Structure of the 70As nucleus

NUCLEAR PHYSICS A EI~qEVII~I~

Nuclear Physics A 584 (1995) 60-83

Structure of the

7°As nucleus

Zs. Podoly~ik, T. F6nyes, J. T i m ~ Institute of Nuclear Research of the Hungarian Academy of Sciences, H-4001 Debrecen, Hungary

Received 29 August 1994

Abstract

y-ray, yy-coincidence, internal conversion electron and y-ray angular distribution spectra of the 7°Ge(p,ny)7°As reaction were measured with Ge(HP) y and superconducting magnetic lens plus Si(Li) electron spectrometers at eight bombarding proton energies between 7.59 and 8.7 MeV. Energies and relative intensities of 113 (among them 60 new) 7°As y rays, as well as 29 new internal conversion coefficients were determined. The proposed level scheme contains 16 new levels. y-ray branching and mixing ratios, level spin and parity values have been deduced. The spins and parities have been determined on the basis of decay properties of levels, internal conversion coefficients, Hauser-Feshbach analysis of reaction cross sections, y-ray angular distribution and other data. The energy spectra and electromagnetic moments were calculated in the framework of the interacting boson-fermion-fermion/truncated quadrupole phonon model for odd-odd nuclei and reasonable agreement has been obtained between the experimental and theoretical results. Keywords: NUCLEAR REACTIONS 7°Ge(p,ny); E = 7.59-8.7 MeV; measured Ey, ly(E,O), yy-coin, [ (ce), O'rel(E, ELEV). 70As deduced levels, y-branching, y-mixing ratios, J,~'. Hauser-Feshbach analysis.

Ge(HP) detectors, combined superconducting magnetic lens plus Si(Li) electron spectrometer.Enriched targets. Interacting boson-fermion-fermion model calculation.

1. Introduction The energy levels of 7°As have been studied earlier from 7°Se fl+-decay and ( p , n y ) reaction by Ten Brink et al. [ 1,2], as well as from heavy-ion reactions by Filevich et al. [ 3] and B~dic~ et al. [4]. These studies extended our knowledge on the level scheme of 7°As considerably, nevertheless unambiguous spin-parity values have been assigned only to seven 7°As levels in the 1993 Nuclear Data Sheets evaluation (Bhat [5] ). The aim of the present work was a detailed 3/ and electron spectroscopic study of the 7°Ge(p,ny)Y°As reaction with special emphasis on the determination o f spins and parities o f levels. This work is part o f a wider program, in which we have investigated the structure o f o d d - o d d 68Ga [6,7], 66Ga[8], 74As [9] and 72As [10] nuclei. The 0375-9474/95/$09.50 (~ 1995 Elsevier Science B.V. All rights reserved SSDI 0375-9474(94) 00486-2

z~. Podolydk et al./Nuclear Physics A 584 (1995) 60-83

61

program includes also a theoretical description of the level spectra and electromagnetic properties on the basis of the interacting boson-fermion-fermion model (IBFFM) and the study of dynamical and supersymmetries in the Ga-As region.

2. Experimental techniques The proton beams of the Debrecen 103 cm isochronous cyclotron were used in the experiments. The energies and intensities of protons were varied between 7.59-8.7 MeV and 3-400 nA, respectively. The 0.3-0.8 m g / c m z thick targets have been prepared by evaporation technique on 4 0 / z g / c m 2 carbon foil backing. For 3,-ray angular distribution measurements we used a 2 mm wide target, deposited on a 340 /xg/cm 2 thick mylar backing. In order to facilitate unambiguous identification of 3, rays we measured the 3, spectra of the 7°'72'73'74'76Ge-l-p reactions, using different isotopically enriched 7°Ge (up to 97.1%), 72Ge (98.2%), 73Ge (81.6%), 74Ge (99.1%) and 76Ge (94.6%) targets. The 3,-spectroscopic measurements were carried out using Compton-suppressed 20% Ge(HP) and 25% coaxial Ge(HP) detectors. (The efficiency values are relative to that of a 7.5 cm x 7.5 cm cylindrical NaI(T1) detector.) The detectors were placed at 90 ° to the beam direction for energy, and at 125 ° for intensity determination. We used 133Ba, 152Eu, 2°7Bi sources for energy and efficiency calibration of the 3, spectrometers. In the low-energy region the X rays of these sources also served as calibration lines. The 3'3,-coincidences were measured with the 20 and 25% Ge(HP) detectors, placed at 125 ° and 235 ° angles to the beam direction. The approx. 16 million 3,3,-coincidence events were recorded in event-by-event mode, with a fixed 60 ns resolving time. The data processing was carried out off-line. After creating the symmetrized two-dimensional coincidence matrix a standard gating procedure was used. Internal conversion electron spectra were measured with a superconducting magnetic lens plus Si(Li) spectrometer [ 11-13], which had ~2.7 keV (at 976 keV) energy resolution and 10% transmission (for two detectors). The background from backscattered electrons was reduced with a swept energy window in the spectrum of Si(Li) detector and with twisted paddle-wheel shaped antipositron baffles. For the efficiency calibration of the spectrometer J33Ba and 152Eu sources were used. We estimated the effect of the angular distribution of electrons on the measured internal conversion coefficients by the use of the available 3,-ray angular distribution coefficients, solid-angle correction factors [13], and normalized directional particle parameters. The result showed that this effect was usually much less than the statistical uncertainties of the measured internal conversion coefficients (ICC). The angular distributions of 3, rays were measured with the Compton-suppressed 20% Ge(HP) detector at five different angles between 90 ° and 135 ° with respect to the beam direction. A control measurement was carried out at another five angles. The solid-angle correction factors for the detector were Q2 = 0.995 and Q4 = 0.987. For normalization of the ?/-ray intensities we used a monitor Ge(HP) 3,-ray detector at fixed position. The theoretical angular distributions for given spin combinations were fitted to the experimental

62

Zs. Podoly6k et al./Nuclear Physics A 584 (1995) 60-83

data in a least-squares procedure using the computer code ANDIST [ 14]. The attenuation coefficients a2 and O~4 were calculated using the CINDY [ 15] program. If the level was fed also by 3 / r a y ( s ) , the reorientation effect was taken into account. The optical potential parameters used in the calculations are given in Section 5. Data reduction was carried out with personal computers using a spectrum analysis program [ 16].

3. Experimental results y-ray spectra of the 7°Ge(p,n3,)7°As reaction were measured at 7.59, 7.75, 7.89 and 8.23 MeV bombarding proton energies. The 3'3,-coincidence measurement was performed at Ep = 8.5 MeV. The enriched targets and the good statistics of 3,3,-coincidence measurement enabled unambiguous identification for most 3, rays. The background, caused by the radioactive decay of the reaction products, was also carefully analysed. If the 3, ray was unresolved or small in single spectra, the energy and intensity was determined from the gate spectra. Typical 3,-ray and internal conversion electron spectra are shown in Fig. 1, and 3,3,-coincidence spectra in Fig. 2. The energies, intensities and 3,3,-coincidence relations of 3, rays assigned to the 7°Ge(p,n3,)V°As reaction are listed in Table 1. Internal conversion electron and y-ray spectra were measured simultaneously (at 8.1 and 8.7 MeV bombarding proton energies). For the normalization of the experimental ICCs we have used the theoretical aK value [ 17] of the 176.17 keV pure E2 [5] 7°Ge transition. Another measurement was carried out at Ep = 8.23 MeV proton energy, where

p

N~

s .........

4 104

2 104

i

7°Ge(p,nqO7°As Ep=8.7 MeV

ram+

;V+

~ c o ,~- ,e ,e -e

x2

Ne-' 4 104 2 104 K L,M 1000

CHANNEL NUMBER I

1500

2000

25100

30bOO

Fig. 1. Typical y-ray and internal conversionelectron spectra of the 7 0 Ge(p,ny) 7 0 As reaction. The energies of y rays are given only for the strongest 7°As lines. Correspondingconversionelectron peaks are also indicated.

Zs. Podolydk et al./Nuclear Physics A 584 (1995) 60-83

N-rr 3000 2000 1000 0

1

L2

500

1000

;'°Ge(p,n.T/)7°As

~

;

Ep=8.5 Mev

~

5

I

Gate: 160.89 keV

~

Gate: 244,10 keV

I ~"~

,q

-~

~

I/

I

I

0 I ~

8

:

l

,.- ,n

S_.o

~ ~

~

.

i l

• N

63

i~

l~

hl,,

t,I

1

I 1500

I/

"

~ ~

'~

~'

"~ "

so:L N-r-~ 800

~

~

N

Gate: 45841+ +458.48 keY

i

i ' ]I

400

0

~

"~

~

r'~

200

400 600 CHANNEL NUMBER

800

100C

Fig. 2. Typical yy-coincidence spectra at different gates. Numbers at the peaks indicate 7°As y-ray energies. The background was subtracted. The Nr7 scales correspond to the first parts of the spectra.

the electron spectrum was measured in coincidence with beam pulses. In this case the formerly deduced 244.10 keV 7°As M1 transition has been used for normalization. The internal conversion coefficients obtained from different electron spectra agreed within experimental errors. The obtained ICCs, as well as the deduced and formerly known multipolarities are given in Table 1. The theoretical and experimental ICCs of the 7°As transitions are shown in Fig. 3. The angular distribution of y rays were measured at Ep = 8.2 MeV. Typical reduced X 2 fits of the theoretical angular distributions to the experimental ones are shown in Fig. 4. In the calculations we have considered only such parity for the initial state, which was in accordance with the internal conversion coefficient measurements, and spins differing from the spin of the final state in max. two units. The error limits of 2 the multipole mixing ratio (8) correspond to Xmin"}-I values. The results of the y-ray angular distribution measurements are summarized in Table 2.

Zs. Podolydk et al./Nuclear Physics A 584 (1995) 60-83

64

Table 1 Energy, intensity, internal conversion coefficient, multipolarity and coincidence relations of 3, rays of the 7°Ge(p,n3,) 7°As reaction Er (keV)

lz' a (relative)

ICC measurements 104 x aK Multip. of 3' ray

32.05 (10) 157.8 (133) 49.45 (3) 1888.8 (1090)

80.04 (6) 81.19 (3)

6.9 (21) 98.4 (53)

86.19 (3)

404.8 (208)

90.96 (8) 93.88 (7) 95.18 (6)

13.0 (16) 9.8 (18) 2.7 (12)

109.84 113.50 132.51 134.63

(6) (4) (4) (5)

9.1 16.1 26.4 1000.0

(17) (19) (31) (575)

Former Coincident 3, rays results E:, (keV) on multip. of 3, ray [5] E2 (MI)

N

N N

N

135.68 (5)

883.4 (457)

148.57 (3)

112.1 (62)

153.18 (3)

71.7 (45)

158.89 (9) 160.89 (3)

17.7 (19) 244.8 (129)

N

166.69 (10) 166.83 (10)

26.7 (83) 230.1 (231)

N

190.52 (6)

18.4 (24)

N

292 (58)

MI(+E2)

217 (18)

M1

86 161 256 327 389 458.5 546 603 906 301.8 D+Q 95 319 597 49 425 648 203 153 81 390 203 49 49 (MI ( + E 2 ) ) 81 254 319 479 597 761 161 414 554 762 49 389 49 389 135 49 622 49 81 287 332 203

114 166.7 263 344 404 465 554 640 945 316 135 332

133 149 244 247 276 301.8 357.8 358.3 414 425 474 490 556 565 659 762 965 1034

161 474 879 256 203 135

216 516

110 244 95 287 332 521 603 773 216 425 562 879 153 465 94 449 166.8 86 675 287 95 293.7 342 578

263 293.6 159 293.7 342 549 656 819 264 474 622

153 254 316 377 449 500 578 857.8

166.8 223.4 302.4 372 479 485 404 520

414 554

166.8 223.4 293.7

313 223.4 298 372 555 657

235 302.4 458.4 577 692

389 516 648

404 520 675

203

254

316

149

316

357.8

136

264

562

389 159 298 521

301.8 223.4 235 302.4 319 555 662

Zs. Podoly6k et al./Nuclear Physics A 584 (1995) 60-83

65

Table 1--continued Ey (keV)

Iy a (relative)

202.66 (3)

597.4 (349)

ICC measurements Former Coincident y rays 104 x aK Multip. results E:, (keV) of y ray on multip. of 3' ray [5]

215.51 (15) 13.1 (25) N 223.38 (9) 9.4 (61) 223.42 (3) 319.6 (171) 235.10 (4) 240.07 (7) 244.10 (3) 247.11 (3) 254.01 (4)

255.96 263.13 263.93 275.52 286.96

51.8 (41) 10.0 (24) N 350.3 (188) 98.1 (57) 34.1 (28)

119 (8)

M1

92 (8)

M1

97 (13)

M1

79 (6)

MI

138 (11)

(4) 85.4 (53) 68 (8) (3) 259.8 (135) 64.6 (52) (14) 9.1 (25) N (7) 11.8 (25) N (4) 58.7 (38) 48.5 (67)

293.63 (3)

283.0 (145)

293.66 296.64 297.51 301.80

70.7 123.4 7.8 655.3

(5) (3) (6) (3)

MI+E2

N

50 (4)

(51) (67) 51 (5) (24) N (331) 24.0 (16)

MI MI

MI M1

M1 El

302.41 (5) 312.62 (5) 315.53 (3)

11.1 (42) 24.8 (28) 242.3 (125)

40.2 (32)

M1

318.60 (3)

252.1 (135)

20.7 (19)

E1

327.37 331.74 342.24 343.81 351.29 357.81 358.32 372.39 376.64 388.96

22.9 15.1 78.2 180.5 71.3 18.7 26.7 15.1 67.3 163.0

35.5 (52) 33.9 (35)

M1 M1

(10) (5) (10) (10) (4) (7) (9) (8) (4) (4)

390.15 (4) 404.15 (8) 413.89 (4)

(28) (27) (49) (96) (46) (48) (49) (26) (47) (105)

105.5 (64) 40.2 (61) 122.0 (77)

(MI+E2)

N

N N N 39.4 (121) MI+E2 29.7 (43) M1 26.2 (42) M1 29.7 (68)

M1

23.7 (29)

MI

N

E1 +M2

91 223.4 449 86 203 95 549 135 49 49 603 49 49 287 485 49 49 86 49 95 485 133 662 95 264 135 49 316 762 81 114 49 240 81 293.7 49 81 135 49 316 49 244 81 49 49 254 235 49 49

94 254 465 136

110 316 705 389

149 191 357.8 389

135 577 166.8 301.8 133 662 264 135 301.8

166.8 656 223.4 316 256 678

235

358.3 565 789 819

149 319

166.8 203 351 389

244 114 136 458.5 135

293.6 546 657 161 247

659 297

167

254

319

256 678 135 622 223.4 80 327 849 319 546 80 301.8 135 302.4 149 135 166.8 578 389 153 293.6 135 657 149 301.8 298 86 86

358.3 565 789 819 166.8 319

603

298

390

390 166.7 240 389 465

485

254 556

485 149 327 167 332 301.8 166.8

153 351 254 372 316 319

203 465 287 692

166.8 319

485

485

203

153 351 136 136

166.7 203

Zs. Podolydk et aL/Nuclear Physics A 584 (1995) 60-83

66 Table 1 --continued Ey (keV)

ly a (relative)

ICCmeasurements 104 × aK Multip. of y ray

424.87 426.11 449.24 458.41 458.48 464.81 474.12 476.75 479.35 485.31

(5) 131.4 (77) 19.4 (34) (3) 231.4 (169) 22.1 (26) (10) 5 0 . 1 (54) N (8) 14.5 (62) (3) 314.1 (169) N 15.4 (18) (6) (3) 164.9 (96) 16.3 (32) (6) 179.8 (116) 16.8 (25) (9) 9.1 (42) (3) 216.4 (133) 7.8 (14)

490.35 500.10 516.11 519.85 520.82 539.92 545.83 549.11 549.50 554.04 555.11 555.66 560.46 561.88

(10) 39.2 (38) (6) 57.9 (47) (36) 2.3 (61) (12) 24.5 (165) (5) 98.6 (183) (3) 201.3 (141) (5) 60.8 (49) (8) 25.2 (43) (10) 1 9 . 9 (43) (15) 8.4 (44) (8) 28.2 (46) (8) 14.5 (45) (4) 101.3 (84) (11) 34.2 (60)

564.78 576.72 578.20 597.05 602.54 621.63 625.17 640.35 647.81 656.20 656.80 659.02 662.10 675.02 678.03 689.88 692.18 704.61 761.30 762.15 772.50 783.35 789.43

(6) (9) (7) (6) (9) (9) (7) (6) (7) (20) (20) (6) (10) (25) (13) (5) (5) (12) (9) (6) (8) (6) (7)

29.8 (37) 8.9 (34) 25.4 (37) 79.2 37.9 83.0 55.6 40.2 4.5

(76) (39) (90) (64) (53) (34)

25.2 12.5 22.4 14.1 76.7

(52) (64) (58) (55) (94)

19.0 (39) 18.7 (39) 28.6 (41) 52.9 (48)

M1 M1

M1 MI E1

N N

N N N N N

N N N N N N N N N N N N N N N N N N N N N N

49 657 49 135 49 49 49

M1

N

d d N 13.0 (14)

Former Coincident y rays results E:, (keV) on multip. of y ray [5]

(El+M2) EI(+M2)

81 81 332 49 49 49 86 135

86

136

153 203 166.8 276 149 203 86 136 135 254 372

319 287 479

301.8 316

485 293.7 302.4 597 692

86 136 136 166.8

MI(+E2) 49 263 313 135 166.8 223.4 390 49 86 136 135 166.8 49 301.8 49 297 49 135 49 81 244 86

86

136

244 223.4 191 135 293.6 136

293.6

49 49 135 133 49 49 86 49

86 223.4 377 263 244 136 244

136 390 426

161

344 319

485

161

247

297

293.6 161 247 293.6

297

135 166.8 319 203 135 166.8 49 149 301.8 135 166.8 49 244

247

293.6

485

Z~. Podolydk et al./Nuclear Physics A 584 (1995) 60-83

67

Table 1--continued Ez' ( keV )

818.78 848.81 857.82 858.40 878.75 896.10 906.32 944.85 964.86 1033.53

ICC measurements 104 x O'K Multip. of y ray

17 a (relative)

(9) (7) (11) (13) (9) (6) (12) (6) (6) (6)

42.3 8.9 29.6 21.7 38.0 26.1 35.1

(43) (39) (43) (42) (42) (35) (38)

Former results on multip. of 7 ray [ 5 ]

Coincident y rays E~, (keV)

N N N

49 149 49

244 301.8

N N N N N N

86

136

293.6

49 49 49 49

a h c J

Intensities at 8.23 MeV bombarding proton energy. At 8.5 MeV bombarding proton energy. OtK = 327(46) X 10 -4 for 134.63+135.68 keV y rays. aK = 18.0(33) X 10 - 4 for 519.85+520.82 keV y rays. D+Q: dipole and quadrupole mixture. N: new y ray (compared with the compilation of Bath [5] ). The numbers in parentheses following the E:,, 1;, and ICC values are experimental errors (in the last numbers).

4. Level s c h e m e of 7°As The construction of level scheme was based mainly on the yy-coincidence measurements, on the energy and intensity balance of transitions and on the y-ray excitation function results. The proposed level scheme is shown in Figs. 5 (low-energy part) and 6 (high-energy part). The y-ray energies and relative branching ratios are weighted aver-

o= ~

10-1

~

o~ K

[ ICC-S

=

O F 7°As T R A N S I T I O N S

]

m~m e4

e,4 o

eo~

-4r--r--~

10 -z

i

M2

10-3

~ 100

~

I-.,/. keY

I

I

I

200

300

400

ff

I

500

600

Fig. 3. Experimental (symbols with error bars) and theoretical (curves) internal conversion electron coefficients of 7°As transitions as a function of the y-ray energy.

Z~. Podolydk et aL/Nuclear Physics A 584 (1995) 60-83

68

Table 2 Results of the 7°As y-ray angular distribution measurements Ei

Ef

Ey

Multip.

(keY)

(keV)

(keV)

ofyray

81.52

32.04

49.45

167.72 234.73

325.65

328.64

(M1)

A2 -0.052

A4 (49)

81.52 86.19 81.52 153.18 32.04 202.66 M1

- 0 . 1 8 6 (64) - 0 . 1 2 6 (106) 0.142 (58)

81.52 244.10 M1 32.04 293.63 M1

- 0 . 1 7 9 (69) 0.304 (90)

167.72 81.52 32.04 383.32 234.73

160.89 M I ( + E 2 ) 247.11 M I + E 2 296.64 M1 148.57

81.52 301.80 E l 390.13

166.73 223.42 M1

485.32

166.73 318.60 E l

508.84 32.04 476.75 M I 539.99 81.52 458.48 M I 566.53 485.32 81.19 D + Q

571.95

y-ray angular distribution measurements a

32.04 539.92 M I ( + E 2 )

-0.091 -0.229 -0.040 -0.051

(59) (165) (87) (235)

-0.165

(53)

0.131

(106)

-0.285

(49)

-0.271 -0.400 -0.413

(133) (104) (104)

0.284 (64)

581.61 167.72 413.89 M I 625.21 390.13 235.10 M1

-0.252 -0.328

(98) (135)

641.84

167.72 474.12 M1

-0.273

(186)

698.86 383.32 315.53 M l

-0.301

(99)

772.28 485.32 286.96 M I

-0.169

(173)

-0.036

Ji c

Ji b Jf (51)

1+ 2+ 3+ 2+ 1+

2+

1+ 3+ - 0 . 0 0 3 (70) 2+ 0.024 (75) 2+ 3+ - 0 . 0 8 6 (62) 1+ - 0 . 2 6 4 (174) 1+ - 0 . 0 4 3 (67) 1+ 0.027 (185) 1-2-0.010 (54) 1-2-- 0 . 1 1 6 (115) 2 + 3+ 5+ - 0 . 0 4 7 (38) 12340.116 (99) 3+ - 0 . 0 0 5 (103) 2 + 0.003 (103) 2 35- 0 . 0 5 6 (71) 2+ 3+ 4+ - 0 . 2 6 7 ( 1 0 4 ) 1+ - 0 . 1 8 0 ( 1 3 7 ) 1+ 2+ 3+ 4+ --0.090 (188) 1+ 2+ 3+ 1- 0 . 0 6 1 (76) 230.076 (172) 2 345-

2+

- 0 . 0 1 2 (50) - 0 . 2 7 8 (115) 0.125 (46)

a Adopted. b Supposed, on the basis of a 0.1% confidence limit for r e d u c e d ,~2 fits. c Adopted, based on all available data.

1+ 1+

1+ 2+ 2+ 1+ 2+ 1+ 1+ 3+

3+

2+ 1+ 4-

2+

2+ 3+

2+

2-

4-

+0.12(31) ~ -0.40 ~ +0.16 +0.03(3) ~-139R +0"52 -- . . . . --0.25 --0.01(27) ~ +19.08 +0.03(3) +0.15(4) ~ +0.45 +0.05(28) --0.16(40) --0.19(24) ~--0.34 +0.14(7) ~--0.62 +0.O3(3) ~-0.47 --0.21(8) ~ --8.14 ,-~ + 2 . 1 4 ~ +0.32 ~-, --1.15 +0.013(14) -0.05(4) --N 1'7+0-12 . . . . -0.19 ~+1.80 ~ +0.27 -0.08(4) +0.11(8) ~ +0.42 ~ - 11.43 +0.05(34) ~ +2.14 ,,~ +0.21 ,,~ - 4 . 7 0 +0.03(6) ~ +1.33 ~ -0.82 +0.03(5) ~+1.33 ~ -1.13 +0.01(3) ,~ + 0 . 5 2 +0.07(11) ~ -0.75 ~ +0.04

1÷

2+ 1+ 1+ 2+ 2+ 1+ 1+ 1+ 223+

4-

3+ 2+ 5-

2+

l+ 4+

3+

3-

3-

69

Zs. Podolydk et aL INuclear Physics A 584 (1995) 60-83 103

,

, .

Io3

,.,

,

,-...~1o 3

,

,

,

:

lO

/

V / ?' t67.7

•

37

101

10 ~

!

101

(~ARCTAN 6 " , , ARCTAN6 -9o-~o-3'o 6 3'0 go so-, ~o-6o-3o 6 ~o 6b 9 o - 9 o - ~ - ~ o

103

I03~ /~

6 ~o ~ 9o

10"~ ' 3 + " ~ - ~

'

'

i

X2 102

I0~

10~

101!-~

© I , , ARCTAN 6 ARCTAN6 -90-~0-3b 6 ~0 *0 90-90-~-~0 6 :io go 90-90-60-30 0 30 60 90 1°3~ . . . . . 1 1 0 3 ~ 103~ . . . . .

/ I0°

-90-60-30

10

0

30 60 9 0 - 9 0 - 6 0 - 3 0

I0° ~

0

30 60 9 0 - 9 0 - 6 0 - 3 0

I-

0

"

30 60 90

Fig. 4. Reduced XX-test plots of 7°As transitions (indicated in the inserts) as a function of arctanS, where 6 2 is the E 2 / M I or M2/E1 intensity ratio of the transitions. Labelled numbers are assumed spins and parities for the initial state in question. Encircled numbers are adopted spins and parities based on all available data. The dashed lines show the 0.1% eonfidenee limits for reduced X 2.

ages of values obtained at different bombarding energies. Many of the y-ray branching ratios are new, the others show good agreement with the corresponding data of Ten Brink et al. [ 1,2]. The spins and parities have been determined from the decay properties of levels, the measured internal conversion coefficients, Hauser-Feshbach analysis, and y-ray angular distribution results. A detailed discussion of the level spin-parity assignments is given in Table 3. The proposed level scheme is in good agreement with that of Ten Brink et al. [2], who have measured it also from the (p,ny) reaction, and it does not contradict level schemes

70

Zs. Podolydk et al./Nuclear Physics A 584 (1995) 60-83

Table 3 Spin and parity ( j r ) assignments to 7°As levels Level energy j r (keV) 0

32.04(3) 81.52(3) 166.73(3) 167.72(4)

234.73(4) 325.65(4) 328.64(4) 344.63(4) 383.32(4) 390.13(3) 425.32(6) 458.15(4) 485.32(2) 508.84(6) 539.99(4) 566.53(4) 571.95(4) 581.61(4) 592.54(4) 625.21(4) 641.84(5) 683.96(7) 687.59(4) 698.86(4) 721.88(5) 772.28(4) 778.95(5) 815.47(5) 868.94(6) 890.46(5) 898.27(6) 928.13(5) 938.95(5) 939.27(5) 950.27(10) 966.86(9)

Basis of the j~r assignment, comments

Spin from atomic beam resonance measurement [181. Supposing 77"f5/2Pf5/2 c o n figuration, the experimental and calculated magnetic dipole moments show fairly good agreement [ 19]. Thus the parity must be positive 2+ E2 transition to ground state [1,2], M1 3' from 235 keV jyr = 1+ 1+ log f t = 4.8(2) from 7°Se decay [ 1 ], 3/-ray angular distribution 3+ M 1 3/to 4 +, (M 1 ( + E 2 ) ) 3/to 2 +, Hauser-Feshbach analysis. B~dic~ et al. give also j r = 3 + on the basis of 3,-ray angular distribution and other arguments [4] 2+ 3/-s to 2 + and 1+ levels, Hauser-Feshbach analysis, 3,-ray angular distribution. The parity must be positive, because the 329 keV level decays by M I ( + E 2 ) transitions to this and to the 81.5 keV 1+ levels 1+ M! 3, to 2 +, transition to 1+, log ft = 5.5(3) from 0 + [1], 3,-ray angular distribution 2+ M1 3/-s to 1+ and 2 +, transitions to 3 + and 1+ states, Hauser-Feshbach analysis, 3,-ray angular distribution 1+ M 1 3, to 2 +, M 1+E2 to 1+, M 1 ( + E 2 ) 3, to 2 +, transition to 1+, Hauser-Feshbach analysis, y-ray angular distribution 0+ M1 3, to 1+, transitions to 1+ and 2 +, Hauser-Feshbach analysis 2E1 3, to 1+, transitions to 1+ and 2 + states, T-ray angular distribution 3+ M 1 transitions to 4 + and 3 +, Hauser-Feshbach analysis, y-ray angular distribution 0+ M1 transition to 1+, 3, to 1+, Hauser-Feshbach analysis 1+ log f t = 4.3(2) from 0 + [ 1 ], M1 3/-s to 2 + and 1+, Hauser-Feshbach analysis 4El 3/-s to 3 + and 4 +, Hauser-Feshbach analysis, T-ray angular distribution (Ref. [4] and present results) 3+ M1 3/-s to 2 + and 3 +, Hauser-Feshbach analysis, T-ray angular distribution 2+ MI 3, to 1+, Hauser-Feshbach analysis, y-ray angular distribution 5(-) Dipole + quadrupole transition to 4 - , Hauser-Feshbach analysis, y-ray angular distribution (Ref. [4] and present results), E2+M3 from 7 ~-) [5] 2+ MI ( + E 2 ) 3/to 2 +, 3/to 1+, Hauser-Feshbach analysis, 3,-ray angular distribution 1+ MI 3,-s to 2 + states, log ft = 5.1(3) from 0 + [1], transitions to 1+ and 2 +, Hauser-Feshbach analysis, 3,-ray angular distribution 1+,2 + M1 3/to 2 +, transition to 1+, Hauser-Feshbach analysis 4+ M1 3, to 3 +, 3/-s to 3 + and 4 +, Hauser-Feshbach analysis, y-ray angular distribution 3+ Ml 3/to 2 +, Hauser-Feshbach analysis, y-ray angular distribution (0) 3,-s to 1+ and 2 +, Hauser-Feshbach analysis 3(+),4(+) M I + E 2 3/-s to 3 + and 2 +, 3, to 3 +, Hauser-Feshbach analysis 3M1 3/to 2 - , Hauser-Feshbach analysis, 3,-ray angular distribution (3) 3,-s to 1+, 2 + and 3 + states, Hauser-Feshbach analysis 3M 1 3,-s to 2 - and 4 - states, Hauser-Feshbach analysis, 3/-ray angular distribution (4) 3/-s to 3 - and 4 - states, Hauser-Feshbach analysis (3) 3,-s to 2 + states, Hauser-Feshbach analysis 6(-) ( M I + E 2 ) 3, to 5 ( - ) , Hauser-Feshbach analysis, B~idic~t et al. [4] give 6 ( - ) on the basis of y-ray angular distribution and y-polarization measurements 1+ log f t = 5.6(3) from 0 + [1], 3/-s to 0 +, I + and 2 + states, Hauser-Feshbach analysis (5) 3/to 5 ~-), Hauser-Feshbach analysis, Ten Brink et al. [2] give (5) 2,1 T-s to 2 + and 3 + states, Hauser-Feshbach analysis 4(-) 3,-s to 2 - and 3 - states, M I + E 2 transition to 5 ( - ) , Hauser-Feshbach analysis 2,1 3/-s to 1+ and 3 + states, Hauser-Feshbach analysis (0) y to 1+, Hauser-Feshbach analysis (5) 3/to 3 +, Hauser-Feshbach analysis 4+

Zs. Podoly6k et aL /Nuclear Physics A 584 (1995) 60-83

71

Table 3 --continued Level energy j r (keV) (0,3)

987.79(8) 1003.61(6) 1026.31(5) 1045.88(10)

1,2 6 ~+/

1046.40(6) 1115.05(6)

1,2 (1,2)

1,2

Basis of the fir assignment, comments

y-s to 1+ and 2+ states, Hauser-Feshbach analysis y-s to 0+, 1+ and 2+ states, Hauser-Feshbach analysis y-s to 1+ and 3 - states, Hauser-Feshbach analysis (El+M2) y to 5C-), Hauser-Feshbach analysis, B~dicifet al. [4] give 6 C+~ on the basis of "y-rayangular distribution and y-polarization measurement y-s to 1+, 2+ and 3+ states, Hauser-Feshbach analysis y-sto 1+and2 + states

obtained from 7°Se fl+-decay [ 1] and other reactions [3,4]. The main differences are as follows: (i) Our level scheme contains 16 new levels, 60 new transitions, 27 new transition multipolarities and many new spin-parity assignments compared with Bhat's recent (1993) evaluation [5]. (ii) We found no experimental evidence for the existence of the 39.4 keV level, which was introduced tentatively by Ten Brink et al. [2]. The 39.4 keV radiation is likely the K-X-ray escape peak of the 49.45 keV y-ray, on the basis of its energy and intensity. In the level scheme o f Ten Brink et al. the 39.4 keV state is fed by a 344 keV transition. According to our yy-coincidence measurements this transition must be put on another place. (iii) The 626.0 keV level decays by a 458.5 keV transition in the level scheme o f Ten Brink et al. [2]. We have found that the 458 keV line is actually a doublet. The stronger component feeds the 81.5 keV level, the weaker one the 166.7 keV state. Instead of the 625.0 and 626.0 keV levels [2], we propose only one with energy 625.2 keV. (iv) Our spin and parity assignments agree well with the J~ values, deduced from log f t [ 1 ], angular distribution [3,4] and linear polarization measurements [4]. On the other hand our spins and parities differ in many cases from values, obtained by Ten Brink et al. [2] on the basis of Hauser-Feshbach calculations. The main reason of these differences is that the calculations were based on different level schemes.

5. Hauser-Feshbach analysis As a result o f detailed y-ray and yy-spectroscopic measurements, the low-energy ( E LEv ~< 1 M e V ) , low-spin level scheme o f 7°As can be considered nearly complete. Thus from In were

the cross sections for the neutron groups feeding the 7°As levels could be deduced transition intensities between different states. order to determine the level spins, theoretical o-eEv(p,n) relative cross sections calculated using the CINDY [15] program, which was based on the compound

Zs. Podolydk et al./Nuclear Physics A 584 (1995) 60-83

72

ELE v , keV (0) 3"~4'+'3

?"'""~,~o

8+

It]rill

,.

5 2+

.~

_~

698.9 6876 664.0

,,,.,:.~=,~==o==%,,==~~', ,+,+2+11 I I I I I I I I 1~-,,.~o.7~==.,~

2

3+

4~+

7; 3.

~ s Illlllll

~

11111]11

I]111111 Ilfllffl

llllllll

2._:+ 0. ;ii iiii

i'

1+

2+

96

4+

52.6

ps

)

i.

i

.

.

IIIIlI

IIIIIT"

illlll

IIIIII

. ~

IIIIII IIIIII

II II1! ]1111-

IIIIII lJllll

II II

T

i-

:

:i- i-

-

~ in

®-,,,-,,,,.,,,,~:~

581.6 5 7 2 . 0

~-o-~

~=~o

5088

I',

1

I I I I I T l I T I~_-o~.=~= - ~.~:~ __I I tl f l II II I TT""~,~*~-.,= :~:~

i-iii! !!

I ~-Ill

641 t~ 625 2

~ta

I I II

] I

II II II i- tI II II lI II TI T':'_~-~,.*=.~-,~ I 7 T •--~¢~t~l~l~o)~

111111-

~

42s.3 36o, ....

~ : o° ~

328.6

~4.6 3257

!111 [I II1 Ill 1T~,667

1" I I i i i i'iiiiil -

rain

u

Fig. 5. Low-energy part of the proposed level scheme of 7°As from (p,ny) reaction. Solid circles at the ends indicate 7y-coincidence relations. Behind the y-ray energies and multipolarities y-branching ratios (and their errors) are given. D and Q mean dipole and quadrupole transitions, respectively.

reaction model. At the calculation of the transmission coefficients we used the optical parameter sets given by Perey and Perey [20]. These parameters were obtained on the basis of the results of Perey [21] for protons and Wilmore and Hodgson [22] for neutrons. The only exception was the real diffuseness parameter for protons, which was reduced in order to adjust the height of the Coulomb barrier. The parameters of the optical potential are given in Table 4. Besides the neutron channels all known (p,p') channels up to 4.5 MeV were also included. Moldauer width fluctuation correction [ 15] was taken into account. The experimental and theoretical cross sections were normalized at the 235 keV 1+ state [ 1 ] for the positive-parity states. For the negative-parity levels the 383 keV 2 - state was used for normalization, in order to get better agreement between experimental and calculated cross sections. The obtained results are shown in Fig. 7.

Table 4 Optical-model parameters used in this work. (The V, W and Vs.o. potential depths are given in MeV and the r range and a diffuseness parameters in fm.)

p+7°Ge n+7°As

V

W

Vs.o.

rre

rim

are

aim

Refs.

58.72 - 0.55E 47.01 - 0.267E-- 0.0018E 2

11.5 9.52 - 0.053E

7.5 6.2

1.25 1.29

1.25 1.25

0.45 0.66

0.47 0.48

121 ] I22]

73

Zs. Podoly6k et al./Nuclear Physics A 584 (1995) 60-83

j Jr'

romO

~,~

~=~2+-~.E_ ,.,,~,..-o~g~ (1.2)

¢q¢~t~tt~

=~

ELEv . keY

~

~t~mmOO~

11151

tot~ o

o~-.r~°=°u~v-'~ ~

6~

~'-~

--1.2

6 ~)

?t-'O 1 (5) I

I

I

(3.z.,-)__ (o,4)+ (3.4}

' .......

¢--'

1003.6 9878 ~1§1~.~ 9503 9ZU.1 8983 890.5 868~

i iiiiiiii'

I

- 6 '+ ~--:

i i i ill

ill

,.3)

illllllll

IIIIIIIII

III

:4--.)3 -

:3,

IIIIIIIll

IIIIIIIIlll

!{!11111

IIliii=lIt

.,6

IIIIIlll

iiiiiiiiii

561.65,~.0 -~.~

:5)

I

3_-(0) 3<+)4(+,

~ * , ~+,+ .

~

2+

o.1+

(1.2) (4)

- - 2 - 3+

(~-)(1+)(0+)

0_++ )+

1+

1+

3+ (2+)

.

.

.

.

'

1+

I

I

I

I

I

.

.

.

.

.

Illlllll I I I

,

l:

.

1+

1+ 2+

.

.

I I I

I,'

t I I I I1 } i III

~ ....

o o ~8~ i i i i i ¢n~,t~-~ "~

, , , a0u~tOmo~ . . . .

I

.

......

III

I I I~®~=%~==~

7790 77za

r~,~,~,~

.,~,1,

I I I I I I I I I I 1

.

~

~ / , I, I L I

: :

: = ' : : :

iii IIII

.

.

.

.

698.9 6876 684C

566! 5,0,,

II

II}I II I ll i I I

458.2 /,25.3

3901 383~

3.6 3~a.0 3~5, 234.7

3+2 +

2~ ........ 4~'~

I

I I I I I I I I I

(5) (3+) (0.4)+

5 1+(,)

1046.41045.9 ~cn ~ ' o w

1677 1667

' 96 ,us 526 rain

4+

81 5 32.(3 0

70

NDS, 1993

33As37

Fig. 6. High-energy part of the proposed level scheme of 7°As. Adopted 7°As levels of the latest Nuclear Data Sheets evaluation [5] are shown on the left side, which contains also the high-spin states, excited in heavy-ion reactions. 6. N a t u r e o f the l o w - l y i n g levels o f 7°As

The experimental information, available on the configuration of low-lying 7°As levels, is very scarce. One-nucleon transfer reaction data are missing, because the neighbouring nuclei are unstable. According to Hogervorst et al. [ 19] the magnetic dipole moment of the 7°As 4 + ground state is ].Zexp +2.1054 (2)/ZN. Supposing 7Tf5/2z'f5/2 configuration for the ground state, the theoretical calculations give /Ztheor = ÷2.04/~N [ 19]. Thus it is very probable that the main configuration of the ground state is 7rfs/2z'fs/2. In order to have more information about the configuration of the other low-lying 7°As levels, we have performed parabolic rule [23 ] calculations. These calculations proved very useful for the description of the energy splitting of different p - n multiplets in the o d d - o d d In [24] and Sb [25] nuclei. In As isotopes rather strong configuration mixing is expected among the close-lying identical spin-parity states, which may imply limitation on the applicability of the parabolic rule. Nevertheless it can be used for a ----

Zs. Podolydk et al./Nuclear Physics A 584 (1995) 60-83

74

91~0 I. >

-

l

¢~

0S6

~ ~

a.

~,

ZLL

669 --

O?S

I o t~

8S~

® ~/ 6g£ t ~

,,>,~

o

~

o

~

o

>

>

~g

,/','/I

I~l

I,~[

~

.

.

o

.

oo_

~

o

~

//;

i

'

=~

~6s.

ZeS--/.~

/~L- //'/I.'/' I//, ~o I , I ~°

/,?//,'/1! l,' l I ; /,'/ I"

~5'-.'f -'~'~' ~,>.,6

ff

_

d, _

&,

~,

-

-

'"

//,. ,~:0~/~,~,, ,~., i o

o

.;o=

o

V89" ,,Z" ,'//' l i d

>

I "'

~'~,;~ ' , 7 1 '

o

~ o .

I

II

® ~,'

m

.

~

~ =

tS

~,~L/ +7~I~ ~_,'~

~

~

~ "~

~e=]

~

.o: o

<.,

:.o

,;'> <.,

o

d,

d,

=

o

~ ~

Zs. Podolytik et al./Nuclear Physics A 584 (1995) 60-83

POSITIVE PARITY

0.8

ELEv. MeV

EREL

03

I

~5/2V~3/;

~. /

ENERGY SPLITTING OF I DIFFERENT p-n MULTIPLETS

IN ~OAs37 ACCOROI.G TO THE PARABOLICRULE

0.E .tl~3/ZV~l/2 0.5

3/2- COLL.

J

~/2v~lt2 NEGATIVE PARITY

0.,~

v~3/2(+COLL

~31zvTs/z / MULTIPLET ' EREL

\

0.3 0.2

75

312COLL.+v~312 3•2- ~312

0.1

(~÷'"1/2-

0

5/2- :rrf'5/2 5/2- vf'5/2 ~A%8

.~1~112vfS/2

\

~3nv~9/z

~5/ZV~V2

\

~uz,,0s~z

v~1/2

69 32Ge37

o~z 3 ~j s

jV

/

~snvis/z

~J

~

/

/ olz3 4 5

s 3 "/

Fig. 8. Predictions of the parabolic rule on the energy splitting of p-n multiplets in 7°As. The abscissa is scaled according to J ( J + 1), where J is the spin of the state.

rough orientation, as the later IBFFM calculations showed. The predicted energy splitting of the 7°As p-n multiplets is shown in Fig. 8. On the left side the low-lying levels of 71As and 69Ge are presented and the main configuration of levels. These latter were obtained mainly on the basis of one-nucleon transfer reaction data [26, 27]. We remark that the level scheme of 69As is known very insufficiently, so we considered here the states of the other neighbouring As isotope: 71As. For the parabolic rule prediction the same proton and neutron occupation probabilities were used, as later in the IBFFM calculation of 7°As levels (see in Section 7). According to Fig. 8 the lowest-lying 0 + states are expected to be relatively pure and they belong to the 7rf.s/2~'fs/2 and/or 7rPl/2~Pl/2 quasiparticle multiplets. Many low-lying 1+ levels are expected and a strong configuration mixing among them. The same is true for the 2 + and 3 + states. The lowest-lying 4 7 state belongs to the ~'rfs/2~'fs/2 multiplet, and it is probably well separated from the 4 + members of the ~p3/zz'fs/2 and 7rfs/2z'p3/2 multiplets. The lowest-lying 2 - and 7 - states are relatively pure and belong likely to the "rrf5/zpg9/2multiplet. In the low-energy 4 - and 5 - states configuration mixing may be expected.

7. IBM, IBFM and IBFFM calculations, discussion In order to get deeper insight into the structure of the low-lying 7°As states, we have calculated the level energies, wave functions, and electromagnetic moments on the basis of the interacting boson-fermion-fermion model. The hamiltonian of the model is [28]

76

Zs. Podolydk et al./Nuclear Physics A 584 (1995) 60-83

HIBFFM = HIBFM(7"r) q- HIBFM(P) -- HIBM q- HRES,

( 1)

where //IBM denotes the IBM hamiltonian for the even-even core nucleus [29-31], HmFM(~') and HIBFM(~') are the IBFM bamiltonians for the neighbouring odd-even nuclei with an odd proton and odd neutron, respectively [32-34], HRES is the hamiltonian of the residual interaction. The hamiltonian of the core has the following form [35]: HIBM = h l N + h2{(d+d+)o[ ( N - N) ( N - N - 1) ]1/2 .q._h.c.} +h3[(d+d+d)o(N-N)l/2+h.c.]

+ ~ h4g[(d+d+)g(dd)L]o, L--0,2,4

(2)

where A/is the d-boson number operator and N is the total number of s and d bosons. The relation of {h} parameters to the parameters defined in Ref. [36] is as follows:

he = V/~ g0, h3 = v2, hOL=

2Lv/2-L-~(O.5cL-V/~H2-2rO.5uo) •

(3)

The IBFM hamiltonian employed here is in the form [30] HmFM(Cr) = HIBM + E

~i(a) q- HBFI(a),

(4)

i where a stands for odd proton ( a = ¢r) or neutron (or = u). The second and third terms are the quasiparticle and boson-fermion interaction hamiltonians, respectively: HBFI(a) = Z

a j { ( d + d ) ° [c;(~)~j(cr)]o}o

J

+~

FH~{Q2 [ c ; (a)~j~ ( a ) ]2}o

JlJ2

+ E

Aj, J2J3 : {[c+(a)d]J3[~J2(a)d+]j3}o :,

(5)

jlj2j3

with Aj = A0x/5(2j + 1),

(6)

F j, j2 = F 0 v / 5 ( u j , u j2 - v j, v j= )
A j,j2j3 = -2Ao ~

v5

(u j, v j3 + vj~u j3 ) (uj3vJ2 + cj3u jz )

×(j3 II Y2 II jl)(j3 Q2;~ - +dV;~/ ~

(7)

II ~ II j2),

(8)

- ~ + ~ / N - Ndu ^ ~ + x(d+d)2t,.

(9)

Za. Podolydk et al./Nuclear Physics A 584 (1995) 60-83

77

The hamiltonian of the residual interaction was taken in the form HRES = 4rrV~( r~ - r. )~( r . - Ro) - x / ~ V ~ ( t r . . try) +Vte,~ [ 3(°'~ " r ' ~ ) (~rv " r~v) •

r2 ~

-

(tr~-o'v)

]

,

(lO)

where r,~ = r,~ - r~, R0 = 1.24/A fm. The hamiltonian of Eq. (1) was diagonalized in the proton-neutron-boson basis: [ ( j ~ j ~ ) j ~ , nol; J), where j . and j~ stand for the proton and neutron angular moments coupled to j~v, nd is the number of d bosons, I is their angular momentum, and J is the spin of the state. The computer codes, used in the calculations, were written by Brant, Paar and Vretenar [37]. First the parameters of the IBM hamiltonian were fitted to the level spectrum of the 68Ge core nucleus. In 3628Ge36 there are two proton and four neutron bosons, thus we have performed the calculations first with six total boson number. Later the calculations were repeated with three total boson number. As the quality of fit was almost the same in both cases (at least for levels below 3 MeV), in the further calculations we have used uniformly three boson number. This substantially simplified the calculations for the single-odd and odd-odd nuclei, without essential modification of the obtained results for the low-lying states. Our earlier calculations on In [24] and Sb [25] isotopes showed also that the restriction of the boson number in the presence of thee U(5) core can be accounted for by renormalization of the parameters. Even the three-boson components were weak in the low-lying states of 7°As, as the IBFFM calculations showed (see later in Table 5). We have used the following parameters in the calculation of the level spectrum of 68Ge: N = 3, hi = 0.9, h2 = -0.15, h3 = 0.06, ha0 = 0, h42 = - 0 . 5 , h44 = - 0 . 0 8 (all {hi} values in MeV). These were not far from the parameters used by Mayer et al. [38] for the description of the 7°Ge level spectrum (hi = 1.036, h2 = -0.17, h3 = 0.03, h40 = 0.2, h42 = - 0 . 4 , h44 = - 0 . 0 8 , all {hi} in MeV, N = 7). The obtained IBM theoretical results are compared with the experimental ones [39] in Fig. 9. In the second step of calculations we fitted the parameters of the boson-(neutronfermion) interaction to the level spectrum of 69Ge37. The neutron-quasiparticle energies and occupation probabilities were taken from BCS calculations, with a slight modification in order to obtain better agreement with experimental data. The quasiparticle energies (E, in MeV) and occupation probabilities (v 2) were as follows: E(vp3/2) = 0.60, E ( v f v 2 ) = 0.24, E ( v p u 2 ) = 0.20, E(vg9/2) = 0.9, /)2(PP3/2 ) = 0.80, O2(pf5/2) = 0.75, U2(VPl/2) = 0.16, U2(/.'g9/2) = 0.09. These values fit also into the systematics of quasiparticle energies and occupation probabilities obtained by Fournier et al. [40] for Ni, Zn, Ge, and Se nuclei. The IBFM theoretical level spectrum, obtained at A~ = -0.05, F~ = 0.35, A~ = 1.3 (all in MeV) boson-fermion interaction parameters (and at N = 3) is shown in Fig. 9 in comparison with experimental results [27]. We remark that when we used total boson number N = 4 (instead of N = 3), we have obtained very similar energy spectrum. There

78

Zs. Podolydk et al./Nuclear Physics A 584 (1995) 60-83 Table 5 Wave functions of some low-lying states of 7°As. Only the strongest components are given. The basis states are [ (j~rj~)j~r~,ndl; J) (see in text)

jr

(j~,j~)

j~;nd 1

[Amplitude I

o+

(53,~) 5

0;00

0.83

o~-

(~3' 3 )

0;00

0.70

1+

3 5 (3,3)

1;00

0.73

1~-

(53' 53 )

1 ;00

0.66

1+

1;00

0.66

2+

(½,½) ( 35, 35)

2+

1 53 ) ( 3' ( ~5, ~5)

2+

3 5 (3,3) 5 ( 3' 3t )

3+

3+ 3 3+ 3+ 4+

( 3l ' ~5) 5 5 (3,~) 5 ( 3 , 35) ( 35' 3 ) ( 33, 35)

4+

( 35' 35) 3 ~5 ) ( 3'

2~-

( g5, g5) 5 39 ) ( 3'

3~-

2;00

0.51

2;00

0.45

2;00

0.56

2;00

0.41

2;00

0.63

3;00

0.51

3;00

0.48

3;00

0.63

3;00

0.78

3;00

0.79

4;00

0.77

4;00

0.56

5;12

0.48

2;00

0.76

3;00

0.75

4["

5 93 ) ( 3' I 9~ ) ( 3'

4;00

0.52

4;00

0.41

4~-

( ~5, 39) ( ~5, 39)

4;00

0.65

( ~5, 39) 1 93 ) ( 3'

5;00

0.56

5 ;00

0.49

5 93 ) ( 3' ( 35, 39)

6;00

0.70

7;00

0.75

51 6~7~-

are only two positive-parity levels below 1 MeV, thus we have calculated the spectrum of negative-parity states only. Using e v = 0.5e and e vm = 0.2e effective charges, X = - ½ x / ~ = - 1 . 3 2 3 , as well as gR = Z/A = 0.464, gut = 0, g~' = --2.04 = 0.533g~'(free) and gt%ns = 0 effective gyromagnetic ratios we have obtained for the magnetic dipole and electric quadrupole moments of the 69Ge 5 - ground state the following theoretical values: /ZIBFM = +0.73/XN, QIBFM = + 0 . 0 4 e.b. The corresponding experimental data are /Zexp = i 0 . 7 3 3 ( 7 ) / x N and Qexp = -t-0.028(7) e-b [41]. The level spectrum of 6 9 A s is very scarcely known. Thus we have fitted the b o s o n -

Zs. Podolydk et al./Nuclear Physics A 584 (1995) 60-83

ELEV

1.C

4 6*

0+

: 4+

2.5 (

3/2-

\5/21/2-

O.C

3.5 3.0

5/2-

MeV 1.1

ELEv'MeV

79

O.E 05

~

2.0

3/2-

0.6

2+ . 0+

05

0+

04

1.5 1.0

2+

~2

0.3 +

3 1 2 - / 3/2-

3 / 2 - ~

0.2 05 0

0.1 0+ EXP.

0+ IBM

0

1/25/2EXP.

1/25/2IBFM

Fig. 9. Low-lying experimental positive-parity levels of 68Ge [ 39 ] and negative-parity levels of 69Ge [ 27 ] in comparison with IBM and IBFM calculations, respectively. (proton-fermion) interaction parameters in zeroth-order approximation to the properties of 713As38.These calculations are described in detail in Ref. [10]. Finally, the parameters of the residual interaction were fitted to the energy spectrum 33As37 . The parametrization applied for 7°As was and electromagnetic moments of 70 as follows: (hi} parameters: as in the case of 68Ge, N = 3. Quasiproton energies: E(77"P3/2 ) = 0.3, E(Trfs/2) = 0, E(7/'Pl/2) = 0.3, E('rrg9/2) = 1.3 (all in MeV). Because of the lack of experimental information on the center-of-gravity energies in 69As, they were fitted after all to the properties of 7°As. Occupation probabilities: u2(Trp3/2) = 0.607, u2(Trfs/2) = 0.309, u2(Trpl/2) = 0.131, u2(Trg9/2) = 0.07, as in the case of 72As [10]. Quasineutron energies: E(~,p3/2) = 0.60, E(~,fs/2) = 0, E(VPl/2) = 0.2, E(~'g9/2) = 0.9 (all in MeV); fitted first to the properties of 69Ge, then to 7°As. Occupation probabilities: as in the case of 69Ge. Strength parameters of the bosonfermion interaction (in MeV): A~" = 0.05, F~r = 0.4, A~r = 0.5, A~) = 0, F~ = 0.2, AU) = 1.3; fitted after all to 7°As. Strengths of residual interaction (in MeV) for positive-parity states: Va = 0, V,~,~ = 0.4, Vtens = 0.015, and for negative-parity states: V8 = - 0 . 4 , V,~ = 0 . 3 , Vtens -- 0.015. Effective charges: e~= 1.5 e, e" =0.5 e, e vm = 0.8 e. X = - 1 . 3 2 3 . Effective gyromagnetic ratios for positive-parity states: g~ = 2.23 = 0.4 g~'(free), g~ = 1.0, g~' = - 1 . 5 3 = 0.4 g~'(free), g~ = 0, gR = Z/A = 0.4714, gtensTr= g,tens = 0. We remark, that the strengths of boson-fermion and residual interactions, as well as the effective charges and gyromagnetic ratios are close to the values, applied for the description of level schemes and electromagnetic properties of 66Ga [8], 68Ga [6,7], 72As [ 10], 74As [9] in our earlier works.

Physics A 584 (1995) 60-83

Zv. Podolydk et al./Nuclear

80

3-

1.1

10 4-

4 f-)

1+

~T

ELEv,MeV ~ ;+

05

0.1(5) 7(--)_. . . . . . . . . .

(3} -'~ 3(+).6÷~

z+~

3"

4+

~

~I _ la.4-.__j (0/,/13.4) (..~.do.4)+._, 1" ~.L..- 51--1

+ o+Z

./T ~ 1+

1+

0.4

3+

o+-~--r+'~-L~ Z.__.m__~ °+ i+ +

(4) --4-

(4) o.2) 10+)~

j"

6-

- -

09

6t-i'3"-.7-

0.8

3-

0.7

- - - , 3551-)

06

-~ -

4- - ' ~

05

z-

--

z-

03

0.3 1+ I+ 3 + O.2

0.4

3+

i+

2+ .,_, _ _ _ 2+

----7

,

"-,

0.1

" ' , I+

3+

(z'4 3+

02

1÷

3.1

2(+)__ 0

4+

3+

4+

4{+llf5/Zvf 5/2 I'-- ND$.1993~

EXPERIMENT

i

~-IBFFM4

Fig. 10. Experimental and IBFFM theoretical energy spectra of 7°As separately for positive- and negative-parity levels. NDS, 1993 is a reference on Bhat's evaluation [5].

The IBFFM theoretical level spectrum of 7°As is compared with the experimental data in Fig. 10. The positive-parity states have been normalized to the 4 + ground state, the negative-parity states to the 2 - 383 keV state. The main components in the wave functions of some low-lying states are presented in Table 5. As Fig. 10 shows the low-lying negative-parity states have been reasonably reproduced in the calculations. The 2{., 3{., 6~-, 7{. levels are rather pure and belong mainly to the 7rf5/2~'g9/2 multiplet (see Table 5 and predictions of the parabolic rule in Fig. 8). The 699 keV 3~- level decays by M1 transition to the 2{. state, in accordance with the expectation for the neighbouring members of the same multiplet. The 4 { , 42, and 5{states have mixed 7Tpl/2vg9/2 and 77"f5/2~'g9/2main configurations. The IBFFM energy spectrum is in reasonable agreement with the experimental one for the low-lying 0 +, 1+, 2 +, and 4 + states. The agreement is not so good for the 3 + states, nevertheless the theory correctly predicted, that there are four 3 + states below 640 keV. According to the IBFFM calculations the 0 + 345 keV excited and 4~- ground states have 7rfs/2vfs/2 dominating configuration. The 7rfs/2vfs/2 components are fragmented in the 1+, 1+, 2 +, 2 +, 3 +, 3 + states with other components. The 0 + state decays by a strong M1 transition to 1+ state, as expected. The low-lying 5 + member of the 7rfs/2vfs/2 multiplet is missing in the experimental spectrum. The ~pt/2vfv2 components are fragmented in the 2 +, 2 +, 3 + and 31 states. The crfs/2vpl/2 doublet is a dominating component in the 2~ and 3+3 states. The ~rp3/2vfs/z multiplet components are strong in

Zs. Podolydk et al./Nuclear Physics A 584 (1995) 60-83

81

the 1+, 1~-, 2 +, 2~-, 3 + and 4 + states. The 7 r p , / z v p , / 2 component is dominating in the 0~- and 1~- states. These results of the IBFFM calculations are in accordance with the prediction of the parabolic rule. The low-lying 1+, 2 +, and 3 + states have many wave-function components, in some cases more than 200. As the y-branching ratios may be influenced very strongly even by the weak components, we did not calculate y-ray transition probabilities. The IBFFM magnetic dipole moment of the 4~- ground state is /ZmFFM = +2.1/ZN, in good agreement with the experimental P~exp = +2.1061(2)/ZN value [19, 42]. The theoretical electric quadrupole moment of the ground state is QIBFFM = --0.023 e-b, while the corresponding experimental m o m e n t : Q e x p = +0.094(24) e-b [19, 42]. Here we remark that B~dic~ et al. [4] have obtained for the electric quadrupole moment of the ground state of 7°As Qtheor = -0.021 e.b, supposing 7rfs/z~f5-/~ configuration. This value is in good agreement with our IBFFM result. According to the measurement of B~dic~ et al. [4], the magnetic dipole moment of the 7 (-) 888 keV state is JZex p ---- 0.75 "4- 0 . 0 5 ] Z N. Our IBFFM calculations give for this state ]JqBFFM = 0.77/ZN, with g~r = 3.63 = 0.65g~'(free). (The other effective charges and gyromagnetic factors were the same, as for positive-parity states.) Prior to our IBFFM calculations the low-lying low-spin states of 7°As were calculated in detail only by Ten Brink et al. [2]. They have used a quasiproton-quasineutron model with exact number projection and Schiffer force for residual interaction. It was supposed that the odd-odd As nuclei are spherical and the lowest states have the lowest seniority (two). The phonon degrees of freedom were neglected. In our I B ( F F ) M calculation it was taken into account, that (i) the 68Ge core nucleus has a small deformation (the h2 and h3 parameters were different from zero), (ii) the phonon degrees of freedom cannot be neglected, (iii) the tensor residual interaction may play an important role in the description of the lowest-spin states (0 +, 1+) [43]. As a result of IBFFM calculations, the 4 + ground state, the positions of the 0 +, 0~and 4~ states, as well as many low-lying 1+, 2 +, (3 +) and almost all (low-lying) negative-parity states have been correctly reproduced.

8. Summary In this work we have studied the structure of the 7°As nucleus from (p,ny) reaction with complex y and electron spectroscopic methods. A new, more complete level scheme of 7°As has been proposed with many new spin-parity values. The IBM, IBFM and IBFFM calculations helped to identify several proton-neutron multiplet states and to understand many characteristics of the low-energy spectrum of 7°As.

82

Zs. Podolydk et aL /Nuclear Physics A 584 (1995) 60-83

Acknowledgements W e are i n d e b t e d to T r a n X u a n Q u a n g , w h o p a r t i c i p a t e d in the w o r k in its early period, to A. A l g o r a , Dr. Z. G~icsi, Dr. J. Gulyfis, Dr. A. K r a s z n a h o r k a y , Dr. S. Mdszfiros, D. Sohler, Dr. A. Valek for t h e i r help in the e x p e r i m e n t s a n d to Prof. S. B r a n t , Dr. Zs. Dombr~idi a n d A c a d e m i c i a n V. Paar for useful d i s c u s s i o n s . W e t h a n k the K e r n f y s i s c h Versneller Instituut (Groningen)

for b o r r o w i n g the C o m p t o n - s u p r e s s i o n shield. T h i s

w o r k w a s s u p p o r t e d b y t h e H u n g a r i a n N a t i o n a l Scientific R e s e a r c h F o u n d a t i o n ( O T K A ) .

References [1] B.O. ten Brink, R.D. Vis, A.W.B. Kalshoven and H. Verheul, Z. Phys. 270 (1974) 83. [21 B.O. ten Brink, J. Akkermans, E Van Nes and H. Verheul, Nucl. Phys. A 330 (1979) 409. [3] A. Filevich, M. Behar, G. Garcia Bermudez, M.A.J. Mariscotti, E. Der Mateosian and P. Thieberger, Nucl. Phys. A 309 (1978) 285. 14] T. B~idic~, V. Cojocaru, D. Pantelic~, I. Popescu and N. Sc~ntei, Nucl. Phys. A 535 (1991) 425. [5] M.R. Bhat, Nucl. Data Sheets 68 (1993) 117. [6] J. Timfir, T.X. Quang, T. Frnyes, Zs. Dombr~idi, A. Krasznahorkay, J. Kumpulainen and R. Julin, Nucl. Phys. A 552 (1993) 149. [7] J. Tim~ir, T.X. Quang, Zs. Dombr~idi, T. Frnyes, A. Krasznahorkay, S. Brant, V. Paar and Lj. Simi~ir, Nucl. Phys. A 552 (1993) 170. [ 8 ] J. Timfir, T.X. Quang, T. Frnyes, Zs. Dombr~idi, A. Krasznahorkay, J. Kumpulainen, R. Julin, S. Brant, V. Paar and Lj. Simi~i6, Nucl. Phys. A 573 (1994) 61. [9] A. Algora, D. Sohler, T. Frnyes, Z. Gttcsi, S. Brant and V. Paar, to be published. [ 10] D. Sohler, A. Algora, T. Frnyes, Z. G~icsi, S. Brant and V. Paar, to be published. [ 11] Z. Arvay, T. Frnyes, K. Fiile, T. Kibrdi, S. IAszl6, Z. M~t6, Gy. M6rik, D. Novfik and E Tfirk~inyi, Nucl. Instr. Meth. 178 (1980) 85. [ 121 T. Kibrdi, Z. G~icsi, A. Krasznahorkay and S. Nagy, Inst. of Nucl. Res., Debrecen, ATOMKI Ann. Rep. (1986) p. 55. 1131 T. Kibrdi, Z. G~icsi and A. Krasznahorkay, Inst. of Nucl. Res., Debrecen, ATOMKI Ann. Rep. (1987) p. 100. [ 14] H. Helppi, Univ. of Jyvfiskyl[i, JYFL Report 1/1976. [ 15] E. Sheldon and V.C. Rogers, Comp. Phys. Commun. 6 (1973) 99. [16] G. Szrkely, Comp. Phys. Commun. 34 (1985) 313. [ 17] E Rrsel, H.M. Fries, K. Alder and H.C. Pauli, At. Data Nucl. Data Tables 21 (1978) 91. [ 18] H.A. Helms, G.J. Zaal, W. Hogervorst and J. Blok, Hypertine Int. 2 (1976) 399. [19] W. Hogervorst, H.A. Helms, G.J. Zaal, J. Bouma and J. Blok, Z. Phys. A 294 (1980) 1. 120] C.M. Perey and EG. Perey, At. Data Nucl. Data Tables 17 (1976) 1. [211 EG. Perey, Phys. Rev. 131 (1963)745. [22] D. Wilmore and P.E. Hodgson, Nucl. Phys. 55 (1964) 673. [23] V. Paar, Nucl. Phys. A 331 (1979) 16. 124] T. Frnyes, Zs. Dombr~idi, A. Krasznahorkay, J. Guly~is, J. Timfir and T. Kibrdi, Fizika 22 (1990) 273. [25] T. Frnyes, Zs. Dombr~idi, Z. Gticsi and J. Guly~is, Acta Phys. Hung. 71 (1992) 239. [261 M.R. Bhat, Nucl. Data Sheets 68 (1993) 579. [27] M.R. Bhat, Nucl. Data Sheets 58 (1989) 1. 128] V. Paar, in In-beam nuclear spectroscopy, vol. 2, ed. Zs. Dombr~idi and T. Frnyes, (Akad. Kiadr, Budapest, 1984) p. 675. [29] D. Janssen, R.V. Jolos and E Drnau, Nuel. Phys. A 224 (1974) 93. 130] A. Arima and E Iachello, Phys. Rev. Lett. 35 (1975) 1069. [311 F. lachello and A. Arima, The interacting boson model (Cambridge Univ. Press, Cambridge, 1987). [32] F. lachello and O. Scholten, Phys. Rev. Lett. 43 (1979) 679. [331 O. Scholten, Prog. Part. Nucl. Phys. 14 (1985) 189; Ph. D. Thesis, Univ. of Groningen (1980).

Zs. Podoly6k et al./Nuclear Physics A 584 (1995) 60-83

83

[ 34] E Iachello and E Van Isacker, The interacting boson-fermion model (Cambridge Univ. Press, Cambridge, 1991). [35] V. Paar, S. Brant, L.E Canto, G. Leander and M. Vouk, Nucl. Phys. A 378 (1982) 41. [361 A. Arima and E lachello, Phys. Rev. Left. 35 (1975) 157; Ann. Phys. 99 (1976) 253; 111 (1978) 201; 123 (1979) 468. [ 371 S. Brant, V. Paar and D. Vretenar, Computer code IBFFM/OTQM, IKP Jiilich (1985), unpublished. I381 R.A. Meyer, R.J. Nagle, S. Brant, E. Frlez, V. Paar and P.K. Hopke, Phys. Rev. C 41 (1990) 686. [39] M.R. Bhat, Nucl. Data Sheets 55 (1988) 1. [40] R. Fournier, J. Kroon, T.H. Hsu, B. Hird and G.C. Ball, Nucl. Phys. A 202 (1973) 1. [411 A.E Oluwole, S.G. Schmelling and H.A. Shugart, Phys. Rev. C 2 (1970) 228. [42] P. Raghavan, At. Data Nucl. Data Tables 42 (1989) 189. [43] V.L Alexeev, I.A. Kondurov, Yu.E. Loginov, V.V. Martynov, S.L. Sakharov, P.A. Sushkov, H.G. BOmer, W.E Davidson, J.A. Pinston and K. Schreckenbach, Nucl. Phys. A 345 (1980) 93.