Investigation of the low-lying levels of 179Hf with the (n, γ) and (n, e) reactions

Nuclear Physics A262 (1976) 273- 300: ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

INVESTIGATION WITH

OF THE

THE

LOW-LYING

L E V E L S O F 179 H f

(n, ?) A N D (n, e) R E A C T I O N S

M R. BEITINS, N D KRAMER. P T PROKOFJEV and J J TAMBERGS

Institute of Ph).stc+, Latvian Academy oJ Scwnce, Rzya. USSR L JACOBS. G VANDENPUT, J M VAN DEN CRUYCE and P H. M VAN ASSCHE

Leuven L'ntt er~ity and SCK/CEN, ,$tol, Belytum and D BREITIG, H A BAADER and H. R KOCH

Techmcal UmtetstO,, Mumch, Fed Rep Germany and Research E3tabhshment. RtsO, Denmark Received 18 August 1975 (Revised 5 February 1976) Abstract:The excited levels of 17')Hf are investigated using the thermal neutron capture 7-ray and conversion electron spectra measured with the bent crystal diffraction spectrometer in R~s¢ and the flspectrograph In Riga The level scheme contams the odd panty rotational bands 7-[514], ~- [510], ~- [5121, ½- [521 '1, 3- [512] and ~- [503] The energies of these levels and the intensity rauos of the transmons between them are calculated taking into account the rotation-particle coupling (RPC) The following even parity levels are proposed 859 0 and 942.2 keV (~ ~ and ~' ofthe ~ ÷[633,1 band), 1004.1 and 1079 2 keV (z5. and ~ + of the 9+ 1-624,1+ Q(22) band); 1186.0, 1199 2 and 1296 4 keV (½", ~+ and a+ z of the ½~[651] band). The levels at 1249 8, 1269 7, 1432 9, 1482 2 and 1755,5 keV, supported by the analysis of the 77 coincidence spectrum and Ge(L 0 singles data, are discussed I

NUCLEAR REACTION l:SHf(n, 7). E = thermal, measured E, 1>, Ic,, 77-com 17°Hf deduced levels, J, n, K, co, transmon mult~polantles Enriched targets

I. I n t r o d u c t i o n

T h e i n v e s t i g a t i o n o f the 179Hf level s c h e m e u s i n g the (n, y) r e a c t i o n was i n i t i a t e d b y M a n f r a s s et al. 1). T h e level s c h e m e u p to 1 M e V was c o n s t r u c t e d u s i n g c o n v e r s i o n e l e c t r o n a n d 7-spectra u p to 660 keV, 77 c o i n c i d e n c e s , as well as the e x c i t a t i o n cross s e c t i o n s for the 179Hf levels seen in (d, p) a n d (d, t) r e a c t i o n s 2, 3). T h i s level s c h e m e 1) c o n s i s t e d o f the s i n g l e - p a r t i c l e states 5 - [ 5 1 4 ] , ½- [ 5 1 0 ] , 25- [ 5 1 2 ] , ½- [521], 3 - [ 5 1 2 ] a n d 27 - [ 5 0 3 ] a n d o f the r o t a t i o n a l b a n d s b u i l t u p o n t h e m . A l e n i u s et aL 4) h a v e s t u d i e d the t h e r m a l n e u t r o n c a p t u r e 7-ray s p e c t r u m o f 17~Hf in the e n e r g y r e g i o n 5 0 0 - 6 0 0 0 keV by m e a n s o f G e ( L i ) a n t i - C o m p t o n a n d p a i r 273

274

M R BEITINS et al TABLI: l Spectrum of ;,-rays. conversion electrons and

E,(AEO

l't(Al,)

(keY)

(rel umts)

42 172(2) 45 8612(7)

1.71(55) 57 1(91)

46 100(2) 46 548(3) 50 411(3) 55445(1)

1 94(52) 1 62(55) 1 66(48) 30 15(392)

55 493(2) 58 078(5) 58 589(6) 66 113(4) 76 024(7) 80 637(10) 82 732(4) 84 299(2) 86 107(4) 86.857(3) 86 978(6) 88 873(3) 93 131(5) 97441(3) 98.439(2) 101 252(6) 101 305(2)

3 94(138) 1 09(34) 117(41) 2 29(55) 1 71(55) 104(38) 1 40(45) 1 55(23) 111(32) 2 19(42) 1.27(48) 1 20(19) 0 92(28) 1 20(16) 5 69(46) 0 84(26) 21 9(15)

101 624(10) 102 082(12) 104 720(5) 105 167(5) 105 904(2)

0 71(18) 0 59(18) 0 91(24) 0 91(24) 15 3(11)

106 410(4) 111.110(12) 111 566(7) 117 606(14) 118 056(17) 118 835(3)

0.79(13) 0 52(14) 0 72(23) 0 57(17) 0.47(16) 11 16(78)

E~(/IE )

I (AI,)

(keV)

(rel umts)

L1 L2 M~ M2 N

34.59 ") 35 12(3) 43.24(3) 43.52(5) 45 32(2)

240(40) 28(8) 70(18) ") 8(2) 23(3)

L1 L2 MI

44 20(3) 4472(5) 52 84(5)

65 (10)") 5(2) 12(4)

L~

87 14(3)

K L1 L2 L3 M2 M3

35 93(5) 90 02(3) 90.57 ¢) 91 74 ¢) 98 96(3) 99 17(3)

15(5) 3 0(15) 23(3) 16(3) 8(3) 7(3)

K L1 MI K

40 55 ~) 94 61(3) 103 37(5) 41 0(1)

38(7) 4 5(10) 2(1) 3.0(15)

K

46 2(1)

2.5(12)

K

53 48 ¢)

Shell

5(2)

21(3)

1;OHf

275

transmon multlpolanties o f 179H f (40- 450 keV) ~(A=)

~ (theor) Multlpol

(exp)

E2

M1

4 2(10) 0.49(17) 1 2(4) 0.14(5) 04(1)

05 40 0 15 9.3

48 0 45 1.03 0 II 03

MI, MI + E 2

2 2(5) 0 17(8) 040(15)

03 16 86

2 75 0 24 068

MI, M1 + E 2

0 9(4)

0.1

05

M1

0 7(2) 0 14(7) 1 1(2) 0 7(2) 0.37(14) 032(13)

0 94 0 092 0 92 0 83 0 235 0215

33 0 475 0 042 0 0054 0 010 00013

E2

2 5(5) 0 3(7) 0.13(7) 4(2)

0 86 0 82 0.38 0.84

2.9 0 46 0 1 28

M1, MI + E 2

3(2)

0 78

25

MI

1 9(3)

067

2 13

Remark

+KLIL 2

M1

M I + E 2 d)

+KLlL3

276

M R. BEITINS et al TABLI:: 1

E (AE)

(keY)

l,(a~,) (rel. umts)

E (AEo) (keV)

UAIo) (tel umts)

M K Ll K L1 L2 L3

107 55(3) 116.27(5) 57 45 ~) 111 58(5) 58.04") 112 0(1) 112 61(5) 113 84(5)

2 5(6) 0 6(2) 6(2) I 0(5) 3(1) 0 3(2) I 5(5) 1 0(5)

K

60 67(5)

1 0(3)

K K K K

75 1(1) 82 1(1) 82 9(1) 86 05(8)

0.7(3) 0 7(3) 0.6(3) 0.6(3)

K

94 00(5)

2 5(10)

KM~ KM 2

92 66(5) 93 14(8)

3 5(5) 1.o(5)

95 355 ~) 149 43 ¢) 149 97 ~) 151 145 ¢) 158 105 15860(5) 160 17 ¢)

Shell

L1

122 797(5)

5 20(31)

123 386(5)

6 18(37)

125 863(5) 125 969(2) 126.002(6) 130 258(4) 133 064(2) 134 989(12) 136 275(8) 136 437(7) 137 524(6) 137 734(9) 137 870(8) 140434(3) 147 477(15) 148.162(4) 151 357(8) 159 060(8) 159 303(11) 159 372(14) 160 706(2)

0 81(19) 1 14(10) } 0 65(19) 0 82(12) 0 92(9) 0 60(11) 0 52(16) 0 52(16) 0.57(14) 044(11) 0 50(7) 0 82(8) 064(13) 0 58(6) 0.53(13) 0 32(9) 0 79(10) 0 32(9) } 29 15(175)

K

95 85(5)

Ll L2 L3 M1

149 97 150 42(7) 151 6(1) 1586o(5) 160.6(1)

505(40) 158(2o) 29(9)") 1oo(14) 47 5(75) 29(5) ") 18 0(35) 28 5(5) 1 5 (calc) 4 (talc) 1 0(5) 0.8(4) 1 (calc) 0 5(2)

K K

106 10 ~) 107 1(I)

3 5(5) 0 5(2)

K LI L2 L3 Ms N 161 202(2) 161 351(3)

166 927(43) 168 176(6) 169 693(9) 171.447(3) 172 456(10)

37 9(26) 446(36) }

0 22(9) 0 37(5) 041(6) 644(39) 0 39(11)

179Hf

277

(continued) (theor)

~(A~) (exp)

Mult~pol E2

MI

0 05(3) 0 24(8) 0 16(8)

1) 066 0 23 061 0 062 06 0 06 0 38 033

03 0 075 19 0 275 18 0 27 0.02 0.003

0.9(4) 11(5)

0 385

115

0 37

1 05

0 21(5) 0 05(2) 1 2(4)

0 2(1) 0.5(2)

1 0(5)

11(6)

17 3(17)

5 4(8) 1 0(3)a)

3 4(5) 1 6(3) 1 0(2)") 0 6(1) 0 75115) 0 305

0 54(8) 1 2(7)

~(M3) h) 19.7 6 27 115 4 O0 I 86 18 0 78

09 0 125 0011 0 0014

0.89

0 0 0 0

0 122 0011 0 0014 0 031

032 11 09 06

0 26

MI + E 2 E2

MI MI M1 M1

M3 +La 16120+K21526 + M ~ 161 20

0 032

0 305

0 76

Remark

MI + E 2 E2 a) - L 2 160 7 1 + K 2 1 5 2 6

+ M 3 160 71

M 1 + E2 M 1

278

M R. BEITINS et al TABI r

I,(A/)

E (AE) (keY)

(rel umts)

173 749(24) 173 998(8) 174 951(8) 176 768(36) 178445(11) 180.628(3) 182 751(3)

0 31(7) } 046(6) 0 44(10) 0 23(8) 0.37(10) 1 34(8) 3.37(20)

183 696(12) 185 248(9) 185 998(27) 191 q64(19] 192 948(6) 193.332(2)

0 34(7) 0 27(4) 0 27(6) 0 20(6) 0 49(9) 61 09(30)

193 8 197 402(26) 201 1 202 302(2)

35 07(18)

203 198(3)

5.52(28)

203 842(4) ~ 204710(4) 205 280(11) 205493(6) 205 965(3) 206 165(5) 9 207 946(39) 211 258(8) 214 360(2)

214 58(2) 214 945(3) 215 053(4) 217.858(16) 224408(31) 224 744(7) 228 390(11) 230 362(18) 231 808(41) 232.461(4)

Shell

E (AE¢) (keY)

l,(Ale) (rel umts)

K

108.4(1)

0 5(2)

K K L1

115 32(7) 117 40 ") 171 55(10)

0 6(3) 2.0(5) 0.5(2)

K K L1 L2 M K

127 55(7) 127 98 ¢) 182 06(5) 182 5(1) 190 7(1) 128.4(1)

< 05 30(5) 4 5(10) 0.4(2) 1 2(5) 1 0(5)

K K L1 K L1 K K K

135 7(1) 136 95 ¢) 190 97(7) 137 80(7) 191 9(1) 138 5(1) 139 3(1) 139.97(7)

K

14061(5)

K L1 L2 L3 M N

149.01 ¢) 203 09 ~) 203 62(5) 204 60(7) 211 9(1) 213 76(5)

K

159 38(7)

0.31(6)

0 72(6) 1 61(10) 1 32(75) 0 49(5) 3 42(24) 0 54(6) 0.22(9) 0 43(5) 1ooo(5o)

1 36(52) 5 52(4O) 1 27(16) 0 37(11) 0.37(5) 1 08(6) 1 48(82) 0 31(9) 0 27(4) 1 55(9)

I 0(5) 15(2) 2 0(7) 1 7(6) 0 3(2) 0 30(15) 0 30(15) 0 30(15) 1 5(5)

51(7) 9 5(25) 1 2(4) 1 0(5) ~) 1 2(4) 0 5(3) ")

0 5(2)

179Hf

279

(continued)

~(A~) (exp)

ct (theor) Multlpol E2

MI

0 45(23) 0.60(15)

0 22

0 66

0 49(9) 0.07(2) 0 006(3) 0.02(I)

0 185 0 024 0 048 0.028

0 55 0 076 0 0066 0 0195

M I + E 2 ~)

0 43(6) 0.06(2) 0 3(1)

0.165 0 018 0 163

0 47 0 066 0.465

M I + E2 a)

0 4(2) 0 2(1) 0 23

0 162

0 465

0 160

0 46

M1 E2 E2

0 45(15)

0 158

0.45

M 1, M 1 + E2

0 051(8)

014 0016 0 032 0 0225 0018

~t(E1) b) 0 0414 0 0048 0 0008 0 0008 0.0014 0 0004

Remark

MI. E2 M1

M1 + E2

0 05(3)

0 0095(25) 0 O012(4) 0 0010(5) 0 O012(4) 0 0005(3)

0 5(2)

0 12

0 35

E 1.nom

+ K 269 88

+ K 279 07

M1

280

M R. BEITINS et al T~,BI I 1 E (AE ) (keV)

1 (AI ) (rel. umts)

233 914(8) 235 481 (62) 238 550(12) 238 718(391 238 989(30) 239 194(3)

0 58(5) 0 20(7) 0 31(51 0.37(181 0 32(15) 11.98(60)

239 432(8) 242 031(7) 244 315(3) 245 325(5) 247 109(8) 254.653(23) 254 987(11) 258 648(5)

0 46(7) 0 38(4) 5 66(28) 1 91(121 0 53(5) 0 38(6) / 0.64(6) j 27 91(140)

259 886(8) 260 719(38) 263 559(25) 264.643(63) '~ 265 467(58) 266 107(15) 266 988(8) 269 881(4) 270 697(201) 271 877(31) 273 186(8) 273 404(18) 274 728(29) 275 29(3) 277.00(1) ? 278 301(141 279 066(4) 279.50(5) '? 280 18(1) 280 75(2) '~ 282 11(2) 282 37(4) 288 50(6) 295 14(2) 296 02(4) 296 44(5) 296.84(2) 297 31(12) 299 04(5) 299 760(4) 302 25(9) 304.024(4) 304 523(7)

0 63(10) 0 23(4) 0 27(4) 0 30(4) 0 20(5) 0 54(4) 1 23(7) 6 11(37) 0 15(10) 0 18(4) 0 93(10) 0 42(5) 0 21(4) 0 18(4) 0.61(6) 0.31(4) 5 72(29) 0 20(8) 0 57(6) 0 33(6) 1 55(87) 0.15(4) 0 21(4) 0 59(5) 0 17(5) 0 22(4) 0 39(10) 0.17(7) 0 20(7) 13 21(66) 0 18 152 3(76) 1.80(14)

Shell

/ :

)~

)

E,(A E,)

1~(AIc)

(keY)

(rel umts)

K LI K

173 84 c) 227 9(1) 174 3(1)

3 5(10) 0 3(1) 0 25(151

K K

178 93(5) 179 8(1)

1 5(3) 0 7(2)

K K L K

189 4(1) 193 30 c) 247.4(1) 194 57(7)

0 5(2) 6(1) 1 0(3) < 03

K K

201 5(1) 204 55 ¢)

0 30(15) 1 2(6) a)

K

208 0(2)

0.3(2)

K

213 76 c)

1.(1(4) a)

K

229.8(1)

0 25(151

K

234 36 ")

1 5(5)

K

238 67 c)

26(4)

179Hf

281

(continued) (thcor) (exp)

Multlpol. E2

MI

0 29(7) 0 025(10) 0 55(35)

0 105 0 0065

0 30 0.021

0.26(5) 0 35(10)

0 092

0 28

0.084 0 033

0 24 0.036

0.21(4) 0 03(1) <05

Remark

MI + E 2 d) M1 MI, M1 + E 2 M1

M 1 + E2 d) (M1)

0 25(13) 0 2(1)

0 074

021

M1 MI + E2

+ L 3 214 36

0 18(7)

0 067

0 19

MI

+ N 21436

0.4(2)

0 058

0.165

0 11(4)

0 056

016

MI+E2

0 17(3)

0 053

0 153

MI d)

282

M R BEITINS et al. TABI r I E(AE

)

(keV)

304.80(4) 305.6 310 17(5) 311 41(4) 311 88(8) 313 30(3) 314 828(8) 315 38(6) 315 93(4) 316 50(4) 318 925(12) 319 26(2) 320 09(4) 324 47(4) 326 057(5) 326 37(4) 328 98(5) 330 92(5) 331 85(9) 337 747(8) 338 57(5) 341 76(1) 345 611(8) 345.81(31 348.43(8) 346 12(2) 351 1(11 9 352 81(31 353 46(2) 354 96(5) 356 16(3) 357 99(2) 366.14(16) 367 28(4) 369 73(5) 372 910(9) 376 69(5) 380 54(24) 384 76(3) 386 30(11 386 85(6) 388 50(3) 395 43(6) 397 72(131

I (M) (rel umts)

Shell

F. ( a E ) (keV)

I (AIo) (rcl umts)

Ll+2 M N

292.75 ~) 301 42 303 7(2)

3 5(5) 0 9(3) 02(11

K

240 3(2)

K

246.4(2)

o 15(5)

K

249 4(2)

o lO(51

K

253 5(2)

o lO(51

K

260 71 ¢)

0 20(5)

K

280 4(2)

o 3(1)

K

288 3(2)

<01

K

291 0(3)

<01

0 27(9) 0.15(5) 0 15(4) 1 28(9) 0 33(10) I 29(9) 0 16(6) o 18(5) 0 23(4) 0.98(8) 0 39(4) 0 36(12) 0 22(4) 4.29(30) 0 30(10) 0 32(4) 0 22(4) 0 22(4) 1 70(10) 0 16(5) 1 09(8) 3 18(22) 0 85(33) 1 62(10) 0 42(8) 0 18(51 o 28(5) o 82(6) o 2o(3/ o 92(37) o 28(6) o 42(8) o 17(6) 0.46(13) o 18(4) 1 99(i 2)

0.27(4) o 20(8) 0 33(10) 1 36(8) 0 23(5) 1 27(42) o 30(5) 0 25(6)

307 8(3)

~01

0 2(11

320 5(4)

<01

323 4(4)

<01

i ~'~Hf

283

(continued) ~(J~) (exp)

(theor) Multtpol E2

MI

0 023(3) 0 006(2)

0 0135 0 0044

0 023 0 005

0 12(4)

0 051

0 142

M1, MI + E 2

0 08(4)

0049

0 140

MI+E2

o lO(5)

0 048

0 136

M 1, M 1 + E2

0 05(1)

0.046

0 128

E2

0.12

0.036

0 103

MI, MI + E 2

00355

010

MI,MI+E2

0031

0089

M1, M I + E 2

< 0 07

0 0305

0 082

M 1, E2

< 008

00303

0081

MI, E2

<

<011

0 10(5)

Remark

284

M R BEITINS et al TABLE 1

E (AE>,) (keV)

I>(AI ) (rel umts)

398 84(8) 402 45(1) 405 02(9) 408 09(2) 409.99(2) 412 15(8) 413 19(1) 416 95(10) 421 24(5) 427 68(6) 429 84(1) 432 76(3) 433 63(3) 435.74(2) 436 22(17) 443 32(6) 443 87(7) 445 29(5)

0 22(7) 3.31(20) 0 23(8) 0 91(7) 1.81(14) 0 31(9) 3 20(19) 0 33(6) 0 59(17) 0.46(9) 3 63(22) 0 69(7) 0 91(8) 2.56(16) 0.38(10) 0 72(12) / 0 55(11) j 0 63(7)

Shell

E (AE~) (keV)

l (dl,) (rel umts)

K

336 5(4)

< 01

K

348 3(4)

K

3646(4)

K

370 5(3)

0 10(5)

K K

378 2(5) 380.2(4)

0 05(3) < 0 05

0.15(5)

< 01

The hnes of 178i_ifand the Auger electrons are vvathdrawn from the spectrum For AE. A 1 and A2, the errors ~) The hne intensity ~sgwen after subtracting the intensity of another hne with the same energy ") Energy calibration hnes d) Intens,ty cahbratlon hnes

spectrometers Beitms and Prade 5) have measured the -t-ray spectrum o f ' 79Hf for the 50- 2000 keV region using a Ge(Li) detector (resolution o f 2 keV at 600 keV) and "/), coincidences between two Ge(Li) detectors. Casten and Kane 6) have investigated both the low- and high-energy ),-ray spectra o f 179Hf with the (n. 7) reaction for resonance neutrons in the 7-energy regions 160--2000 keV and 4 45 MeV. Hill and Meyer v) located eighteen 7-transitions, observed in the/~-decay o f 179Lu between ten levels o f 179Hf up to 1200 keV. In this work, the spectrum o f 7-rays m 179Hf following the (n,),) reaction has been studied using the curved crystal spectrometer in Rls0. The 179Hfconversion electron spectrum has been measured using the 3-spectrograph xn R~ga but with a better resolution and sensitivity than in previous work 1).

2. Experimental methods and results The Ris~ curved crystal spectrometer 8), located at the D R - 3 reactor, was used to analyse the low-energy spectrum o f 179Hf after thermal n e u t r o n capture in an enriched target. An energy resolution for the bent-quartz diffractometer ofAE(keV) = 4 8 E 2 / n was obtained, where E is the 7-ray energy m MeV, AE the F W H M and n the diffraction order.

17OHf

285

(continued) ~t(Act) . (exp)

< 0 03

0 05(2)

< 0 03

0 04(2)

< 0 08

ct (theor) . . . E2 M1

Multlpol.

0 026

0 074

E2

0 024

0 068

M 1 + E2

0 022

0 062

E2

0 021

0.060

M 1, E2

0 020

0 056

M1

Remark

are gweu m umts of the last digit b) The quoted conversion coefficients apply only for the transmon of the gwen energy

The sample quantity was 30 mg H f O 2 , enriched to 89.1 9o~ in 178HF. The mare contaminant in the y-spectrum arose from the capture in 177Hf, but these lines are well known from the paper of Smither 28). The y-ray spectrum measured in the energy region 40-1150 keV is listed in tables 1 and 2. These tables contain only the lines assigned to t79HF. The energies are relative energies only. They can differ from the absolute transition energies by about 1 0 - , E~. This difference is not included in the quoted errors, as it only would hamper the apphcation of Ritz combinations. The intensity values have been normalized to the 214.36 keV line; the intensity value of which is assumed to be 1000. The (n, e) spectrum of t 7 9 H f in the energy region 30-600 keV was investigated by means of a/3-spectrograph with a homogeneous magnetic field 9). The target was made from hafnium oxide with an enrichment to 95.9 ~,, m iVSHf, that was vacuum evaporated on an alummium foil of 0.2 mg/cm 2 thickness. The evaporated target had a thickness of 0.I mg/cm z. After improving the spectrographlcal resolution and sensitivity, this target allowed us to obtain a resolution of 0.08 ~ for the line L 3 160.71 keV (E e = 151.15 keV). The energy calibration was made using the curved crystal spectrometer data. Intensity calibration was performed with the transitions for which the multipolarities are known from the level scheme (table 1). The (n, e) spectrum and transition multipolarities are reported in tables I and 3.

M. R BEITINS et al

286

TABIr, 2 Spectrum of ":-rays t79Hf (450- 1150 keV)

Er(A E :)

l~(d I,)

E>,(AE)

I>(A1:)

(keY)

(tel umts)

(keY)

(rel umts)

450.12(11) 455 40(5) 456 47(7) 459 41(16) 465 29(5) 466 43(3) 470.93(2) 476 48(12) 477 73(6) 478 43(4) 480 49(8) 482.41 (13) 483 18(4) 484 95(6) 486 80(3) 499 94(5) 506 31(4) 510 53(9) 511 03(3) 511 28(16) 512 61(4) 514.84(2) 516 27(8) 518 64(3) 520 58(8) 528.67(4) 532 87(12) 535 71(24) 536.09(11) 548 84(4) 549 49(10) 552 86(13) 564 49(22) 565 99(13) 568 36(8) 570 00(7) 571.73(4) 573 75(7) 582 44(20) 588 86(8) 589.99(10) 596 82(I 1) 600 03(5) 608 92(24) 612,51(8) 614,03(30) 615 36(14)

0 32(8) 0.52(9) 0 78(8) 0 43(7) 2 54(18) 1 55(12) 8.52(51) 0 88(13) 0 91(25) 2 85(17) 0 68(14) 0 42(12) 3 32(23) 3 39(24) 3 34(20) 1 02(13) 1 19(32) 0 66(20) 2 84(176) 0.88(22) 0.52(15) 0 70(18) 0 39(12) 5 62(34) 1 07(21) 6.07(36) 0 59(15) 1 06(28) 0.64(15) 3 07(25) 1 02(17) 0 59(15) 1 41(17) 0.65(16) 1 24(20) 1 70(24) 7 24(43) 3 44(24) 0.96(15) 4 02(28) 2 58(23) 1 00(18) 2,42(17) 0,57(17) 1,60(22) 1,06(25) 0 80(18)

616 85(9) 628 22(31) 635 31(3) 644 76(44) 648.67(11) 653 28(3) 655 42(5) 656 23(7) 658.94(18) 665 27(11) 669 38(13) 670.74(27) 694 04(12) 709.42(19) 712 36(13) 721 82(22) 728 94(7) 729 74(7) 731 46(20) 736.15(16) 738 96(20) 744 05(21) 761 46(11) 765 10(5) 778 34(15) 782.78(53) 788 01(11) 788.89(29) 810.83(5) 819 38(16) 829 50(24) 847 98(25) 852.14(26) 859 02(14) 867 89(25) 870.14(16) 873 71(16) 894 66(31) 914 85(40) 918.19(11) 925 97(16) 956.41(30) 976 04(37) 986 20(29) 1004 14(25) 1012.83(38) 1017 27(41)

1 94(2'5) 0 93(23) 7 26(51) 0 86(17) 1 44(18) 9 70(56) 8 25(58) 2 26(36) 0 79(20) 1 64(15) 1 89(34) 1.60(32) 1 50(20) 1.34(31) 3 00(30) I 02(26) 7 10(213) 13 10(341) 1 83(41) 2.14(26) 1 27(29) 1 94(29) 6 28(44) 11 53(69) 3 01(36) 1 49(33) 8 03(273) 1.25(37) 10.76(75) 2 84(40) 2 35(52) 2.26(41) 3 21(64) 7 00(70) 3 73(74) 7.13(93) 5 75(63) 2 63(63) 3.00(I 20) 7 62(76) 13 91(476) 7 96(159) 3 67(88) 5 35(106) 35 81(251) 7.96(253) 9 27(130)

179Hf

287

TABLE2 (continued)

E~(AE e)

I e(A~ )

Er(A Ey)

I ,(A Iv)

(keV)

(rel. units)

(keV)

(rel. units)

1035.53(31) 1039 54(71)

13 97(140) 8.63(181)

1082.73(28) 1103.66(35)

16.0(22) ") 17.1(31) ")

1055 66(19) 1062.61(32) 1067 53(32) 1079 16(28)

24.54(270) 8 84(159) 9.22(157) 15.5(22) ")

1111 55(42) 1121 43(37) 1141 52(66) 114470(71)

14.03(308) 17 56(350) 10 06(302) 9 3(31) d)

a) The sum intensity of nonresolved 178Hf and 179Hf lines

The Auger electron and 178Hf lines are drawn from the tables. We also used Ge(Li) singles and y~ coincidence data; the main part of this work was pubhshed previously by Beitins and Prade 5).

3. Discussion 3 I SINGLE-PARTICLE STATES OF ODD PARITY AND THEIR ROTATIONAL BANDS

The scheme containing the levels of the rotational bands ~-[514], ½-[510], 5-[512], ~-[521], 3-[512] and ~-[503], as well as the transitions observed in the spectra measured in our work, is given in fig. 1. The scheme of fig. 1 has essentially more precise energy values than the scheme proposed earlier 1). Besides, several new rotational levels are proposed and a greater number of transitions are located in the scheme due to the higher resolution and sensitivity: e.g., the 160.7 keV 7-line observed previously is now resolved into different lines, 160.706, 161.202 and 161.35 l keV, all fitting into the scheme. The same is true for the 304.0 keV line and for several others. The parameters of the rotational bands are calculated from the branching ratios for lntraband transitions and the value lo) Qo = 6.85(18) b: 27- [514]"

(gK--YR) 2 = 0.55(40),

5-[512]"

(gK--gR) 2 = 0.59(18),

½-[521]" ~-[510]:

(gK--gR)2(1 +bo) 2 = 1.99(36), (gK--,qg) 2 = 5.7(8),

b o = 0.36(5).

The 98.8 keV transition between levels I = ~zand ~ in the band ~- [510] has not been observed in the spectrum; the intensity estimated from the above-mentioned parameters is ~ 0.28, which is indeed lower than the lowest measurable intensity

288

M R BE1TINS et al ...g

~,7

L__

g

oj

I I

,/2-[5m]

7/f [503]

i °I!'j --,.~

m

|)y~*

:-.

(d,t)N~--J td,p}

' Hf 72

I07

7/2- [5t4]

y2" ~5~]

Fig 1 T h e odd p a n t y levels o f ' 79Hfbelow 1 M e V T h e short arrow shows that the level is populated from a capture state ,n the (n, 7) react,on T h e t r a n s m o n s m a r k e d w~th an asterisk are located twice m the level scheme.

for this energy region. The transition 45.86 keV (3 ~ ½) in the same band has a conversion line intensity ratio L1/L 2 = 8.5(10). Thts value corresponds to 62 = E2/M 1 = 0.0030(15) or M 1 + 0.3 i% E2. The calculation from the branching ratios of the 7-transitions 25.~ ½ and ~ ~ 3 gives a mixing ratio 6 z = 0.0035(5). This 62 value agrees well wxth the one obtained from the converszon spectrum. The value of (~/K--gr) e within the band 31512] is not calculated because the mtraband transitions are not observed here. The conversion electron lines of the transitions 160.71 kcV (½- [510] --*-~- [514]) and 214.36 keV (~- [514] --* 9+[624]), which depopulate the isomeric level (t = 18.6 s) at 375.07 keV, are clearly observed m the spectrum. Relative experimental and theoretical intensities for the conversion lines of the 160.71 keV M3 transition normalized to the L 3 line are given in table 4. It can be seen from the table that the 160.71 keV transition has M3 multipolanty without an E4 admixture. This result does not confirm the value 6 z = E4/M3 = 0.14(14) gwen in ref lz).

179Hf

289

TABLF 3 Multlpolantles of some transitions (460-660 keV)

E, (AE~)

IT(AI)

(keY)

Shell

(rel. umts)

465 29(5) 466.43(3) 470 93(2) 477 73(6) 478 43(4) 483 18(4) 484 95(6) 486 80(3) 518 64(3) 528 67(4) 548 84(4) 549 49(10) 571 73(4) 573 75(7) 588.86(6) 589 99(10) 635 31(3) 653 28(3) 655 42(5) 656 23(7)

2 54(18)) 1 55(12))? 8 52(51) 0 91(25)~ 2 85(17)) 3 32(23) 3.39(24) 3 34(20) 5 62(34) 6 07(36) 3.07(25) 1 02(17)J 7.24(43) 3.44(24) 4 02(28) 2.58(23)) 7 26(51) 9 70(56) 8 25(58) ~ 2 26(36) f

K

E¢(AEc)

I,(AI )

(keY)

(rel umts)

400 5(4)

0.05(3) ,~ 0 05

ct(A~)x 102 (exp)

ct x 102 (theor)

Multi-

E1

E2

M1

,~ 0.6

0 63

I 75

4.9

El

< 0 05 0 05(2) ,~ 0.05 0 05(2) 0 30(15) 0 2(1)

1.5(6) ,~ 1 5 1 5(6) 5 4(27) 3 3(17)

0 0 0 0 0

59 59 59 51 49

1 65 1 63 1 62 1 42 1 33

4 4 4 3 3

E2 E1 E2 MI MI

~ 07 3.0(15)

043 0 43

1.10 1.08

295 2 90

E1 M 1, M 1 + E2

2(1) < 1

034 032

089 0 83

225 2 10

M1, M I + E 2 E2, E1

K K

412 6(6) 417.8(5)

K K K

421 3(5) 453 3 a) 463 3 a)

K

483 6(6)

K

508 3(5)

< 0 1 ,~ 0.05 0 10(5)

K K K

524 2(7) 570 0 ~) 587.3(7)

< 005 0 15(8) < 0 1

K

590 2(7)

0 2(1)

polarities

55 52 50 85 65

a) Energy cahbrauon hnes TABLE 4 Relauve converszon hne mtenslt,es for the transmon 160 71 keV

cxp theor theor

M3 E4

K

LI

L2

L3

M1

M2

Ms

N

505(40) 492 5 18 5

158(20) 157 73

29(9) 28 8 167

100(14) I00 100

48(8) 39 2 1

75 43 5

29(5) 27 26 2

18(4) 19 6 18 7

The following values of the anomalous factors 29) d = 0~exp/~Ztheor (where ~ stands for the internal conversion coefficient) are determined for the conversion lines of the E1 transition of 214.36 keV with A K = l, for which nuclear size effects are essential: A(K) = 1.2(2), A(L1) = 2.0(5) and A(L2) = 1.5(5). The obtained values of A correspond to rather small values of the hindrance factors 13)

F w-B(E1)sp B(El)exp

--8x104 ,

FN-- B(E1),~ _ 16, B(E1)exp

becaase the internal conversion anomaly and the delay of the E1 transitions are strongly correlated.

290

M R BEITINS et al

From branching ratios for the M1 transitions between the rotational levels of different bands, we have also calculated the Mikhailov mixing parameters a, parametrlzing in this way the deviations from the Alaga rules. For M1 transitions, the Mikhailov formula for Ig,-Krl = 1 and Ki 4:½ reads B(M1; l,g, ---, IfKf) = (I,1K, K f - K , IIfKf>2M2{1 + [ I f ( I f + 1)--Ii(I,+ 1)]a +3K, , ( - 1)1' + ~(If+ !~ 2 - "jbf2 ,,'~2 •

TABI F 5 The ~alculat~ons of the mlxmg parameters a for the MI transmons K,

Kf

I,

Ir

E~

~-[512]

~-[514]

z 2

2 ~ ~

402 45 279 07

3 3(2) 5 7(3)

~-[5123

~-[5123 2

~ ~ 2, 22

269 88 171 45 380 54 282.11

6 6 0 I

t 32 _5 2

345.61 299 76 244 32

3 18(22)) 13 21(66) ~, 5.66(28) )

0 21(2)

~ ~ ~

367 28 311.88 205,96

0 46(13)) 1 28(9) ~3.42(24) )

020(6)

~-[512]

½-[5103 z 32

1/

a ].

1(4) 4(4) ) 20(8) ] 55(87) J

0 024(2)

0.041(4) 0035(20)

It is seen from table 5 that the mixing parameter for transitions between the levels of the bands 3-[512-] ~ ½-[5103 is greater than the same parameter for the transitions of the bands ~- [512] -~ _~- [514] and 3- [512] ~ 3 - [512]. The Coriolis mixmg calculation, given in table 6, also shows the wave functions of both these first states to be less pure, considering the values of the admixed components, than the wave functions of the 52-[512-] and ~--[514] states. The Mikhailov parameter is the smallest for transitions between the latter states, which are found to be rather pure. The parameter is also larger for transitions between the state 3-[512], which is less pure, and the pure ~- [512] state, and a is the largest for transitions between the 3-[512] and ½-[510] states, which both have larger admixed components. For the transitions from the band 3-[512] to the ~-[521] band, which is even more Coriolis mxxed than the ½-[510-] state, the corresponding Mtkhailov parameter is expected, in th~s quahtative picture, to be even larger. As no branching ratios are available this could not be checked. It might be noted that from all levels of the band 7-[503] only the -~- level at 870.7 keV has a large (d, p) cross section is. 27). Therefore, we have not sufficient

179Hf

291

TABLr 6 Energles and mixing amphtudcs for Conohs coupled negahve panty bands m 179Hf

K'~[NnzA]

I-[510]

21-[521]

J~

Eale

(keV)

½15101

½1521]

31512]

2~_32 g122

375.08 420 94 476 38 582 29 681 09

375.23 421 19 475 36 582 25 681.78 848.56

0 9977 0 9956 0.9872 0.9818 0.9716 0 9611

-0.0684 - 0 0482 -00963 - 0 0638 - 0 1073 - 0 0782

00799 -01268 - 0 1763 - 0 2039 - 0 2597

00110 0 0298 0.0265 0.0515

0.0021 0.0031 0.0074

0.0001 0 0001 0 0002

~

61427 679 58 701 12 849 28

61423 679 86 701 01 849 21 896 06 1126 96

00684 0 0722 0 1213 0.1547 0 1583 0 2298

09977 0 9403 0 9709 0 8047 0 9561 0 7389

0.3327 0 2072 0 5730 0 2464 0 6329

0.0043 0 0144 0 0123 0 0259

0 0006 0 0009 0.0021

0.0001 0 0 0003

720.69 788 25

71881 790 I 1 905 96 1023.48 1208.66

00591 0 1030 0.1048 0.1729 0 1414

-03370 - 0 2200 - 0 5903 --0 2728 - 0 6692

09396 0 9700 0.8002 0 9460 0 7291

0 0135 0 0162 0 0259 0.0221

0.0006 0.0015 0 0016

0 - 0 0001 0

51838 616 82 742 78

51903 616 70 742 25 895 74

-00128 -00332 - 0 0323 -00593

-00001 -000t31 -0.0019 - 0 0003

-00126 -0.0160 - 0 0221 -00191

0.9998 09972 0 9944 0.9901

00651 0 0977 0 1255

0.0021 0.0031 0 0040

21436 337 75 485.23

21551 336.78 485 04

-0.00Ol - 0 0002 - 0 0004

0 0.0001 0.0001

0.0006 0 0012 0 0019

-00652 -0.0978 -0.1258

09975 0 9949 0 9917

00266 0 0266 0.0265

8707 996 7

87070 994 15 1145.04

-00001 0 - 0 0002

0 0.0001 - 0 0001

-00003 - 0 0005 -0.0007

-00267 -0.0267 -0.0268

09996 0 9996 0 9996

~,2_ i ;t2~2~-[512]

~2 1-

~2 2~-[512]

~_72

x2! ~-[514]

2112

}-[503]

~_ 2

__

Mixing amphtudes

Ee~p

(keV)

0 0 0

~[512]

~[514]

7[503]

information on the moment of inertia for this band. For the nearby ~83W and 185w nuclei the inertial parameter A for this 7 - [ 5 0 3 ] state has been determined ~6, 27) as 15.8 and 16.4 keV respectively. The analysis of the o/-ra.y spectrum has shown that the level ~ - [ 5 0 3 ] in 179Hfhas an energy of 870.7 keV, which is confirmed also by the coincidence between transitions 656.23 and 214.36 keV. We propose that the level at 996.7 keV has a rotational character. Its depopulation is shown in fig. 1. This energy agrees well with the calculations listed in table 6, which predict an energy of 994.15 keV. In this way, an inertial parameter A = 14.0 keV is obtained for this band. We have compared the experimental values for the ratios between the MI reduced transition probabilities between the levels of the bands 7- [503] and 7- [514] with the calculated probabihty ratios taking into account Coriolis interaction. Experimentally one finds, B(~--* _i)/B(_ ~ i7 __., 9) = 2.1(6) and B(9 ~ 7)/B( 9 --, 9) = 1.1 (4),

292

M . R . BEITINS et al

while the calculated values are 3.5 and 0.06, respectively. Also the Alaga branching rules, in the latter case, lead to a value of 0.36. which still results in an intensity for this -~ -~ -~ transition below the limit of observability. It could therefore be quite possible that this transition fits only by accident this energy sum, especmlly taking into account the larger error of 0.5 keV, masking in this way a weaker deexcitation. To draw attention to this, the transition is dashed in the level scheme (fig. 1). Let us consider now the 935.7 keV level. It is weakly excited in the (d, p) and (d, t) reactions. In the (n, y) spectrum, nine ~-transitions could be found, which depopulate this level to the rotational levels of the bands ~-[514], ½-[510], -15-[512] and ~- [512]. This decay pattern allows us to assign for this level the spin and panty P = 7 or 5- (fig. 1). In a previous work 1) the assumption was made that the 935.7 keV level has the structure ~-~[512]. The great difference ( ~ 50 keV) for the position extrapolated from the } and -25level energies of the same band was explained as a consequence of the Coriolis interaction with the levels 7- i[503] 7 5 and ~ - 2[512] which are located not far from 935.7 keV (fig. 1). However the calculations given in table 6 did not support this assumption because the calculated value of the -~-~[512] level is now 906.0 keV. We propose a level at 898.9 keV which deexcites to the levels of the bands ½-[510] and ~-[512]. The calculations of the mixing parameters a (table 5) confirm the depopulation of this level to the ~z- [-512] band. This is not in contradiction with the quantum numbers 2-31512]. The structure of the 935.7 keV level remains an open question taking into account the above-mentioned facts. 3.2 CORIOLIS M I X I N G C A L C U L A T I O N S

Our experimental data on the 179Hf negative parity states show that there exist deviations from the adiabatic unified model both in the level energetics and in the depopulation of the rotational bands. This is most evident in the deviations from the energy values defined by the I(I+ 1) rule and, besides, in the existence of':-transitxons which are forbadden by AK in the adiabatic theory (i.e., for these 7-transitions with 2 < IKI- KrL). These phenomena can only be explained by taking into account band mixing due to nonadiabatic effects. Our approach to the explanation of band mixing is based on Coriolis interaction calculations. This method is treated in detail in refs. ~7-19). Six interacting bands, based on the Nilsson states ½-[510], ½- [521], ~-[512], ~-[512], ~-[514], ~- [503], contain eighteen known levels and these levels are described by seventeen parameters. A fit to the experimental energies (see table 6) was performed, resulting in a mean deviation A = IEcxp-Ecalc I = 0.81 keV of the energy for a single level and ~2 ~--- 11.72 for one degree of freedom. The ratlos of the reduced ),-transition probabihties have been calculated for all M 1 transitions with AI = 0, 1 and for E2 transitions with AI = 2 between the levels of th~s six band mixed system. The calculations were made in two ways:

179Hf

293

TAB[ L 7

Ratios of the reduced MI and E2 y-transition probabdltles in the system o f mixed if" = 12 ~2±- s 2a- ~252- and 22- bands in 179Hf Level energies (keV)

Ratios of reduced 7-transition probaNhtics t, f

-

Eo

21436

337 75

375 08

420 94

476 38

518 38

E .... or Er, 2 a)

Energies of 7-transmons (keV) E~,/E~2

exp. ratios

~alc ratios

ratios

error d)

mixed

unmixed

33775 7 701 12J

l

12339/48680 h)

110

10

170

518 38} 616 82

~

"~04 02/402 44

110

10

140

518.38 701 12 J

1

304 02/486 80 b)

190

15

76

485 23 616.82.1

I

147 48/279 06

485.23 849.28 J

l

147 48/511 28 b)

30

10

19

616 82 742 98 J

I

279 06/405 02

76

26

170

849 28 ~ 8707 J

~

511"28b)/53287

420 94 72069)

l

476 38 } 701 12

1

101.30 ¢)/326 06 c)

614 27 } 679.58

l

239 19/304.52

582 29 / 898.9 )

l

161 35 c)/478 43 c)

614 27 51838J

1

19333/ 9744 b)

614 27 720 69 )

1

193.33/299 76

17

1

582 29 720 69 I

I

10590/24431

33

3

19

1 8 x 104

679 58 788.25 J

l

203.20/311 88

16

1

55

2 3 x 103

679.58 "~ 849 28 J

1

203 20/372 91

17

1

60

45

701 12~ 849 28 {

1

224 74/372 91

25

3

72

34

720 69 } 788 25

l

244 31/311 88

92

7

7 1

214 36~ 420 94 )

f

304 02/ 97 44 b)

4.2

5

2 1

616.82 701.12)"

l

9844/182.75 b)

4586/34561

0 76

17

15

6

26

13

1 8 × 103

2

170

14

1

30

360

35

70

9

13

11

I

40

2.4

0.18

7.7x I03

6.5

4.5

4.0x 103

96

23

29x103 7 0 x 104 82 4 1 x 10°

91

0 22

M R BEITINS et al

294

T~,BI I" 7 (continued)

Level energies (keY)

Ratios of reduced 7-transition probabilities l, f

Eo

E,, 2 or

E,,.2 ")

679 701 788 849 582.29

58 12 25 28

701 12 788 25 701.12 870 7 849 28 898 9

614 27

701 1 2 788 25

616 82

476.38 337 75 518 38 337 75 742 98 849 28

679 58

420 94 375.08 476 38 375 08

681 09

849 28 898 9

701.12

476 38 420 94 582.29 214 36 582 29 616 82 614 27 375 08 616 82 518 38

720 69

Energies of ?-transitions ' (keV) E ~,/E~

420 94 375 08 518 38 476.38 614 27 420 94

cxp ratios ratios

calc. ratlo~,

error d)

mixed

unmixed

l

161,20 h)/182 75 b)

16

I

1

269.88/330,92 b)

51

9

22

l

118.84/205,97

17

2

15

l

118 84/288 50 b)

760

180

830

l

267 00/316 50

14

11

1 lxl03

40

33

560

i f f

86 86 c)/174 O0 ~) 140 43 ~)/279 06 98 44/279 06

89 150 1,1 23

1

2

70

220

0 36

27

440

l

125 96/232 46 b)

f

258 65/304 52

f

203 20/304 52

1

168 18/217 86

22

7

19

5.9 x 103

f

224.74/280 18

37

4

15

1.1

f

118 84/486 80 b)

20

67

f

118.84/ 84.30 b)

4

25

f

86 86 c)/326.06 c)

f

84 30 b)/182 75 h)

f

299 76/345.61

f

202 30/244.31

f

106 41/299 76

4.6

5

4 1

25

2

99

I0

1

230 26 380

75

15

180

24 58

7 4 x 104

47

7

64

5

34

0 80

1

19

2 2 x 104

11 14

2

21

3 8

160

179Hf

295

TABI I: 7 (continued) Level energies (keV)

Ratios of reduced y-trans,tlon probabilities Energies of y-transitions (keV) E~/E2

,, f E0

78825

E,,., or

E<~ ")

47638 21436 51838 42094 61427 375 08

t

f

31188/57375 b)

~

f

269.88/367 28

J

}

exp ratios

calc. ratios

ratios

error d)

mixed

23

2

24

unmixed

34

9

19

I 6 x 10a

I1

2

48

6.5x 10a

f

174.00~)/413 19 ~)

476 38 } 51838 61682 } 47638 681.09 t 518.38 )

f

372.91/33092 b)

64

11

45

f

23246 b)/37291

3.2

2

20

f

168.18/330.92 b)

13

2

17

3377017512t

f

14816/511.28 b)

27

7

38

70112 ~ 61682 J

f

14816/23246 b)

.15

2

054

8707

214.36 / 33775 J

f

65623/53287

21

6

35

898.9

616 82 l 518.38 J 61682 ~ 681.09 J

f

282.11/38054

f

282.11/21786

1.9

12

22

51 x 103

68109 ~ 58229

f

21786/31650

50

16

53

0.35

4207206994}

f

17844 ")/47843 ¢)

849.28

J

)

")&,2=Eo+E

2, E , , 2 = e 0 - e

19

18

13

5

10

43

3.5 11

23

x 10 6

2

b) The AK forbidden 7-transitions in the adlabatlcal theory. ~) The E2 transitions d) In units of the last significant digit

(i) takmg into account band mixing using the mixing amplitudes which were determined in the calculations of level energies (table 6); 0i) without band mixing, i.e. taking for the "main" component of the given state ~gi = 1, and for all other admixture amplitudes UK, = 0. The results of the calculations are given in table 7. The calculated 47 mdependent ratios between M1 transitions and six ratios for E2 transitions are in agreement with the experiment within an order of magnitude, when band mixing is taken into account. Without mixing, deviations of three orders of magnitude and more occur. As mentioned above, the ),-transitions, forbidden by AK, cannot be explained at all using the adiabatic model without band mixing. Among the above

296

M. R, BEITINS et al

mentioned 47 M1 reduced 7-transition probability ratios, twenty refer to one or two ":-transitions forbidden by AK. Taking into account band mixing, these twenty ratios can be well described, i.e. the deviation from the corresponding experimental value does not exceed a factor of ten. The same consideration can be applied to the partial hfetimes of y-transitions. For the 137.9 keV E2 transition, depopulating the 614.3 keV level, with T ~ p = 118 ns [ref. 20)], the calculated value with mixing is T ~ , ¢ = 116.9 ns, and without mixing T½¢~l¢ = 2.93 × 104 ns. The obtained results show that taking into account band mixing improves essentially the agreement between the calculated and experimental ratios of reduced 7transiuon probabilities. 3 3 THE STATES OF EVEN PARITY

3.3.I. The yround-state band oJ 179Hf This band has the asymptotic quantum numbers 9-[624]. The rotational levels of this band up to a spin ~ + have been observed 21) m the decay of the 179mHf level at 1106.0 keV (T~ = 24.8, U = ~ - ) . This isomeric level, having a three-quasiparticle structure n[624]]'+p[404]~,+ p[514]T, was excited m the 176yb(~, n)179Hf reaction. In the (n, ~,) reaction, only the first rotational level in the ground-state band ~ - is excited. The --121+~ 9 + transition has a multipolarity M I + E 2 (table 1). It is shown in ref. 21) that (9r--gR) 2 = 0.131(7) for the 9+[624] band. 3.3.2. The y-vibrational band. The y-vibrational level ~+ for the ground state Is given at 1254 keV in the 179Hf level structure calculations based on the superfluid model 22). The structure {~+ [642] 18 ''//o,9+[ 624] +QI(22) 81 ~o} is assigned to this level. A weak 7-transition, which therefore might have an E2 character, from the capture state to the level at 1004 keV is observed in ref. 4). Therefore the quantum numbers ~+ are proposed for the level of 1004 keV. A very intense ~,-transition at 1004.14 keV is observed in our ),-ray spectrum (table 2). This 7-transition is not in coincidence with any transition, indicating that it could indeed go directly to the ground state. All these data support the location of the v-vibrational level (K 0 - 2) at 1004.1 keV. For this transxtion of 1004.1 keV one can estimate an upper limit of ~T, admitting I~ < 0.1 at this energy, equals ~X = IJI: < 0.1/35.8 < 0.003. This value does not exclude an E2 character as ~,h(E2) = 0.0035 and .~th(Ml) = 0.007. The cross-section calculations for the excitation of levels in the (d, t) reaction 15) show that for the even panty bands arising from the neutron i~ shell-model orbit the excitation of the -~, 9 and ~ levels should be observed. The 1004.1 keV level is weakly excited in the (d, t) reaction 3). In the case of pure y-vibration, the distances between the rotational levels in the 1004.1 keV band would correspond to a value for the inertial parameter, close to the value A = 11.2 keV of the ground-state band. However, the 1004.1 keV rotational band should have a lower A-value, as its structure is complex, containing admixtures of the ~+ [642] state with a rotational parameter A of about 8 keV [ref. 16)-]. We propose the level 1079.2 keV as the ~+ rotational

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level of the I + vibrational state (A = 10.7 keV). The 1079 keV level depopulates to the 9 and -12-1levels of the ground-state band (fig. 2). The Alaga rules predict equal intensities for these E2 transitions, and this equality Is obtained approximately m the experiment. The 9+ level of the ~ band, should be excited in the (d, t) reaction. Its energy, ifA = 10.7 keV, should bc 1175.5 keV. The peaks at the energies 1167 and 1200 keV m the (d, t) reaction 3) have a complex structure. Calculations based on the Alaga rules show that the transition intensities to the ground-state band 9 ~ 9 and 9 ~ ~ have a ratio 1:2; this means that it is more probable to observe the transition 9 ~ ~ . Such a suitable transition m the -/-spectrum can be the transition at 1055.7 keV. This intense transition is located in another place of the scheme. However, it is possible that part of it may be located as the transition 9+, ~ ~ 11 T + , _92.Then the level 9+ has an energy of 1178.5 keV, and the z~+ band has parameters A = 10.27 keV and B = 18.75 eV. 3.3.3. The ~+[633] band. The superfluid model calculation of the lV9Hf level structure 2z) shows that the single-particle state ~7+ [ 6 33], already known in the neighbouring nuclei, must have an energy of about 870 keV in 179Hy. It is known 15) that the 9 and ~ levels of the rotational band built on this state must be excited in the (d, t) reaction. The cross sections for their excitations would have almost equal values. The energies for such levels in the 1 MeV region can be 937 and 1167 keV, because the inertial parameter of the ~+[633] band must be ~ 10 keV from the systematics in neighbouring nuclei 16). The -~+ and 9+ levels of this band can be

298

M R BEITINS et al.

reached in the (n,'D reaction. We propose that these states may be the levels at 859.0 and 942.2 keV, which deexclte to the levels of the bands 9+1-624] and ~-[514] (fig. 2). Calculations with the Alaga rules show that the transition from the 9+ level to the ground-state band 9 + 7 ___,~ + , ~ is three times more intense than the transition 9+ 2 7 _..¢ 9 + 5 , 9, i.e., the latter should not be observed. The parameter of the band ~+ [633] has a value A = 9.1 keV 3.3.4. The tentative 3 + [651] band. A coincidence between the transitions at 571.73 keV with E1 multipolarity (table 3) and at 193.33 keV, deexciting the level -~--t[521], is observed in the I'7 coincidence spectrum. The proposed level has an energy E = 1185.98 keV and decays to the levels ~i - , ~3- , 25--, 31510] and 3-11-521]. This allows us to assign to this level spin values 3 or 3. A transition from the capture state to the 1186.0 keV level has not been observed, which could be explained by an even parity for this level. We propose that the 1186.0 keV level refers to the orbit 3 ÷ [651 ]. A rotational band has been constructed: the -25+ level with an energy of 1199.2 keV [-excited in the //-decay of ~79Lu, ref. 7)] and the 3+ level at 1296.4 keV [very weak population from the capture state in the (n, ";) reaction with resonance neutrons 6)]. A good energy agreement with the analogous band in 175Yb [ref. 23)] is obtained: the energies in 175Yb are U-E(keV): 3~-1356.5, 2~+-1368.1 and 3+-1468.9. The parameters of the 3+[651] band in lVsYb are A = 8.65 keV, a = 3.33 and in 179Hf, A --- 8.68 keV and a = 3.24. This value does also not conflict with a Nilsson model pre&cuon a6), for a deformation parameter 6 = 0.22, of 3.09. However, it must also be taken into account that the 3 + and ~+ levels of the particle state ½+ [651] must be strongly excited m the (d, p) reaction as shown by the excitation cross-section calculations. The level at 1199 keV in ~79Hf is only very weakly excited in the (d, p) reaction, in&cating then that the 3 + [651] band m 179Hf has a complex structure with strong collective components if this band ~s correctly assigned. 3 4. ADDITIONAL LEVELS ABOVE 1 MeV The analysis of the 179Hf )'7 coincidence spectrum measured by Beitins and Prade s) m Rossendorf has shown that. besides the previously discussed level at 1186.0 keV five more levels can be constructed. A new level ~s proposed at 1249.8 keV. Its decay pattern and the M I multipolarity for the 635.3 keV transition allow assigning spin and parity 3- to the 1249.8 keV level (fig. 3). Levels at 1269.7, 1432.9. 1482.2 and 1755.5 keV correspond to levels that are determined using y-transitions following thermal 4) or resonant capture 6). Part of them are supported by 7'7 coincidence data. For the levels at 1755.5 and 1432.9 keV the coincidence data are e~ther scarce or not available, to support these levels seen elsewhere 4, 6). In the work of ref. 6) these levels are suggested to be ~-. The decay of

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4. C o n c l u s i o n s

In general, it can be concluded from the comparison of the Z79Hf level scheme below 1 McV with those of the neighbouring nuclei and superfluid model calculations zz), that almost all expected rotational bands based on single-particle states are found in this region. The ZVgHf single-particle levels above I MeV are already strongly fragmented and have large collective admixtures. This is confirmed by the weak excitation of levels from 900 at 1200 keV in the (d, p) and (d, t) reactions 2.3). Additional information is needed to clearly determine the structure of these levels. such as reaction experiments wzth 179HE,multipolarity determinations above 500 keV etc. Prewous conclusions on the single-particle levels in ~79Hfare also discussed in some detail in refs. z4-26).

300

M R BEITINS et al.

The authors are indebted to M. N. Plate for his assistance in the numertcal calculations and Prof. O. Schult for his constant support of this work. The majority of the authors received kind hospitality at the AEK, Rise. Part of thts research was performed under the agreement between the SCK/CEN, Mol and Leuven University. References l) P Manfrass, A Andreeff, R Kastner, W Bondarenko, N Kramerand P Prokofjev, Nucl. Phys Al02 (1967) 563 2) M. N Vergnes and R K Shehne, Phys Rev 132 (1963) 1736 3) F A. Rickey and R. K. Shehne, Phys. Rev 170 (1968) 1157 4) G Alenlus, S E Arnell, C. Schale and E Wallander, Nucl Phys A168 (1972) 209 5) M R Beitms and H. Prade, Izv Akad. Nauk SSSR (set fiz) 37 (1973) 1813 6) R F. Casten and W R Kane, Phys Rev C7 (1973) 419 7) J C Hdl and R. A Meyer, Bull. Am Phys Soc 18 (1973) 1379 8) H. R Koch, H A Baader, D. Breltlg, K. Miihlbauer, U Gruber, B P K. Materand O. W. B Schult, m Ncutron capture gamma-ray spectroscopy (IAEA, Vtenna, 1969) p 65 9) M K Balo&s. V. A Bondarenko and P T Prokofjev, Izv. Akad Nauk SSSR (set fiz.) 28 (1964) 262 10) O. Hansen, M O. Olesen, O Skilbrelt and B Elbek, Nucl Phys 25 (1961) 634 l l ) R. S. Hager and E C Seltzer, Nucl. Data Tables A4 (1968) 1 12) T Katoh, J Phys Soc Jap 25 (1968)51 13) K E. G. Lobner and S G Malmskog, Nucl Phys 80 (1966) 505 14) V M Mlkhatlov, Izv Akad Nauk SSSR (set fiz)30 (1966)1334 15) D G Burke, B Zcldman, B Elbek, B Herskmd and M Olesen, Mat. Fys Medd Dan. Vtd Selsk 35 (1966) no 2 16) M. E Bunker and C W Retch, Rev Mod. Phys. 43 (1971) 348 17) J J Tambergs, M K. Balo&s, M K Mduna, L A Nelburg, M N. Plate and P. T. Prokot]ev, Izv Akad Nauk SSSR (ser fiz ) 39 (1975) 177 18) J J. Tambergs, M K. Balo&s, M K Mduna, L A Nelburg, M N Plate and P T. Prokofjev, Izv Akad. Nauk Latv SSR (ser fiz-techn nauk) NI (1975) 8 19) J J Tambergs, M K Balodls, M N Plate and P. T Prokofjev, Izv Akad Nauk SSSR (ser fiz.), m prmt 20) W Andrejtscheff, P Manfrass, K D Schdhng and W Seldel, Nucl. Phys A225 (1974)300 21) H. Hfibel, R A Naumann and P K. Hopke, Phys. Rev C2 (1970) 1447 22) F A Gareev, S. P Ivanova, V G Solovlev and S. I Fedotov, FIT Elem Chastlts At. Yadra (SSSR) Dubna 4 (1973) 357 [Enghsh transl :Sov J Part and Nucl 4 (1973) 148] 23) D Brettlg, Z Naturf 26a (1971) 371 24) P T Prokofjev, M K Balo&s, M R. Beitms, J J Berzm, V A Bondarenko, N D Kramer, A. J Krumma, G L Rezvala and L I Slmonova, Spectra ofelectromagnettc transitions and level schemes following thermal neutron capture by nuchdes with A = 143-193 (Zmatne, Rtga, 1973) 25) L. Jacobs, G. Vandcnput, J M Van den Cruyce. P H M Van Assche, D Breltlg, H A Baader, H. R Koch, I. K Alskms, M K Balo&s and P T Prokotjev, Conf on nuclear structure study with neutrons, Hungary (1972) A66 26) M R. Beltms, N D Kramer, P T Prokoljev, P H M Van Assche and L Jacobs, 25th USSR Conf on nuclear spectroscop3, and structure of atomic nuclei, Lenmgrad, January, 1975 (Nauka, Lenmgrad, 1975) p 143 27) R F Casten, P Klemhem7, P J Daly and B Elbek, Mat. Fys Medd Dan Vld Selsk. 38 (1972) no 13 28) R K Smlther, Phys. Rev 129 (1963) 1691 29) E L Church and J Weneser, Nucl Ph),s 28 (1961)602