Nuclear structure studies of 177,178,179,181Ta using (3He, d) and (α, t) reactions

Nuclear Physics A 778 (2006) 125–152

Nuclear structure studies of 177,178,179,181Ta using (3He, d) and (α, t) reactions D.G. Burke a,∗ , W.P. Alford b,1 , D. Elmore c,2 a Department of Physics and Astronomy, McMaster University, Hamilton, ON, L8S 4M1, Canada b Department of Physics, University of Western Ontario, London, ON, N6A 3K7, Canada c Nuclear Structure Research Laboratory, University of Rochester, Rochester, NY 14627, USA

Received 22 June 2006; accepted 21 August 2006 Available online 20 September 2006

Abstract 176,178,180 Hf(3 He, d) angular distributions and 176,178,180 Hf(α, t) spectra were measured using 32 MeV 3 He and 30 MeV α particles at the University of Rochester MP tandem van de Graaff accelerator laboratory.

Reaction products were analyzed with an Enge split-pole magnetic spectrograph. New nuclear structure information is reported for each of the residual nuclides 177,179,181 Ta, and the systematic behavior of bands based on the 7/2+ [404], 9/2− [514], 5/2+ [402], 1/2− [541], 1/2+ [411] and 1/2− [530] bands can now be observed. Some limited measurements of the same reactions on a target of 177 Hf, taken to facilitate identification of isotopic impurity peaks in the main spectra, provide useful new structure information and a proton separation energy for 178 Ta. © 2006 Elsevier B.V. All rights reserved. PACS: 25.55.-e; 25.55.Hp; 27.70.+q; 21.10.Pc; 21.10.Re Keywords: N UCLEAR REACTIONS 176,178,180 Hf(3 He, d), E = 32 MeV; measured σ (E, θ). 177 Hf(3 He, d), E = 32 MeV; 176,177,178,180 Hf(α, t), E = 30 MeV; measured σ (E). 177,178,179,181 Ta deduced levels, -values, spectroscopic strengths, Nilsson band assignments. 178 Ta deduced proton separation energy. Enriched targets, magnetic spectrograph.

* Corresponding author. Fax: +905 546 1252.

E-mail addresses: [email protected], [email protected] (D.G. Burke). 1 Present address: Courtenay, BC, Canada. 2 Present address: Physics Department, Purdue University, West Lafayette, IN 47907-2036, USA.

0375-9474/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2006.08.010

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1. Introduction Nuclear structures of the odd-mass tantalum isotopes 177 Ta, 179 Ta, and 181 Ta have been studied by a number of experimental techniques [1–3]. However, these are among the few nuclides in the 150  A  190 deformed region which are accessible to single-proton-stripping studies using stable targets, but for which no data of this type are available in the published literature. The present work reports (3 He, d) and (α, t) measurements which confirm and extend known rotational bands, and permit new assignments of single-proton states in each of these nuclides. Experimental details and results are presented in Section 2, and methods used for the data analysis are described in Section 3. The interpretation and discussion of nuclear structures for the three odd tantalum isotopes are found in Section 4, while Section 5 is concerned with the odd–odd nuclide 178 Ta. Although the original objective did not include a study of 178 Ta, a few relatively short (3 He, d) and (α, t) measurements were made with a 177 Hf target to help identify peaks it contributed as an isotopic impurity in the other targets. These limited data provide useful support for some previous interpretations of levels, and permit new band assignments in 178 Ta. The structure of 178 Ta has been an interesting challenge. It has two levels which decay by electron capture but thus far it is not known which is the ground state. Proton separation energies for specific levels, determined from the present work, provide information relevant to this issue. 2. Experimental details and results The experiments were performed with 32 MeV 3 He and 30 MeV α particles from the MP tandem van de Graaff accelerator at the University of Rochester Nuclear Structure Research Laboratory. Targets were prepared from samples of isotopically enriched HfO2 , purchased from the Isotope Sales Division of the Oak Ridge National Laboratory, with the stated compositions shown in Table 1. From intensities of elastically scattered beam particles it was determined the target thicknesses were all in the range of 30 to 40 µg/cm2 . Reaction products were analyzed with an Enge split-pole magnetic spectrograph and detected with Kodak NTB50 photographic emulsions. For each of the 176,178,180 Hf targets deuteron spectra from the (3 He, d) reaction were recorded at 10 angles ranging from 7.5◦ to 50◦ , and (α, t) measurements were made at two reaction angles. Figs. 1 to 8 show the (α, t) and (3 He, d) spectra from each of the four targets. The overall energy resolution was between 15 and 20 keV full width at half maximum (FWHM) for the (α, t) reaction and between 20 and 25 keV FWHM for the (3 He, d) reaction. Q-values, and hence excitation energies, for levels corresponding to peaks in the spectra were obtained using a magnet calibration which had previously been determined using alpha particles from a radioactive source of 212 Pb. Table 1 Isotopic compositions of hafnium targets Target 176 Hf 177 Hf 178 Hf 180 Hf

Isotopic abundance (percent) 176 Hf

177 Hf

178 Hf

179 Hf

77.49 0.76 0.52 0.22

11.43 91.67 4.36 0.74

5.84 4.85 89.14 3.01

1.95 0.92 2.9 1.21

180 Hf

3.29 1.80 3.07 94.82

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Fig. 1. Spectrum of tritons from the 176 Hf(α, t)177 Ta reaction at θ = 60◦ . Solid lines with the data points show results of the peak-fitting program. Labels for the bands indicate I π and the Nilsson quantum numbers K π [N nz Λ]. Some isotopic impurity peaks are indicated by the residual nuclide and the level energy. Impurity peaks are designated by an asterisk if only part of the observed peak is due to the impurity.

Fig. 2. Spectrum of deuterons from the 176 Hf(3 He, d)177 Ta reaction at θ = 30◦ . See caption for Fig. 1.

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Fig. 3. Spectrum of tritons from the 178 Hf(α, t)179 Ta reaction at θ = 60◦ . See caption for Fig. 1.

Fig. 4. Spectrum of deuterons from the 178 Hf(3 He, d)179 Ta reaction at θ = 30◦ . See caption for Fig. 1. At least half the intensity of the peak near 565 keV labelled with an asterisk can be attributed to the 289 keV level of 178 Ta.

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Fig. 5. Spectrum of tritons from the 180 Hf(α, t)181 Ta reaction at θ = 60◦ . See caption for Fig. 1.

Fig. 6. Spectrum of deuterons from the 180 Hf(3 He, d)181 Ta reaction at θ = 25◦ . See caption for Fig. 1. The spectrum at θ = 25◦ is shown for this case because an impurity group obscures the ground state peak at θ = 30◦ .

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Fig. 7. Spectrum of tritons from the 177 Hf(α, t)178 Ta reaction at θ = 60◦ . See caption for Fig. 1. For this odd–odd residual nuclide the bands are labelled by the Nilsson orbital into which the proton is transferred and coupled to the 7/2− [514] neutron in the target ground state. As it is not known which level forms the ground state, zero for the excitation energy + − scale has been set at the {7− , 72 [404]π + 72 [514]ν } bandhead, as in Refs. [33,34].

Fig. 8. Spectrum of deuterons from the 177 Hf(3 He, d)178 Ta reaction at θ = 30◦ . See captions for Figs. 1 and 7.

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Normalization factors to convert intensities of peaks in the spectra to absolute cross sections were obtained by using a NaI scintillator monitor counter in the target chamber, which recorded elastically scattered beam particles at θ = 45◦ . The solid angles for the monitor and spectrograph were known, and elastic scattering cross sections at θ = 45◦ were obtained from distorted wave born approximation (DWBA) calculations described below. (3 He, d) angular distributions for levels populated in 177 Ta, 179 Ta, and 181 Ta are shown in Figs. 9, 10 and 11, respectively. The curves in these figures are DWBA predictions for the values indicated, each multiplied by a scaling factor to give a best least-squares fit to absolute cross sections of the data. These scaling factors yield the spectroscopic strengths as described in Section 3. Tables 2 to 5 list the levels populated in 177 Ta, 179 Ta, 181 Ta, and 178 Ta, respectively. In each of these tables the first three columns show excitation energies from the two reactions compared with accepted values, where available, from previous works. Additional columns show (3 He, d) cross sections at θ = 30◦ and the (α, t) ones at θ = 60◦ , as well as level interpretations. 3. General comments on methods of analysis Quantitative analyses of single-nucleon-transfer results in deformed nuclei usually make use of the Nilsson model description of single-particle states. Several review articles have described this approach and demonstrated its success. The theoretical cross section for a single-nucleon transfer reaction leading to a rotational band member of spin If in a deformed residual nucleus can be written [4,5]   2   dσ dσ 2 , (1) = Ng ai (Cj  )i Pi I0 K0 j K|If Kf  dΩ dΩ DW j,

i

where N is a normalization factor for the DWBA cross sections, (dσ/dΩ)DW , and the first summation extends over all possible j and  values leading to the final state. The factor g 2 has a value of 2 if the initial or final state has K = 0 with all nucleons in time-reversed orbitals (e.g., as in ground state bands of even–even nuclei), but otherwise g 2 = 1. The Cj  values are expansion coefficients describing the Nilsson orbital of the transferred nucleon in terms of spherical states. The Clebsch–Gordan coefficient couples the initial target spin and its projection I0 , K0 with the transferred j, K to form the final state If , Kf . Pi is a pairing factor, and for the stripping reactions in this work Pi2 = Ui2 , the emptiness probability in the target for the orbital to which the nucleon was transferred. In Eq. (1) the final state is assumed to be a mixed configuration, with amplitudes ai for the various components. The mixing could result from Coriolis or other interactions. The distinctive set of Cj  coefficients for each Nilsson orbital produces a characteristic pattern of cross sections, or fingerprint, predicted by Eq. (1). These fingerprints have proven to be a very powerful and successful tool for identifying bands populated in many nuclides. The main part of this study involves even–even hafnium targets, for which I0 = 0, so j = If , for which the Clebsch–Gordon coefficient has a value of unity, and g 2 = 2. Eq. (1) then reduces to 2    dσ dσ = 2N ai (Cj  )i Pi . (2) dΩ dΩ DW i

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Fig. 9. Angular distributions for selected transitions in the 176 Hf(3 He, d)177 Ta reaction. Points with downward-pointing arrows indicate upper limits to cross sections. The curves are from DWBA calculations for the -values indicated, multiplied by a scaling factor for each curve to give the best fit to the data. For the 220 keV doublet the data have been fitted to the sum of an  = 1 and an  = 5 DWBA curve as shown, and the sum is indicated by the solid curve. For some peaks the data do not clearly distinguish between  = 2 or  = 3 and a curve for each -value is shown.

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Fig. 10. Angular distributions for selected transitions in the 178 Hf(3 He, d)179 Ta reaction. See caption for Fig. 9. Data for the 679 keV doublet are fitted to the sum of an  = 1 and an  = 5 curve.

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Fig. 11. Angular distributions for selected transitions in the 180 Hf(3 He, d)181 Ta reaction. See caption for Fig. 9.

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Table 2 Population of levels in 177 Ta by the (3 He, d) and (α, t) reactions Excitation energy (keV)a

Cross section (µb/sr)a

-valued

Previousb

(3 He, d)c

(α, t)c

(3 He, d)θ =30◦

(α, t)θ =60◦

0.0 70.59(13) 73.36(15)

0(1)

−1(1)

12(2)

29(2)

4

70.6

70.6

207(7)

74(2)

2

187(1)

130(2) 185(1)

84(4)

2(1) 28(2)

3

220(1)

220(1)

75(5)

54(2)

1&5

245(1)

25(3) 65(4)

36(2) 2(1) 4(1)

5

371(1)

245(1) 286(1) 372(2)

492(2)

497(1)

20(2)

7(1)

523(1) 640(1)

524(1) 641(2)

738(2)

738(1) 898(1) 1011(1) 1046(2)

45(4) 36(3)e  15 18(2)e,f 130(6) 298(8) 40(5)

10(1) 3(1) 2 8(1)e 6(1) 13(1) 13(1) 3

48(4) 159(6) 153(6) 24(4) 9(3) 26(4) 96(5) 77(5) 65(4) 22(2)

19(2) 45(2) 26(2) 4(1) 17(2) 7(1) 4(1) 2 ∼3 15(2)

131.05(14) 186.15(6) 216.62(7) 220.03(16) 245.85(20) 288.55(14) 372.57(7) 487.62(6) 497.41(6)

639.95(7) 690.30(10) 737.0(3) 899.36(15) 1044.94(11)

1010(1) 1045(1) 1086(3)

1

1487.71(17) 1512.54(10)

1120(2) 1162(2) 1264(2) 1341(2) 1365(2) 1447(3) 1488(3) 1638(4) 1804(2)

+ 7/2,

7/2 [404] 5/2, 5/2+ [402] 9/2, 9/2− [514]

9/2, 7/2+ [404] − 5/2,

1/2 [541] 1/2, 1/2− [541] 11/2, 9/2− [514] 9/2, 1/2− [541] 11/2, 7/2+ [404] − 3/2,

1/2 [541] 1/2, 1/2+ [411] 3/2, 1/2+ [411] 7/2, 1/2− [541]? 5/2, 1/2+ [411] 3/2, 3/2− [532]b 11/2, 1/2− [541] 11/2, 11/2− [505]b

3 1 (2)

3/2, 1/2− [530] (1/2, 1/2− [530])b

1094.19(10) 1120(1) 1161(1) 1264(1) 1336(2) 1362(3) 1448(3) 1484(2) 1510(2) 1634(2) 1800(3)

I, K π [N n3 Λ]

2 or 3 3 (2) 2 or 3 (3)? (2 or 3)? (3)? (2)?

7/2, 1/2− [530]

(1/2−)b (1/2−, 3/2−)b

a The uncertainty in the last digit of each value is indicated by the number in parentheses. b Results from the Nuclear Data Sheets [1]. c Experimental energies were measured relative to the strongly-populated 70.59 keV level. Uncertainties shown are

statistical only. In addition there is a calibration uncertainty which is  1 keV for levels up to ∼ 1 MeV, but increases and may be as large as ∼ 10 keV at an excitation energy of ∼ 2.5 MeV. d From (3 He, d) angular distribution. e A significant fraction of this cross section is due to 179 Ta as an isotopic impurity. f Peak is obscured at θ = 30◦ by an impurity. Value shown is for θ = 40◦ .

 The quantity [ i ai (Cj  )i Pi ]2 is often called the nuclear structure factor. Its value can be calcudσ dσ lated from model wavefunctions and compared directly with [( dΩ )/2N ( dΩ )DW ] obtained from the experimental results.

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Table 3 Population of levels in 179 Ta by the (3 He, d) and (α, t) reactions Excitation energy (keV)a

Cross section (µb/sr)a

-value

I, K π [N n3 Λ]

4

7/2, 7/2+ [404] 9/2, 9/2− [514] 9/2, 7/2+ [404] 11/2, 9/2− [514] 5/2, 5/2+ [402] 1/2, 1/2+ [411] 3/2, 1/2+ [411] − 5/2, ⎧ 1/2 [541] − ⎪ ⎨ 9/2, 1/2 [541] 5/2, 1/2+ [411] ⎪ ⎩ 1/2, 1/2− [541] 7/2, 1/2+ [411] 3/2, 1/2− [541]

Previousb

(3 He, d)c

(α, t)c

(3 He, d)θ =30◦

(α, t)θ =60◦

0.0 30.7(1) 133.78(11) 180.79(14) 238.56(9) 520.23(18) 527.52(15) 627.99(15) ⎫ 628.03 + x d ⎪ ⎬ 673.01(22) ⎪ ⎭

3(2) 32(2) 131(1) 180(1) 238.6

0(1) 32(2) 135(2) 181(1) 238.6

12(2) 4(1) 5(1)e 22(3) 192(7)

29(4) ∼2 2(1) 50(3) 89(5)

527(1) 629(1)

527(2) 629(1) ⎧ ⎫ ⎪ ⎨ 673(1) ⎪ ⎬

22(3) 77(4)

6(1) 30(2) ⎧ ⎫ ⎪ ⎨ 60(4) ⎪ ⎬

(2) 3

679(1)

⎪ ⎩ ∼ 680 ⎪ ⎭

82(5)

⎪ ⎩ 12(2) ⎪ ⎭

1&5

855(1) 891(2) 994(1) 1064(1) 1122(1) 1177(1) 1231(2) 1335(1) 1394(2) 1420(1)

855(1) 891(1) 995(1) 1066(1) 1125(1) 1178(1) 1234(2) 1338(1) 1398(2) 1422(2)

58(4) 15(2) 35(3) 103(5) 60(4) 34(4) 13(3) 84(5) 16(4) 240(8)

4(1) ∼2 16(2) 10(1) 9(1) 8(1) 5(1) 18(2) 9(1) 14(2)

1 2 or 3 2 or 3 0 2 or 3 2 or 3

1

3/2, 1/2− [530]

1461(1) 1496(2) 1524(1)

1468(2) 1492(2) 1528(2)

53(5) 42(5) 114(6)

14(2) 10(1) 38(3)

0 1 3

1/2+ (1/2, 1/2− [530]) 7/2, 1/2− [530]

1555(1)

1558(2) 1665(2) 1875(3) 1939(3) 1996(4) 2146(3) 2272(2)

50(5)  12 45(4) 47(5) 21(3) 63(5) 6

9(1) 4(1) 6(1) 5(1) 5(1) 3(1) 7(1)

3

5 2

696.00(21)

2

1423(10)

1527(10) 1561(5)

1874(3) 1938(3) 1995(3) 2137(3) ∼ 2270

1/2+

a The uncertainty in the last digit of each value is indicated by the number in parentheses. b Results from the Nuclear Data Sheets [2]. c Experimental energies were measured relative to the strongly-populated 238.56 keV level. Uncertainties shown are

statistical only. In addition there is a calibration uncertainty which is  1 keV for levels up to ∼ 1 MeV, but increases and may be as large as ∼10 keV at an excitation energy of ∼ 2.5 MeV. d x = 45 ± 10 keV (see Ref. [2]). e Peak is obscured at θ = 30◦ . Value shown is for θ = 22.5◦ .

For the present work, DWBA calculations were performed using the program DWUCK4 [6] with optical model parameters from the study of 183,185,187 Re by Lu and Alford [7], except that no lower cutoff was used in the radial integration. This parameter set has been used for single-

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Table 4 Population of levels in 181 Ta by the (3 He, d) and (α, t) reactions Excitation energy (keV)a Previousb



0.0 6.237(20) 136.262(13) 158.554(24) 482.168(23) 590.06(23) 615.19(3) 618.99(5) 994.2(10) 1022.6(10)

1205.7(6)

Cross section (µb/sr)a

-valued

(3 He, d)c

(α, t)c

(3 He, d)θ =30◦

(α, t)θ =60◦

0(1)

0(1)

11(7)e

29(2)

4

157(1) 482.2

134(2) 159(1) 482.2 588(2)

29(3) 174(7)

2.3(6) 43(2) 109(3) 2.3(6)

5 2

619(1)

619(1)

15(2)

9(1)

2

771(1) 996(1) 1025(1) 1085(1) 1135(2) 1205(1) 1235(2) 1294(1) 1357(2) 1393(2) 1487(2) 1567(1) 1650(2) 1735(2)

772(1) 996(1) 1024(1) 1087(2) 1134(2) 1208(2) 1236(2) 1294(1) 1353(2) 1388(2?) 1487(2) 1565(1) 1641(2?) 1733(2)

1782(2) 1804(2)

11(2) 63(4) 37(3) 25(3) 6(1) 25(3) 25(3) 90(5) 27(3)e 25(3) 17(2) 67(4) 23(3) 13(2)

1848(2) 1860(2) 1900(2) 1989(2) 2024(2) 2075(2) ∼2150 ∼2191 2231(2) 2316(2)

58(6) 70(6) 24(3) 20(3) 23(3) 35(3) 31(3) 20(0) 39(4) 45(4) 41(4)

4(1) 32(2) 70(3) 5(1) 3(1) 11(1) 4(1) 22(2) 4(1) 6(1) 6(1) 25(2) 4(1) 15(2)

20(2) 16(2) 40(5) 22(5) 7(1) 8(1) 3(1) 6(1) 4(2) 3(1) 6(1) 5(1) 2

1785(1) 1849(2) 1861(2) 1896(2) 1988(2) 2021(2) 2074(2) 2151(2) 2194(2) 2234(2) 2314(2) 2345(2)

240(8)

I, K π [N n3 Λ]

3 5 1

1 (0)

7/2, 7/2+ [404] 9/2, 9/2− [514] 9/2, 7/2+ [404] 11/2, 9/2− [514] 5/2, 5/2+ [402] + 7/2,

5/2 [402] 1/2, 1/2+ [411] 3/2, 1/2+ [411] 5/2, 1/2+ [411] 5/2, 1/2− [541] 9/2, 1/2− [541] 1/2, 1/2− [541]

3/2, 1/2− [541]

2 2 (3)

1

(3/2, 1/2− [530])

3

(7/2, 1/2− [530])

1 1 (0) 2

a The uncertainty in the last digit of each value is indicated by the number in parentheses. b Values from the Nuclear Data Sheets [3]. c Experimental energies were measured relative to the strongly-populated 482.18 keV level. Uncertainties shown are

statistical only. In addition there is a calibration uncertainty which is  1 keV for levels up to ∼ 1 MeV, but increases and may be as large as ∼ 10 keV at an excitation energy of ∼ 2.5 MeV. d From (3 He, d) angular distribution. e Peak is obscured at θ = 30◦ by an impurity group. Value shown is for θ = 25◦ .

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Table 5 Levels in 178 Ta populated by the (3 He, d) and (α, t) reactions Excitation energy (keV)a,b Previousc

(dσ/dΩ) (µb/sr)b (α, t)

(3 He, d)

(α, t)

(3 He, d)

(θ = 60◦ )

(θ = 30◦ )

2(2) 24(3)

0(4)

16(2) 4(1)

101(1) 128(3)

101(2)

151(2) 180(2)

151(2)

219.7

222(1)

289.1

289.1

0



Presentd

Interpretatione [I, K π ]

Configuration

8(2)

7, 7−

7+ 7− 2 [404]π + 2 [514]ν

23(2) 4(1)

35(6)

1, 1−

7− 5+ 2 [402]π − 2 [514]ν

16(2) 9(2)

26(4)

2, 1−

7− 5+ 2 [402]π − 2 [514]ν

225(2)

18(2)

21(3)

289.1 ∼ 324? ∼ 351? 381(4)

45(3)

250(3)

383(3)



8, 8+ 3, 1−

4(1)

4(1)

88(7) 9(3) 7(3) 4(3)

6,6−



7− 9− 2 [514]π − 2 [514]ν + 5 [402] − 7 − [514] π ν 2 2 5 + [402] + 7 − [514] π ν 2 2

⎫ 422.1 ⎪ ⎬

422(3)

418(5)

33(4)

⎫ ⎪ ⎬

⎪ ⎭

434(4)

433(4)

24(4)

⎪ ⎭

486(2) 525(2)

484(3) 524(3)

20(2) 10(2)

12(3) 41(5)

(6, 4+ )

9 − [514] − 7 − [514] π ν 2 2 − − ( 12 [541]π − 72 [514]ν ) − − ( 12 [541]π − 72 [514]ν ) − − ( 12 [541]π − 72 [514]ν )

564(2) 584(2)

564(3)

12(2) 4(1)

21(3)

(7, 4+ )

( 12 [541]π − 72 [514]ν )

38(5) 8(2) 38(5) 11(3) 19(5) 15(5) 13(3) 17(8) 27(6) 16(5) 11(3) 18(5) 79(8)

(8, 4+ )

( 12 [541]π − 72 [514]ν )

119(15)

(3, 3+ )

96(10)

(4, 3+ )

( 12 [530]π − 72 [514]ν )? − − ( 12 [530]π − 72 [514]ν )?

97(10)

631(5) 671(2) 715(3) 768(3) 808(3) 881(3) 901(4) 1005(3) 1032(3) 1053(4) 1098(4) 1131(4) 1173(4) 1203(4) 1224(3)

672(3) 708(5) 771(3) 815(4) 880(4) 902(5) 925(5) 1004(5) 1032(4) 1055(5) 1097(4) 1134(5) 1172(3) 1222(3)

⎧ ⎪ ⎨ 74(8)

⎪ ⎩



9, 8+ (4, 4+ )

(5, 4+ )

5(2) 11(2) 4(1) 7(2) 4(1) 6(2) 2(1) 5(1) 7(2) 2(1) 3(1) 3(1) 11(2) 5(2) 12(2)

1281(4) 1311(5) 1331(4)

1280(3) 1324(4)

20(3) 5(1) 7(2)

1393(3)

1386(4)

15(2)

66(10) (5, 3+ )

−

−

−

−

−

−

−

−

( 12 [530]π − 72 [514]ν )? (continued on next page)

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Table 5 (continued) Excitation energy (keV)a,b Previousc

(dσ/dΩ) (µb/sr)b

Presentd

(α, t)

(3 He, d)

(α, t)

(3 He, d)

(θ = 60◦ )

(θ = 30◦ )

1430(4) 1462(4) 1497(4) 1519(3) 1540(3) 1604(5) 1623(4) 1710(4)

1429(5) 1459(3) 1491(4)

5(1) 18(3) 8(2) 11(2) 22(3) 4(2) 7(2) 5(2)

29(8) 78(8) 45(5)

1531(4)f 1599(5) 1619(5) ∼ 1700

Interpretatione [I, K π ]

Configuration

145(10)f 41(10) 38(10) 20(4)

a It is not known whether the ground state of 178 Ta is the {7− , 7 + [404] + 7 − [514] } or the {1+ , 9 − [514] − π ν π 2 2 2 7 − [514] } bandhead, and here the 7− level has been used as a baseline and assumed as the ground state, as in ν 2

Refs. [33,34]. b Uncertainties in the last digits of the values are given in parentheses. c Previous energy values are from Kondev et al. [34]. d Energy values are given relative to the stongly populated 6, 6− level at 289.1 keV. e Assignments of levels at 0, 219.7, 289.1, and 422.1 keV were previously proposed [33,34], and are supported by the present results. Assignments for other levels are from this work. See text. f Observed particle group shows multiplet structure.

proton transfer studies of many nuclei in this mass region, including isotopes of promethium [8], europium [9,10], terbium [11,12], holmium [13], thulium [14], lutetium [15,16], rhenium [7] and iridium [17]. The standard value of N = 4.42 was used for the (3 He, d) reactions [6]. For the (α, t) reaction the value of N is not well established, and has commonly been chosen so as to make (α, t) strengths for well-known transitions agree with those from (3 He, d) data. In the works cited above, values ranging from N = 46 to ∼ 140 have been used, depending on the reaction conditions. In this study, N = 102 has been adopted so the strong  = 2 transitions populating the 5/2+ [402] bandheads at 70, 239, and 482 keV in 177 Ta, 179 Ta, and 181 Ta, respectively, have the same strengths in both reactions. The angular distributions shown in Figs. 9 to 11 for many prominent peaks in the (3 He, d) spectra can determine the orbital angular momentum, , transferred, and this information is also listed in Tables 2 to 4. Experience and DWBA calculations have shown that, for conditions of the present experiments, (α, t) angular distribution shapes for different -values are too similar to be very useful as indicators of . The main value of the (α, t) results is in helping to locate levels populated by higher -values, such as  = 4 or 5. This is because (3 He, d) cross sections at typical reaction angles (in the range of θ = 30◦ to 60◦ ) decrease at least an order of magnitude as  increases from 1 to 5, so even fairly strong transitions with high -values can have their peaks obscured by those for other levels, or by impurities. In contrast, absolute values of (α, t) DWBA cross sections for the conditions of these experiments do not depend strongly on -value, so the high- transitions can also have prominent peaks. The usefulness of ratios of the (3 He, d) and (α, t) cross sections as indicators of transferred -values has been shown in the previous studies mentioned above. In most cases, however, there is enough uncertainty in these ratios to preclude quantitative assignments of . In practice, it can be concluded that levels with large (3 He, d) peaks and very small (α, t) ones most likely have  = 0 or 1. On the other hand, levels with prominent

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Table 6 Nuclear structure factors for assigned bands in Ta nuclides Band and spin

Nuclear structure factor Calculated No mixing

7 + [404] 2

Experimental Coriolis

177 Ta

179 Ta

mixed

(3 He, d)

(α, t)

(3 He, d)

181 Ta

(α, t)

(3 He, d)

(α, t)

U 2 = 0.45

7/2 9/2

0.45 0.00

0.46 0.00

0.43 –

0.53 –

0.38 –

0.47 –

0.32 –

0.45 –

5/2 7/2 9/2

0.75 0.03 0.02

U 2 = 0.8 0.75 0.02 0.02

0.73 – –

0.77 – –

0.78 – –

0.76 – –

0.83 – –

0.82 – –

9/2 11/2

U 2 = 0.8 0.01 0.01 0.79 1.01

– 0.89

– ∼ 0.81

– 0.75

– 0.69

– 0.65

– 0.58

3/2 5/2

0.11 0.04

U 2 = 0.2 0.11 0.04

0.07 –

0.10 0.04

0.08 Obs.a

0.06 Obs.a

0.07 –

0.08 –

1/2 3/2 5/2 7/2 9/2 11/2

0.03 0.04 0.19 0.05 0.57 0.02

U 2 = 0.9 0.03 0.07 0.25 0.14 1.03 0.07

0.08 0.19 0.45 (0.2) 1.07 –

– 0.03 0.24 0.09 0.71 –

0.07 0.10 0.44 – 1.6 –

0.09 0.03 0.24 – 1.14 –

0.05 0.05 0.43 – 1.6 –

0.03 0.07 0.22 – 1.29 –

3/2 5/2 7/2 9/2 11/2

0.01 0.11 0.05 0.71 0.03

U 2 = 0.9 0.00 0.05 0.04 0.31 0.05b

 0.02 – – – –

 0.03 – – – –

– – – – –

– – – – –

– – – – –

– – – – –

1/2 3/2 5/2 7/2 9/2 11/2

0.02 0.22 0.00 0.47 0.15 0.08

U 2 = 0.95 0.02 0.20 0.00 0.41 0.09 0.05

– 0.42 – 0.65 – –

– 0.17 – 0.52 – –

0.06 0.38 – 0.24 – –

0.11 0.15 – 0.37 – –

– 0.42 – 0.34 – –

– 0.18 – 0.34 – –

5 + [402] 2

9 − [514] 2

1 + [411] 2

1 − [541] 2

3 − [532] 2

1 − [530] 2

a Level obscured by another large peak. b This level is predicted to be very strongly Coriolis-mixed.

(α, t) peaks and very small (3 He, d) ones have  = 4 or 5. Levels with  = 2 or 3 have significant peaks in both reactions. Transition strengths are very important for determining and testing model assignments for the levels. For this purpose, nuclear structure factors as defined above, extracted from the experimental cross sections, are compared with Nilsson model predictions in Table 6. Results are presented

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for bands based on the various single-particle orbitals discussed in the following subsections. The first column lists the band assignment and the next two columns show predicted strengths. Values in column 2 are Cj2 U 2 for the pure Nilsson orbitals from a model calculation with parameters κ = 0.0637 and μ = 0.600 as recommended by Lamm [18], deformation δ = 0.27, and pairing emptiness factors U 2 as indicated in the table. Column 3 shows the predicted strengths  [ i ai (Cj  )i Pi ]2 from a typical Coriolis-mixing calculation in which the unperturbed band energies were adjusted to give perturbed energies in approximate agreement with experimental values for 177 Ta. The unperturbed band parameters and energies were essentially those used by Hjorth and Ryde [19] for a Coriolis calculation of 177 Ta levels. The purpose of this calculation was not to find a best ‘fit’ to the observed strengths but to show typical effects of the Coriolis mixing for the various bands. Separate predictions are not shown for 179 Ta and 181 Ta because the effects are similar to those for 177 Ta, as discussed in subsequent subsections. The last six columns of Table 6 dσ dσ )/2N ( dΩ )DW ] from the (3 He, d) and (α, t) data for each of the list experimental strengths [( dΩ three isotopes. For transitions with low -values such as 0 and 1, which correspond to dominant peaks in the (3 He, d) spectra, the extracted (3 He, d) strengths are expected to be more reliable than those from the (α, t) reaction. However, for high- transitions the (3 He, d) strengths have been extracted from weak peaks, as described above, so for such cases the (α, t) strengths may be more reliable. 4. Level structures in 177 Ta, 179 Ta, and 181 Ta 4.1. The low-lying 7/2+ [404], 5/2+ [402] and 9/2− [514] bands Angular distributions and spectroscopic strengths from the present results are consistent with and provide additional support for previous assignments of these bands, which were known in all three nuclides. In 177 Ta the 11/2, 9/2− [514] level at 220 keV was not resolved from the 1/2, 1/2− [541] one at 217 keV, but the (3 He, d) angular distribution in Fig. 10 has been fitted to the sum of an  = 5 and an  = 1 DWBA curve to extract the respective strengths given in Table 6, using the approach described in previous works for cases of mixed- transitions [20,21]. The 7/2+ [404], 5/2+ [402] and 9/2− [514] orbitals originate from the 1g 7 , 2d 5 and 1h 11 shells, 2 2 2 respectively, and this is reflected in the Cj  coefficients having large values for only j = 7/2, 5/2, and 11/2, respectively. Thus the transfer strengths are large only for rotational band members with these j -values. This can be seen clearly in Table 6, where the predicted strengths are large for only these j -values and all others are much smaller. The experimental patterns are in good agreement with these predictions; the prominent peaks for these bands in the spectra of Figs. 1 to 6 are for the j -values above, and in most cases the peaks expected to be weak were not actually observed. It is noted that in the 1973 Nuclear Data Sheets [22] the 5/2+ level at 482 keV in 181 Ta had been interpreted as the 5/2+ [402] bandhead, but this assignment was not adopted in the 1991 revision [23]. High spin studies by Saitoh et al. [24] and Dracoulis et al. [25] again proposed 5/2+ [402] character for this level and reported additional rotational members, and the most recent revision of the Nuclear Data Sheets [3] has again adopted this assignment. The strong  = 2 population of the 482 keV level in the stripping reactions of the present work provides very conclusive evidence for the 5/2+ [402] nature of this level. It is also noted from Table 6 that strengths for the 7/2+ [404] and 5/2+ [402] bands are not affected significantly by Coriolis mixing. This is because there are no bands at higher excitation energies originating from the same shells, which would have significant stripping strength to mix

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into these levels. For the 9/2− [514] band a small increase in the j = 11/2 strength is expected from Coriolis mixing with the higher-lying 11/2− [505] band. 4.2. The 1/2− [541], 3/2− [532] and 1/2− [530] bands These bands are discussed as a group because there appears to be significant Coriolis mixing among them, as predicted. The 1/2− [541] band is known in many nuclides in this region, and has a characteristic pattern of cross sections easily identified by significant  = 1, 3, and 5 transitions to the spin 1/2, 3/2, 5/2, and 9/2 members. The large decoupling parameter (a ∼ 3 to 7) is also an important aid to identification. Low spin members (I  5/2) of the band in 177 Ta were known from electron capture decay studies [27], and many higher levels with 9/2  I  45/2 were known from high spin studies [28], but the 7/2 level had not been identified. Interpolation among energies for the known j =  + 1/2 sequence predicts the 7/2 member near ∼ 520 keV, so it is reasonable to associate it with the 523 keV level observed in this work. The experimental strengths in Table 6 are consistent with this interpretation. In 179 Ta the 5/2− member of this band was assigned at 628 keV and the j =  − 1/2 sequence was observed for 9/2  I  45/2 [26], but the absolute energies were not known because the 9/2 → 5/2 gamma transition was not observed. In the Nuclear Data Sheets [2] the separation of the 5/2 and 9/2 levels was designated as ‘x’, and its value was estimated to be 45 ± 10 keV from interpolation of corresponding values in neighboring isotopes. In the present experiment the 9/2 level is found at 673 keV due to its strong (α, t) population, indicating the value of ‘x’ is actually 45 ± 1 keV. The spin 1/2 and 3/2 members have also been newly identified at ∼ 680 and 855 keV, respectively. Although the spin 1/2 and 9/2 members are unresolved, the energies were obtained from peak centroid positions in the (3 He, d) and (α, t) spectra, respectively, and the (3 He, d) strengths given in Table 6 were obtained by separating the angular distribution into  = 1 and  = 5 components as shown in Fig. 10. The 5/2 member of the 1/2+ [411] band is known to exist at 673 keV, but as this orbital is below the Fermi surface its cross section is not expected to be large. The corresponding 5/2+ level in 181 Ta has a (3 He, d) cross section of only ∼ 10% of that for the unresolved multiplet in 179 Ta. In 181 Ta, tentative assignments for several j =  + 1/2 members of the 1/2− [541] band were proposed by Saitoh et al. [24], starting with the 5/2 level at 994 keV. This interpretation is confirmed and extended by the present work, in which the spin 1/2 and 3/2 members have also been located (see Table 4). It is seen from Table 6 the Coriolis calculations predict the 1/2− [541] band to gain a significant amount of strength from the mixing, especially for the j = 9/2 member, and the experimental results support this expectation. This happens primarily at the expense of the 3/2− [532] band, as both these orbitals originate from the 1h 9 shell. The net result is that the 3/2− [532] 2 band is predicted to have no strongly populated members in the stripping experiments, and it has not been identified in any of the isotopes in this study. In 177 Ta the bandhead was previously assigned at 690 keV [1,27], but the strength expected in the present experiment is too small to be observed. The 9/2 member may have enough strength to be observable, but could have been unresolved from other large peaks in the spectra. The 1/2− [530] band, which originates from the 2f 7 shell, has appreciable strength for 2

j = 3/2 and 7/2. In 177 Ta the 3/2− level known at 1045 keV [27] was previously suggested as a member of this band [1], and the strong  = 1 transition (giving rise to the largest peak in the (3 He, d) spectrum) provides convincing evidence for this interpretation. The level at 1161 keV,

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populated by a strong  = 3 transition, is assigned as the 7/2− member. This band is expected to mix with the 1/2− [541] and 3/2− [532] bands, and it appears some of the j = 7/2 strength may have been transferred to the 1/2− [541] band as predicted by the Coriolis calculation. The spin 1/2 bandhead was previously assigned tentatively at 1094 keV, and although an observable (3 He, d) strength is predicted the peak would have been obscured by a larger one nearby. A similar pattern of strong transitions with  = 1 and  = 3 is observed to levels at 1420 and 1524 keV in 179 Ta and is therefore interpreted as the 3/2 and 7/2 members of the 1/2− [530] band. In this case the 1496 keV level, which is populated weakly with  = 1, is a likely candidate for the spin 1/2 bandhead. In Table 3 the 1420 and 1524 keV levels are shown on separate lines from the 1423 and 1527 keV levels, respectively, known previously from (p, t) studies. These must be different levels because the ones populated in (p, t) are assigned positive parity. In 181 Ta, levels at 1785 and ∼ 1860 keV have  = 1 and  = 3 transitions, respectively, and are tentatively assigned as 3/2 and 7/2 members of the 1/2− [530] band. Some comments can be made concerning the systematics of these bands. It appears the energy separation of the 1/2− [541] and 1/2− [530] bands does not change appreciably although the excitation energy for both bands increases with neutron number, being ∼ 800 keV higher in 181 Ta than in 177 Ta. One possible cause for this shift could be a small decrease in deformation with increasing mass number, since these negative parity levels are all downsloping in the Nilsson diagram while the 7/2+ [404] ground state orbital is upsloping. However, the excitation energy increase of ∼ 400 keV for the 5/2+ [402] band between 177 Ta and 181 Ta cannot be easily explained by deformation changes, as this orbital slopes parallel to the 7/2+ [404] one for variations in both 2 and 4 . (See Fig. 5 of the review article by Jain et al. [29].) It is interesting to note that 1/2− [530] bands were observed in (3 He, d) and (α, t) studies of odd-mass lutetium isotopes [15,16], at energies of 800 to 900 keV above the 1/2− [541] band, comparable to those in the tantalum nuclides reported here. A similar situation was reported for iridium nuclei [17], where the 1/2− [530] bands were tentatively assigned about 600 keV above the 9/2, 1/2− [541] level. In similar studies of odd-mass rhenium [7] the 1/2− [541] band was observed systematically but no 1/2− [530] assignments were reported. Although large peaks about 800 keV above the 9/2, 1/2− [541] level were observed in 183,185 Re they were ascribed to positive-parity levels [7]. 4.3. The 1/2+ [411] band The 1/2+ [411] band was previously assigned in the Nuclear Data Sheets, with bandheads at 488, 520, and 615 keV, for 177 Ta, 179 Ta, and 181 Ta, respectively. This orbital is below the Fermi surface so is populated weakly in the stripping reactions, and as it originates from the 2d 3 shell its largest strength is for j = 3/2. The respective 3/2 rotational members at 497, 527, 2

and 619 keV in these nuclides have  = 2 (3 He, d) angular distributions, and the strengths listed in Table 6 are consistent with expectations. The spin 5/2 member is expected to be populated weakly, but in 177 Ta and 179 Ta is not resolved from other peaks. In 181 Ta it was previously unknown and has been assigned at 772 keV on the basis of the present results. 4.4. Other levels In the Nuclear Data Sheets for 177 Ta [1] the 899 keV level is tentatively assigned I π = 11/2− and suggested as the 11/2− [505] bandhead. In this case it should be populated in these experiments with a strong  = 5 transition. This level was not observed in the (3 He, d) reaction, and the

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(α, t) cross section corresponds to a nuclear structure factor of only 0.10 for an  = 5 transition, much smaller than the value of ∼ 0.7 predicted by the Coriolis calculation for the 11/2− [505] bandhead after some of its strength has been transferred to the 11/2, 9/2− [514] level discussed earlier. Thus, the data do not support the 11/2− [505] assignment, and indicate that only a small component of that configuration may exist at this energy. Dasgupta et al. [28] concluded the value of I π was most likely 11/2− for the 899 keV level, but that 13/2− was not completely ruled out. They considered the 11/2− [505] assignment, and also suggested a possible alternate interpretation as a quadrupole phonon based on the 9/2− [514] bandhead. The latter configuration is expected to have negligible single-proton-transfer populations, so although the present results may be consistent with it they should not be regarded as strong evidence for such a description. The highly selective single-nucleon-stripping reactions have significant cross sections only for single-quasiparticle components of levels near or above the Fermi surface, and do not distinguish among many types of weakly populated configurations. It is quite possible the 899 keV level has a minor 11/2− [505] component, as part of a complex configuration. In 181 Ta the level at ∼ 1205 keV populated in the present reactions may be the same one previously known at 1205.7 keV [3] and assigned as the K π = 3/2+ , K0 − 2 gamma vibration based on the 7/2+ [404] ground state. The 3/2+ [402] orbital is above the Fermi surface and forms the ground states of iridium nuclei. It is coupled by a strong E2 matrix element to the 7/2+ [404] one, so a significant component of the 3/2+ [402] configuration is expected to be mixed into this K = 3/2 gamma vibration. An early calculation with the quasiparticle phonon nuclear model [30] predicted this K π = 3/2+ vibration in 181 Ta at 1140 keV, with a 3/2+ [402] admixture of 4%. This could be an explanation for the population observed in these experiments. The 3/2+ [402] orbital originates from the 2d 3 shell and most of its strength is for j = 3/2. 2

For a pure 3/2+ [402] band the nuclear structure factor for the 3/2+ bandhead is ∼ 0.85, so the observed value of 0.08 would correspond to an admixture of ∼ 10% of this single-proton configuration in the γ -vibration. Several levels at higher excitation energies have angular distributions consistent with  = 0 transitions, in which case they would have I π = 1/2+ . These could be due to admixtures of the 1/2+ [400] orbital, which appears at very low excitation energies in odd iridium nuclei. 5. Levels of 178 Ta 5.1. General comments As mentioned earlier, two known levels in 178 Ta decay by electron capture (EC) to 178 Hf, but it is not known which of these is the ground state [31]. One is the 9.3 min activity, assigned − − as the {1+ , 92 [514]π − 72 [514]ν } configuration because it is fed by an allowed unhindered (log f t = 4.65) EC transition from the 0+ ground state of 178 W, and it also decays by allowed unhindered transitions to the ground state band of 178 Hf [32]. (The notation used for two-quasiparticle configurations is {K π , followed by the Nilsson quantum numbers Ω π [N nz Λ] for the proton and the neutron}.) No other 178 Ta levels are known to be populated from the decay of 178 W, for which the available energy is small. The 2.36 hr activity in 178 Ta is as+ − signed as the {7− , 72 [404]π + 72 [514]ν } configuration. This, and a number of other levels, have been reported from high-spin studies. Dubbers et al. [33] studied γ -rays following the (α, 2n), (d, 2n) and (p, n) reactions and proposed a 178 Ta level scheme including the {7− , 7+ 7− 2 [404]π + 2 [514]ν } band, starting at an energy they call 0 keV, as well as ones based on the

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Fig. 12. Partial level scheme for 178 Ta, showing some of the levels populated in this work, and (at right) the tentative − − placement for the {1+ , 92 [514]π − 72 [514]ν } band discussed in the text. In order that the lowest level has an energy of zero, excitation energy values shown to the left of levels populated in the present work are labelled E + x, as in the Nuclear Data Sheets [31], where values of E are those from Table 5. The K π = 7− , 1− , 6− , and 8+ bands are considered − − − − well-established. Assignments for the {4+ , 12 [541]π + 72 [514]ν } and {1+ , 92 [514]π − 72 [514]ν } bands are based on tentative interpretations in both the high-spin study of Kondev et al. [34] and the present work. Gamma-ray transitions (from Ref. [34]) that establish the relative energies of the K π = 4+ and 1+ bandheads are shown. If these tentative interpretations are correct, the value of x is 28 ± 4 keV. While all data in this work and Ref. [34] are consistent with this interpretation, there is a discrepancy with the reported β + endpoint energy [40] for the 178 Ta EC decay more than twice the stated uncertainty on that measurement (see text). 9− 7− + 2 [514]π + 2 [514]ν } Gallagher–Moszkowski partner of the 1 band mentioned above, + − + − {6− , 52 [402]π + 72 [514]ν }, and the {9− , 92 [514]π + 92 [624]ν } configurations. The first

{8+ ,

the three of these can be populated in the present single-proton stripping reactions, and are shown in the partial level scheme of Fig. 12. The K π = 9− band cannot be observed in these reactions, because two-quasiparticle configurations can be populated only if their odd neutron is the same as − the one in the 177 Hf target ground state, which is the 72 [514]ν orbital. Fig. 7 and Table 5 show that prominent peaks are found with energy spacings consistent with those of the four known levels expected to be populated significantly in these three bands. These are the K π = 7− and 6− bandheads, and the 8+ and 9+ members of the K π = 8+ band. A more recent study of 178 Ta levels by Kondev et al. [34] using the (11 B, 5n) and (7 Li, 5n) reactions confirmed the assignments of Dubbers et al. and extended the bands to higher spins. − − They also tentatively proposed the {4+ , 12 [541]π + 72 [514]ν } band and its decay to the band −

based on the {1+ , 92 [514]π −

7− 2 [514]ν }

9.3 min isomer. These two bands were not connected

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to the ones assigned by Dubbers et al. with any gamma rays, so their relative excitation energy was unknown. Following Dubbers et al., Kondev et al. use an excitation energy scale in which + − the {7+ , 72 [404]π + 72 [514]ν } bandhead is at 0 keV, and define the unknown excitation energy −

−

of the {1+ , 92 [514]π − 72 [514]ν } bandhead to be X keV. These earlier studies have thus not determined which of the 1+ or the 7+ activities forms the ground state of 178 Ta. In the 2003 evaluation of input data [35] for the 2003 mass tables, the 7− bandhead is estimated to be 100 ± 50 keV above the 1+ one. In principle, it could be possible to settle this question with the proton stripping reactions, as both bands should be populated. However, the 1+ band is difficult to identify unless very good statistics are available, because the transfer is primarily  = 5, j = 11/2, and the strength can be distributed over band members from spin 1 to spin 9. Therefore, further discussion of the relative energies for these bands will be postponed until the interpretation of identified peaks in the spectra is considered. To simplify discussion of present results in terms of previously known levels, the excitation energies in Table 5 and Figs. 7 and 8 use the same scale as in Refs. [33,34], with the + − {7+ , 72 [404]π + 72 [514]ν } bandhead designated as 0 keV. It will be seen below that with this choice the values for some levels are negative, so the level scheme of Fig. 12 uses a slightly different approach (similar to that of the Nuclear Data Sheets [31]), in which this 7− level has an excitation energy of x + 0 keV. Thus, energies of levels observed in the present experiments are labelled in Fig. 12 as E + x, where E values correspond to those in Table 5, Figs. 7 and 8, and Refs. [33,34]. The lowest level is then designated to have 0 keV in Fig. 12, and one aim is to try − − to establish the value of x. (If the ground state is the {1+ , 92 [514]π − 72 [514]ν } bandhead, the quantity X used by Kondev et al. [34] is then the negative of x.) 5.2. Interpretation of strongly populated levels The (3 He, d) and (α, t) strengths from these experiments provide additional support for the 6− , and 8+ bands assigned by Dubbers et al. as discussed above, and also permit some new levels to be identified. For this purpose, program GREATER [36] was used to perform Coriolis mixing calculations, and to predict cross sections for rotational members of all bands according to Eq. (1). The DWBA and Nilsson model parameters, and the pairing emptiness parameters, Ui2 , used were the same as for the neighboring even-mass targets. Spectroscopic strengths are not readily extracted from these limited data because, in general, the transitions involve a mixture of -values. Instead, predicted (α, t) cross sections at θ = 60◦ and (3 He, d) ones at θ = 30◦ for bands discussed below are listed in Table 7, where they are also compared with experimental values from Table 5.

7− ,

5.2.1. Transfer of the 7/2+ [404] proton Since the only Cj  coefficient of significant magnitude for this orbital is for j = 7/2, essen+ − tially all the transfer strength to the {7+ , 72 [404]π + 72 [514]ν } band goes to the bandhead. As seen in Table 7 the predicted cross sections of 13 µb/sr for (α, t) and 8 µb/sr for (3 He, d) are in good agreement with the observed values of 16(2) and 8(2) µb/sr, respectively. The + − {0+ , 72 [404]π − 72 [514]ν } Gallagher–Moszkowski partner has not been identified. Its bandhead is expected to be about 250 keV above the 7− one (see Fig. 27 of Ref. [34]), similar to the separation observed for these bands in 176 Lu, and the transfer strength is expected to be distributed over several rotational members. Thus, the predicted cross sections are small (see Table 7).

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Table 7 Comparison of predicted and observed cross sections for 178 Ta levels Configuration and level

Energy (keV)

dσ ) predicted (µb/sr) ( dΩ

7 + [404] ± 7 − [514] π ν 2 2 K π = 7− I =7 I =0 K π = 0−

0

14 2 4 4 2 1

289 101 151 ∼ 223

I I I I

I =2 I =3 I =4

9 − [514] ± 7 − [514] π ν 2 2 K π = 8+ I =8

K π = 1+

I I I I I I I

=9 =1 =2 =3 =4 =5 =6

1 − [541] ± 7 − [514] π ν 2 2 K π = 4+ I =4

K π = 3+

I I I I I I I I

=5 =6 =7 =8 =3 =4 =5 =6

I I I I I I I I

=4 =5 =6 =7 =4 =5 =6 =7

1 − [530] ± 7 − [514] π ν 2 2 K π = 3+ I =3

K π = 4+

(3 He, d)(θ =30◦ )

8 1 3 3 2 1

16(2)

8(2)

40 16 15 8 3

112 40 38 22 8

45(3) 23(2) 16(2)  18a

88(7) 35(6) 26(4)  21a

220 422

11 16 0 4 8 8 5 2

6 10 0 2 4 4 3 1

 18a  33a

 21a  37a

(∼ 420) (∼ 434) (485) (564) (672?)

11 21 23 15 4 7 10 9 5

18 22 18 9 3 15 17 10 4

 33a ∼ 24 20(2) 12(2)  11

 37a  37a 12(3)  21  38

(1222?) (1280?) (1386?)

9 20 21 12 4 3 3 2 1

46 72 54 27 7 23 12 5 2

12(2) 20(3) 15(2)

119(15) 96(10) 97(10)

=1 =2 =3 =4

5 + [402] ± 7 − [514] π ν 2 2 K π = 6− I =6 I =1 K π = 1−

dσ ) observed (µb/sr) ( dΩ

(α, t)(θ =60◦ )

(α, t)(θ =60◦ )

a Value shown is total cross section for an unresolved multiplet.

(3 He, d)(θ =30◦ )

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Some of the weak peaks expected could be obscured by larger ones in the spectrum, or could be part of the unassigned populations at 128, 180 or 250 keV in the (α, t) spectrum. 5.2.2. Transfer of the 5/2+ [402] proton + − The known {6+ , 52 [402]π + 72 [514]ν } bandhead at 289.1 keV has the largest peak in each of the (3 He, d) and (α, t) spectra, and the predicted cross sections are in fairly good agreement + − with those observed. The {1+ , 52 [402]π − 72 [514]ν } triplet Gallagher–Moszkowski partner was not previously known. It is expected lower in energy, with reasonably large cross sections. The prominently populated levels at 101 and 151 keV can be identified as the spin 1 and 2 − − members. The spin 3 member is not resolved from the {8+ , 92 [514]π + 72 [514]ν } bandhead, which is known at 219.7 keV. The observed energy of 222 keV for this doublet in the (α, t) spectrum would be an average of comparable intensities from the  = 5 transition to the 8+ level and the  = 2 one to the 3− level, while the (3 He, d) value of 225 keV would be dominated by the  = 2 component. Thus, the 3− level has an energy close to ∼ 225 keV. The peak for the spin 4 member would probably be in the tail of the large one for the 289.1 keV level. 5.2.3. Transfer of the 1/2− [541] proton − − The {8+ , 92 [514]π + 72 [514]ν } bandhead at 220 keV has been mentioned above, and its 9+ rotational member is known at 422 keV, located in an unresolved multiplet in these reactions. To explain the observed results a new level is proposed near the 9+ one known at 422 keV, in addition to another new one at ∼ 434 keV, and both “new” levels must be populated with low -value components in order to have such strong (3 He, d) cross sections. The peak-fitting computer program finds a doublet in this region of the (α, t) spectrum with 33 µb/sr at 422 keV and 24 µb/sr at 434 keV. This cross section at 422 keV is twice as large as the 16 µb/sr predicted for the 9+ level alone. The (3 He, d) spectrum at θ = 15◦ also shows a doublet, with 33 µb/sr at 418 keV and 42 µb/sr at 433 keV. In the (3 He, d) spectrum at θ = 30◦ this multiplet, with 74 µb/sr, was not resolved, but the centroid energy was 425.8 keV. Since this energy is near the average of 418 and 434 keV the cross sections near ∼ 434 keV and near ∼ 420 keV would have comparable intensities, of 30 to 40 µb/sr each. The 9+ level at 422 keV is predicted to have a (3 He, d) cross section of about 10 µb/sr at θ = 30◦ and only ∼ 1 µb/sr at θ = 15◦ , so a new level is proposed at about 420 ± 4 keV. These fairly large cross sections are attributed to transfer of the 1/2− [541] proton, which is associated with the only other band observed with such large intensity at simi− − lar excitation energies in the neighboring odd isotopes. The {K π = 4+ , 12 [541]π + 72 [514]ν } −

−

band should be lower in energy than its {K π = 3+ , 12 [541]π − 72 [514]ν } band Gallagher– Moszkowski partner, and Coriolis coupling could be expected to transfer significant stripping strength from the K π = 3+ to the K π = 4+ band. Kondev et al. [34,37] tentatively proposed the K π = 4+ bandhead at 447.7 + X keV, and suggested the 5+ → 4+ gamma transition had an energy too low to have been observed in their experiment, so the spacing between the (4)+ and (5)+ members was unknown. A sequence of levels up to spin (18)+ was then built up from the (5)+ level. Table 7 shows the spin 4, 5, 6, and 7 members of this band have quite large predicted cross sections and should be observed in the present reactions. In this region of excitation energies the only set of peaks having spacings consistent with the spin (5), (6), and (7) levels tentatively proposed by Kondev et al. are those at ∼ 434, ∼ 485, and ∼ 584 keV. If these three peaks were associated with the spin (5) to (7) levels of Kondev et al. the newly-found level at ∼ 420 keV could be the 4+ bandhead. The peak at ∼ 671 keV would also be at an energy consistent with the spin (8) level of Kondev et al., but the observed intensities are larger than predicted,

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suggesting some other unresolved level would have to be present. This interpretation explains a number of the large peaks in the spectra, and the cross section pattern is reasonable (see Table 7), so is shown as a tentatively proposed assignment in Fig. 12. Although some of the experimental cross sections appear larger than predicted, two factors must be noted. One is that for 1/2− [541] bands in the odd-mass tantalum neighbors the observed peaks were also stronger than calculated (as seen from the strengths shown in Table 6). The other is that the predicted values depend somewhat on details of the Coriolis mixing with the K π = 3+ Gallagher–Moszkowski partner, and with bands formed by transfer of the 3/2− [532] proton, all of which are unassigned and at unknown excitation energies. With this tentative interpretation for the K π = 4+ band the value of X would be −28 ± 4 keV and the spacing between the 4+ and 5+ rotational members would be 14 ± 4 keV. 5.2.4. Other levels Many large peaks are seen in the spectra at excitation energies between about 1000 and 1600 keV. As the largest peaks in this energy range for the neighboring 177 Ta and 179 Ta nuclides are for the 1/2− [530] band it is most likely the levels populated strongly in 178 Ta belong − − − − to the {K π = 3+ , 12 [530]π − 72 [514]ν } and {K π = 4+ , 12 [530]π + 72 [514]ν } bands. The K π = 3+ one should be lower in energy, and Coriolis mixing should transfer strength to it from the K π = 4+ band. As shown in Table 7, the largest peaks in this region are thus predicted to be the spin 3, 4, 5, and 6 band members of the K π = 3+ band. One might suggest that three of the largest peaks observed, at about 1222, 1280, and 1386 keV, could be the first three members of this band. Although the populations are larger than predicted it is noted from Table 6 this was also true for transfer of the 1/2− [530] proton to odd-mass tantalum isotopes. Also, the high level density at these excitation energies makes it likely that many of the observed peaks are multiplets, so any suggested assignment would be quite speculative. +

5.3. Relative spacing of the {7+ , 72 [404]π + bands

7− 2 [514]ν }

−

and {1+ , 92 [514]π −

7− 2 [514]ν }

Two different approaches can be used with the present results to determine a value for the quantity X defined by Kondev et al. [34] for the separation of these bandheads. As seen in Section 5.2.3, one method is to assume the tentative assignments of Kondev et al. are correct − − − − for the {1+ , 92 [514]π − 72 [514]ν } and {4+ , 12 [541]π + 72 [514]ν } configurations, and also π + to assume the K = 4 band members have been correctly identified in the present spectra, to + − determine their energy relative to the {7− , 72 [404]π + 72 [514]ν } bandhead. The value obtained in this way was X = −28 ± 4 keV. The other approach is to make use of energy separations within a spectrum, of peaks from different residual Ta nuclides, to get Q-value differences for the different isotopes. These can be compared with proton separation energies, Sp , from the 2003 mass table [38]. In the mass table the value Sp (179 Ta) = 5211.0 ± 0.4 keV is precisely known for the 179 Ta ground state, and Sp (178 Ta) = 4907 ± 15 keV is for the 1+ level of 178 Ta, because it was obtained from the measured EC decay energy of the 9.3 min activity. From positions of peaks due to the 178 Hf isotopic impurity in the 177 Hf target (and also those due to the 177 Hf isotopic impurity in the 178 Hf target), the reaction Q-value populating the ground state of 179 Ta was found to be 276 ± 3 keV greater than that for the 7− level of 178 Ta. Combined with Sp (179 Ta) from the mass table, this yields Sp = 4935 ± 3 keV for the 7− level of 178 Ta. Similarly, positions of peaks due to the

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isotopic impurity in the 176 Hf target can be used with the mass table value Sp (177 Ta) = 4435 ± 3 keV to obtain a value of Sp = 4927 ± 4 keV for the 7− level of 178 Ta. This result is considered less reliable than that from Sp (179 Ta) because Sp (177 Ta) has a significantly larger uncertainty in the mass table. If a weighted average of 4934 ± 3 keV is adopted from these measurements for the 7− level of 178 Ta, and the mass table value of 4907 ± 15 keV were used for the 1+ level, it would be concluded the 7− level is X = 27 ± 15 keV below the 1+ one. This does not agree with the value of X = −28 ± 4 keV obtained above. However, it will be seen below there are additional complications involved. An examination showed no simple way this discrepancy could be attributed to misidentification of peaks in the spectra used to obtain the proton separation energy for the 7− level described above. In addition to considering the reliability of the K π = 4+ and K π = 1+ band assignments, another relevant issue is the reliability of the mass table value of Sp (178 Ta) = 4907 ± 15 keV (for the 1+ level). That result was obtained from the EC decay energy for 178 Ta, which is listed as 1937 ± 15 keV in the evaluated data [39] used for the 2003 mass table. However, the experimental positron end point energy was reported as 890 ± 10 keV [40] which, by adding 2m0 c2 corresponds to an EC decay energy of 1912 ± 10 keV. A comment in the evaluated data [39] indicates the value was adjusted because the ratio of β + intensities to the 0+ ground state and 2+ level at 93 keV in 178 Hf did not agree with the theoretical value of 2.7. The reported endpoint energy was regarded as a weighted average for two β + groups, increased by 25 keV, and the uncertainty was increased from 10 to 15 keV. The procedure for this correction may be questioned, because Gallagher et al. [40] actually reported two positron groups, with endpoint energies differing by about 90 keV, and the value of 890 ± 10 keV is for the one of higher energy. They commented that the discrepancy between observed and predicted intensity ratios could be due to energy degradation of positrons in the relatively thick source used. If the 25 keV correction had not been applied, the mass table proton separation energy for the 1+ level of 178 Ta would be 4932 ± 10 keV rather than 4907 ± 15 keV as in Ref. [38]. The method of using separation energies to determine X would then yield X = 2 ± 11 keV, corresponding to the 1+ level being only 2 ± 11 keV above the 7− one. Although this would remove almost half the discrepancy between values of X from the two approaches, the remaining discrepancy is still more than twice the stated uncertainty on the β + endpoint energy measurement. Nevertheless, the arrangement of levels discussed above, with the K π = 4+ and K π = 1+ bands as proposed by Kondev et al., is shown as a tentative interpretation in the level diagram of Fig. 12. − − Another way to determine X would be to identify the {1+ , 92 [514]π − 72 [514]ν } band directly in the (3 He, d) and (α, t) spectra. Unfortunately, the peaks are expected to be weak because the transitions have  = 5 and the strength is distributed over several band members (see Table 7). Several weak unassigned peaks observed in the (α, t) spectrum, at energies of about 24, 128, 180, and 250 keV, could be candidates for some of these levels. For example, in the band structure of Kondev et al. the 2+ member is at X + 46 keV, which would correspond to an energy of ∼ 18 keV in the present spectra. The weak peak at ∼ 24 keV is thus a possible candidate for the 2+ member. The 3+ member is 73 keV higher [34] and would be close to the prominent peak at 101 keV. (The data in Table 7 show the latter peak may have some otherwise unexplained high- strength.) The 4+ member could be responsible for part of the unassigned peak at 180 keV. In searching for this band it must also be noted that a significant odd–even staggering may exist. The corresponding K π = 1+ band in the isotone 176 Lu has a very significant staggering, which − − Covello et al. [41] could explain by the {0+ , 72 [523]π − 72 [514]ν } band having a large Newby shift, and mixing with the K π = 1+ band via the Coriolis interaction. The net conclusion is that 177 Hf

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all data from these experiments are internally consistent with X = −28 ± 4 keV; that is, with the 1+ level being 28 ± 4 keV below the 7− one, but this would require the β + endpoint energy to differ from its reported value [40] by more than twice its stated uncertainty. 6. Concluding remarks These experiments have identified many new levels in 177 Ta, 179 Ta, and 181 Ta, and the spectroscopic information obtained has permitted spin-parity assignments and model interpretations for many of these. Single-proton stripping strengths provided additional support for previous assignments of the 7/2+ [404], 9/2+ [514], and 5/2+ [402] bands in each nuclide, and identified new rotational members for the 1/2− [541] and 1/2+ [411] bands. Present results confirm the previous tentative assignment from EC decay data for the 1/2− [530] band in 177 Ta, and also locate this band in 179 Ta and 181 Ta. The 899 keV level in 177 Ta was previously considered a possible candidate for the 11/2− [505] bandhead [1] but less than ∼ 10% of the strength expected for the pure 11/2− [505] state is observed at this energy. The (3 He, d) and (α, t) spectra from the 177 Hf target, originally intended only for use as an aid in identifying peaks due to isotopic target impurities, have provided useful new structural + − information for 178 Ta. Specifically, the {K π = 1− , 52 [402]π − 72 [514]ν } band was assigned, 188 keV below its known K π = 6− Gallagher–Moszkowski partner, and a tentative assignment − − for the {K π = 4+ , 12 [541]π + 72 [514]ν } band was made. Although a new value for the proton separation energy of the {K π = 7− ,

7+ 2 [404]π

−

+ 72 [514]ν } bandhead was obtained, this has still −

−

not firmly settled the question of whether this level or the {K π = 1+ , 92 [514]π − 72 [514]ν } one forms the 178 Ta ground state. Data from the present experiments and those of Kondev et al. [34] are fully consistent with the 1+ level being 28 ± 4 keV below the 7− one. However, this depends on tentative interpretations in both Ref. [34] and the present work, and would require the β + endpoint energy for EC decay of the 1+ level to be ∼ 860 keV rather than the value of 890 ± 10 keV reported by Gallagher et al. [40]. Thus, additional work to settle this question is desirable. This should be possible with a thorough proton-stripping study on a 177 Hf target. It would be necessary to have good statistics and good resolution, and measurements with the (α, t) reaction − − would be very important because identification of the {1+ , 92 [514]π − 72 [514]ν } band involves searching for weak  = 5 transitions. Acknowledgements The authors wish to acknowledge the importance of Dr. Zygmunt Preibisz in suggesting and initiating this project. The operations staff of the MP tandem van de Graaff accelerator are thanked for providing many days of stable 3 He and α beams for the experiments. We are also very grateful to Mrs. I. Wolansky for her careful work scanning the photographic plates. Useful discussions with Balraj Singh and Jim Waddington have been very helpful, and Filip Kondev has kindly provided supplemental information to his published report. Financial support from the US National Science Foundation for support of the Rochester Nuclear Structure Research Laboratory, and from the Natural Sciences and Engineering Research Council of Canada for operating grants, is gratefully acknowledged.

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