The rotational bands 12 +[411]and 12 −[541]in 175Lu

11.E.l: 2.Bj

Nuclear Physics A223 (1974) 320-332;

@

North-Holland

Publishing

Co., Amsterdam

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

THE ROTATIONAL

BANDS &+ [411] AND +-15411 IN 175Lu

G. WINTER, W. ANDREJTSCHEFF, Zentralinstitut

fiir Kernforschung,

L. FUNKE, Bereich

P. MANFRASS

2, Rossendorf/Dresden,

and H. SODAN DDR

Received 13 August 1973 Abstract: In a study of the y-radiation emitted in the reaction 176Yb(p, 2n) excited states of the nucleus 175Lu up to spin I = -%j have been investigated. The main results concern the rotational bands &+14111and $- [541] with the corresponding band heads found at 626.60 and 370.88 keV, respectively. The half-life of the )+ [411] level has been determined to be T+ = 10.710.5 ns. Furthermore, the band heads $- [532] and $+ [411] are proposed at energies of 999.0 and 1150.8 keV, respectively. Experimental El transition probabilities between both K = i bands are compared with calculations including the Coriolis and pairing effects, as well as theoretically deduced quadrupole deformation parameters. E

NUCLEAR

REACTIONS 176Yb(p, 2ny), E = 6.8-10 MeV; measured Ey, a@,), yv(t), yy-coin. 175Lu deduced levels, J, TJ., 7~.Enriched target.

1. Introduction

Although the excited states of the stable nucleus 175Lu have been investigated in several works I-‘), t h e results concerning the rotational bands of the Nilsson orbitals If z 14111 and Q- [541] are still rather incomplete. From the study of the radioactive decay of the neighbouring nuclei 175Yb and ’ 75Hf, the Nilsson configurations 3 [404] , 3’ [402], 4- [514] and the isomeric 4- level of the band 3- [541], as well as a few rotational states have been identified. The lifetimes of most of these states are already known (see fig. 6). Furthermore, very important details of the 175Lu level structure have been obtained from the study 4, “) of the particle transfer reactions (a, t) and (z, d). However, the rotational band 3 [41l] could not be established. The aim of the present work was the identification of the Nilsson orbital $+ [411] and the investigation of the probability for the El transitions to members of the $- [541] band. Such interband transitions have been found in several other oddproton nuclei ‘-11 ). From the discussion of these transition probabilities we expected that in ” 5Lu the band head +’ [411] would have a measurable lifetime. Moreover, the rotational excitations in 175Lu should be further clarified. After our experiments had been finished 12) we learned of similar work 13) on ’ 75Lu in which fragmentary results concerning the K = 3 bands are also given. 2. Measurements The levels in ” 5Lu were excited by the reaction ’ ’ 6Yb(p, 2n)’ 75Lu using the proton beam of the new tandem accelerator in Rossendorf. A self-supporting metal 320

175Lu ROTATIONAL

BANDS

L’ZLQ 33,: I’<; L’LLB

I

L’OOQ

-

-

;

e*soL -

c3

1'9296'909

-

7’9%

O’EBS =

62’96E

-

--;

?

48.‘Iz

E5Z -

--====4 _g95: =

S’LSZ sL’972

-

321

322

G. WINTER

et al.

TABLE 1

Transitions in

-

~'%LI

observed in the reaction 176Yb(p, 2n) at & = 10 MeV

Er (kev)

Ir

89.35 111.9 113.8 113.6 “) 124.57 130.80 132.92 137.6 137.9 “) 140.73 143.89 147.4 b) 156.07 158.23 161.20 161.2 “) 203.0 “) 216.74 232.78 246.15 251.5 “) 251.5 “) 255.72 257.86 261.9 “) 279.25 282.52 289.43 298.52 319.29 324.0 343.46 353.57 396.29 419.9 432.8 461.6 471.3 484.2 518.1 524.0 538.5 “) 548.6 583.0 “) 586.4 608.9 ‘) 628.1 709.8 780.9 “) 800.7

8.4 z I z 14 w 8 6.8 0.7 4.8 w 5 w 4 5.7 5.6 3.7 2.0 1.6 G 12 z 4 0.8 3.6 1.5 2.1 z 4 % 2 36.8 7.2 1.8 6.8 8.9 18.3 2.7 8.3 1.5 100 “) 216 20 2.3 6.8 1.7 2.1 2.0 1.4 2.8 1.2 2.7 1.4 2.3 4.9 4.6 4.9 1.7 2.4

Ii, Kin

If, IV’

175Lu ROTATIONAL

323

BANDS

TABLE 1 (continued)

Er (keV)

'Y

817.7 872.1 “) 940.9 ‘) 957.5 ‘) 961.9

4.0 3.8 1.8 2.9 2.5

Ii, Ki”

If, KP

(4, a-

8, t-)

1 1(21 r

Q, *- )

First column: The mean errors of the energies are smaller than 0.1 keV for energies given with two decimals and smaller than 0.4 keV for the others. “) These transitions are identified only in the coincidence experiments. “) The intensity has been corrected for a 20% content of a 176Lu transition. “) Not placed in the level scheme, the assignment to 175Lu is not certain. Second cohmn: Gamma-ray intensities measured at an angle of about 90” to the beam axis. The errors are of the order of 10 to 30% depending on the line strength. “) Normalization value. Third andforrrth columns: Assignment of the transition.

target of 176Yb (enriched to 96 %), with a thickness of 0.9 mg/cm’, was irradiated in different experiments with protons of energies between 6.8 and 10 MeV. The y-radiation emitted during the irradiation was studied using both singles and coincidence arrangements. Fig. 1 shows a y-ray spectrum measured at an angle of about 90” with respect to the beam axis during the bombardment of the target with 10 MeV protons. Several y-ray transitions belonging to 176Lu are caused by the (p, n) reaction on the target. Since the energies of these transitions are precisely known from (n, y) experiments 14) it was possible to determine the energies of the new y-rays of ’ 75Lu with good accuracy. The results of the singles measurements are summarized in table 1. The y-ray spectra recorded at different bombarding energies facilitate the assignment of the stronger lines to 175Lu, but for the weak lines this assignment is not certain (see table 1). Using a proton energy of 10 MeV to initiate the (p, 2n) reaction, we performed the following coincidence experiments: (i) Measurement of prompt y-y coincidences using two Ge(Li) detectors. A summary of the results is given in table 2. Some important spectra are shown in fig. 2. (ii) Measurement of the spectrum of y-rays populating the known “) 1.49 ps isomeric state at 353.57 keV (populating spectrum). This experiment was performed by the use of a fast-slow coincidence circuit “). The time-to-pulse-height-converter was started by the pulses of one y-ray detector (Ge(Li) or NaI(T1)) and stopped by delayed pulses from a second y-ray detector (Ge(Li)). In the slow channel of the starting branch we selected the isomeric transition in question. The spectrum of y-rays preceding this isomeric transition was recorded with the Ge(Li) detector of the stopping branch in coincidence with the selected pulses from the start detector and further, by gating this stop channel with pulses within a window of the time distribution curve set on the left-hand side of its maximum. In one of the first experiments we used

324

G. WFNTER

et al.

Ge(Li) detectors to select the 353.57 keV line and to detect the populating spectrum up to 400 keV. In order to study this spectrum up to 900 keV the efficiency was improved by the use of a 7.6 cm x 7.6 cm NaI(T1) detector for selecting the 353.57 keV transition. The results are shown in fig. 3. (iii) Lifetime measurements in the nanosecond range by the method of delayed y-y coincidences using a NaI(T1) and a planar Ge(Li) detector. The details of such experiments are described in a previous publication “>. For the 255.72 keV transition we obtained a time curve (see fig. 4) revealing an experimental half-life of Z!?& = l&7&0.5 ns.

GATE 256 keV

GATE 273 keV ;; z

%

GATE 283 keV

Y iii

GATE 343 keV

, 100

200

CHANNEL

300

400

50

NUMBER

Fig. 2. Selected part of prompt y-y coincidence experiments. Transitions supposed to be in coincidence are marked by their energy values in keV. Peaks caused by coincidences with the continuous part of the spectrum are labeled b.

e

0

a

5

200

400

600

800 CHANNEL NUMBER

1000

1200

1400

1EOO

Fig. 3. Spectra of y-rays populating the 1.49 ys isomer. Both spectra have been recorded with a 26 cm3 Ge(Li) spectrometer, which was gated on the photopeak of the 353.6 keV transition, using a second 20 cm3 Ge(Li) detector (A) or a 7.6 cm x 7.6 cm NaI(T1) detector (B). In the measurement of spectrum (13) the trigger level of the timing system was set at about 150 keV. Peaks caused by chance coincidences are labeled b.

N

2

Y 10

I;:

tl co

z

f

5

z

5

6

WI

z

326

G. WINTER

et al.

(iv) Measurement of the spectrum of y-rays populating the new isomeric level, in order to assign the 255.72 keV transition. An example of populating and de-populating energy spectra is presented in fig. 5. TABLET

Summary of the 7-y coincidence experiments Transitions favoured in the gate “)

E, (gate) 89 114 125 161 256 279 283 289 319 343 396 256 353

b): ‘):

114, (137), 343 89, 133, 138, (145), (161), 202, (226), 283, 299, 343, 433 (129), 217, 233, 256, 279, 289, 343, 462 (89), 114, 138, 158, 251, 484, 549 125, 131, 141, 217, 233, 246, 462, (518), 524 125, 141, (462) 114, 133, 156 125, 141, 217, 246, 343, 462, 518 none 89, 114, 125, 138, 141, (203), 217, 233, 246, 251, 289, (341), 518 133, 156 125, 131, 141, 217, 233, 246, 462, 518, 524, 586 (112), 125, 144, 147, 161, 256, 258, (261), 279, 319, 324,420,471,484, 549, 586, 628, 710, 818, 872, 941

518, 524,

Energies are given in keV. “) Numbers in parentheses mean weak or uncertain coincidences. “) Populating y-lines, measured in the time interval from 5 to 20 ns before the maximum of the time curve (see fig. 5). ‘) Populating y-lines, measured in the time interval from 0.1 to 3 ps before the maximum of the time curve.

3. Level scheme A level scheme of 175Lu, taking into account our new results, is shown in fig. 6. By means of the (p, 2n) reaction at E,, = 10 MeV excited states in 175Lu have been found with an angular momentum of up to I = y. The following discussion has been limited to the newly established levels and/or transitions. In the rotational band $- [514], the SL level, which is also excited in particle transfer reactions 5), was confirmed. An additional state, introduced on the basis of coincidence experiments has been assigned as the J$ member. The band 3’ [402] was observed up to I = 9. According to our results, the energies of the transitions between the rotational states of this band are practically the same as for the corresponding transitions in the ground state band. Levels of the rotational band $- [541] have been established up to I = q. All transitions introduced in this band are observed in the populating spectrum to the 1.49 ,USisomeric state. In agreement with the decay studies “) the 3 member was found at 514.77 keV. However, the hitherto existing proposal “) for the g level could not be confirmed. From our results this level is placed at 370.88 keV. Arguments for this new placement follow from the energies of the rotational transition 4 -+ 3

175Lu ROTATIONAL

0.51nslCHANNEL’

t 0

Fig. 4. Time distribution

50

100 CHANNEL

327

BANDS

NUbI&

curves obtained by lifetime measurements l’5Lu.

l

200

on the 255.72 keV transition in

and of the 255.72 keV transition de-populating the band head 4’ [411]. The 5 member is introduced on the basis of a coincidence between the 161 and 158 keV y-lines. According to the particle transfer experiments “) the 4 level is expected at 417 keV. In the new level scheme this state is fixed at 415.1 keV. Then the y-ray energy of the deexciting transition to the 3 isomeric state is close to that of the KB X-rays. Therefore, this transition was not directly observed. The -‘$ and 9 members are placed on the basis of transitions measured in the populating spectrum to the 1.49 ,us isomer. In the present work the rotational band built on the configuration 3’ [411] has been found up to I = y. The 3 member is de-excited to the band head 3’ [402] as well as to the isomeric 3- state of the $- [541] band. By means of unambiguous coincidences with the 289.43 and 279.25 keV y-rays it was possible to establish the 3 and 3 members of the 4’ [411] band. The energy of the band head follows from the 130.80 keV transition de-exciting the 3 member and is supported by the 255.72 keV transition to the +- band head. All the transitions introduced in this band were observed in the spectrum of y-rays populating the 10.7 ns isomeric state (see fig. 5 and table 2). Among the levels supposed by O’Neil et al. “) to be possible candidates for the ++[411] configuration, those at 635 and 761 keV may correspond to our proposal for the (-$ and 3) and (3 and 9) levels, respectively. The interband transitions 255.72 and 279.25 keV connecting levels of both K = 3 bands have already been mentioned. Two additional transitions of this type with energies 111.9 and 419.9 keV have been placed on the basis of their appearance in

328

G. WINTER

et al.

START NaJ (Tl), El-256 STOP.

I

L@ 3-

2-

keV

Ge(LI) PLANAR

my B I

ABC

‘4

t

POPULATING

d

w”

-T

PROMPT

Iv ;

DE- POPULATING

CHANNEL

NUMBER

Fig. 5. Time-related y-spectra associated with the 10.7 ns isomeric state. Peaks belonging to 176Lu are marked by crosses.

the populating spectrum to the 1.49 ps isomer (see figs. 3 and 6). From the ratio of y-ray intensities of the transitions 140.73 and 419.9 keV one can deduce lo) the transition probability to be B(E1; 3, +’ -+ 3, $-) = 3.9 x 10m8e2 - b [the intrinsic quadrupole moment of the nucleus in the contiguration &‘[411] has been assumed 21) as Q, = 8.03 b]. Some levels at higher energies have been identified on the basis of coincidence experiments. These states are partly excited also in particle transfer reactions. In fair agreement with O’Neil et al. “) we obtained the band head $- [532] and the corresponding first rotational state at the energies 999.0 and 1063.4 keV, respectively. TWO

I’IJLu ROTATIONAL

BANDS

329

330

G. WINTER

et al.

other states at 1150.8 and 1219.1 keV are de-excited to members of the 4 [411] band and have been tentatively assigned to the +* [41 I] band. From particle transfer reaction studies, one may conclude that the level at 1219.1 keV possibly corresponds to the unclassified 1222 keV level. In connection with the proposal of O’Neil et al. ‘) for the configuration +- [530] we assume two levels at 1315.5 and 1332.5 keV, deduced from the energies of transitions in the singles spectrum. The most intense of these transitions with an energy of 817.7 keV has been observed in the populating spectrum to the 1.49 ps isomer. 4. Discussion The most important results of the present work are concerned with the rotational bands of the con~gurations 3’ [411] and 4- [541] in ’ 75Lu. Recently these two bands have been thoroughly studied in several other isotopes of lutetium ’ 1*I5 - ’ ‘)_ In these investigations not only both rotational bands have been analyzed in terms of the Coriolis interaction, but also the interesting El interband transitions between them have been examined g-11, ’ 7*’ *). E xperimental energies of the band heads and the values of the rotational parameters A and AI (for notations see ref. ““>) for these bands are listed in table 3 for odd-mass nuclei of lutetium. The new data for “‘Lu are in agreement with the general tendency within the group of Lu isotopes considered. TABLE 3 Analysis of the

rotational bands

gt [41t ] and j- [541] in odd-mass Lu isotopes

l69Lu

I’lLu

l73LU

175&

97.4 13.68 -9.x

208.1 13.65 -9.1

425.3 13.55 -10.3

626.60 13.67 -11.6

29.0 9.3 34.9

71.1 9.6 34.6

128.3 8.6 36.5

370.88 7.3 41.3

“‘LU

$‘I4111

Eexp(kev) A A1

(keV) (keV)

569.63 14.41 -13.1

g- 15413

G, WV) A AI

(keV) (keV)

761.25 “)

For the experimental data see refs. 11.15-17). “) I = 52state.

Comparing the experimental El transition probabilities with the prediction of the Nilsson model, one finds considerable discrepancies. In the present case the hindrance ‘factors FN = B(El),/B(El),,, are much greater than unity (see table 4). A correction due to the pairing correlations between nucleons reduces the theoretical values considerably, since the transition takes place between a particle state (4- [541]) and a hole state ($* [411]). It should be noted that in this case small admixtures of

“5Lu

ROTATIONAL,

331

BANDS

other configurations may cause an appreciable change in the value of the transition matrix element 1“). In table 4, the results of our calculations of El transition probabilities are presented. The Nilsson hindrance factor Fz for I’lLu is different from the corresponding value given by Liibner et al. “). Th is is mainly due to the pairing factors P_ = UiUf-ViVf which are rather small in the present case of particle-hole transitions. Although the pairing factors used in ref. ‘*) are expected to be more accurate than ours, the uncertainties of these small values are still considerable. Furthermore, in our case the Coriolis admixtures slightly increase the hindrance factors while in ref. I*) they lead to somewhat smaller values. This is probably an effect arising from the sign of the pairing factors relative to that of the small admixtures. In both cases, the Coriolis effect does not significantly influence the transition probabilities.

Electric dipole transitions

TABLE4 between the states &+[411] and Q- 15411in Lu isotopes 1’ 5Lu

l7lLu

l73Lu

*+ .+&137.0 30

g+ +g-

Er WV) T;;;; (ns) Tlexp (ns) 2 FN F’N

34.5 305 12

1.0 72 2.6

11 740 45

146 3100 500

3.0

48

870

Nucleus Ji + Jr

FPC p”c

F, (ei + Q) Ref.

In the hindrance

15 2.0 9.20 )

I+

z

0.56 9.18.20

+&-

255.7 10.7

296.9 0.82

)

6.5 this work

l7’Lu g-+-F

3+

188.1 35

84 11 )

factors Fi the pairing effect is taken into account (FE = FNPz). Pairing and

Coriolis interactions are included in the hindrance factors F PC N calculated with equal and different (E, + sr) deformations of initial and final states. The experimental information and some calculation results are taken from the references quoted.

The hindrance factors for the 419.9 keV transition 3, $‘[411] to 3, &- [541] in 175Lu with a reduced probability evaluated to be B(E1) = 3.9 x lo-’ e2 - b (sect. 3) were deduced as FN = 187 and Fs = 11. Compared with the corresponding values for the band head transition, which are about four times larger (column 4 of table 4) an influence arising from the Coriolis effect with increasing spin values is indicated. This is in good accordance with the tendency found lo) in I’lLu. For transitions between the intrinsic states f’ [41 l] and &- [541] it was shown that better agreement with the experimental B(E1) values 20) is achieved by taking into account different deformations of initial and final states. In the present work, the pairing factors as well as the quadrupole deformation parameter E for each one-quasiparticle state are obtained by the standard BCS procedure, including the blocking

332

G. WINTER

et al.

effect and minimizing the total energy of the nucleus. Details of these calculations and of the Coriolis coupling analysis are given in refs. ’ 6*““). In all cases considered, the best agreement with the experimental transition probabilities is obtained by including the individual quadrupole deformation of each state. We are indebted to the Soviet specialists and to the staff of our tandem generator for adjusting the machine during these experiments. Support for this work from the Ministerium fiir Wissenschaft und Technik and the Akademie der Wissenschaften der DDR is gratefully acknowledged. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15)

16) 17) 18) 19) 20) 21)

E. Bashandy and M. S. El-Nesr, Ark. Fys. 21 (1962) 65 K. H. Johansen, B. Bengtson, P. G. Hansen and P. Hornshoj, Nucl. Phys. Al33 (1969) 213 G. G. Seaman, E. M. Bernstein and J. M. Palms, Phys. Rev. 161 (1967) 1223 M. M. Minor and R. K. Sheline, Phys. Rev. C3 (1971) 766 R. A. O’Neil, D. G. Burke and W. P. Alford, Nucl. Phys. Al67 (1971) 481 M. Hiijeberg and S. G. Maimskog, Nucl. Phys. Al34 (1969) 77 Y. Dar, J. Gerber, A. Macher and J. P. Vivien, Nucl. Phys. A171 (1971) 575 P. G. Hansen, P. Hornshoj and K. H. Johansen, Nucl. Phys. Al26 (1969) 464 W. Andrejtscheff, F. Dubbers, P. Manfrass and K.-D. Schilling, Nucl. Phys. A190 (1972) 489 G. Winter, L. Funke, P. Kemnitz and H. Sodan, Nucl. Phys. A199 (1973) 1 P. Manfrass and W. Andrejtscheff, Nucl. Phys. Al94 (1972) 561 G. Winter, W. Andrejtscheff, L. Funke, P. Manfrass and H. Sodan, Proc. XIII Symp. on nuclear spectroscopy and nuclear theory, Dubna 1973, p. 129 C. Foin, D. Barneoud and S. A. Hjorth, AFI 1972, Annual report, p. 11 M. K. Balodis, J. J. Tambergs, K. J. Alksnis, P. T. Prokofjev, W. G. Vonach, H. K. Vonach, H. R. Koch, U. Gruber, B. P. K. Maier and 0. W. B. Schult, Nucl. Phys. Al94 (1972) 305 C. Foin, D. Barneoud, S. A. Hjorth and R. Bethoux, Nucl. Phys. A199 (1973) 129 P. Kern&z, L. Funke, K. H. Kaun, H. Sodan, G. Winter and M. I. Baznat, Nucl. Phys. A209 (1973) 271 S. A. Hjorth, H. Ryde and B. Sksnberg, J. de Phys. 33 (1972) 23 K. E. G. Lobner, M. J. Bennet and M. E. Bunker, Nucl. Phys. Al97 (1972) 553 W. Ogle, S. Wahlborn, R. Piepenbring and S. Frederiksson, Rev. Mod. Phys. 43 (1971) 424 W. Andrejtscheff, F. R. May, L. Miinchow and S. Frauendorf, Phys. Lett. 44B (1973) 351 K. E. G. Lobner, M. Vetter and V. Hiinig, Nucl. Data A7, no. 5 (1970) 495