Levels in 178Hf studied in the (n, γ) reaction

Nuclear Physics A171 (1971) 353-383;

@ North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

LEVELS IN 178Hf ~TUD~D IN THE (n, y) REACTION B. FGGELBERG and A. BACKLXN Institute of Physics> Uni~rsjty of Uppsa~ and The Swedish Research Council’s L&oratory, Studsvik, Sweden Received 22 February 1971 (Revised 23 April 1971) Abstract: Conversion electrons and y-rays from the reaction 177Hf(n,~)178Hf have been studied by a double-focussing @-spectrometer and Ge(Li) detectors. A w coincidence measurement has also been performed. A level scheme has been constructed with rotational bands as follows: five members of a K = 2+ band based at 1174.80 keV, three (possibly five) members of a XT= 2- band at 1260.57 keV, two (possibly three) members of a K = 2- band at 1362.44 keV, three members of a 4+ band at 1513.88 keV, three members each of O+ bands at 1198.0 and 1433.9 keV. Levels at 1860.20 and 1353.7 keV may possibly be the first two members of a K = 3’ band and levels at 1818.6 and 1957.0 keV may be the 2’ and 4+ members of an additional O+ band. A level at 1403.21 keV, most probably with KZn = 22-, may indicate the presence of a third 2- band at low excitation energy. A KZn = OF level at 1443.5 keV and an (0)2+ level at 1561.91 keV implies the presence of two more O+ bands, although other members of these bands have not been detected in the present work. E

I

NUCLEAR REACTKIN “‘Hf(n,y) thermal neutrons. Z,,, yy-coin. 17sHf deduced ievels Z, n, K, ~m~tipol~ty.

Measured I$, Z,, E,,, Enriched target, ‘Ge(Li)

I

The nucieus “‘Hf has been the subject of several studies, but only sporadic information on the level structure has been obtained so far. In the B-decay of the I+ state of “‘Ta six positive-parity levels are populated, which have been assigned as the O+ and 2’ members of three K = 0” bands l -“). The decay of the high-spin isomer in “*Ta populates the two 8- states in 178Hf [ref. *)I, Further information on the rotational band based on the 1148 keV 8- state has been gained from a study of the decay of an isomer in “*Hf with K 2 1S produced by thermal neutron capture in 177Hf [ref. “)). The thermal neutron capture cross section of “‘Hf is relatively large, 370 b [ref. “)I, and the spin of the oapture state is 3 or 4. The (n, y) reaction can therefore be expected to yield rather complete information about the levels with spins up to about 5 units in the energy region below % 2 MeV. Attempts have been made by Smither “) and Groshev et d ‘) to analyze the complex y-ray spectra obtained from this reaction, but for lack of resolution and precision 353

354

B. FOGELBERG AND A. Ba&CKLIN

it was only possible to establish minor parts of the level scheme in a reliable way. The positions of some of the levels may be obtained from the primary Y-rays, which have measured by Namenson et al. “). Further information on primary y-rays have been reported after the completion of this work by Faler et al. “). The present work was undertaken in order to establish the existence and characteristics of as many as possible of the expected but so far not observed collective bands and two-particle bands in 17’Hf. For this, singles and coincidence y-ray spectra were studied in the energy region OS-2 MeV using Ge(Li) detectors. Furthermore, the corresponding conversion electron spectra were studied with a nJ2 P-spectrometer. A first paper reporting the establishment and characteristics of the y-vibrational band has been published earlier ’ “).

2.1. CONVERSION

ELECTRON MEASUREMENTS

The conversion electron spectrum resulting from neutron capture in ’ 77Hf was measured with a momentum resolution of about 0.2 % FWHM with the rrJ2 pspectrometer rl* r2) placed at a tangentia1 beam hole of the R2 reactor in Studsvik. A thermal neutron beam passes through the spectrometer, giving a ffux density of about IO* n/cm2 * s at the target position. Three targets of different thicknesses, ail of the voltage gradient type ’ 2, ’ 3), were used in the present measurements. The target thickness was chosen depending on the energy region so that electron energy losses in the target never contributed more than 20-30 % to the line width. The spectrum was measured in two parts, from 20 to 450 keV and from 840 to 1490 keV, since previous measurements ‘) have shown that no lines in the intermediate region are strong enough to be seen in the present internal conversion measurement. A special run was also made to record the K lines of two strong transitions at about 1650 keV. Energy calibration was carried out using the procedure described in ref. 14). In the low-energy region we used the Lrt, conversion line of the 100.107 [ref. ‘“)I keV transition in le2 W. A good agreement was found with the energies reported by Smither “) from a crystal diffraction measurement of the “‘Hf(n, Y)‘~~H~ y-ray spectrum. The accuracy of the latter measurement was better than in the present study of conversion electrons, and we have preferred, with a few exceptions, to use y-ray energies as well as intensities from ref. “) in conjunction with the present low-energy conversion electron intensities, as displayed in table 1. The norma~zation constant for the K-shell conversion coefficients was obtained as an average of the values for the E2 transitions in the ground state rotational band. Theoretical conversion coefficients were taken from the work of Hager and Seltzer r6). The high-energy ( > 840 keV) part of the conversion spectrum turned out to be highly complex, containing several unresolved structures. Some of these could be resolved

339.23

348.26

356.83 363.29 399.64 403.64 424.39 426.21 430.81 435.57 466.83 473.44 494.22 491.79

2.RO 6.60 1.10 1.65 1.30 75.00

20.

20.

K K K K K K

1x K LI’L2

5.93 1.90 1.04 0.20

c 0.14 c 0.14 ( 0.M 0.26 CO.16 so.25

K x

0.22 0.35 0.22

413.50 K 29.00 Lt 497.00 L2 460.00 13 19.00 K 14.00 K 3.00 Ll+L2 1.50 13 1.40 K 2.80 K 2.20 Ll+L* 1.10 L3 1.40 r. 1.40 K 100.00 K 34rSOLt+L2 ‘yg “,3 . 1.00 I 0.90 K 2.30 K 1.30 x 1.00 K 1.90 K 0.31 P (: 0.70 K < 0.80 K

30.

:3: 15. SD.

::: 40.

::: 60. 15. 20. 40. 15. 40.

20. 20.

:::

:o”: 60.

::: 60. 49. 40. 60.

15. 30.

0*4?5E-01 00

O.llnE 00 D.944E-01 c 0.470E-01 < 0.49bf-01 < 0.333f-01 O.Z74f-01 < 0.397E-01 < 0.362E-01 < 0.307f-01 0.619f-01 c 0.531E-at < 0,9fiSE-02

0.117E:

cm oo

00

< 0.149E < p”,-CJ; . 0.126f O.lOlf 1).470f-41

00 Of) 00 00 00 00 00

0.72if 0.283f b.32S.E D.240f 0.138E 0.192E 0.30665

DO a0

01 111

QX

00 00 (10

x

013798 0.62Of D.13lf

< 0.453E 0.5456

0.8SbE 0*29BE

OILPlE

EXPERIMENT

ALPHA

36.

54.

28. 25.

25.

25.

63. 28* 45. 22.

32. 94. 63. 7% 28. 43. 25,

54.. 36. 20.

45.

63. 45.

25,

9,

ERROR

0.119GOI D.lOtE-01 0.9148-02 0.894f-02 0.7978-02 0.79OP-02 D.YflE-02 O.YSt&-02 0.644&Z-02 O.b24E-02 O.%Bf-U2 0.559C-02

D.lZbE-01

0.134EQl

0.226&-01 O.l9bE-01 O.l7t%-Ul O.l62E-01 O.l57f-01 O.f40f-61

0*405E-01 0.3586-01 0.349f-01 0.2988-01 0.295E-01 0.265f-01 0.264E-01

0.471+X-01 0.469f-01 01419f-01

0.122E 0.114E

0.261E O.lblE

0.356E

El

00 00

00 00

PO

00 #O OB

00 00

00 00

0%

0.34QE-01 0.29OE-01 0‘26ff-01 G&.254+01 0.224E-01 0.222E-01 0.216E-01 O.ZlOE-01 Q.l78E-01. O.l?ZE-01 0.155E-01 G.i52E-Oi

0.372E-01

O.39BE-01

0.713E-01 D.608E-Cl 01522E-01 0.492E-01 0.475E-01 f).444E-01

5.136E 00 i).118E 00 0.1IS.E 00 0.969E-01 0.959E-01 O.B51E-01 0.84bE-01

0.160E 0.159E O.141E

o.43SE O.407E

0.875E 0.570E

O.lllE

E2

Cl0

00

00 00 00 00 00 00

a0 00 OO 00 00 00 00

00 DO 00

61 01

01 01

01

O.lOOE 00 O.@Z9f-01 0.741f-ut 0.723f-01 O.b34E-01 O.bZYE-01 o.LIOE-01 O.S93E-01 0.4998-01 0.4776-01 0.427E-01 O.C19f-01

0.107E

0.115f

O.ZO!% 0.17% O.lSlE 0.142E 0.137E 0.128E

0.3898 0.339E 0.33If 0.278E 0.27% 0.2458 0.24%

0.45BE 0.456E 0.403E

0.129E O.lZOE

0.297E Q.174E

0.42lE

fll

0.349E 0.2798 0.244f 0.23X 0.203E O.ibtE 0.194E o.188E O.ISZE 0.146E 0.1ZBE 0.12Sf

4.3tlE

0.409t:

0.824E 0.4BlE O.S67f 0.928E 0.50&E 0.46%

0.179E O.lP2E 0.147f O.llQE O.IIBE O.tOZE O.XOiE

0.220f O.ZlQF: 0.11X%

0.18EE 0.72OE

0.22X Q.llSE

0.3458

HZ

00 00 00 00 00 00 00 00 00 00 00 00

00

00

00 DO 00 DO 04 00

ox 01 OX 01 01 01 01

01 Ok 0%

0% 0%

02 02

02

HI

OR

RI 81 Ef El EL E7 El fl f1 #l El El

III

EE*H

f2 EZ ii!

m?

E,

rsa E? n:: F? I% YL

OP IW :w

1

Et Ofi Et El IJP El E7.MI E7M1 62+EI 1 E?

E?+Ml HI

eiJ*oi

El+ffZ EC+nl Hl EZ+ni

rnl f2

I!:? r,

EZrF’iff%I

El 0; El ELt<5OZ tit

fli E2+<50X

82

The conversion electron intensities have: been measured in the present work, while the y-ray intensities are taken from ref. 6). The transition energies are also to a large extent the ones ofref. 6), only the values for the 213.43, 325,53., 339.23, 383.29, 473.44 and 491.79 keV transitions have been determined in the present work.

:“o: 20. ZD. 20. 70. 16.

::.

20. .

:Oa: 20. 20. 2%

4.20 2.90 1.40 I. eo 2.50 6.40 2.10 2.30 3.10 2.50 1.90 15.10

0.050

273.09 289.4’1 306.37 313.32 317.37 325.53

::: 20. 20” 20.

20. 20.

0.050 a.100 a.090 0.090 0.170 0.140 5.300 0.140 0.404 0.205 u.100 C.OSD

0.030 0.030 0.040 0.100 0.100 0.055

256.56

1.25 2.10 1.65 5.70 5.60 3.10 3.70

20. 20. 20.

25.

6.020 c.azo 0.020 0.020 0.020 G.050 0.050

216.29 227.20 229.32 244.23 245.23 256.01

2.20 1.44 4SS.00

20. 20.

5.50

0.040 6.040 a.030

203.75 204.03 213.43

2. to 3.m

0.050

0.010 0.010

14C.tlb 144.49

20. 20.

1.32 2.8Q

20.

0.010 0.010

1a5.14 126.58

20.

199.05

12.50

0.005

KEV

KEV

93‘13

ERROR

LNERGV

Low-energy transitions observed in the 177Hf(n,y)17sHf reaction

E

0.200 0.300 G.ZOG 0.200 0.500 0.700 0.403 G.30@ 0.300

0.300 0.400 0.250 0.250 0.150 0.300

0.150 c.150

1230. la 1232.66 1241.64 1255.21. 1269.27 1276.40

1291.21 1310.04

G.150 C.6CO 0.2oo C.600 0.600 0.2co 0.600

1161.40 1110,bO 1175.20 1183.40 1190.39 1198.00 1205.60 1207.16 1221.05

1085.24 1102.90 3106.92 1126.35 1144.78 1156.76

0.500 G.150

1014.33 1017.94 1061.52

o.osn c.3oc C.jOG L.2CO 0.3co *.*60 0.400 0.3GG 0.3GO O.WO G.COC 6.300 0.300 G.4UO 0.300 0.400 0.300 0.300 Cd00 c.150 a.150

497.19 544.40 548.46 bC7.31 618.57 629.14 633.26 645.78 649.66 658.29 717.19 745.62 753.02 819.7b 844.12 BSQ.Ri 868.54 Be?.38 901.37 92l.?H 962.2C

0.2OG 0.250 0.400 0.300 0.250 0.200 0.250 0.400

KEY

KEV

969.86 965.39 993.16 1005.OG 3008.39 1015.11 1030.9R 1059.14

ERROR

ENERGY

17.00

:::

20. ZP. 40. 15. 15. 7. 20.

5. 25.

5.

36; 35. 5. 20.

30; 7.

25. 30. 30. 30. 7. 7.

:::

ii:

1::

40.

15;

40. 20. 25. 50.

30. 40. 25.

40;

t5. 20. 25. 3G. 40. 25. co.

10. 20.

‘I

ERRGR

K

K K tc u K K K K K K K

=c*.5a 6.70 13.60 4.90 10.90 8.50

SC.

4c.

:E: 3c.

SC. ZC. 5C. 2c. 3c.

40. It, 15. 15. 3c.

DE$WEC

2C. 5.

.

OBSERVED 7. 4c. If.

2C*

OBSERVED 5c. SC. 7. 7.

K KCOMP

I( K K

ND’;;i$RD;S . 12.20 57.00 27.80 22.2c 10.30

IP.CC 111.00

lS.5C 9.50 43.50

15.10 K <4.,LJ K NO ELECTRDNS

c4.50

c4.50 K 10.60 K C3.50 K 6.9C K <5.50 K NO ELECTRONS 6.30 K a.sc K 5G.CO K 55.50 K

:1*::

,” . t.90 lc

ELECTRCNS ELECTRONS ELECTRONS

NO

NP

4LPHA

K

,;‘:t;=“,: . O.l23E-02 0.245E-02 O.L97E-02 0*893E-03 0.230E-02 CC.2CZE-02 0.221E-02 0*99SE-03 0.4t8E-(12 0.1&E-02 O.l12E-02

D.,38E-02 >C.225E-CI 0.24-/E-02

0.165.S02 0.412E-02

0.454E-02 0.430E-02 0.410E-02 0.319E-02

0.434E-02 0.336E-02 O.Zb4E-02 <0.274E-C2 >C. lCCE-Cl

EXPERIHENT

N N

OBSERVED OHStRYED OBSERVE0 NOELECTROMS OBSERVED OBSERVEO NC ELECTRGNS oaswwm NU ELECTROQ5 ELECTRONS CBSCRVEU OBSERVED NC ELECTRONS ELECTRONS OBSERVE0 GRSERVED NG ELECTRONi NC ELECTRONS OBSERVED NC ELECTROWS CBSERVED OBSERVED NO ELECTRONS OBSERVED NO ELECTRONS OBSERVED NC ELfCTRONS NC ECECTROYS CBS ERYED NO ELECTRONS OBSERVED GBSE?tVED NC ELECTRJNS OBSERVED NO ELECTRONS NC NC

IYTENSITY

x

tNTENS1TV

15.10 2.50 5. TO 4.10 2.50 2.70 2.70 3.20 1.70 1.50 2.70 l.60 2.00 2.50 2.40 3.40 1.60 2.60 4.30 10.10 12.20 5.80 3.60 <1.5c 2.90 4.60 6.30 1.90 3.10 4.60 21.10 38.10 3.60 36.60 6.50 2.00 23.10 4.50 70.00 <1:.cc tco.ec COCP 17.40 2.50 cz.00 6s 22.00 N 52.00 3i.40 55.30 10.00 4.90 6.70 30.30 2.60 13.00

ECECTRil\I-

ERRCK

GArvA-

:t : 25. 34.

52.

50.

:::

7.

9. 45. 25. 20.

21.

10.

2: 10.

54.

40.

34.

:::

$

ERROR

0.462E-02 O.C54E-02 G.367E-02 0.3546-02 0.342E-02 0.331%-02 0.3241-02 0.32CE-02 O.PlZf-02 0.2636-02 0.243t-02 0.239f-02 0.202&Y-02 0.191E-02 O.l85E-02 0.181E-02 0.176f-02 0.1699-02 O.l62E-02 0.1498-02 O.lClE-02 O.l43E-02 O.l41E-02 O.l3EE-02 0.1371-02 O.l35E-G2 0.13lE-02 O.l25E-02 O.lZZE-(it O.lZlE-02 O.l2GE-02 O.l20E-02 O.llbf-02 O.l15E-02 0. LlZE-02 O.l09E-02 O.lO?E-02 O.l05E-02 O.l04E-02 O.l04E-02 O.lOZE-02 O.lOlE-02 O.lOOE-02 0.9928-03 0.989E-03 0,96&E-03 0.957E-03 0.954E-03 0.9348-03 0.9248-03 0.90bE-03 O.W?E-03 0.8?9E-03 0.8576-03

0.559E-02

El

THEORtTIthC

(i.22bE-02 0.2216-02 O.TtBL-02 0.2338-02 O.Z11E-02 O.ZO?E-02 O.ZOlE-02

G.Z3bE-02 O.I35E-02 0.228E-02 0.22?E-02

G. L%?E-01 O.l23E-01 0. LZlE-01 &962E-02 0.924E-02 0*890E-02 0.67?f-02 0.840E-02 0.829E-02 G.&06E-02 3.67OE-02 0.6171-02 0.60X-02 O.SO?E-02 ‘,.47?E-02 0.460E-02 0.4506-02 0.436E-02 0.4181-02 0.399E-02 0.3666-02 0.3608-02 0.349E-02 0.344E-02 0.336E-02 0.334E-02 0.329E-02 0.3191-02 0.303E-02 0.294E-02 0.293E-02 G.291E-02 G.289E-02 O.ZBOE-02 G.278E-02 0.269E-02 0.260E-02 G.255E-02 0.251E-02 0.249E-02 0.24lE-02 0.244E-02 0.24lE-02 0.238E-02

E2

CONVERSION

0.4328-02 0.420E-02 0.414E-02 0.403E-02 0.397E-02 0.38bE-02 0.3?3f-02

O.C63E-02 0.45bE-02 0.45X-02 0.437E-02 O.C34E-02

0*419f-01 0.332E-01 0.326E-01 O.ZSlE-31 0.2396-01 0.229E-01 0*225E-01 O*‘?lrlE-01 O.ZllE-01 0.204E-01 O.l64E-01 O.l49E-01 O.l45E-01 O.littk-01 O.IOPE-01 O.l04f-01 O.lOZE-01 0.980E-02 0.930E-02 o.aaoE-02 O.?92E-02 0.77bE-02 0.747E-02 0.732E-02 O.lllE-02 0.706E-02 O.b93E-02 0.648E-02 0.6261-02 0.6041-02 0.599%-02 0.5948-02 0.589E-02 0.567i-02 O,!ibZE-02 0.5388-02 0.51lE-02 0.504f-02 0.493E-02 0.490E-02 0.4BSE-02 0.477E-02 0.470E-02

nk HZ

0.109E-01 O.lO?E-01 O.l07E-01 0.103E-01 Q.lOZE-01 O.l02E-01 0.984E-02 0.969E-02 0.942E-02 O.Q28E-02 0.901E-02 O.%69E-02

O.l25E 00 0.9+A?E-01 O.Q41E-01 O.b99E-01 O.b63E-01 0.632E-01 0.620E-01 0*586E-01 0.576s01 0.555E-01 0.435E-01 0.39OE-01 0.380E-01 0.300E-01 0.277E-01 0.263E-01 0.256E-01 0.245E-01 0.2321-01 O.ZlBE-01 O.lQ4E-01 O.lPOE-0 L o.la2e01 O.l18E-01 O.l73E-01 0.171E-01 0.168E-01 0.162E-01 O.lSlE-01 O.l45E-01 0.144E-0, 0.142E-01 O.l41E-01 O.l35E-01 O.l34E-01 O.l28E-01 O.l23E-01 O.lZOE-01 O.l17E-01 O.llbE-01 O.l15E-01 O.l13E-01 O.lllE-01

COEFFICIENTS

Conversion electrons and y-rays in the OS-2 MeV region as obtained in the present work

TABLE 2

+%)I?)

E” E, E2 EZ El E2 El EJ Et E2I E2 E,

+#I?)

El NOT rll EZ EZ+Hl+EO

EL E2 Elt E2 El

W z

0.600 a.400 ‘3.430 C.400 0.400 U.5UO 0.40@ 0.400 0.400

1469.30 1473.20 149t.fl3 1512.40 1542.50 1640.70 1647.10 lb50.4G 1483.40

C,. slrc, k.430 1.COO 0.500 C.%C C.4CL’ t.*c’)

The theoretical conversion

c *40”

lbP0.5G

1711.80 1725.00 1780.50 lR41.6U lwt9.lP 1e95. li 19C4.40

1633.93 1443.50

1426.67

0.500 0.150 0.150 0.150 O.ZOCl 0.200 0.200 a.200 C.bPO l.COO

Kk”

KEV

1323.03 1329.34 1333.50 1340.58 1345.30 1384.91 1403.15

FKHOR

ENERGY

ZR: 30. 40. 40. 2c. 20. 4C. 25. 25. 25. 25.

60. 30. 15. 2@. 15.

i9.CG

34.CC 2?.5C 14.2C 6.4C ELECTRONS 25.50

ELECTRWS

K K K K K

K K K K

5.50 4.5G 3.90 NC ELECTRONS 4.2c I( NO ELECTRONS NC ELECTRONS NC ELECTRONS lO.CC K 11.10 K NC ELCCTRIINS NO ELECTROi~S “C ELECTRUNS NC ELECTRONS NC ELECTRUYS NC ELECTRUNS vu tiLECTRU\S YC ELECTRONS YC ECCCTRONS

NC

Yf

ELECTRON-

OBSERVEU OBSERVED OBSERVED 3c. 3C. ORSERYED OBSERVED OBSEt7YED OBSERVE0 OBSERVED ORSERVED OBSERYED OBSERVED OBSERVED

SC. OBSERVED 40.

OBSERVED IC. 15. SC. EC.

1c. 1c. zc. 4C.

OBSERVED

ERROR

coefficients are taken from ref. 16).

9rPC 6.90

2.60 LO. 60 15.10 2.90 9.00 b.8”

10. 15. IO. 20. 30. 15.

IO.

30.

IO

ERRCR

27.00 21.00 30.60 5. LO 2.50 7.50 27.90
2.

CACY‘t-

42. 42.

43.

0.347E-02 0.455E-02

76.

18. 18.

14. 18. 22. 45.

ERROR

O.l40E-02

P,OF-Iv

K

>O.hT”E-“Z 0.34bE-02

>n.

0.757E-02 0.183E-62

0.280E-02 0.249E-02 0.103E-02 0.281E-02

ALPhA

TABLE 2 (continued)

0.457E-03

0.461E-03

O.b48E-03 o.sa4t-03 0.5ElE-03 0.579E-03 0.5606-03 0.55bf-03 0.545E-03 0.538E-03 0.510E-03 0.493t-C3 0.4BOE-03

0.6828-03 O.b70E-03

0.734E-03 0.72bE-03 0.7OCE-03 C.701E-03

0.7628-03 0.74bE-03

0+843E-03 0.836E-03 0.83lE-03 0.824E-03 0.819E-03 0.779E-03

THEORETICAL

t. 154E-02 0.148E-02 O.l33E-02 0.132.E-02 “. 13lE-02 u. lZbE-02 U.IZbE-02 O.l23E-02 O.lZlE-02 U.l14E-02 O.lOEE-02 O.l07E-02 0. IOZE-02 0. LOlE-02

O.l97E-02 t.l9bE-02 O.l94E-02 O.iBZE-02 O.l91E-02 U.lBlE-02 O.l77E-02 O.l73E-02 0. I70E-02 U. lb8E-02 O.lbZE-02 b.l61E-02 O.l57E-02

CONVERSION

0.264E-02 0.252E-02 0.217t-02 0.215f-02 0.214%-02 0+205t-02 0.203E-02 0.197.5-32 O.l93E-02 O.l79E-02 0.165E-02 O.l64E-02 0.155E-02 O.l53t-02

0.3648-02 0.3bOE-02 0.357E-02 0.353E-02 0.350E-02 0.32bE-UZ O.llbE-62 0.307E-02 0.300t-02 0.295E-b2 0.283E-02 0.281E-02 O.J7LE-02

COEFFlCIENlS

0.604E-02 0.575E-02 0.493E-02 0.4BBE-02 0.486E-02 0.462E-02 0.458E-02 0.444E-02 0.4351-02 0.402E-02 0.370E-02 0.367E-02 0.345E-02 0.341E-02

0.847E-02 O.B37E-02 O.B30E-02 O.BlPE-02 O.BlZE-02 0.754E-02 0.730E-02 0.707E-02 0.691E-02 0.6791-32 O.b50E-02 0.645E-02 0.62OE-02

!, I E:+rlLtE”

E2

EZ+ll,tC* E? El, El) El’ “R

Ml

EL( r,,, rlnt ELI thl?, EI EZL+“I?I

B. FOGELBERG

AND A. B;4CKLIN

l’*Hf

LEVELS

359

I . ..-.

.!

I

.--.

-. ::. . -, . I-

_

.:::

..

-5.:

.:..

. .. . .. *.*... .*..: : :_. ..: .* . . I’.. . .( . :. .; .

_ . .. -

a’. ’ :’ *.* 5

..*. .*

* .

.**

.

.

.:

.

,.. :

.

.a;.*

*_..: 2.. . : .:I . . ::, ) : . :* .

360

B. FOGELBERG

AND A. Br?iCKLlN

by first subtracting all L and M conversion lines of lower energy transitions, as calculate from theoretical conversion coefficients and the experimental K line intensity, and then carefully fitting ex~erime~ta~~y determined fine shapes to the re-

1167+ bkg. j (1175

177 Hftn 1 a1’78Hf

1403 1421 1385

CHANNEL

I

,

bkg

NUMBER

Fig. 2. The region 1.0 to 1.5 MeV of the neutron capture pray spectrum of *‘*Hf, measured with a 30 cm3 coaxia1 Ge(Li) detector.

The K conversion Xine of the 1173.226 [ref. r7)] keV transition in “Ni was used as energy standard for the high-energy part of the spectrum. ~ormal~zation of the conversion coefficients was made using the theoretical 16) value for the pure E2 transition at 1175.20 keV. In all, conversion electron lines belonging to 72 transitions were detected and in addition several significant upper limits of conversion line intensities could be established. Fig. 1 shows parts of the measured conversion electron spectra, and the results are compiled in tables 1 and 2. 2.2. GAMMA-RAY

~EASU~MENTS

Gamma rays from the reaction ’ “Hf(n, y) ’ 78Hf were measured with 25 and 30 cmJ Ortec true coaxial Get&) diodes using an external target. The neutron beam, extracted from a central beam hole of the R2 reactor at Studsvik, passed through a cooled quartz crystal and was collimated to a diameter of 12 mm at the target. This was situated inside a tube of 6Li, CO, with a wall thickness of 5 mm. A 5 mm thick lead absorber was inserted between target and detector to reduce the Iow-energy count rate which was not measured in the present work, since the lowenergy region has been studied earlier “). The neutron flux density was about 4 x lo6

“8Hf

361

LEVELS

n/cm’ * s, and the target to detector distance was about 30 mm. The target consisted of 80 mg of 91.7 % enriched 17’Hf02 contained in a small bag of 0.6 mg/cm2 Melinex foil, which was found to give a negligible background. Several spectra were recorded, each measurement lasting 50-80 h. The background AT 90’ IN

THE

ANGLE EXPERIMENT

I LIN AMP

SCA

I

1

DELAY AMP 427

DELAY %p ND 3300

0

100

200

300

keV

Fig. 3. Top: schematic view of the electronic system used to recordcoincidences. Bottom: lowenergy “‘Hf(n, y)17 *Hf y-ray spectrum obtained with the 7.6 cm x 7.6 cm NaI(Tl) detector showing the coincidence gates as dashed regions.

was recorded after each measurement with the target replaced by the same amount of material with low capture cross section to simulate scattering in the target of neutrons and y-rays from the reactor. Background lines could thus be identified with a rather good accuracy. A special measurement of the spectrum above 2 MeV was performed to ensure that eventual escape peaks at lower energies were identified.

362

B. FOGELBERG

AND

A. BACKLIN

Results of the y-ray measurement combined with the conversion electron data are shown in table 2. One of the measured y-ray spectra is shown in fig. 2. Energy and efficiency calibration was performed using a set of accurately calibrated standard sources obtained from IAEA, Vienna, and a 24Na source. 2.3.

GAMMA-GAMMA

COINCIDENCES

A coincidence experiment was performed with a 7.6 x 7.6 cm NaI crystal placed at an angle of 90” to the Ge(Li) detector, both counters being about 30 mm away from the target. A schematic view of the set-up, and the fast-slow coincidence system is shown in fig. 3. Four gates were selected in the NaI spectrum in one ADC by a digital gate system, and the other ADC was used to record coincident Ge(Li) detector spectra into the corresponding quadrants of the analyzer memory. Two of the gates were set to accept photopeak events from respectively the 2+ + O+ and 4+ -+ 2+ transitions in the ground state band, and the other two were placed on the background on the high-energy side of these photopeaks as shown in fig. 3. The large dynamic range of the pulses from the (n, 7) spectrum gave rise to a rather bad time resolution (Z 20 ns) which forced us to use a time window of about 60 ns, thereby accepting a relatively large number of random coincidences. Some unwanted coincidences also arise from the low-energy background in the NaI crystal, which partly consists of Compton events of high-energy y-rays which directly or indirectly form cascades with the y-rays in the 1 MeV region. The ratio of true photopeak to random plus background coincidences was generally about 7 to 1. TABLE 3 Results of the yy coincidence Gamma-ray energy keV 962.2 1077.9 1081.5 1102.9 1144.8 1167.4 1175.2 1183.4 1205.6 1207.1 1227.0 1230.1

Coincidence relation with gs. band c4 c4 c2 c4 c4 c2 (60&10) % C 2 c2 c4 c4 c4 c2

measurement

Gamma-ray energy keV 1269.3 1291.2 1310.0 1329.3 1333.5 1340.6 1403.2 1420.7 1542.5 1647.1 1650.4 1725.0

Coincidence relation with g.s. band c2 c2 c2 c4 c4 c2 c2 c2 c 2”) c 4 “) 1 c 28)

“) These assignments are not definite, but turned out to be the most probable ones from a statistical analysis of these parts of the coincidence spectra. The labels C2 and C4 indicate a coincidence with respectively the photo peaks of the 2+ -+ O+ and 4+ + 2+ transitions in the ground state band.

363

l’*Hf LEVELS

w Cfu)

3%

iz f--

._..S.--

zs= _-__

_____---

s-~_.~IIxz===-

------m

__ --%*_

VI

--z.C=-

t--

--_

-===f

lINNiH3

/ SlNfl03

x

-g_

364

B. FOGELBERG

AND A. BXCKLIN

The results of the coincidence measurements are collected in table 3 and the most relevant parts of the coincidence spectra are shown in fig. 4. 3. Construction of the level scheme The presently constructed level scheme of ’ “Hf has been based mainly on the data obtained in the present work but also on the high-resolution measurement of the lowenergy (< 500 keV) neutron capture y-ray spectrum reported by Smither “). In all about 220 transitions have been involved in the work and 71 of these are placed in the level scheme finally arrived at. Although only about one third of the transitions are placed in the scheme, it contains 85 “/, of the total y-intensity in the spectrum below 2 MeV, of which about 3 % have been taken from ref. “). The main part of the levels are established on the basis of coincidence relations. A few states could be identified as previously known from the decay of “*Ta [refs. 2*“>I. 0th er states are strongly supported by primary y-rays **“). Only four levels rest solely on energy combinations. Naturally the possibility of obtaining random combinations has to be considered in these cases. In the region 1100-2000 keV there is a large number of level candidates, suggested by combinations of two transitions with two established levels. In the present case one can estimate that more than 50 % of these combinations do not represent true levels. The number of random combinations can, however, be drastically reduced if further restrictions are imposed on the level candidates. In the present work an energy combination has been approved as representing a true level only if (i) the combination is situated within the limited energy region where a level with certain decay characteristics can be expected, e.g. by assuming the rotational model to be valid or where a primary y-ray suggests a level. {ii) The sum of the intensities of the y-rays de-exciting the level candidate has to agree within reasonable limits with the expected population of the level. (iii) The combination fulfils expected decay characteristics with regard to multipolarities (when these are known), and relative transition probabilities. With these restrictions in mind, it is not very likely that a random combination has been included in the level scheme presented here (fig. 5 and table 9). 3.1. THE GROUND

STATE ROTATIONAL

BAND

Three prominent transitions at 93.17, 213.43 and 325.53 keV observed in the conversion electron and y-ray spectra can be identified with the 2+ -+ O+, 4+ -+ 2+ and 6’ 3 4f transitions between the well-known levels in the ground state (g.s.) rotational band. The g.s. band has been studied up to the 8+ level by Coulomb excitation lg) and from the decay of the 8- isomeric state at 1148 keV [refs. i8* I’)]. A precision measurement of y-ray energies from this decay is reported in ref. ‘), in which the energy of the 8’ -+ 6+ transitions is given as 426.371 kO.015 keV, very close to the value 426.21 kO.14 keV observed for a y-line in the neutron capture y-ray spectrum “). The intensity of the Bf -+ fZif transition can be estimated from

Fig. 5. Levels and transitions in ’ 78Hf as obtained in the present work. The energies of the levels in the ground state band have been taken as averages of the presently measured energies and the ones of refs. S*6). Transitions with double arrowheads have been placed in the level scheme by using the measured coincidence refations, and transitions labelled by a star may be placed at alternative positions in the scheme. An upward flag to the left of a level means that the level have been excited in the (d, p) reaction and a downward Bag indicates excitation by the (d, t) reaction, both reported in ref. 25). Short vertical arrows ending at a level shows that the level has been reported to receive feeding by primary y-rays in the A question mark at a level indicates (n, y) reaction a*9), while a level fed in the b-decay of the 1+ state in ltsTa is indicated by an inclinedarrow. that the rotational relationship with other levels is uncertain (see the text). Bands with bandheads at 1174+80, 1198.0, 1260.57 and 1513.88 keV are identified as respectively y-vjbration, /?-vibration. the K = 2- (#- [5 12]-8’ [624]) and the K = 4+ (%- [514] +i- [SlO]) two-quasiparticle bands, The two latter assignments are taken from ref. 25), For a discussion of the level scheme, see sect. 3 in the text.

366

B. FOGELBERG

AND

A. BtCCKLIN

population systematics, and by comparison with other nuclei with similar capture states, i.e. 168Er [ref. ‘“)I, 166H~ [ref. “‘)I and to some extent also ’ 62Dy [ref. 22)] and ‘(j4Dy [ref. 23)J. It turns out that the intensity of the 426.21 keV y-line is 2-4 times higher than what is expected for the transition depopulating the 8+ level, which is an argument against an identification of the 426.21 keV y-line with the 8+ + 6+ transition. As will be shown later, the 426.21 keV y-ray fits well in another place in the decay scheme. It is thus not improbable that the observed y-line in fact is an unresolved doublet. The accurately known energies of the levels of the g.s. band can be used for a determination of the parameters in the rotational formula: E = Eo+AZ(Z+1)+BZ2(Z+1)2.

(1)

The 2+ and 4+ level energies inserted in eq. (1) yields: A = 15.613 keV,

B = - 14.129 eV.

Inclusion of a term CZ3(Zf 1)3 gives parameters: A = 15.618 keV,

B = -15.157

eV,

C = 0.0398 keV.

The calculated energy between the 6+ and 8+ levels comes out as 420.07 keV using the first set of only two parameters and as 428.56 keV using the second set, which can be compared with the experimentally ‘) measured distance of 426.37 keV. 3.2. THE I/-VIBRATIONAL

BAND

From the coincidence relations, four levels are established at 1174.80, 1268.86, 1384.53 and 1533.60 keV. The multipolarities of the de-exciting transitions indicate positive parities of these levels, and a spin sequence of 2,3,4 and 5 is implied by their modes of decay. The level spacings agree roughly with the Z(Z+ 1) dependence expected for a rotational band, and the absence of levels with spin lower than 2 is compatible with a K quantum number of 2. The terms expected to dominate the energy formula for K = 2 bands is in the rotational model 24): E = Eo+A2Z(Z+1)+B2Z2(Z+1)2+D2(-l)r(Z-1)Z(Z+1)(Z+2).

(2)

With the level energies as given above, we find for the coefficients: A,

= 16.23k0.13 keV,

B, = -45.0&2.0eV,

D, = -7.Okl.O

eV.

The significance of the coefficient D,, taking care of the odd-even shift, is clearly illustrated in fig. 6 showing (E,, 1 - E,)/2(Z+ 1) plotted versus (I+ 1)‘. From the energy formula (2), the 6+ level is expected at % 1675 keV, not too far away from an energy combination at 1691.41 keV of two transitions of expected intensities, which combine with the 4+ and 6+ members of the ground state rotational band. The conversion coefficient is measured for only one of these transitions, indicating E2 or Ml multipolarity. Support for the interpretation of this combina-

367

‘78Hf LEVELS

tion as the 6+ level of a K = 2+ band is given in a recent measurement on the “‘Hf(d, p)“‘Hf reaction *‘), where the spin 2+ to 6+ levels of a collective K = 2+ band were found at 1175, 1269, 1384, cz 1530 and x 1698 keV. One may note that exclusion of the last term of eq. (2) makes the agreement between the experimental energy and the calculated 6+ energy still worse by x 10 keV. A special study was made of the relative E2 transition probabilities from the yvibrational band to the ground state band. The experimental values of conversion coefficients are all consistent with E2 multipolarity, and a possible small Ml admixture in some transitions has been neglected in the calculations. The experimental ratios TABLE 4

Decay properties of the y-vibrational Rel.yintensity

Ratios of Alaga 26) zz - lo2 reduced E(E2) values

1,

I,

Transitionenergy keV

Multipole assignment

2

0

1175.20

40

2

2

1081.52

38.7h2.7

2

4

868.54

1.650.8

3

2

1175.20

60 i1oq

3

4

962.20

12.2*1.2

E2+ <15%Ml

4

2

1291.21

13.0&2.0

E2+ ~40%

4

4

1077.94

27.1f1.9

E2+ < 25 % Ml

4

6

753.02

2.0*0.5

5

4

1227.05

31.4f6.3

5

6

901.37

6

4

6

6

&lop)

band

E2 2+0 m

= 0.62112

0.70

2.013.5

2+4 ~ 2+2

= 0.11&0.06

0.05

8

3-+4 __ 3+2

= 0.46+0.08

0.40

i.o*1.3

4-+2 z4

= 0.17&0.03

0.34

4.6Al.2

4-+6 4-+4

= 0.29&0.08

0.086

4.311.7

S-+6 5-+4

= 0.6610.26

0.57

0.6+1.7

1384.91

2.510.8

6+4 6+6

= 0.21*0,09

0.27

l.Oil.0

1059.14

3.151.0

E2+

< 25 % Ml

f8

E2

b) E2+

Ml

(9 -f3) Y


E2 or Ml

Weighted average:

1.451.0

“) These transitions could not be resolved in the single spectrum. The intensities are obtained from the coincidence measurement. b, This value can be caused by other transitions coinciding with the 753 keV line. The value of z2 has been omitted in the average. In the first two columns the initial and final spins of the connected states are given. Columns 3 and 4 contain energies and intensities of the connecting y-rays. The multipole assignments are based on conversion coefficients measured in this work. The next column gives the ratios of the reduced S(lZ2) values, assuming all transitions to be pure E2. In the last two columns are shown the prediction of Alaga’s rule, and the values of the band-mixing parameter z2 obtained from the deviations from Alaga’s rule z6).

368

B. FOGELBERG

AND A. BACKLIN

of B(E2) values are collected in table 4 together with the theoretical ratios obtained from the Alaga rule 2”). The deviations of the experimental values from the adiabatic theory are usually interpreted in terms of the band mixing parameter z2, which is given in the last column of table 4. The band mixing parameter has been calculated

Fig. 6. Plots of the quantity (I$+,-Er)/2(1+1) versus (/+I)’ for the X = 2 bands in “‘Hf, showing the different rotational parameters for the odd and the even spin members of the bands. The numerical values of the rotational parameters A and B shown in the figure are obtained from the zero crossing points and the slopes of the heavy lines. Further details on the energy parameters of rotational bands are given in the text and in table 8.

approach by several authors 27-29). In the present for l’*Hf in the microscopic experiment the value of z2 comes out as (1.4 + 1.O) x 10m2, in good agreement with the calculations of refs. 27, 29) but far smaller than ref. ““). In fig. 7 we show theoretical and experimental values of z2 as a function of mass number. In this figure are also included .z2 values corresponding to the E2 branching ratios predicted by the hydrodynamic R-V model of Faessler, Greiner and Sheline 30). Band mixing effects seem to be highly overestimated also in this model. A different formula for the effects of band mixing is given by Michailov 31). B(E2; 21, ~ OZ,) = (Zi22-21ZrO)2[Mr

+M,(Z,(Z,+l)-Zi(Zi+l))],

(3)

where M2/M1 is the angular momentum independent part of the admixed amplitude, when only mixing with the ground state band is taken into account. The parameters

1’8Hf LEVELS

369

M, and M2 are related to z2 by 32) z2

=

2M2

(4)

Ml AM,

from which we have: 3

= (0.7105)

* 10-2.

Ml

Adopting the adiabatic collective model 26P33) further information can be gained from a study of intra-band transitions. In the low-energy y-spectrum “) there is a 264.59 keV y-ray, which fits energetically between the 5+ and 3+ levels of the y-band. Assuming this to be an intra-band transition, and using a quadrupole moment Q2 of the y-vibration equal to Q, = 6.8 b [ref. ““)I of the ground state band, we have: B(E2; 25+ + 23+) = 0.89 e2 - b2 x 150 s.p.u. The E2 branching from the 5+ level then gives B(E2; 25+ -+ 04+) = 1.2 * lo-’

e2 * b2.

This corresponds to 2 s.p.u. and is in rough agreement with experimental B(E2) values obtained by Coulomb excitation of ylvibrational bands in other rare-earth nuclei 35) an d a 1so with what is predicted by BBS2”) and Soloviev 36). No other low-energy y-rays can be fitted as intraband transitions in the K = 2+ rotational band, which is in accordance with the expected intensities of these transitions. 3.3. THE

K = O+ BAND AT 1198.0 keV

Two levels, assigned as I” = O+ and 2+ with K = 0 have been observed 2*“) in ’ '*Hf at 1199 and 1276 keV, respectively, in the decay of ’ '*Ta. In the present work, a weak transition with cr, > aK(M2)at 1198.00 keV is observed, which is identified as the O+ -+ 0” transition. The coincidence relations establish a level at 1276.47 keV, the decay mode of which indicates a 2+ assignment. The conversion coefficient of the 1183 keV 2+ -+ 2+ transition agrees well with the value observed in b-decay 3), which is compatible with a strong EO component, and we identify this level with the earlier known 2*“) KZ" = 02+ level. Another transition, at 1145 keV with a conversion coefficient suggesting EO admixture, which is coincident with the 4+ + 2+ transition in the ground state rotational band, defines a KZ" = 04+ level at 1451.45 keV. Assuming these three levels to form a K = 0 rotational band, application of the energy formula (l), yields coefficients A,,= 13.25 keV and B, = -29.0 eV. Support for the assumption that these levels belong to the same rotational band is given by the relative transition probabilities to the ground state band, as discussed below.

B. FOGELBERG

370

AND A. BACKLIN

The branching ratio to the ground state band B(E2;02+ is a factor of 3.5 smaller than expected from the adiabatic

+ OO+)/B(E2;02+ -+ 04+) theory ‘“). Assuming this

to be due entirely to mixing with the ground state band we can express the reduced E2 transition probabilities to the g.s.b. as 31) B(E2; Ii0 --) Z,O) = (Z~200~Z~0)2~M~+M~[Z~(Z~+1)-Z~(Z~+1)])2~ where M2/M1 often is denoted z0 [ref. 37)]. We obtain z0 = -0.036+0.010, is in decent agreement with the value -0.026+0.010 obtained in radioactive studies 38). TABLE

(5) which decay

5

Decay properties of the K = O+ band at 1198 keV in “‘Hf Initial level KP energy -.

Final

Exp.

WV

oo+

Relative reduced y-intensities

level KP

Alaga

Xa)

P< E2

r0 = -0.036

oo+

0.20+0.06 ‘)

1198.00

02+

02+ 1276.47

oo+ 02+ 04+

0.76hO.15 7.6 f0.4 6.7 &I.0

2.6 3.7 6.7

0.72 1.67 6.7

100 0.26iO.04

100 24i.5 ‘) 100

04+ 1451.45

02+ 04+ 06+

< 0.28 12.0 kO.6 6.7 f2.7

4.2 3.8 6.7

0.25 1.22 6.7

0.15 50.07

100 11*5=:) 100

< 3.1

Weighted average X = 0.22-10.05 “) The parameter X is defined in the text. b, From relative intensities given in ref. 3). ‘) Percentage required to explain the E2 branching for a za of about -0.03 1. See also ref. ’ *) and the text.

Also the 4+ level exhibits an E2 decay different from the Alaga rule 26), see table 5. The lower limit of the ratio B(E2; 04+ -+ 06+)/B(E2; 04+ -+ 02+) corresponds to z. 2 0.030. It was earlier shown 38) that the relative E2 transition probabilities from the 2+ member of the band were all consistent with a single value of zo, since the 02+ + 02’ transition was shown to contain (83 + 10) 0/0M 1. Assuming the same value of z. to be valid also for the 4’ level we obtain an Ml component of (89 f 5) PI, in the 04+ -+ 04+ transitions when taking z. = -0.031 (average of ref. 38) and present work). The EO admixture in the AZ = 0 transitions from the O+ band to the g.s. band is evident from the large conversion coefficients of these transitions. For the Of -+ Of transitions one may express the EO transition probability 39) T(E0)

= Qp2,

(6)

ltsHf LEVELS

371

where Q is an electronic factor, and p is the nuclear “EO strength parameter”. may relate the EO and E2 transition probabilities through the expression 40)

x=

e2p2Rz

=

2.55

. lo-6

B(E2; 0+’ --f 2+)

L&O)

E%W

Z,(E2) -%--

A’

’

One

(7)

where the value of Q is obtained from interpolation in fig. 1 of ref. 39). One may express reduced EO transition probabilities also for other Z -+ Z transitions between the O+ band and the g.s.b. in terms of the X-parameter (7) by assuming the E2 transition probabilities between the bands to be regulated by a model. Assuming eq. (5) to be valid we obtain for the 2 -+ 2 transition

x=

e2p2Rz

(2200]40)2

B(E2; 2 + 4) (0200120)=

A similar expression is obtained for the 4 + 4 transition. The calculated X-values are given in table 5 using the value of z. and the value of the Ml mixing in the 4 -+ 4 transition deduced from the present data. It is seen that the X-values are very similar for all Z + Z transitions as expected for levels in the same band. The magnitude of the X-parameter is smaller than what is calculated microscopically for /I-vibrations by B&s41) who obtains X z 0.5 for i’*Hf. It is also slightly smaller than the value X = 4fi2 z 0.30 obtained by Rasmussen 40) in the hydrodynamic model. Of all the O+ bands found in 17*Hf, this band has the strongest EO transitions to the ground state, and it therefore seems likely that it to a large extent consists of the P-vibration. 3.4. THE

K = 0+ BAND AT 1433.9 keV

A weak conversion electron line corresponding to a transition of 1433.9 keV can be identified as a O+ + O+ EO transition also observed in the decay of 1“Ta [refs. ‘, “)I. The corresponding O+ + 2+ transition is in the present measurement masked by the stronger 1340.6 keV El transition. Another level at 1496.48 keV is established by the coincidence of the 1403.15 keV y-ray with the 2” + O+ transition in the ground state band. Part of the 1403 keV transition may be placed from the 1403 keV level to the ground state, but the coincidence spectrum clearly shows that the main part of the transition proceeds to the 2+ state in the g.s.b. The spin and parity of the 1496.48 keV level can be assigned as 2+ from the mode of decay. The EO admixture to the 1403.15 keV 2+ + 2+ transition indicates a strong K = 0 component in the state. The similarity between the X-parameters derived for the O+ and 2” states, table 6, indicate that these levels belong to the same band. The rotational energy parameter is 10.42 keV, yielding z 1640 keV as the expected energy of the 4+ level. This is very close to a 3+ or 4+ level at 1635.83 keV, which is defined by the coincidence of the 1329.34 keV E2(+Ml) y-ray with the 4+ + 2” transition of the ground state band, the energy fit of the 1542.5 keV transition to the 2+ level of the ground state band, and a primary transition ‘* “).

372

B. FOGELBERG

AND A. BACKLIN TABLE 6

Decay properties of the K = O+ band at 1433.9 keV in “*Hf Initial level KP energy

Final level

% E2

KI”

Alaga

Exp.

(kev)

oo+

x

Relative reduced y-intensities za = 0.01

oo+

0.11~0.03 “)

1433.90 02+ 1496.48

oo+ 02+ 04+

0.89f0.14 1.40&0.21 1.00*0.25

0.89 1.27 2.30

0.89 1.03 0.97

0.21&0.09

100 74*14 ‘) 100

04+ 1635.83

02+ 04+ 06+

0.97f0.15 7.3 +0.7 < 1.5

0.97 0.88 1.54

0.97 0.66 0.46

< 0.20 b)

100 9* 2”) 100

Weighted average X = 0.15 &to.06 “) From intensities given in ref. 3). b, The 04+ -+ 02+ y-intensity has been used for the relative E2 transition probability of the I --, 1+2 transition. “) Percentage required to explain the E2 branching for a r,, of 0.01. See also the text.

instead

Application of the energy formula (1) yields coefficients with reasonable values, table 8, suggesting that the 4+ level may well belong to the band. This interpretation is not contradicted by the upper limit of the EO parameter Xfor the 4+ + 4+ transition, table 6. The ground state decay properties of this proposed second excited O+ band turns out Z2

Sm

Gd

Dy

Er

Yb

Hf

w

A i R-V-UODEL(HYDRCDYNAUlC o: .i

UARSHALEK BE5

0i

PAVLICHENKOV

/

150

1)

EXPERIMENT

160

im

Fig. 7. Plot of theoretical and experimental

180

190

MASS

NUMBER

values of the band mixing parameter .z2 as a function of mass number.

17rHf LEVELS

313

to be similar to those of the band with the bandhead at 1198 keV. As is shown in table 6, the intensities of the AI = 2 transitions from the 1496.48 keV 02+ and 1635.83 keV 04+ levels are fairly consistent with a small band mixing parameter z. = 0.01. However, the AZ = 0 transitions exhibit an excess y-intensity. It is natural to ascribe this to an Ml admixture, which we obtain as 25 % in the 02+ -+ 02+ transition and 91 ‘A in the 04+ 3 04+ transition. One may note that Michailov 42) predicts the Ml amplitude in AZ = 0 transitions between bands with K = 0 to be proportional to Z(Z+ l), which seems to be approximately verified in this case. The origin of this band is not certain. The relatively weak EO transitions to the ground state band indicate a weak contribution of the B-vibration. The small logff values observed for the p-feeding of the O+ and 2’ states from ’ '*Ta [ref. 3)] indicate a strong component of the ($- [514]-3- [514]) proton state, which Gallagher and Soloviev 43) predicted at 1.7 MeV. 3.5. THE K = 2-

BAND

AT 1260.6 keV

Three negative-parity levels are established at 1260.57, 1323.18 and 1409.51 keV through the coincidence relations of the intense 1167.40, 1230.10 and 1102.90 keV El transitions. Spin assignments of 2,3 and 4 respectively are indicated by the modes of decay. Strong support for the levels is obtained from primary transitions “) which feed the 1323 and 1410 keV states. The decay mode of the levels and their relative population, fig. 8, suggest that the levels belong to the same band. No I = 1 level was observed, indicating K = 2 for the band. This is supported by the fairly large retardation factors for the El transitions to the g.s.b. (see below). In the (d, t) experiment of ref. 25) the 5- level is found at z 1506 keV. Several levels are populated in the (n, 7) reaction around this energy, giving rise to complex lines in the spectra. From the coincidence measurements we place the 1205.6 keV El transition to the 306.61 keV level yielding a 3-, 4- or 5- state at 1512.2 keV. However, as discussed below we also expect a 4- level with about the same population as the 25- level at thisenergy, so from the transition to the g.s.b. we can only obtain a crude value of x 1512 keV of the 25- level energy. It may be possible to find the level position more accurately from a study of intraband transitions and transitions to the K = 2+ band, since these may compete favourably with the Kforbidden transitions to the g.s.b. Three low-energy y-rays in the spectrum of ref. “) do in fact combine at 1510.48 keV with the KZ” = 23-, 24- and 24+ levels. No multipolarities are known for the transitions involved, and we can only tentatively assign the combination to represent the 5- level of the K = 2- band. Also the population of the 6- level is expected to be sufficient for a detection of the y-rays from its decay. Application of eq. (2) yields a 6- energy about 7 keV above the energy of a possible 5- or 6- level at 1636.81 keV, which is defined by an El transition to the 6’ level of the g.s. band and an E2 transition to the KZ” = 24level.

374

B. FOGELBERG

AND

A. BiiCKLIN

Two low-energy y-rays found in ref. “) fit energetically as 4- --f 2- and 4- -+ 3intra-band transitions. The probability that each of these fits is accidental can be estimated to about 5 ‘A. Assuming the energy fits to be true and the Alaga rule to be valid we find for the 4- + 3- transition an E2/M1 mixing ratio 6’ > 2. By using the expressions for the intra-band transition probabilities B(E2) = ~

B(M1) = t

Q~(li 2KOllr K)‘,

~~ K2(g,-g,)‘(1i

(9) 1KOllr K>‘,

(IO)

we obtain, by inserting Q, = 6.8b [ref. 34)], a value of lgK-gsl < 0.1. From the (d, t) reactions ’ “) the 2- band is deduced to have a predominant character of the two-neutron state ($‘[624]_3- [512]). The contributions to gK of the two orbitals will therefore have different signs giving a resultant 95

gK

[624] - -%- [512] ,

9s free

9s

free

I

which according to systematics “) should be appreciably smaller than one. The experimental value of l&-&l is thus reasonable since gR is typiCally about 0.4. Using the value 6.8 b for the quadrupole moment of the 2- band we also derive a hindrance factor 45) for the 24- -+ 04+ transition to the g.s.b. of F,(El;

24- + 04+) = 0.4 - 105.

This is a reasonable value for a once K-forbidden transition. For the 24- + 23+ transition we deduce F,(El;

24- -+ 23+) = 1.3. 103.

An expression for the transition probabilities of n times K-forbidden transitions due to admixtures has been given by Michailov 31), which, for Kr > Kf and Ki # +, reads: B(;i, Ii + If) = (Zi, J.9Ki-n,

Kf+n-KiJIf, x

Kf)’

1

(li+Ki)!(li-Ki+n)!

[~,(1+~)]2,

[ (Ii-Ki)!(Ii+Ki-n)!

where A = [lf(lf+

l)-Ii(Ii

+ I)]A.

(11~)

(Ilb)

The parameter A is the angular momentum independent part of the admixed amplitude. In this case we obtain A from the branching of the transitions from the 3- level to the g.s. band, and M,, from the intraband/interband branching from the 4- level with a further use of a Q, of 6.8 b.

““Hf

LEVELS

375

The result is A = -0.042 3.6. THE K = 2-

BAND

(01-0.313)

and

Mi = 0.9 - lo-*e - b.

AT 1362.4 keV

Three El transitions, with energies of 1269.27, 1310.04 and 1340.58 keV, all coincident with the 2+ + O+ transition in the g.s. band, define negative-parity levels at 1362.44, 1433.75 and 1403.21 keV. None of the levels decays directly to the ground state, thus not likely having spins less than 2. The 1433.75 keV level combines energetically with the 4+ level of the g.s.b. via a weak y-ray of 1126.35 keV indicating a 3assignment. Support for the level is obtained from a primary y-ray defining a state with spin 3 or 4 at 1434 keV [ref. ‘)I. The absence of other transitions than to the 2+ state in the g.s.b. for the 1362.44 and 1403.21 keV levels, together with the fact that these levels are weakly populated in the 1+ ground state decay of “*Ta (the y-rays are observed but not placed in the level scheme of ref. “)) makes 2- assignments plausible. The branching ratio of the El transitions from the proposed 1433.75 keV 3- level to the g.s. band shows serious disagreement with K quantum numbers of 0 or 1 but agrees to within less than a factor of two with the El branching from the KZ” = 23level at 1323.18 keV. The K = 3 alternative is not probable since no transitions to the K = 2’ band have been detected, which are favoured as compared with the transitions to the g.s.b. It is thus not unreasonable to assign also the 1433.75 keV level as the 3- rotational state of one of the 2- levels. The 2- band-head can possibly be distinguished through a study of population systematics, fig. 8. It is seen that the 1403.21 keV 2- level is a less probable choice for the band-head, since the population is a factor of two lower than expected, while the population of the 1362.44 keV level fits fairly well to that of the 3- level. If the 1362.44 and 1433.75 keV levels are adopted as members of a rotational band, one would expect the 4- level at w 1510 keV with a population of about 15 units of table 2, i.e. almost the same expectation values for energy and population as for the 5level in the K = 2-(3- [512] - 4’ [624]) band. The 1205.6 keV El y-ray, defining a level at x 1512 keV through the coincidence relationship with the 4+ + 2’ transition, is likely to be a superposition of the 4- + 4+ and the 5- --f 4+ transitions. An argument supporting the 24- level at 1512 keV is that this is the only level that can be inferred from the data with strong enough population. The El branching from the 1433.75 keV 3- level yields roots of A = -0.061

(or

A = -0.24)

for the mixing parameter in eq. (11). Gallagher and Soloviev 43) predict only t wo 2- bands below 2.3 MeV, the (3- [512] -$‘[624]) neutron state at 1.7 MeV and the (4- [514]-$+ [402]) proton state at 1.8 MeV. Since the two-neutron state has been identified as contributing strongly to the

376

B. FOGELBERG

AND

A. BiiCKLlN

2- band at 1260.6 keV, it is tempting to suggest the 2- band at 1362.4 keV to be the two-proton state. The intensity of the 1270 keV y-ray observed in the P-decay of the [e-(514)_2-(514)] ground state of 178Ta [ref. “)I implies a logft value of about 7 for the transition to the 1362 keV level, which is not unreasonable for a first-forbidden, hindered transition 46). It should, however, be noted that a third 2- state is observed at 1403 keV (see below), which is also very likely fed in the decay of 178Ta [ref. “)I. Neergard and Vogel 47) have calculated the energies of the octupole states expected in even deformed nuclei. The 2- state in ’ '*Hf is expected at 1.32 MeV, which is only 40 keV away from the 1362 keV 2- state. The question of whether this state should be characterized as an octupole vibration or a two-particle state remains open. 3.7. THE

K = 4+ BAND

AT 1513.88

keV

Two intense E2 y-rays of 1420.67 and 1207.10 keV, which are strongly coincident with respectively the 2+ --f O+ and 4’ 4 2+ transitions in the g.s. band, define a positive-parity level at 1513.88 keV. The level is further supported by a primary y-ray ‘) and by the energy fit of two strong and one weak transition “) to the K = 2+ band. Another level is defined at 1640.37 keV by the coincidence between 1333.50 keV E2 transition and the 4+ + 2+ transition in the g.s.b. and by the energy combination between the 1333.50 and 1008.39 keV transitions. Also three low-energy transitions combine with the 3+, 4+ and 5+ levels in the K = 2+ band. Furthermore the 126.58 [ref. “)I keV E2 transition fits to the state at 1513.88 keV. The decay mode of these levels suggests that they are the two first members of a K = 4+ band. This interpretation is supported in the (d, p) measurements of ref. ’ “). The 6+ state is expected at an energy of about 1790 keV and to have a strong enough feeding to be observed. At 1788.38 keV we find a combination of two low-energy transitions “) to the 44+ and 45+ states and a fairly strong E2 transition to the 6+ state in the g.s.b. Since this is the only level candidate in this energy region showing the expected population and relative intensities we assign the state as 46+. Using the value obtained for the g.s.b. of Q, = 6.8 b [ref. 34)] we may calculate absolute transition probabilities from the 46+ level from the intensity ratios with the 274.69 keV 6+ -+ 4’ transition. Similarly the absolute transition probabilities from the 45+ level may be calculated from comparison with the E2 part of the 126.58 keV 5’ -+ 4+ transition. From the L-subshell ratios we obtain a2 2 1, which corresponds to ]gK-g,J < 0.16 for the Ml transition. This quantity-can also be obtained from the intensity ratio of the intraband transitions from the 6+ state assuming the Alaga rule to hold. For the 6+ + 5+ transition we then obtain a2 = 0.41tz:T,, which corresponds to (gK-g,J = 0.2510.16 for the Ml part of the transition. As an average for the band we somewhat arbitrarily set ]gK-gR] w 0.13, which corresponds to a2 z 1.5 for the 5+ + 4+ transition. Absolute transition probabilities from the 45 ’ level were calculated using this value together with the g.s.b. value Q, = 6.8 b. The transition probabilities from the levels of the K = 4+ band are given in table 7.

2.3 - 10-2(E2) 2.0 * 10-2(E2) 8.4 * 10-2(E2)

1.4. 10m4e2 * b2

* b2

1.2. 10e4e2 5.3 * 10e4e2 * b2

6.5 f1.3 12.4 k2.5 90 f20

(5.0 kO.8) * 1O-3

(4.5 rtO.9). 1o-3

(1.9 ztO.4) * 10-e

2.7 kO.54 1.1 AO.22 (9.8 &2) * lo3 (9.8 &2) * lo4 0.33f0.06 6.6 f1.3 (2.2 hO.4) * 1o-3 0.16&0.03

245.23 129.33 126.58

1333.50

1008.39

371.74

256.01 107.31 230.74

128.09 274.69

148.07 1156.76 463.64

24+ 44f

04+

06+

23+

24” 25” 2424” 44+

4s+ 06+ 24+ 1.9. 10-3e2 * b2 0.15ee. b2

2.2 - IO- *e2 * b 2.2 * 10-7e2 * b 0.29e” - b2

7.4 * 10m2e2 * b’; 3.3 . 10-3p2N 3.0 * 10e2e2. b2., 1f9 * 10m2E1N 2

1.3 4 10m3e2 - b2; 5.5 - 10-5~2n 3.2 * 10-3e2 * b2* 3 5 91O-s PN2 1.49e; - b2

0.31 (E2) 23(E2)

12.5(E2); 2.0 * 10-3(M1) 52(E2); 1.2 * 10-2(M1) 1.0 * 10-6(E1) 1.0 * 10-5(W) 48 (E2)

0.23@2); 3.3 * 10-s(M1) 0.55(E2); 2.1 * 10-5(M1) 250@2)

O.l2(E2)

23’

7.0. 10e4e2 * b2

2.7 f0.5

339.22

< 1.8 * 10-4(E2)

< 1.0 - 10-%r2 * b2

22+

4.10-3

<

881.7

06”

1.2 * 101~(E2)

5216.2 * 10s6e2 * b2

w 24 - 10-s

1207.10

1.7 - 10-4(E2)

* bZ

1.0 * 10m6eZ

04+

(4.0 rfrO.4) - 10-z

(s.p.u.)

1420.67

&eW

Estimated reduced transition probabilities (ez - b2, e2 . b, p2n)

0.33 1.84

1.90 - 10-a 0.92. 1O-2

1.90 * 10-Z

1.51 OS34

2.70

5+4 n

s4

(Ml)

At = -0.008 (Ml) -+ A2 = 0.21

_, ;’ 1 “d;y 2 .

Normalized Value of the mixing parameter in eq. (11) for some KAlaga value for E2 forbidden transitions

from levels of the K = 4+ band

02+

KI”

Relative reduced y-intensity

TABLE7 probabilities

The first two columns gives the initial and final states, the third column shows the transition energy. Column four contains relative intensities, reduced by the energy factor. All positive-parity transitions have been treated as E2:s. Columns five and six show estimates of absolute transition probabilities, obtained by using Q0 = 6.8 b for the intrinsic quadrupole moment of the 4+ band. In cases where transitions to the K = 2+ band show y-intensities in excess of the Alaga rule, column 7, the excess has been treated as Ml admixture. For further details see the text. The last column rr\ntnine thm rnnts nf .w I1 11 fnr ~nrn~ K-fnrhiridm tmncitinns.

46+

45+

44+

KI”

Initial Final Transition level level energy

Relative, and estimated absolute, y-transition

3

d G

2

378

Et. FOGELBERG

AND A. BiiCKLIN

All transitions to the g.s.b. were assumed to be pure E2. For the transitions to the K = 2+ band the large transition probabilities to the 4+ and 5+ states may indicate that these transitions are predominantly Ml, which is supported by the conversion coefficients measured. The twice K-forbidden E2 transitions to the g.s.b. may according to Michailov 31) take place through AK = 2 admixtures with a spin-independent amplitude A, see eq. (1 I). Table 7 also shows the values obtained for the admixed amplitude for the K-forbidden transitions from the 4+ band. A very small value of A seems to be consistent for all transitions to the g.s. band while A % 0.22 applies for the Ml part of the transitions to the K = 2+ band. It is possible also for the transitions from the 44+ state, to obtain an estimate of the absolute transition probabilities by assuming a constant matrix element for the E2 transitions to the K = 2+ band. For this one may compare the 44+ -+ 22+ transition either with the 4~5~+ 23+ or with the 46+ -+ 24’ transition, We see in table 7 that the strengths of these transitions are very different. The intensity of the latter transition is almost of rotational magnitude, which would imply a very strong AK = 2 mixing between the bands. On the other hand the 45’ -+ 23+ transition is remarkably weak. The strength of the 46” + 24’ transition may possibly be due to an accidental energy coincidence with another line, and we have used the 45 -+ 23+ transition to calculate the transition probabilities from the 44” level in an absolute scale. The results are included in table 7. 3.8. A POSSIBLE

K = 3+ BAND AT 1860.20 keV

The (d, p) measurements 2s) suggest the K = 3* [~-~514~~-(510)] neutron state with the first three levels at 1867, 1956 and 2073 keV. From population systematics, fig. 8, we find that in the (n, 7) reaction the 3+ state can probably be expected to have a population of lo-20 units of y-intensity of table 2 and the 4+ state 5-15 units. Provided that these states decay strongly only to a few states, which is normal, transitions from the 3+ and 4’ states should be observed in the present work and ref. “). We find only one combination, at 1860.20 keV, of strong enough transitions, within 10 keV from the energy obtained in the (d, p) measurements for the 3+ state. The energy is somewhat low, but also for the K = 4’ band we find the energies to be in average about 5 keV lower than found in the (d, p) measurements. The combination consists of the 497.79 keV El transition and the 426.21 keV El or E2 transition, which can be placed to the upper of the K = 2- bands. A problem is that the 426.21 keV transition also fits well between the 8+ and 6+ levels in the ground state band “). As discussed in subsect. 3.1 is, however, the intensity of the 426.21 keV y-line, as inferred from population systematics, about 2 to 4 times higher than expected for the 8+ + 6+ transition, of the ground state band. If the population systematics is applicable in this case, more than 50 % of the 426.21 keV y-intensity can be interpreted as the El transition between the KZ” = 33+ and 23- states. The intensities then give a satisfactory agreement with the Alaga rule for

r’aHf LEVELS

K=O* 1196 keV 23456

0:l

K.Z-

K.2-

1261 kcV

K=O+

1362 keV

2m

234 -

lL41 kcV 0:

K.4+

K.3+

1514 krV

1660 ke\

4

J

Fig. 8. Relative population of levels of excited rotational bands in I’sHf plotted as functions of the spin of the levels. For a given band, the population is a smooth function of angular momentum, and it is evident that the population of a level can be predicted to within 50 % if an adjacent member of the same band is known, and probably to within a factor of 2-3 if no other band members are known. The dashed curves represent visual fits to the points. Bands with the same principal K quantum number have been fitted with the same curve.

TABLE 8

Parameters

in the rotational

energy formulae obtained for the rotational

bands in I’sHf

Band-head energy (keV) K= 0.00

1174.80 1198.0 1433.9 1443.5 (1818.6) b) 1260.57 1362.44 1513.88 (1860.20) b,

See the “) This The latter “) The

o+ 2+ 0+ o+ o+ o+ 224+ 3+

15.618 16.23 13.25 10.57 11.8 “) 9.88 10.51 14.55 13.37 11.68

-

15.157 45.0 29.0 28.8

1.43 -148.5 - 14.3

0.0398 -7.0

4.00

text for further &tails. value is obtained from the distance between the 1443.5 keV OO+ and 1515 keV 02+ levels. level has not been observed in the present work, but has been studied by refs. 2*s). rotational relationship between these states and higher-lying ones is not certain.

380

B. FOGELBERG

AND

A. BjlCKLIN

the El branching. The accuracy of the measured conversion intensity of the 426.21 keV transition is unfortunately too poor to decide whether it is dominantly of El or E2 multipolarity. Further support for the 3+ level is obtained from a primary y-ray transition defining a level at 1864k 3 keV [ref. s)]. Also the 4+ level should be visible in the (n, 7) reaction. The only strongly enough populated level candidate, which is situated within 10 keV from the energy suggested by the (d, p) data, is found at 1953.7 keV. Itis defined by the 1647.10 keV Ml transition, which is coincident with the 4’ + 2+ transition in the g.s.b. and by a primary y-ray a) defining a level at 1954 keV. It is possible that this level is the 34+ state, but if so, the decay modes of the 33+ and 34+ states are remarkably different, indicating unexpectedly strong odd-even effects in the K = 3+ band. 3.9. ADDITIONAL

K = Of BANDS

The O+ state at 1444 keV, observed in studies of the decay of ’ 78Ta [ref. “)I is only weakly populated in the (q,,, y) reaction. No trace can be found of the transition to the 2+ level of the ground state band and the EO transition of 1443.5 keV is barely detectable in the present work. The 2+ level at 1515 keV [ref. 3)] which probably forms the first rotational state to the 1443.5 keV O+ level could not be detected in the present work, since the depopulating transitions were obscured by the intense gamma and electron lines from the y-decay of more strongly populated levels around this energy. Another state with K = 0 and I” = 2+, also reported in ref. 3), is revealed at 1561.91 keV through an energy combination of the 1469.3 keV E2/Ml and 1255.21 keV E2 y-rays with the 2+ and 4+ levels of the ground state band. The alternatives K = 1 and K = 2 are not compatible with the low intensity of the presently not detected transition to the ground state. It is, however, difficult to understand why the O+ band-head expected at % 1500 keV cannot be found in the P-decay studies since the geometrical factor of the P-decay matrix element is expected to favour decay to a Of state by a factor of two relative the 2+ rotational level. The presence of still another possible K = O+ band is implied through the coincidence of the 1650.4 keV transition with the 4+ + 2+ transition in the g.s. band. The probable EO admixture in the 1650.4 keV transition suggests K = Of.This 1957.0 keV 4+ level has also been observed to receive feeding by primary y-rays from the capture state “). With a reasonable moment of inertia the 2+ level of this band would be expected around 1800 keV. A level is found at 1818.6 keV, defined by the coincidence of the 1725.0 keV y-ray with the 2’ -+ O+ transition of the g.s. band, and an energy combination of the 1512.4 keV y-ray to the 4” member of the g.s. band. The y-ray branching from this level is compatible with KZ" = 02+ or 12+ assignments, but the lack of knowledge of the conversion coefficient of the 1725.0 keV transition makes a definite K = 0 assignment impossible. Also the 1818.6 keV level has been observed in studies or primary y-rays 8*“).

“sHf

LEVELS

381

3.10. OTHER LEVELS

in addition to the two K = 2- bands we find a negative-parity level at 1403.21 keV (see also subsect. 3.6). This level does not decay to the K = 2’ band, which suggests a low K quantum number. However, both KI” = 01 -, 03 - and 11- assignments imply considerably stronger transitions to theOO+ or 04+ statesin the g.s.b. than is observed (the predominant part of the 1403 keV transition is coincident with the 2+ -+ O+ ground state transition). A KI” = 12- assignment would imply the existence of a KP = 11- level rather close to 1403 keV, which should have been populated strongly enough to be seen (the de-exciting y-rays might of course be obscured by stronger ones). Conversely, a 1I- assignment would indicate the presence of a 12- level which has not been detected. It is also likely that the band head in this case should have been populated in the p-decay of l’*Ta. We therefore tentatively suggest the 1403 keV level as a KI” = 22- state. TABLE9 Levels in l’*Hf for which unique quantum number assignments could not be made, or which could not be safely assigned as belonging to any rotational band Level energy GceV) 1403.21 AO.10 1561.91 kO.20 1805.0 &IO.5 1818.6 kO.4 1873.0 &LO 1953.7 rto.4 1957.0 &to.4 *) 3 ‘) “)

The The The The

Possible assignment K in

Main mode of &cay Transition(s) final level(s)

1,2 0

22+

0, 1

2,3,4 2, 394

0

2, 334 2, 3,4+ 4*

1310.04 El 1255.21 E2/Ml 1561.0 E2/Ml 1711.8 1512.4 1725.0 1780.5 1647.1 E2/Ml 1650.4 E2+MI+EO

93.17

306.61 93.17 93.17 306.61 93.17 93.17 306.61 306.61

Comments

‘1 1

b.C

2+ 24 4+

‘1 &c.d

)

2’ f:

:;

44

a.c.d )

level is established through the coincidence measurement. level has also been observed in studies of r’*Ta decay 3). level is populated by direct transitions from the 3, 4- capture state s* p)+ 1818.6 and 1957.0 keV Ievels may possibly belong to the same K = O+ band.

Table 9 contains the decay data for levels observed, for which it has not been possible to make certain assignments concerning rotational relationships or quantum numbers in the present work. 4. Concluding remarks Through a detailed study, primarily of the transitions in the 1 MeV region following the thermal neutron capture in l”Hf, it has been possible to establish several new bands and find additional information on the already known bands in “sHf. As is common in thermal neutron capture reactions the ~-vibrational band is especially

382

B. FOGELBERG

AND A. BACKLIN

strongly populated. A remarkable feature of r7*Hf is the large number of K = Of bands; in addition to the three known bands “) we find evidence for possibly two additional bands. Another feature is the existence of two low-lying K = 2- bands only 100 keV apart. Several bands expected at comparatively low energy are not observed. We note here that in spite of a careful search for it no evidence is found for the K = 1octupole band, which is predicted at 1.4 MeV [ref. “‘)I. As discussed in subsect. 3.10 is the 1403.21 keV level not likely to be a K = I- state. If the band exists at this low energy we expect it to be rather strongly populated in the present experiment and we therefore suggest that the energy of this band may be several hundred keV higher than predicted. The K = O- and K = 3- octupole bands are predicted to be at 1.8-1.9MeV [ref. 47)], wh’tc h ex pl ains why they are not observed. A study of conversion electrons from neutron capture in ’ 77Hf has recently been reported by Prokofjev and Rezvaja 4s). They present a level scheme containing three levels of the K = O+ band based at 1198 keV, four levels of the y-vibrational band, three levels of a K = 2- band at 1249 keV, three levels of the K = 4+ band, three levels of a K = 3+ band at 1873 keV and two levels of a high-lying K = 5+ band. Of these, only the levels of the K = O+ band, the first three levels in the y-band the 4- level at 1409 keV and the first two levels of the K = 4+ band agree with the present work. We are indebted to Dr. P. Kleinheinz for communicating results prior to publication. The work was supported by the Swedish Atomic Research Council. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21)

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I’sHf

LEVELS

383

22) A. Biicklin et al., Phys. Rev. 160 (1967) 1011

23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48)

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