1.2 mg . cm-’ at 45” to the beam, an experimental energy resolution of 2.6 keV at 1 MeV was obtained. Part of the electron spectrum and the corresponding y-ray spectrum are illustrated in fig. 5. Using three different magnet sets in the electron spectrometer, electron intensities were measured in the range 25&l 400 keV. Normalisation of the electron yields in the 1 MeV region presented a problem, due to the lack of transitions with known conversion coefficients. However, measurements of conversion electrons from 17’Yb were made *) both immediately before and after some initial 17’Yb measurements at MSU, with the same experimental conditions (apart from the target itself). These were used for an initial normalisation. When taken together with the y-ray angular distribution results, certain strong transitions in 17’Yb (e.g. that at 1068 keV) could be shown to be almost pure El transitions; this was used to renormalise the spectrum, together with some stretched E2 transitions. The resulting aK values are given in table 2, along with the multipolarity assignments and the corresponding theoretical values “). The detailed results are discussed in sect. 3.

P. M. Walker et al. I Rotational bands

70

‘68Er(a.2n)‘70Yb

I

Sin&s 1000

a, E if&

500

a (0

z 2

0

1000

5oc

0

I

lob0

900 y-ray

energy

llb0 (keV)

Fig. 5. Comparison between singles electron ( 120°) and y-ray (90”) spectra in the energy region 900 to 1100 keV, following the ‘68Er(c(,2n) 170Yb reaction. The electron spectrum is shifted so that K-conversion transitions are aligned with corresponding y-ray transitions in “‘Yb.

3 . The “‘Yh

level scheme

Level schemes for I’OYb are presented in figs. 6 and 7. Only transitions identified following the r6’Er(a, 2n)“OYb and the 17’Er(a, 4n) r”Yb reactions are illustrated. Fig. 6 shows the yrast band and the negative-parity side bands, while the positiveparity side bands are shown in fig. 7. The schemes have been established on the basis of the y-y coincidence relationships, for which sample spectra have been illustrated in figs. 2 and 3. The illustrated data represent only a small fraction of the total information used. The spin and parity assignments are discussed in the following sections. For convenience, the rotational bands have been given K-quantum number classifica-

P. M. Wulker et al. i Rorationui hands

K-electron

conversion

coeffGents

for transitions

71

in ““Yb Theoretical

E, (keV)

296 339 341 370 390 401 417 474 506 541 546 609 698 739 772 804 817 840 844 909 936 940 948 951 955 975 981 991 1000 1017 1028 1043 1046 1052 1068 1087 1096 II31 II82 1244 1252 I330 I383

2;‘“’ X IO”

60 fl0 86 +I8 42 +I0 27 +_ 6 31 f 5 49 *lo 26 f 5 20 f. 4 25 k 5 27 f 7 I2 + I’) 4.6* 1.2 30 flOd) 7.3& 1.9 2.4* 0.4 2.7* 0.6 8.3+ 2.8 I2 * 3 9 &4 2.0* 0.4 5.1 * 1.2 2.0* 0.7 X.9 5 2.4 I.92 0.6 5.2* 1.6 5.8* 2.5 1.3* 0.2 4.4+ 0.8 1.5+ 0.3 ‘) 5.0* I.2 3.1 f 0.7 1.2+ 0.4’) 2.g* 0.7 2.6+ 0.8 ‘) 1.1+ 0.1’) l.8* 0.4’) 2.9* 0.6 2.6& 0.6 2.0* 0.5 ‘) 2.0& 0.2’) 2.2* 0.5 0.7& 0.2 2.5+ 0.5

Assignment

E2 Ml(+E2) E2 E2 F.2 Ml +E2 E2 E2 Ml +E2 Ml(+E2) F.2 El Ml(+EO) (Ml +E2) El El (Ml +E2) (& El (Ml +E2) El Ml El MI+E2 (MI +E2) El Ml +E2 El (Ml +E2) (MI +)E2 El (Ml +)E2 (MI +E2) El (El +E2) (Ml +)E2 (Ml +E2) (E2) (M&E2 El (El + M2)

values “) x 10’

h, El

E2

Ml

17 12 I2 10 9.0 8.4 7.7 5.8 5.0 4.3 4.2 3.3 2.6 2.3 2.1 I.9 I.8 1.7 1.7 I.5 I.4 1.4 I.4 1.4 I.4 1.3 1.3 I.3 1.3 1.2 1.2 I.2 1.2 1.2 I.1 1.1 I.1 I .o 0.9 0.9 0.9 0.8 0.7

55 38 38 30 27 25 22 I6 I4 I2 I2 9.0 6.8 5.‘) 5.3 4.9 4.1 4.4 4.4 3.7 3.5 3.5 3.4 3.4 3.4 3.3 3.2 3.2 3.1 3.0 2.9 2.8 2.8 2.8 2.7 2.6 2.6 2.4 2.2 2.0 2.0 1.8 I.7

I40 100 97 78 67 63 57 40 34 29 28 22 I6 I3 I2 II IO 9.1 9.5 7.Y 7.3 7.2 7.1 7.0 6.9 6.6 6.5 6.1 6.2 6.0 5.8 5.6 5.6 5.5 5.3 5.1 5.0 4.6 4.1 3.6 3.6 3.1 2.9

“) Ref. 9). “) Angular distribution coeflicients may be significant in determining multipolarity parentheses indicate tentative assignments. ‘) Used to calibrate data; see text. “) Unresolved doublet; assumed El component has been subtracted. ‘) L-conversion component (from transition at E, - 5 I keV) has been subtracted. r) Unresolved doublet; total zk is given.

assignments

72

P. M. Walker et al. / Rotational

bands

193.3

*;3 170yb,,,

K=O

Fig. 6. Partial level scheme for r”Yb, deduced following the r7’Er(a, 4n) and 16sEr(x, 2n) reactions at 50 MeV and 27 MeV, respectively. Dashed transitions and parentheses indicate tentative assignments. Dashed levels are known from other work (see text). Only the yrast band and negative-parity side bands are illustrated. Other side bands are shown in fig. 7.

tions. However, in general K is not a conserved quantity, and the degree of validity of the K-assignments will be considered in sect. 4. In general, y-ray multipolarities are assumed to be dipole (El, Ml) or quadrupole (E2) for prompt transitions (T+ 5 5 ns). No side-band structure (at least above Z = 4) has been previously established in l”Yb so that most of the states seen in the present work are reported here for the first time [apart from those given in our preliminary report ‘)I.

13

P. M. Walker et al. I Rotational bands 3307.6

(14+)

4810.2 I

2+ o+

193.3 84.3 + 4 17’Yb

Fig. 7. Partial

3.1. THE

level scheme

for 170Yb , as fig. 6 , except that only positive-parity

POSITIVE-PARITY

YRAST

BAND

side bands

are shown.

(K” = 0+)

The positive-parity yrast band, which includes the extension of the ground-state band (g.s.b.) through the backbending region, was already known ‘) up to I = 18. We confirm these assignments and tentatively identify the 20+ -+ 18+ transition at 631 keV. 3.2. THE

NEGATIVE-PARITY

YRAST

BAND

(K” = 4-)

A preliminary account of the negative-parity yrast band has been given ‘). The band had not been reported before, although the levels at 1345 keV (5-) and 1573 keV (7-) could be the same as those identified lo) at similar energies from the (d, t) reaction. Two examples of coincidence spectra, that lead to the placement of the levels in the band based on the 1259 keV level, are shown in fig. 2. The high-resolution planar Ge detector is seen to separate clearly the 192 and 193 keV transitions.

P. M. Walker et al. / Rotational bands

74

The spin and parity assignments are established from the decay of the odd-spin members to the g.s.b. For example, the angular distribution coefficients (table 1) for the 1068 keV (A,/& = -0.23) and 772 keV (A,/& = -0.12) transitions from the 1345 keV level imply almost pure dipole AI = 1 transitions, and hence I = 5 for the 1345 keV level. Furthermore, the weakness of the conversion electrons corresponding to the 1068 keV transition (fig. 5) establish, even in the initial normalisation, aK < 3 x 10m3, hence El (rather than Ml) multipolarity, and negative parity for the 1345 keV level. The same argument may be used for the 1573 keV, 7- level and, less rigorously, for the 1872 keV, 9- level. Both cascade (I + I- 1) and crossover (1 -+ I- 2) in-band transitions are observed from most of the excited band members, leading to the other spin and parity assignments. The only tentative assignments are at the top of the band, where the transitions have low intensities. The I” = 4- band head is found to be isomeric, with a half-life of 370& 15 ns (from the y-y-time measurements). Thus the 981 keV, 4- + 4+ transition is strongly K-forbidden, and the band may reasonably be given a K = 4 assignment. This assignment is considered in greater detail in sect. 4. 3.3. THE K” = (3)-

BAND

The 1661 keV level is assigned 1 = 5 on the basis of the angular distribution coefficients for the 1383 keV transition (A,/& = -0.22) to the 4+ member of the g.s.b., since these imply AI = & 1, and the presence of the 1087 keV transition to the 6+ member of the g.s.b. establishes the higher-spin alternative. Similarly, the 1904 keV level can be assigned Z = 7. Further Ievels (1763,2045, . . . keV) are placed in a band based on the 1661 keV level, connected by cascade and crossover transitions. These levels are only weakly populated, but the many branches involved give confidence in the assignments. Representative y-y coincidence spectra are shown in fig. 3 (102 and 282 keV gates). The negative-parity assignment for this band comes from the El decay of the outof-band transitions (940, 1087, 1330 keV) to the g.s.b. (see table 2). In the decay properties~of its members, the band has similarities with the K” = 4band based on the 1259 keV isomer. For example, the even-spin members have no out-of-band branches, in contrast to the odd-spin members. However, in this case no isomeric band head is located and, indeed, the 1661 keV level might not be the band head. Both the out-of-band branching ratios and the (a, xn) population mechanism are unfavourable for the observation of lower band members, if they exist. A tentative K = (3) assignment is made on the basis of the y-ray transition properties and the available Nilsson quasiparticle configurations, discussed in subsect. 4.5.

P. M. Walker et al. / Rotational 3.4. THE K” = 6-

bands

15

BAND

The sequence of levels above the 1852 keV level is reasonably interpreted as a rotational band. The A, < 0 and A, N 0 angular distribution coefficients for the in-band transitions determine their dZ = 1 character, while the crossover transitions are generally too weak to be observed. The 1852 keV band head decays by two transitions to the negative-parity yrast band. The 506 keV transition to the 5- level is a dZ = 1 transition (A,/& = - 0.18) while the 401 keV transition to the 6- level may be dZ = 0 or 1 @,/A,, = 0.28, A, 2 0), establishing Z = 6 for the band head. The electron conversion coefficients for these transitions (table 2) establish Ml/E2 character, hence negative parity for the i852 keV level and its associated rotational band. The half-life of the 1852 keV band head is not well established, due to isomeric side feeding from the 2190 keV level (T+ = 2.8 ns). However, there is a “prompt” component evident in the TAC spectrum (with respect to the beam) for the 506 keV transition, enabling a limit of T+ 5 1 ns to be set. This short half-life is consistent with the decay of the Z = 7 1965 keV level, for which out-of-band decay (514 keV) is observed to the negative-parity yrast band, in competition with the collective inband decay (114 keV). The K = 6 assignment is based on Z = 6 for the band head. This band is identified only up to Z = 10, which is surprising consdering its low excitation energy. There may be an 11 + 10 transition unresolved from the 193 keV, 4’ -+ 2’ g.s.b. transition, but it is difficult to establish experimentally. 3.5. THE K” = 7-

BAND

Another well-defined sequence of levels is that above the 2190 keV level, with both cascade and crossover transitions within the band. The 2733 + 2342 keV crossover transition is not established, but this may be due to its energy (391 keV) being unresolved from the 390 keV 6+ -+ 4+ g.s.b. transition. A sample coincidence spectrum (339 keV gate) is shown in fig. 3. The Z = 7 assignment for the band head is established from the AZ = 1 character of the 339 keV transition (A,/& = - 0.18) to the Z = 6, 1852 keV level. The Z = 5 possibility is discounted because of the strong population of the band; furthermore, branches are observed to the 6- and 5- members of the negative-parity yrast band, but not to the 4- member, supporting the Z = 7 assignment. The 2190 keV band head is assigned negative parity primarily on the basis of the Ml character of the 339 keV transition (see table 2) to the 6-, 1852 keV level. The levels above the 2190 keV level are placed in a dZ = 1 sequence on the basis of the observed cascade and crossover transitions. The angular distribution coefficients for the cascade transitions (A, N 0.25) do not, in themsleves, establish the spin sequence because, in general, stretched quadrupole assignments would also be possible. We note, however, that A, > 0 for the 152 keV transition, supporting its

76

P. M. Walker et al. / Rotational

bands

AI = 1 assignment, and the presence of the crossover transitions (335 keV and 435

keV) removes ambiguities. The TAC spectrum for the 339 keV transition (see fig. 4) yields a half-life of 2.8kO.3 ns for the I = 7, 2190 keV level, establishing this level as the band head and suggesting the K = 7 assignment. 3.6. OTHER

SIDE BANDS

The preceding sections have described rotational bands that are well defined, in the sense that all the observed levels are connected by in-band transitions. Numerous other levels are established in r7’Yb from the present work. Using the spin-parity assignments, and the expectation that in a well-deformed nucleus rotational bands should follow (at least for I 5 14) a smooth E versus 1(1+ 1) behaviour, these levels can also be classified into rotational bands. This classification is inevitably more tentative, especially since many of the levels are only weakly populated. 3.6.1. The probable K” = I- side band. Odd-spin levels with 5 5 Z 5 15 (lig. 6) can be placed in a negative-parity side band, from the present work. Following 17’Lu decay, Camp and Bernthal “) identify I” = 1 -, 3- levels at 1365, 1397 keV respectively; these can reasonably be placed in the same band. The 3- level is strongly excited by inelastic deuteron scattering lo) (with a B(E3) - 4 s.p.u.) suggesting that this is an octupole-vibrational band. The branching ratio rl) from the l- level to the g.s.b. indicates a K = 0 assignment. However, we prefer a tentative K = 1 assignment, because a K” = l- band is known “) at low energy in 17*Yb and it seems likely that we have observed the equivalent band in 170Yb. This is fuither discussed in subsect. 4.5. We note here that a K = 1 assignment is not inconsistent with the branching ratio data, since a few percent K = 0 admixture would lead to dominating El, AK = 0 transition strength. Our failure to find even-spin band members may simply be a consequence of their unfavoured energies, leading to insufficiently strong population. 3.6.2. Theprobable K” = O+ side band. Even-spin levels with 4 5 I 5 12, observed in the present work, are placed in a K” = Of band (fig. 7). The I = 0, 2 members (at 1069, 1139 keV) are known from other work ‘OP1*). Although the present data do not show significant EO components in the AZ = 0 transitions to the g.s.b., we have some confidence in the assignment of the levels to the same K = 0 band, based on a comparison with the data for 17*Yb. In each case the collectivity of the K = 0 excitation is small ‘*) (< 1 s.p.u.) and the higher spin members decay by Al = 0, Ml transitions to the g.s.b. 3.6.3. The probable K” = 2+ side band. Levels observed in the present work with 4 5 I 5 14 are placed in a K” = 2+ band based on the Z = 2, 1146 level (fig. 7). The I = 2, 3, 4 members are known from other work 1o-12). We observe odd-spin band members up to I = 7 (and tentatively I = 9). This band is apparently based l OSl’) on the y-vibrational mode.

P. M. Walker

et al. ! ~5t5t~o~ol bands

77

3.6.4. Remaining levels. The remaining levels that can unambiguously be placed in 17’Yb appear to form a positive-parity band above the 1409 keV level, with 4 s I 5 10 (fig. 7). There are no candidates for lower-spin band members. Since the detailed ’ “Lu decay study of Camp and Bernthal ’ ‘) might be expected to provide candidates for I = 0, 1 or 2 levels, if they exist, we suggest that K = 3 or 4 for this band. Probably this is a K = 3 band, equivalent to the low-lying K” = 3+ band known ‘) in 17’Yb. 3.7. UNPLACED

TRANSITIONS

Most of the transitions not assigned to 17’Yb, following the (a, 2n) and (cx,4n) reactions, were placed in other nuclei. However, several transitions could not be placed, and remain candidates for being in the “‘Yb level scheme. In particular, an apparent sequence of transitions at 220.2, 303.0, 381 .O and 450 keV is unplaced. Also, an isomeric transition at 198.3 keV (?” = 132+_17 ns) is distinct from the 197 keV 19F contaminant, and could be in “*Yb. Possible transitions above the isomer are at 217,257 and 294 keV. The 198 keV transition could feed into the g.s.b_ through an 815.4 keV transition, but this is very weak, and poorly resolved from the assigned 8 17.1 keV transition. 4. Discussion 4. I. POSITIVE-PARITY

SIDE BANDS:

S-BAND

CANDIDATES

The positive-parity side bands identified in 17’Yb are illustrated in fig. 7. Due to the lack of connecting in-band transitions, these bands are only tentatively assigned, as outlined in sect. 3. We restrict our discussion to the excited K” = O+ band. The excited K” = Of band is the positive-parity ypare band and has a rapidly rising moment of inertia: for the 2+ + O+ and 12+ + 10’ transitions, 2$/h’ = 87 and 118 MeV- I, respectively ; this compares with yrast band values, for the 2’ -+ 0’ ) 12+ + 10’ and 20 ’ + 18+ transitions, of 71, 84 and 124 MeV-l, respectively. A reasonable extrapolation of the excited K” = Of band gives a crossing with the g.s.b. at about I = 18, the spin at which backbending is observed experimentally. We speculate that the observed levels in the excited K” = O+ band could be the low-spin members of an (i+)” Stockholm band (or S-band) that crosses the g.s.b. and causes backbending in the yrast states. We note that a remarkably similar situation exists *) in 17’Yb , inasmuch as extrapolations of the g.s.b. and the first excited K” = O+ band suggest a crossing at about f = 20. The present evidence is very limited. However, “lOYb is a suitable candidate for a renewed study: using the 16’Gd(14C, 4n)17’Yb reaction, it might be possible to identify the yrare states in the crossing region. Further aspects of the backbending in 17’Yb are considered in subsect. 4.6.

78

P. M. Walker et al. / Rotational

4.2. CORIOLIS

COUPLING

AND

ITS CONSEQUENCES

bands IN THE

K” = 4-

BAND

The negative-parity yrast band has unusual properties, in that its band head is isomeric (T+ = 370 ns) characteristic of deformation coupling, but the odd-spin band members have prompt branches to the g.s.b., characteristic of rotation alignment. These features have been discussed qualitatively 7), and can be understood as a consequence of Coriolis effects on the i, neutron that contributes to the Nilsson configuration for the band. In this section, the configuration assignment is considered first, followed by the results of a two-quasiparticle-plus-rotor band-mixing calculation. The latter gives a more quantitative basis to the discussion in ref. ‘). 4.2.1. Quasiparticle assignment. Information on the quasiparticle structure of the band may be obtained from an analysis of the mixing ratios for AZ = 1 transitions within the band, using the Nilsson and rotational models. Mixing ratios, 6, may be calculated from both y-ray angular distributions and branching ratios. For the latter:

ii2 4=1+62=

2K2(2Z - 1)

T(E2,Z -+ Z-2) T(Ml+E2,Z+Z-1)’

(Z+l)(Z-l+K)(Z-1-K)

where the quadrupole admixture, q = T(E2, Z + I- l)/T(Ml +E2, Z + I- l), and T represents the y-ray transition intensity; the sign of 6 is not determined, and the value depends on K. Using the y-ray angular distributions, the sign of 6 is determined ’ 3, and the value is independent of K; however, the attenuation of the nuclear orientation is needed. The attenuation parameters, a, are expected to increase monotonically with spin, tending to unity. The present data for a2 = AyP’/Ay are illustrated in fig. 8, using the stretched E2 transitions in the positive and negativeparity yrast bands. Evidently the bands have similar behaviour, and the shaded region, which follows essentially the g.s.b. values, is taken to represent the K = 4band also. These a, values and the corresponding &values are given in table 3 for the low-lying members of the K = 4- band, together with the values of gK-gR according to the rotational model formula gK-gR

= 0.93

E1+1-1 e,.

(126

Here the g’s represent gyromagnetic ratios, and the quadrupole moment Q, = 7.6 b [ref. ‘“)I. The constancy of the gK-gR values lends support to the placement of the levels in a single rotational band. Further, since gR z 0.3, it follows that gK x 0, corresponding [ in the Nilsson model, ref. 15)] to a two-quasi-neutron singlet configuration (i.e. a neutron configuration in which the intrinsic spin magnetic moments cancel). Considering also the reasonable assumption of K = 4 for the band, on account of the isomeric Z = 4 band head, the band is assigned the {$‘[633],,

P. M. Waker et al. 1 ~otat~~~

0.5’

4

6

79

bands

10

12

Fig. 8. Attenuation coefficient of the nuclear orientation, Q = Ay@/A’;““, as a function of spin, for stretched quadrupole transitions in “OYb. The shaded area represents the estimated values (+ cr) for all bands.

+-[521],),Tao-quasineutron singlet co~g~ation, since this is the only low-lying Nilsson con~guration (see fig. 9) that satisfies the experimental criteria. A problem arises when one considers the 161values from the branching ratios TABLE3 Mixing ratios and g-factors in the negativeparity Initial spin

g2

7

yrast band of “‘Yb

64

IO

ang. dist.

branching -0.30*0.05

5

87

0.67+ 0.03

-0.42+0.07 -1.65+0.20

6

I05

0.75kO.03

-0.41+ 0.05 -1.75+0.15

0.64+0.09

-0.3110.04

7

122

0.81 t-o.03

-0.37*0.07 -1.95kO.25

0.61 +O.lO

-0.34+0.06

8

143

0.85 rfr0.03

-0.517tO.06 - 150~0.20

0.59+0.04

-0.25t0.03

‘) Attenuation coefficients from fig. 8. ‘) The A, coefficient is insufficiently accurate to distinguish the two possibilities for each I, but the lower magnitude is favoured by the branching ratio result; also see text. ‘) Assumes pure K = 4. d, From angular distribution &values.

80

P. M. Waiker et al. J Rotational bands -I

1/2+[660] 43y

! ;42-

i

54

I

53

[541]

‘I;[6241

-

%J514]

-

5Gf5f2]

-

‘/;[521]

-

“f; [402] “,; [514]

-

ii ‘/2’[404] 6 & 5

(70)

ar g41-

-

‘/2+[411]

/

(100)

52

$;[633]

cf

40-

5/;[523] 3,; [4ff]

-

51

“,: [642]‘9J505]

5$[413] 5/;[532]

Protons

3/G[521] “4 1651 ] -

50

Neutrons

Fig. 9. Single proton and single neutron energies for *‘OYb, calculated in the Nilsson model with Ed = 0.264, sq = 0.025, KP = 0.0634, yP = 0.603, k;, = 0.0637, K, = 0.414. The approximate region of the Fermi surface is indicated for protons (70) and neutrons (100).

(see table 3) since these differ significantly from the angular distribution results. This could be taken to imply lower K for the band; for example, if K = 3 is used for the I = 6 level, then ISI = 0.32, compared with ISI = 0.64 when K = 4, and 161= 0.41 from the angular distribution result. However, it should be noted that the proposed quasiparticle contiguration includes the 3+[633] neutron from the i, orbitals, and the strong Coriohs effects on this particle lead to mixing with lower K configurations. Hence, we cannot assume good K for the band. Nevertheless, the {f+E6W,, 5C5211,),- configuration may still dominate the band structure, and the constancy of the gK- g, values is still significant because the principal admixed configurations are also of the two-quasineutron singlet type. Further discussion of these features is delayed until the results of a Coriolis band-mixing calculation have been described. 4.2.2. ~u~d-~i~i~g de~cr~pt~~~of the negative-parity yrast states. Since the quasiparticle configuration proposed above involves an i, neutron, and these high-j neutrons are known 16) to be strongly affected by the Coriolis force, a two-quasi-

P. M. Walker et al.

I Rotational bands

81

particle-plus-rotor Coriolis coupling calculation has been carried out in order to gain a more detailed understanding of the band properties. Relevant aspects of the calculation have been described recently a). Briefly, the band con~g~ation is taken to be, in this case, composed of a +-[521-j quasineutron (assigned above) and an i, neutron (a = a, 3, . . . y) with BK = 1 band mixing. A variable moment-of-inertia parameter is used such that Elevel = EzqP +(A+B(l(l+ l)-K2>)(Z(I+ l)- K’), with A = 14.05 keV from the 2+ + Of g.s.b. transition energy, and B = - 6 eV which is taken to be half the g.s.b. value to allow for the extra blocking in the excited band. The value of d (half the pairing energy) is treated as a parameter. Initially, a constant reduction (01x) of all off-diagonal matrix elements was employed, but the level spacings could only be reproduced qualitatively (dashed line in fig. 10). Good agreement with experiment was obtained

----

6”

. . ._

u-7

* f

,>-q-._

-.-.-

c? f(,=o(K2=o.7 ocK,=o.9 i tiK2=0.65 o(K,=cxK2=o.6

l

Fig. 10. Moment-of-inertia parameter, @/2X = (El-El_ 421 as a function of spin for side bands in I’OYb. In the top section, the experimental values (dots) are compared with two-q~si~~icie-Pius-rotor calculations (lines) for various attenuations (cQ of the Coriolis mixing matrix elements. These attentuations, and the values of other parameters, are discussed in the text. In the bottom section, for the K = (3) band, only experimental values are shown.

“)

“1

- 0.003 -0.00s - 0.009 -0.012 -0.015 -0.019

2200 2349 2531 2737 2965 3211

I

0.000 0.001 0.001 0.002 0.003 0.004

0.006 0.014 0.027 0.033 0.062

*42

0.000 0.006 0.000 0.023 0.000 0.053 0.000 0.098 0.000 0.150 0.000 0.200

itO

0.023 0.036 0.048 0.060 0.072 0.083

0.065 0.111 0.154 0.194 0.236

334

0.031 0.056 0.085 0.177 0.140 0.182 0.192 0.248 0.236 0.307 0.272 0.354

$:2

- 0.000 -0.000 --o.ooo -0.000 -0.001 -0.001

-0.003 - 0.004 -0.012 -0.002 -- 0.032

$31

-0.006 -0.015 -0.023 - 0.041 - 0.048 - 0.080 - 0.076 -0.127 -0.104 -0.176 -0.127 -0.219

4fl

-0.165 -0.210 - 0.244 -0.271 - 0.294 -0.315

- 0.240 -0.326 - 0.385 -0.428 -0.465

535

-0.173 - 0.248 - 0.304 -0.351 -0.385 - 0.420 -0.439 - 0.465 - 0.473 - 0.489 -0.495 - 0.494

543

0.000 0.000 0.000 0.000 0.0~ 0.000

0.000 - 0.004 0.000 -0.030 0.000

-550

0.024 0.047 0.070 0.097 0.120 0.150 0.166 0.197 0.205 0.235 0.235 0.260

3:2

G&K

0.986 0.915 0.881 0.850 0.845 0.833

0.968 0.919 0.875 0.833 0.795

%#6

0.978 0.947 0.914 0.877 0.843 0.798 0.715 0.714 0.714 0.628 0.662 0.549

$44

0.000 0.000 0.000 0.000 0.~ 0.000

0.000 0.016 0.000 0.066 0.000

$31

-0.075 -0.114 -0.147 -0.175 -0.200 -0.218 -0.237 - 0.242 -0.261 - 0.248 -0.274 - 0.242

3$3 ei5

0.000 - 0.343 -0.402 - 0.427 -0.439 - 0.444

0.000 -0.186 -0.239 - 0.266 -0.279

fQ7

0.000 0.000 0.000 0.000 0.000 0.000

0.000 - 0.005 0.000 - 0.024 0.000

342

-0.086 -0.061 -0.037 -0.012 0.011 0.030 0.049 0.060 0.076 0.076 0.095 0.083

q:4

representation

0.000 -0.140 -0.192 -0.225 -0.247 -0.257 - 0.269 - 0.259 -0.274 -0.242 -0.270 -0.217

“) Q, for an i13,2 neutron; 0, for a 4-[521] neutron; ~~~ = 0.8, ma2 = 0.6; IC:,,, 1,2 KI < 0.01; A = 0.72 MeV. b, Q, for an i,,,, neutron; Q,for a4-[512] neutron; cxK1= 0.9, aKZ = 0.65; (C:,,, 5,2 J < 0.01; A = 0.72 MeV. ‘) 0, for an h 11,2proton; Q2,for a 3”[404] proton; gKl = aKZ = 0.6; A = 0.97MeV.

8 9 10 11 12

-0.017 -0.035 - 0.056 - 0.077 -0.109

tz?3

- 0.005 -0.013 -0.019 - 0.038 - 0.038 - 0.077 - 0.059 -0.130 - 0.080 -0.188 - 0.099 -0.243

1830 1943 2079 2236 2413

1264 1351 1457 1580 1724 1880 2065 2247 2418 2614 2960 3157

4 5 6 I 8 9 10 11 12 13 14 15

it1

6 7 8 9 10

Energy WV)

I

Ci coefficients for negative-parity bands in 17’Yb calculated in a two-quasiparticle-plus-rotor

TABLE4

0.000 0.000 0.023 0.034 0.042 0.048

0.000 0.000 0.024 0.037 0.047

938

0.000 0.000 0.014 0.023 0.032 0.038 0.045 0.047 0.054 0.050 0.060 0.049

Y$6

0.000 0.000 0.000 0.000 0.0~ 0.000

0.000 0.001 0.000 0.005 0.000

IL33

0.000 0.011 0.013 0.012 0.009 0.006 0.002 -0.002 -0.006 -0.009 -0.013 -0.013

945

F $. g ; 9 @

p F $ & 2 2 F --

w

P. M. Walker et al. / Rotational

bands

83

when matrix elements connecting the i, orbital nearest the Fermi surface (s2 = 2) were reduced (c+J more than other matrix elements (o(&. The results of the calculations are compared with experiment in fig. 10, through the variation of the level spacings with spin. The experimental irregularities can be well reproduced. The energies and matrix elements for the better fit are compiled in table 4. It should be noted that the high moment of inertia (h2/2~ z 9 keV) is reproduced, even though the lower g.s.b. value (h2/2$ = 14 keV) was used in the unmixed bands. We may now reconsider the &value calculation using y-ray branching ratios. For the mixed band

BW, Z + Z’) = &e’@,

C CI,Ci

((zZQOIZ'K)I~,

K

in the usual notation; hence, we find for Z = 8 (for example) 16) = 0.55 +0.04 compared with the pure K = 4 value of 16) = 0.59 kO.04. This brings the &value closer to the angular distribution result of 6 = -0.51 kO.06. We next address the problem of the out-of-band transitions to the g.s.b. There appears to be an anomalous situation, in that the band head has a 370 ns half-life, while the odd-spin members decay promptly to the g.s.b. If it is assumed that the decay is by El, AK = 0 or 1 transitions only, then the relative transition probabilities to the K = 0 g.s.b. can be calculated using the K = 0 and 1 components from the wave functions given in table 4. We further assume constructive interference between different components from the same state, and that the AK = 0 part of the transition is a factor of 100 stronger than the AK = 1 part. The latter assumption is based on the results *) for the lowest K = 1 band in 17’Yb, where decays to the g.s.b. are observed from both odd and even spin excited members. We note that, in the particles-plus-rotor model used here, the even-spin members of the negativeparity yrast band have no K = 0 component. Using, then, the experimental value of T+ = 370 ns for the 981 keV 4- + 4+ transition from the band head, the 1000 keV 7- + 6+ transition, for example, is predicted to have a partial half-life of about 0.4 ns (implying T+ rz 0.2 ns for the 1573 keV, 7- level). Therefore, the out-of-band 7- + 6+ El transition is able to compete with the collective in-band transitions, a result that is consistent with its experimental observation. The out-of-band transitions from the even-spin members, however, are predicted to have partial half-lives of many nanoseconds (like the 4band head) so that the fact that they are not identified experimentally is not surprising. In the corresponding band of 168Er which also has an isomeric Z = 4 band head, the 6- --f 6+ transition is observed as ‘a weak branch: see subsect. 4.7. In summary, a two-quasiparticle-plus-rotor description of the negative-parity yrast band in ’ 70Yb is able to account for two important features : the level spacings in the band (i.e. the staggering in AEj2Z shown in fig. 10, as well as the high moment of inertia); and the prompt out-of-band decay, which is observed from the oddspin states but not the even-spin states. These features arise from the mixing between

84

P. M. Walker et al. / Rotational

bands

configurations that involve an i ‘1neutron. The dominant configuration for the band is the {3’[633],, +[521],},- two-quasineutron singlet. Within the model, the +-[521] neutron is understood to be deformation coupled (i.e. strongly coupled to the quadrupole deformation) while the i, neutron becomes rotation aligned at high spin. The band may be described as being “semi-aligned” [see also ref. *)I, giving experimental properties that are at first sight contradictory but can be well described theoretically. 4.3. ROTATION

ALIGNMENT

IN THE K” = 6-

BAND

The band based on the Z = 6, 1852 keV level is not found to have an isomeric band head. However, the out-of-band branching is weak except from the 1852 keV level, so that this may be reasonably interpreted as being the band head, with K= 6. The band has significant features that are similar to the negative-parity yrast band. These include a high moment of inertia (24/h’ x 115 MeV- I) and negative A, angular distribution coefficients for in-band Z + I- 1 transitions. The latter may be taken to imply a two-quasineutron structure and we assign the ($‘[633],, 2-[512],},configuration to the band. This is the only low-lying Nilsson configuration (see fig. 9) consistent with the experimental criteria. The high moment of inertia is interpreted as arising from the partial rotation alignment of the $‘[633], i, neutron, similar to the, alignment in the K = 4- band (subsect. 4.2). This is another “semi-aligned” side band. The level energies may be calculated in the particles-plus-rotor model (see subsect. 4.2) leading to the results shown in fig. 10 and table 4. Although the agreement is only qualitative when the parameters are exactly the same as for the K = 4- band, modest adjustment of the Coriolis attenuation parameters leads to the good agreement shown by the dotted line in the figure. The band does not show the oscillations in the value of AE/2Z that are evident in the K = 4- band. This is consistent with the calculation, and results from the different mixing with K = O- bands. The K = 6- band in 17’Yb may be compared with the better studied *) K = 6- band in 17’Yb . Both bands have the same quasiparticle configuration, and very similar properties. 4.4. INTERMEDIATE

ALIGNMENT

IN THE K” = 7-

BAND

The Z = 7 level at 2190 keV has a half-life of 2.8 ns, and is reasonably interpreted as a K = 7 band head. The Z --f I- 1 in-band transitions have large positive A, angular distribution coefficients (A,/A, N 0.25). Using the most well defined transition (152 keV, 8 + 7) we find gK-gR w 0.5 (cf. subsect. 4.2), indicating the dominance of a two-quasiproton singlet configuration (gk fi: 1). Considering the available low-lying Nilsson configurations (fig. 9) the {3-[523],, $‘[404],},assignment is

P. M. Walker et al. / Rotational bands

85

made. Again a unique-parity high-j nucleon is involved. In this case it is an h, proton, and Coriolis effects might be expected in this band also. The Coriolis effects depend on the difference betweenj2 and GZ2,so that for an 52 = 3, h, proton (j” - G2 = 18) the effects should be significantly less than for an s2 = 3, i, neutron (j2--a2 = 30). One manifestation of Cpriolis effects is band compression, i.e. a high apparent moment of inertia, and the expected differences are indeed evident in the moments of inertia: for the K = 4- band, 21/fi2 M 115 MeV- ‘, reflecting the influence of an iii, neutron; for the K = 7- band, 22/h’ z 100 MeV-“, reflecting the influence. of an h, proton; while for the g.s.b., 24/h2 % 75 MeV- ’ at comparable rotation frequencies. Equivalently, these differences are evident in the value of i,, the intrinsic angular momentum that is aligned 17) with the rotation. At ho = 0.27 MeV i, = 422in the K = 4- band, and i, = 21Fz in the K = 70 band. It can be seen that the alignment in the two-quasiproton band is at an intermediate value. The results of a two-quasiparticle-plus-rotor calculation for the ($-[523-j,, S+[404],},_ configuration, where the $-[523] proton is allowed to mix with the other hY proton orbitals, are given in fig. 10 and table 4. A good description of the K = 7 band is seen to be possible, supporting the proposed assignment. Since we are here dealing with proton con~~ations, some of the parameters of the calculation are necessarily different from the previous calculations for neutrons. For the K = 7 band we use A = 0.97 MeV (to approximately match the band-head energy) and B = -0.010 keV (i.e. the g.s.b. value, because the i, orbitals are no longer blocked). The level spacings (in particular the S- -+ 7- energy) are a sensitive function of the Fermi surface; good agreement with experiment could not be found for the expected position of the Fermi surface, half way between the ++[41 l] and $+[404] orbitals, and the results displayed are for the Fermi surface 150 keV below the ++[411] orbital. The Fermi surface is not very close to any of the h, orbitals, and the attenuation of the Coriolis matrix elements was chosen to be the same (aK1 = 01x2 = 0.6) for all elements. 4.5. POSSIBLE AK = 2 MIXING BETWEEN THE K = (3) BAND AND THE K = (1) BAND

The band assigned K = (3) in the level scheme (fig. 6) presents significant problems in its interpretation. Considering also the weak population of the band, the suggestions that follow must be considered to be tentative. First the K = (3) assignment is considered. Since levels down to I = 5 are observed, we can assume K 5 5. It has been noted in subsect. 3.4. that the failure to observe states in the band with I < 5 may be a consequence of unfavourable branching ratios, rather than a termination of the band. The A, coefficients for in-band f -+ I- 1 transitions are negative, implying the dominance of two-quasineutron structure. Indeed, the A, magnitudes are rather small compared with the I + 1- 1 transitions in the K = 4- band, implying larger fgK- gRj, hence a two-quasi-

86

P. M. Walker et al. / Rotational

bands

neutron triplet configuration, but the uncertainties are too great to come to a definite conclusion. The only negative-parity two-quasineutron configurations expected at low energy involve the 5+[633], i, neutron and either of the +-[521] and 3-[512] neutrons (see fig. 9), i.e. the only ones with K 5 5 are the {:‘[633],, +-[521]n}3-,4and the {4’[633],, &-[512],}1- configurations. The K = 4- configuration is already accounted for in the band based on the isomeric 1259 keV level, and the K = l- configuration is unlikely because in 17’Yb the equivalent band *) is very strongly perturbed. Furthermore, we already have candidates for the K = lodd-spin band members (fig. 6). Therefore, the ($‘[633],, +[521]n}3- assignment is preferred, and is in fact a triplet configuration. Next, the level spacings in the band are considered. The average moment of inertia is high (29/h’ z 110 MeV- l), which is consistent with the involvement of an i, neutron in the quasiparticle configuration (see previous subsections). However, the moment-of-inertia parameter calculated from the dl = 1 spacings (Ft2/2j = dE/21) has anomalous behaviour, illustrated in fig. 10 (bottom section). Two features are important: first, the phase of the oscillations is opposite to that in the K = 4band, i.e. the even spins are favoured energetically, rather than the odd spins; second, the oscillations decrease with spin, whereas in the K = 4- band they increase. Within the framework of the particles-plus-rotor calculations discussed in subsect. 4.2, these features cannot be reproduced. A plausible explanation can be offered if AK = 2 mixing is permitted between the {$‘[633],, +-[521],},and the {$‘[633],, 2-[512],},configurations. Oddspin states based on the latter configuration are tenetatively identified in “‘Yb. Also, their energies may be estimated from the equivalent band known 8, in 172Yb and the position relative to the band based on the {$‘[633],, $-[512],}6configuration, which has been located in both 17’Yb (subsect. 4.3) and 172Yb [ref. 8)]. Since these K = 1 and K = 6 configurations involve the same neutron orbitals. but in opposite couplings, their relative energies should be similar in the two isotopes. In 172Yb the K = l- states of even spin (Z) are almost degenerate with those of odd spin ;1+ 1). In ’ 70Yb the K = 1 - even spin (I) states are estimated to lie above the K = (3) even spin (I) states; whereas the odd spin (1+1) states lie below the K = (3) odd spin (I+ 1) states, consistent with their experimental energies. Thus, if AK = 2 mixing is permitted between the two bands, the K = (3) even-spin states would be shifted down in energy, while the odd-spin states would be shifted up. This corresponds to the experimental observation that the even-spin K = (3) states are favoured energetically. The behaviour of the experimental K = (3) band (fig. 10) can be reproduced if the magnitude of the mixing matrix elements is about 20 keV at low spin and may increase with spin. A detailed tit has not been carried out because there are too many uncertainties for such a fit to be meaningful.

P. M. Walker et al: / Rotational bands 4.6. BACKBENDING AND THE RELATIONSHIP NEGATIVE-PARITY YRAST BANDS

BETWEEN

THE POSITIVE-PARITY

87 AND

It is well established that ba~kbending in the deformed rare-earth region is strongly influenced by the i+, neutrons 16), and the fact that the degree of backbending is not a smooth function of neutron number is now more clearly understood, since it is known l*) that the mixing between the g.s.b. and the crossing band (the S-band) is an oscillating function of the neutron number. The observation that no N = 98 nuclei show ba~kbending, while N = 96 and N = 100 nuclei do, is seen to be a consequence of the stronger mixing for N = 98. However, the N = 100 nuclei themselves show significant differences. The yrast bands in lT4W and 17’Yb [refs. l, 2)] backbend, while in the intermediate isotone, 172Hf [refs. 3*4)] the yrast band does not backbend. The present work confirms the back~nding in ’ 70Yb. The difference between ’ 74W and ’ “Hf has been understood in a simple empirical model ‘?I‘), in which the properties of the (i?)>”S-band are derived from the negativeparity yrast band, whose configuration was presumed to involve one i,: neutron. Now that the negative-parity yrast band is also known in l”Yb, the method may be extended to this nucleus. The even-spin S-band is constructed from the odd-spin negative-parity states in the following ’ 35, manner. Observed states with spin and excitation energy I-, E in the negative-parity band become postulated states with (I+ l)+, ES-E in the Sband. Thus the level spacings remain the same (giving the S-band a higher moment of inertia) but the whole S-band is shifted by E. The appropriate values of E were l, “) 75 keV in lT4W and 100 keV in 17’Hf. For 17’Yb E = 75 keV is again used. A twoband-mixing calculation was carried out to locate the mixed yrast states, with both 20 keV and 40 keV mixing matrix elements. A good description ‘a495, of the yrast bands in 174W and 172Hf was obtained with th_eweaker mixing. The present results for “‘Yb are shown in fig. I1 ; backbending is predicted in good agreement with ex~iment, though this time better agreement is obtained for stronger mixing. The stronger mixing is consistent with the results of Coulomb excitation of the yrast states up to I = 20 [ref. I’)]. This simple approach correctly predicts the occurrence (or otherwise) of backbending in these N = 100 isotones. The success comes about because we are able to use an observed band that involves a single i, neutron to predict the location of unobserved states based on an (iq)” con~guration. Previously 134* 5, the involvement of an i, neutron in the negative-parity yrast states had no direct experimental support. However, the present measurement of the AI = 1 angular distribution coefficients gives strong support to this supposition (see subsect. 4.2). We have speculated in subsect. 4.1 on the possible observation of the low-spin members of the S-band in 170Yb.

P. hf. Walker et al. 1 Rotationalbands

88

I

I

3

0.06

0.08 ii*w*

0.10

&leVF

Fig. 11. Moment of inertia, 2X/a/A’= (41-2)/(&-E,_,), as a function of rotation frequency hw = j((E,-E,_,), for bands in 17’Yb. The experimental yrast band (0) is compared with that calculated with 20 keV ( x ) and 40 keV (+) mixing between the extrapolated g.s.b. (dashed line) and the postulated S-band (0).

4.7. COMPARISON

BETWEEN NEGATIVE-PARITY

YRAST BANDS IN N = 100 ISOTONES

It has been seen in the previous subsection that the location of the negativeparity yrast states is linked with the position of the positive-parity yrast states, which show significant differences in behaviour. A comparison between the negativeparity yrast states in the N = 100 isotones is itself worthwhile. The contrast between these bands is most strikingly shown through the I -+ I- 1 energy level differences, in fig. 12 (left section) : the oscillations (or degrees of decoupling) are much stronger in the heavier isotones. Only limited regions of spin are included, for the sake of clarity. Since the neutron Fermi level (N = 100) may be presumed to be the same for all these isotones, the larger ,oscillations, which reflect greater degrees of Coriolis coupling, probably arise from either smaller moments of inertia or, in a different sense, from smaller quadrupole (EJ or larger hexadecapole (Q) deformations. A smaller moment of inertia gives larger Coriolis coupling matrix elements, while smaller Ed or larger Ed values lead to compression of the i, orbitals, and hence to greater Coriolis mixing between them. These features may be incorporated into a two-quasiparticle-plus-rotor description of the negative-parity yrast states (see subsect. 4.2). Deformation parameters (Ed and EJ are taken from refs. 20,21), and moment-of-inertia parameters are taken from the g.s.b. values (A = &+, B z +(g.s.b. value). These are listed in table 5. Other parameters are kept the same as for 17’Yb.

89

P. M. Walker et al. / Rotational bands

N=lOO

N=lOl

Calc.

Expt.

xw o HF .

9

I lo

Yb

I

I

,I ,

8

I

11.

12

9

10

11

I ‘I I 12

I?/2

, 191’2

/ 2112

I 231’2

I/t,

Fig. 12. Moment-of-inertia parameter, h2/29 = (E, - _I?,_ ,)/21 as a function of spin for W ( x ), Hf (0) and Yb (0) isotones with N = 100 and 101. The experimental oscillations (over a limited spin range) in the N = 100 isotones (left section) are compared with those calculated in a two-quasiparticle-plus-rotor representation (middle section) and those found in the i,,,, bands of the N = 101 neighbours (right sectionl.

Results of the calculation (where no fitting has been done for 172Hf and 174W) are shown in fig. 12 (middle section). The qualitative observation that the heavier isotones have larger oscillations in A&‘21 is reproduced by the calculation, indicating a satisfactory inte~retation. There are, however, si~i~cant quanti~tive differences, which either may reflect the necessity of varying the parameters of the calculation TABLE5 Parameters used in two-quasiparticle-plus-rotor

I’OYb 17’Hf ‘74W

0.264 0.259 0.238

0.025 0.024 0.019

0.414 0.412 0.409

0.0637 0.0637 0.0637

“) Refs. ‘“,‘q. “) Off-diagonal matrix element reduction parameters; neutron; tlKl is for all other elements.

14.05 15.87 18.83

sz

calculations

-6 -9 -17

0.72 0.72 0.72

0.8 0.8 0.8

0.6 0.6 0.6

is for elements involving the $‘, iIS,*

P. M. Walker et al. / Rotational

90

bands

(in which case the physical significance of the variations becomes unclear) or else other quasiparticle configurations and/or octupole couplings may become significant in the higher-mass isotones. It is also interesting to compare the behaviour of the i, bands in the neighbouring odd-mass nuclei. This feature is again illustrated in fig. 12 (right section) showing the same qualitative agreement with the behaviour of the N = 100 nuclei, and indicating the significant influence of the i, neutrons in their negative-parity yrast bands. Other features of the N = 100 negative-parity yrast bands are compared in table 6. At moderately high rotational frequency (ho = 250 keV) the rotation-aligned angular momentum (i.e. the intrinsic contribution, i,) is about 4h, and varies little between isotones. The decay of the 4- levels, however, shows significant differences. Here data “) on 16*Er are included. The negative-parity yrast band in ‘@Er is only known (j) to 1 = 8, precluding it from the firevious discussion; but the partial y-ray half-life of 1.l ps for the 4- + 4+ transition may be compared with 370 ns for 17’Yb, about 1 ns [ref. ‘3)] for 17’Hf and less than about 20 ns [ref. ‘)I for 174W. The corresponding Weisskopf hindrance factors (Fw) are given in the table, and show decreasing hindrance for increasing neutron number, consistent with stronger Coriolis effects in the heavier isotones. Finally, the El hindrance factors for 11- -+ 1O+ transitions are compared in the table, showing remarkable similarity. It is the similarities noted above that are harder to explain than the differences. Stronger Coriolis effects might be expected to result in greater alignment and smaller hindrance factors in the heavier isotones. The similarities at high spin could be taken as an indication of a saturation of the Coriolis effects, but it is important to remember that the g.s.b. has been used as a K = 0 reference, and band-mixing effects in the g.s.b.‘s at high spin may be disturbing the comparison. As noted in subsect. 4.2 the negative-parity yrast band of 168Er has a weak 6- + 6+ branch ““) as well as an isomeric I = 4 band head. Assuming that the intrinsic quadrupole moment is the same as in the g.s.b., the 2+ + O+ half-life ““) TABLE 6 Comparison

Isotone

r6sEr ““Yb i7’Hf ‘,‘%W

‘)

between

negative-parity

yrast bands b

i.@) (hx

= 250 keV)

4.1 4.2 4.1

in N = 100 isotones

(4- :;+

)g.s.b.)

2.7 x IO9 1.6x lo9 N 6~10~ < lo8

Fw ‘1 (11- --f IO+ g.s.b.)

1.3 x lo4 1.0 x lo4 2.3 x lo4

‘) Data from refs. 1,3,6.22,2a), and present work. “) Hindrance factor calculated from electronically measured half-lives (assumes El multipolarity). “) Hmdrance factor calculated from branching ratios using B(E2, 2+ + O+) g.s.b. values from ref. “) and assuming Q, is the same in the two yrast bands. The ‘74W B(E2,2+ --t O+) is taken to be as for isaW. El multipolarity is assumed for the 11 - + lO+ branch.

P. M. Walker et al. / Rotational bands

91

may be used to calculate the expected 6- -+ 4- half-life. The partial 6- -+ 6+ half-life is thus found to be 80 ns, 18 times faster (allowing for transition energies) than the 4- -+ 4+ transition. In the two-quasiparticle-plus-rotor representation, the I = 6 level is calculated to have a R = 1 component 16 times larger than that of the I = 4 level, accounting well for the observed difference in transition rates. It should be noted that the negative-parity yrast band in 16*Er may contain a significant two-quasiproton component 26), but this does not affect the above result if the proton component is the same in the I = 4 and the 1= 6 levels, since we are concerned with relative values.

5. Conclusions Eight side bands have been identified up to high spin in “‘Yb. Five of these have negative parity, necessarily involving high-j unique-parity nucleons. The strong Coriolis dK = 1 mixing effects on these bands are described in a two-quasiparticleplus-rotor representation, giving generally good agreement with experiment. Evidence for dK = 2 mixing is found in one side band with K = (3). In these negative-parity side bands the high-j nucleon becomes rotation aligned, giving a high effective moment of inertia and an intrinsic contribution to the total nuclear angular momentum. The second nucleon remains deformation coupled, and the side bands are called ‘~semi-aligned’. The lowest positive-parity side band (K = 0) has a rapidly rising moment of inertia, and could cross the g.s.b. at about I = 18. This work has been supported in part by the US National Science Foundation under grant No. Phy 78-22696, and the Danish Natural Science Research Council.

References 1) G. D. Dracoulis,P. M. Walkerand A. Johnston,J. of Phys.64 (1978)713 2) A. J. Hartley, R. Chapman,G. D. Dracoulis,S. Flanagan,W. Gelletlyand J. N. MO,J. of Phys. A6 (1973) L60 3) P. M. Walker,G. D. Dracoulis,A. Johnstonand J. R. Leigh,Nucl. Phys.AZ93 (1977) 481 4) P. M. Walker,G. D. Dracoulisand A. Johnston,Phys. Rev. CZl(l980) 464 5) G. D. Dracoulis,P. M. Walkerand A. Johnston,J. of Phys. 63 (1977)L249 6) H. R. Koch, Z. Phys. 192(1966)142 7) P. M. Walker,S. R. Faber, W. H. Bentley,R. M. Ronn~gen, R. B. Firestoneand F. M. Bernthal., Phys. Lett. 86B (1979) 9 8) P. M. Walker,S. R. Faber, W. H. Bentley,R. M. Ronningenand R. B. Firestone,Nucl.Phys.A343 (1980)45 9) R. S. Hagerand E. C. Seltzer,Nucl. Data, A4 (1968)1 10) D. G. Burkeand B. Elbek,Mat. Fys. Medd.Dan. Vid. Selsk.36 (1967)No. 6 1040 11) D. C. Camp and F. M. Bernthal,Phys. Rev. C6 119721 12) L. L. Riedkger, E. G. Funk, J. w. Mihelich,G. s. &hilling,A. E. Rainisand R. N. Oehlberg,Phys. Rev. C20(1979)2170

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13) I$ der Mateosian and A. W. Sunyar, Atomic Data and Nucl. Data Tables, 13 (1974) 407

14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24)

25) 26)

K. E. G. Liibner, M. Vetter and V. Hiinig, Nucl. Data Tables, A7 (1970) 495 T. L. Khoo, J. C. Waddington and M. W. Johns, Can. J. Phys. 51(1973) 2307 F. S. Stephens, Rev. Mod. Phys. 47 (1975) 43 A. Bohr and B. R. Mottelson, J. Phys. Sot. Japan, 44 (1978) Suppl. 157 R. Bengtsson, I. Hamamoto and B. R. Mottelson, Phys. Lett. 73B (1978) 259; R. Bengtsson and S. Frauendorf, Nucl. Phys. A314 (1979) 27 D. Cline, Lecture Notes in Physics 92 (1979) 39 S. G. Nilsson, C. F. Tsang, A. Sobiczewski, Z. Szymanski, S. Wycech, C. Gustafson, L-L. Lamm, P. MBller and B. Nilsson, Nucl. Phys. A313 (1969) 1 C. Ekstr(im, H. Rubinsztein and P. Miiller, Phys. Ser. 14 (1976) 199 L. R. Greenwood, Nucl. Data Sheets, 11 (1974) 385 D. R. Haenni, Y. Gono, D. R. Zolnowski and T. T. Sugihara, Proc. Int. Conf. on nuclear structure, Tokyo, 1977 (Organising Committee, Tokyo) p. 413 W. F. Davidson, D. D. Warner, K. Schreckenbach. H. G. Barrier, J. SimiC, M. StojanoviC, M. BogdanoviC, S. Kiocki, W. Gelletly, R. F. Casten, G. B. Orr and M. L. Stelts, J. of Phys. G7 (1981) 455: and addendum, in press W. Andrejtscheff, K. D. Schilling and P. Manfrass, Atomic Data and Nucl. Data Tables, 16 (1975) 515 A. Furusawa, M. Kanazawa and S. Hayashibe, Phys. Rev. CZl(l980) 2575