Signature-dependent ml and e2 transition probabilities in 155ho and 157ho

Nuclear

Physics

@ North-Holland

A424 (1984) 365-382 Publishing

Company

SIGNATURE-DEPENDENT

G. B. HAGEMANN,

Ml AND E2 TRANSITION PROBABILITIES IN “‘HO AND 15’Ho

J. D. GARRETT,

B. HERSKIND

and J. KOWNACKI*

The Niels Bohr Institute, University of Copenhagen, Denmark B. M. NYAKt)**,

P. L. NOLAN

AND J. F. SHARPEY-SCHAFER

Oliver Lodge Laboratory, University of Liverpool, PO Box 147, Liverpool, L69 3BX, UK and P. 0. TJOM Instituie of Physics, University of Oslo, Norway Received

20 January

1984

Abstract: lssHo and l”Ho have been populated in the reactions ‘41Pr(‘80,4n) and ‘46Nd(‘5N,4n) at 85 and 74 MeV, respectively. In both nuclei bands built on the i-C5231 configuration were established to spin values considerably above the first backbend. A signature dependence in the excitation energies as well as in the ratio of Ml to E2 transition rates is observed below, but not above, the backbend in both nuclei. In 15’Ho lifetimes were measured with the recoil-distance method. The dl = 2; E2 transition probabilities obtained show very little variation with either signature or spin and no irregularity at the backbend. The signature dependence and strong rise in the ratio B(Ml)/B(E2) observed at the backbend in “‘Ho therefore must be caused by the B(M 1) values. A signature dependence in the B(E2, I + I - l)/B(E2, I + I - 2) ratios also found in “‘Ho below the backbend is mainly the result of signature dependence in the dl = 1; E2 transition rates. Qualitatively, most of the features observed can be explained by nonaxial deformations, which change from large negative to slightly positive values of y at the backbend.

1. Introduction Odd proton nuclei with neutron number around 90 have been studied in only a few cases ’ -3). This region is characterized by small Ed deformations, and du’e to a rather shallow potential energy minimum deformation changes especially in the nonaxial regions are expected to take place4). Indeed, changes in signature splitting in the routhians (excitation energy in the rqtating frame) have been

* Present Technology, ** Present Hungary.

address: Institute for Nuclear Studies, Department 05.400 Swierk, Poland. address: Institute of Nuclear Research of the Hungarian 365

of

Nuclear

Academy

Spectroscopy

of Sciences,

and

Debrecen,

366

G. B. Hagemann et al. / ‘55, ls7Ho

ascribed to changes in the degree of y-deformation 4*5). Such changes are observed to occur after a pair of i, quasineutrons have been aligned. We have studied the iV = 88, 90 nuclei f55.157Ho and analyzed the data in terms of transition rates of Ml and E2 character between and within the two signatures of the decoupled lthT band which at low frequency mainly has the Nilsson configuration j-[523]. In 15’Ho absolute transition rates were obtained from recoil-distance measurements of lifetimes. A discussion of the relative Ml and E2 transition rates in ls7Ho is given in ref. ’ ). The data cover three ranges of the rotational frequency kti: (i) at low frequency, a strong signature dependence in both excitation energy and transition probabilities (especially Al = 1) is present ; (ii) in the crossing region where mixing between the bands is present very large changes in B(M1) values are observed; (iii) at higher frequency above the crossing no signature dependence is found. Throughout this region there is very little variation in the B(E2, I -+ I-2) vaiues measured in 157H~. The data are compared to the nonaxial particle-rotor-model calculations of Hamamoto and Mottelson 6).

2. Experimental procedure and results 2.1. SPECTROSCOPY

OF ‘-Ho

AND 15’Ho

The nuclei 155H~ and f57H~ were populated with the reactions “‘Pr(‘s0, 4n)15”Ho and ‘46Nd(15N, 4n)15’Ho using beams of 85 MeV I80 and 74 MeV 15N ions, respectively from the FN tandem accelerator of the Niels Bohr Institute. Targets were self-supporting i mg/cm’ metallic foils with a recoilstopping layer of h 4 mg/cm 2 208Pb evaporated onto them. The isotopic enrichment of 14(jNd was 97.5%. The y-r ay s were detected in an array of 4 Compton-suppressed Ge(Li) detectors with an additional “ball” of 14 BGO crystals in a 4~ geometry close to the target. [This experimental setup is a preliminary version of that described in ref. “).I These 14 detectors were used both to produce a fold value (number of detectors firing) and also a sum energy signal which gives a clean selection of the exit channel at the highest spin values. The Ge(Li) detectors were 22 cm from the target at angles of &37O and i_ 123”. Events recorded required at least 2 Ge(Li) detectors and one BGO counter to be in coincidence within 80 ns. Angular distribution measurements were also performed using a fixed monitor counter at - 150° and two rotatable Ge(Li) detectors at a distance of 12 cm from the target. The calibration was performed with y-rays from ls2Eu and 177LU. sources placed at the position of the beam spot detected at the various angles utilized. These data were used to construct the level schemes shown in fig. 1. For 157H~ a discussion of the level scheme is given in ref. I). For ls5Ho agreement has been found with the level scheme information of ref. 7, which has been extended in

5516*X

Is5Ho

“-
Fig. I. (a) Level scheme of “‘Ho

01

-==.39_0

(‘7/2-)

The energy x for the missing

smx

transition

‘57H~

_.

is 5 40 keV. (b) Level scheme

(

of 15’Ho [ref. ‘)I.

wri 1

_

5364

368

G. B. Hagemann et al. J 155, 15’Ho

the present experiment to spin values of y(y) and y(*$), respectively, in the two signatures built on the $-[523] configuration. In the lower part of the level scheme a connection between the y- and an excited state of 110.3 keV is missing. A search for this transition was made in a special yycoincidence experiment using one low-energy photon (LEP) and 2 Ge(Li) detectors, and also in an experiment to detect conversion electrons with a miniorange electron spectrometer. In both experiments beams pulsed over a large range of frequencies were used. In the search for delayed conversion electrons a target of 1 mg/cm* r4i Pr backed with 1 m&m * “‘Pb to SIOWdown the recoils was placed 2 cm upstream from the target position at which a thin (60 pg/cm’) Cfoil was placed to stop the recoils. With the sensitivity obtained we conclude that the energy of the unobserved transition is less than 40 keV. In table 1 the relative intensities, angular distribution coefficients and assignments for transitions which have been placed in the level schemes of fig. 1 are collected. Values of 6 for the I -+ I - 1 transition are also given, whenever the data allowed these to be extracted. 2.2. RECOIL-DISTANCE

MEASUREMENTS

IN “‘Ho

A ‘46Nd target with a thickness of 470 ,ag/cm’ evaporated onto a stretched 2 mg/cm* Au foil facing the beam was bombarded with 74 MeV 15N ions. The recoiling nuclei (F/c = 0.0092) were stopped at various distances d from the target by an 8 mg/cm2 movable Au stopper controlled by a precision micrometer ‘). Data corresponding to d = 0 were obtained with 470 pg/cm* of 14’Nd evaporated directly onto an 8 mg/cm* Au stopper. A 2 mg/cm* foil in Front of the target ensured the correct beam energy in this case. The target-stopper distance was measured using the capacitance method. Gamma spectra for different target stopper separations were detected in a Compton suppressed 27 ‘i: Ge(Li) detector at O* at a distance of 19 cm from the target. In order to enhance the 4n reaction channel 4 NaI(T1) detectors placed in a close geometry near the target were used as a multiplicity filter. At least two of the counters in the filter were required to be in coincidence with the Ge(Li) detector. Spectra obtained at various distances (d)are shown in fig. 2. The spectrum at d = 0 pm is unshifted and that at 7.9 mm is completely shifted. The areas of the shifted (f,) and unshifted (I,) peaks from the decay of the moving and stopped recoils are obtained as a function of distance and used in the expression Jo(d) e - dll’r R(d) = Z,(d)+&(d) = '

where z is the mean life. The mean recoil velocity t? was determined from the experimentally observed Doppler shifts. In several cases the area of either the

499.1 16.3“) 581.5 44.0 “) 660.3 76.0 “) 712.8 119.2y 673.6 251.7 560 305.3 627 344 308.1 396 19.3“) 463.6 482.8 559.8 543.5 628.3 5154.3

W’)

E,

Ii--I I,

0.20+0.03 -O.OJIO.O3 0.42i:O.O2 0.08~0.02 1.23? 0.3 0.23+0.03 -0.08If;O.O2 0.38+0.04 0.04f0.04 0.26iO.03 -0.07~0.02 0.301;0.03-0.02*0.02 0.42 t-O.06

f07 107

0.07rt:0.02 0,121:0.02

0.15&0.02 0.43+O.O2

154 93 12.5 106

1000-13QOd)

J

'i 21+6d)

i 200fW) i 67+_25“) .I

>

i

,

I

+o.i

1.1820.12

1.0

1.5k0.3b)

0.07LO.04 i 4.0+12

8

43 97

0.0s -t_0.08

0.27&0.02 -0.13&0.02

- 0.09 to.07

:tb) 18

64

81

0.25 +0.02

130 -0.06aO.02

0.25&0.02 -0.08 ho.02

252

A4

'=Ho 0.24,0.02 -0.03 kO.02

A,

454

Ao b2

0.245rtO.025

0.107~0.012

0.053rirO.Oi8

OJ8-tO.04

0.18&0.05

0.5OkO.14

0.44_tO.l4 +-I_

0.17+_0,12

B(EZI+I-I)** &Ii) B(E2.1 -+1-2)

0.021~0.011 0.7.?1:0.30d)

1.63~0.36")

0.X8&0.18")

1.5*0.4

3.6&1.0d)

3.0f1.2d)

2.91-0.8

512d)

ez..

BfM1,1-+-If ___._..__* B(E2,I-+1-2j

far transitions in the bands observed in ‘55H~ and ‘57H~ built on the $-[523] configuration

Energies, intensities, angular distribution coefricients and extracted values of mixing ratios, branching ratios and ratios of reduced transition probabilities

35 12 16 22 20 b) 21 71 b) 57

268 558 389 289 453 150 198 4gb) 110 47 75 b) 72 38

669.6 594 540.7 421.5 506.3 254.7 588 282.1

315.5 147.7 424.0 178.2 512.8 202.8 583.0 223.7 630.6 241.2 566.1 205 501.3 263.3 590.5 318 682 360

47b)

A,

E, (kev)

lJ7Ho

0.0 kO.08 0.0 +0.19

-0.16+0.08 0.18+0.19

I: 0.02 * 0.02 & 0.02 + 0.02 kO.02 & 0.04 +0.03

- 0.08 + 0.04 0.02 * 0.05

-0.05 0.05 -0.07 0.03 - 0.05 0.02 -0.08

0.07 + 0.04

0.28 f 0.03 - 0.02 kO.04

0.29 +0.02 0.04 * 0.02 0.31 kO.02 0.10~0.02 0.24 + 0.02 0.02 f 0.04 0.29 * 0.02

-0.30+0.04

- 0.03 + 0.06 0.06 rt 0.03

0.33 + 0.06 -0.13*0.03

cont. - 0.04 + 0.02

“‘Ho

A,

0.25 kO.03

A,

6

0.07

0.13

0.17

0.22

0.20

-0.04

kO.07

to.03

to.03

,0.02

50.02

rto.07

0.75kO.30

2.8 +0.25

1

j

1

i

>

+0.1s

4.0+ 1.5b)

1.8,0.6b)

0.81 +o.lZh)

0.54rtO.20”)

0.86 _f 0.26 “)

1.46 +. 0.22 “)

4.53 + 0.69

1.03+0.15y

1.02+0.011”)

0.95&0.11

1.18+0.12

1.33+0.14

1.73+0.42a)

1.44f0.32”)

0.57

2.10+0.022

4.1 k0.4b)

J

SF’ b=

0.156~0.0~7~)

B(Ml,I-+I-I) _-_-* B(E2,1+1-2)

2.3420.24

3.0 +0.3

1.35+0.13

j

1

> 0.48 20.05

1.25f0.2b)

0.96+0.20?

1

/

I

I (continued)

0.065 + 0.024

TABLE

0.78 +0.X0 0.78

0.87+:.:;

0.98’;:::

2.59 +0.50

3.50*0.70

0.02 f 0.02

B(E2, I -+ 1-2)

B(E2,I+I-1) -**

-$

a(1,)

5

t, .? K

“) b, ‘) d, I+2 ‘)

- 0.03 * 0.02 0.03 kO.01 - 0.06 i 0.02 0.04 f 0.02 - 0.06 rt 0.02 0.04 & 0.02 - 0.05 & 0.04 0.05 * 0.05

0.01+0.07

0.22 + 0.02 0.11+0.01 0128f 0.02 0.14+0.02 0.30 & 0.02 0.17+0.02 0.28 f 0.03 0.06 kO.05

0.50 & 0.07

q-+ 1-2) 16~ = 0.0693 x -5 E;(I -+ r--l)~(l+s2)

260 930 199 293 1.50 121 125 77 80 40h) 31 b) 39 44b) 88

e2. b’.

0.12 +0.03

>

0.52+0.2a)

5.5k2.0b)

1.01kO.035 “)

1.73kO.35”)

0.56,0.22”)

0.5kO.l b)

\

f.46k0.37

4.0+ 1.4h)

0.8f0.2b)

) >

2.OkO.7 b,

1 0.5110.18”)

0.50 ): 0.05

1.6210.16

)

0.20 +0.04

0.52 CO.05

1.24,O.ll

0.23 kO.10

0.22 f 0.08

0.58 + 0.09

1.08+0.17

0.61 kO.06

} 0.68+0.07 > I

2.78 + 0.44

0.28 + 0.03 0.74 $: 0.08

0.28 kO.02

o 27 +0,02 . -

0.27 +0.02

-i-r

Assuming 6 = 0. In most cases the error introduced IS considered < 22,. Intensity could only be obtained in coincidence data. Unobserved transition. Branching ratio obtained indirectly by observing the I - 1 -) Z-3, I- 1 + I-2 and I -+ 1-2 transition intensities in a spectrum gated with the + 1 or I+ 1 + I transition. Conversion is taken into account by a value of 6’ in accordance with 0.1 < Q,/Q,, < 10. The transition has increasing spin. This is corrected for m the B(M I)/B(E2) value of column 8.

B(E2,I+I-1) ** _. B(E2,1+ 1-2)

B(Ml,I-+I-1) * _ B(E2,I -1-2)

271.6 166.8 393.7 244.8 488.7 309.6 561.4 358.3 613.6 389.2 603.0 361.1 441.9 236.8 537.4 273.2 638.5 321 731 370

,”

;

.m G.

G. B. Hagemann et al. / 15’r 15’Ho

312

d = 9.5,um

2% -L 272- 1?/243/2I

300

500

400 ENERGY

Fig.

2. Gamma-ray separations,

spectra from the ‘46Nd(‘5N, d. Shifted and unshifted positions

( keV) 4n)15’Ho reaction for various target-stopper for some of the transitions are marked.

shifted or the unshifted peak could not be determined due to overlap with neighbouring transitions (see fig. 2). In such cases the “R” values have been derived from the observable component alone after an intensity normalization at each distance. Corrections for changes in detector solid angle and efficiency affected the lifetime by less than 1% and were disregarded. In order to derive the lifetimes z of the individual decaying states corrections for both cascade arid side-feeding have been taken into account. Least-squares fits to the experimental intensities (R(d)) by means of the program RECOIL9), in which the feeding pattern and lifetimes of 3 directly feeding and 3 sidefeeding transitions have been taken into account, are shown in fig. 3 for both signatures of the $-[523] band in 15’Ho. In many cases a

G. B. Hagemann et al. { ls51 “‘Ho

373

A -J.--i_ ‘- %- .b) * r;l’.~~ 22

&zX_B22

1.0

I

I

50

100

I

I

50

150

I

100

I

150

d @ml Fig. 3. Values

of

from states with

R(d)

=

r = -$

I,(d)) as a function of target-stopper separation d for transitions (a) and cz = +$ (b). The solid curves show least-squares fits ‘) with feeding corrections included.

1&)/(1,(d)+

value of the lifetime could be determined from both interband transitions. The extracted values are given in table 2.

and intraband

3. Analysis 3.1. ENERGIES IN THE ROTATING

FRAME

The level scheme energies of fig. 1 have been transformed to the routhians lo), e’, which are the excitation energies in the rotating frame in fig. 4. The references used have parameters ypo and 9, in a Harris expansion 1‘) chosen to give constant alignment (-de//do) above the first crossings which result from the alignment of a pair of i, quasineutrons. For comparison the routhian for 15’Ho also is included 12). Values of $0 and fl are given in the caption to fig. 4. The three Ho isotopes show in their energy spectra, and therefore also in their routhians e’, a strong dependence on neutron number (N = 88, 90, 92). Large-deformation changes are indeed expected to take place near N = 90. The values of (Q. Q) of the Lund systematics 13) for these nuclei are (0.157, -0.02), (0.198, -0.02) and (0.228, - 0.02), respectively.

G. B. Hagemann et al. / “‘.

374

TABLE

Lifetimes

and transition

I

probabilities

determined

2 from interband

and intraband

B(E2,1 -. 1-2) (e’. b’)

TP) (ps)

‘I’ y 9 y y y 9 y

157Ho

transitions

B(Ml,I+I-1) (eh/2Mc)2

@(I)

66rl: 18 14.9k2.1 b, 9.oi_ 1.4b) 3.5+0.8b,C) 3.0+0.4 1.0+0.8 2.2+ l.Ob) 1.5+0.5

0.90 + 0.26 0.36 k 0.06 0.3 1 * 0.05 0.45*0.10 0.30 f 0.04 0.54 f 0.‘43 0.28kO.13 0.70+0.24

0.18+0.06 0.48 + 0.07 0.37 kO.06 0.44*0.11 0.31 kO.05 1.12+0.91 1.27 + 0.46 1.04+0.36

-$

18.2+_3.0b) 8.8 kO.8 b, 2.3 kO.6 b, 2.2_tl.Ob) 2.1+_1.0
0.44f_o.10 0.35 *0.04 0.67+0.18 0.4OkO.18 0.29+_0.14 > 0.44 0.38 + 0.08 > 0.3

0.32+_0.06 0.21+0.02 0.32 +0.09 0.20 & 0.09 0.15+_0.08 > 0.63 0.66+0.11 > 0.30

+f

“) r(y) is first determined. Observed lifetimes are utilized in the feeding pattern to succeeding states. The intensity of feeding from unknown states is generally i 30 % of the known sidefeeding. Best fits are obtained with r of the unknown feeding < 1 ps except where stated. The error given includes this uncertainty. b, Average of 5 from the I + I-2 and I + I - 1 transitions. ‘) Best fit for r of unknown sidefecding 2.7 ps. d, Upper limit for the state. The value includes (unknown) feeding.

3.2. RELATIVE

The

TRANSITION

experimental

PROBABILITIES

branching

IN ‘55,‘5’Ho

ratios

I = T,(Z -+ Z -2)/T,(Z -+ I - 1) and mixing ratios 6, where ~3~= T,(E2,1 + I- l)/T,(Ml, 1 + I- 1) of table 1 can be converted and B(E2,Z+Z-l)/B(E2,Z-+Z-2). to ratios of B(M1, Z + Z - l)/B(E2, Z -+Z-2) For the c1 = -$ part of “‘Ho the splitting is so large that some of the Z + I- 1 transitions could not be observed due to their very small transition energy. A value of A is then deduced from the observed strength of transitions deexciting the state Z - 1 in a gate feeding into the state 1. A complication in this procedure arises from not knowing the total conversion coefficient of the missing transition. If the Ml and E2 conversion coefficients are comparable, this complication adds only little to the uncertainty in A, but at the lowest energies @(Ml) and c((E2) differ by several orders of magnitude. It has then been assumed that the variation of the ratio Qi/Qe is limited to 0.1 < Qi/Qc < 10, where B(E2, Z + Z - 1) f (ZK201Z -2K)

Ql/Qo= B(E2, I -+ Z - 2) > (ZK20lZ - 1K) ’

(2)

G. B. Hagemann

et al. / “‘, l”Ho

I

.2

375

2

.4

few (MeV) Fig. 4. Experimental routhians I”), e’, as a function of ho for the yrast and open circles connected by solid and broken lines correspond CL= -i bands, respectively. A reference frame with 2 = f,,+~,w’ and fI = 120, 90, 90 MeVm3 .h4 has been subtracted for ‘55Ho,

bands in 155~‘57~‘59H~. The solid to transitions in the a = +f and with f,, = 10, 20, 26 MeV-” h2 15’Ho and “‘Ho, respectively.

which seems a rather small restriction. Even though some signature effects < 20% around QJQ,, = 1 are expected 6), the highest observed excursion is Q1/Qo = 2 in l”Ho as discussed below. The signature effect on the energies in “‘Ho is so large that the I = _?iz state is higher in energy by 19.3 keV than the I = y’state. Therefore, the Ml(y + 9) matrix element extracted from coincidence results as described above is compared to a B(E2,y + 8) within the band with signature c1 = +s instead of the GL= -i band. Fig. 5 shows the values of B(Ml,I -+ I-l)/B(E2,1 + 1-2) for “‘Ho (left) and for “‘Ho (right), as a function of I. In the favourable cases of “clean” transitions a value of 6 can be extracted from the angular distribution data. This is of course not possible for unobserved transitions which imply that the B(E2, I + I- l)/B(E2, I -+ Z-2) values from the

G. B. Hagemann et al. I ‘55.

376

15'Ho

r

15?Ho

'=Ho 0 a =- 112

0

a=-112

. a=tl/2

l

a = + l/2

I

I

I

I

‘s/2

25/2

3512

4512

I Fig. 5. Experimental values of B(M1, I + I- lMB(E2.1 -+ 1--2) as a function of I “‘Ho (left) and 15’Ho (right). The open and closed points represent transitions e = -4 and +$, respectively: The full and broken lines are drawn to guide the parentheses at I = y for “‘Ho corresponds to B(E2,y -+ 4) rather than B(E2, y + inversion at I = y. For this point the denominator therefore has c( =

ct = -$ band are presented

cannot be obtained below the band crossing in 155Ho. The values as a function of I in fig. 6 for both nuclei converted to Q,/Qo,

according to eq. (2). In this conversion value of K would increase Q1/QO.

3.3. ABSOLUTE

for transitions in from states with eye The point in ‘I’) due to a level +$

TRANSITION

The lifetimes z measured mixing ratios, be converted B(E2, Z + Z-2)

we have used a value of K = ;. A smaller

PROBABILITIES

IN i5’Ho

in 157H~ can, by means of experimental branching to absolute E2 and Ml transition rates using = [z x 1.23 x 1013E,5(Z -+ Z-2)(1

+a,,,(Z + Z-2)

+;(l+a,,(Z-I-l))]-‘&b2,

B(Ml,Z-+Z-l)=

(3)

[rx0.57x10’3E,3(Z+Z-1)(41+cc,,,(Z+Z-2)) 2

+1+dl*,,(Z

and

-+Z-l))(l+P)]-i

)

& (

>

G. B. Hagemann et al. / L55*15’Ho

371

Fig. 6. Values for Q, in part (a) and B(MI) in part (b) for transitions in 15’Ho extracted from the measured lifetimes through eqs. (3) and (6) with K = 3 and eq. (4). The value of Q. corresponding to I = 9 is shown in parentheses because the extraction for this low value of I z K depends strongly on admixtures of low K-components. (A lower K would decrease the Qo.) The dependence on K decreases strongly with increasing I and is considered to be negligible compared to other sources of error for 1 2 y. The dashed curve shown in part (b) corresponds to the triaxial particle-rotor model calculations of ref. 6, with 1’ = - I5O.

where cr,,,(Z + I-

1) = &

(h2a(E2)+4M1))

(5)

also depends on the mixing ratio 6. Since the mixing ratio in all the cases measured is predominantly of in 15’Ho gives l/(1 +S2) 2 0.93, i.e. the Z --f I - 1 transition Ml character, we have assumed 6 = 0. The error introduced this way is negligible compared to the direct errors in the lifetime z and branching ratio A. The values of B(E2, I + Z-2) and B(M1, Z -+ Z - 1) are given in table 2.

378

G. B. Hagemann et al. 1 ls5, 15’Ho

4. Discussion The most striking

feature

of the routhians

e’ shown

in fig. 4 is the change

at the

crossing frequency from a large signature splitting into no splitting at all or even a slight inversion for both “‘Ho and “‘Ho . Such an effect has been explained 4,5) by a change in y-deformation from rather large negative values, which reproduce the energy splitting at smaller rotational frequencies, to a slightly positive value at frequencies above the vi I; crossing +. Similar behaviour is also found 2*3) in i5’Tm which has 90 neutrons and is intermediate in deformation 13) between “‘Ho and 15’Ho. This effect is also seen ‘*) in “‘Ce, where the odd neutron is in the equivalent Nilsson orbit (h,: [523];-). For both Ho nuclei investigated a large change is also observed in the B(M1, I + I - l)/B(E2, I + 1-2) ratio at the value of I where the i,& neutrons become aligned (see lig. 5). With the lifetimes measured in 15’Ho it is for the first time demonstrated that the rise in the B(M1, I + I - l)/B(E2, I --+ I - 2) values at the crossing is due to an increased B(M1) and not to a decreased B(E2) value. Indeed, the measured B(E2, I -+ I - 2) values in 15’Ho of table 2, which have been converted to Q. using

B(E2,I

-+ I-

2) = &

Q; (IK20(1-

2K)Z,

show very little variation with I (see fig. 6). In this conversion a value of K = s has been used throughout although some admixture of K = * (and thus also 3 and 2) must be present to cause the signature dependence in the energies. The I = 2, AZ = 2 Clebsch-Gordan coefficient of eq. (6) depends very little on K, except for the lowest Z-value. Indeed, the Q. of I = y appears at a value of Q. = 11 e. b compared to an average of Q. w 4 e. b with no pronounced systematic the remaining higher values of I. The explanation for the apparently extracted at I = 9 is most likely the greater sensitivity of the K-value

trend for high Q,, used. In

order to explain the signature effects in the energies in 15’Ho, values of y = -7” before and +4“ after the crossing have been proposed 4). Such a change in y would imply a decrease in Q. (proportional to cos (30°+y)) by lo’/, at the crossing, provided that no change in s2 occurs simultaneously. The data are not conclusive to this accuracy - but are not in contradiction to such a change in triaxiality. The average value of Q. - 4 e. b can be converted to p = 0.18 or s2 = 0.16, which is somewhat smaller than expected from the Lund systematics 13) given in subsect.

’ Recent interaction introducing

quasiparticle-plus-rotor calculations 14) with seem to reproduce a part of the observed triaxial degrees of freedom.

a rotation-dependent change in signature

core-quasiparticle dependence without

G. B. Hagemann er al.

3.1. An average of Q. below I=” 13 (excluding Qo(r = +j)/Qo(r

=f’-f)

the

‘=‘1.2~‘01.

: ‘55. l”Ho

379

backbend within each signature individually , . give Of above) would The absolute B(M1.I -+ I-l)avaht:~~picted

in the upper part of fig. 6 therefore show a slightly smaller signature dependence than the B(M1, I --+ 1- l):‘R(E2. I + I-2) ratios of fig. 5 even though the overall structure is preserved. Since both nuclei show effects which can be ascribed to a changing triaxiality, a comparison with a schematic triaxial particle-rotor-model calculation of the transition probabilities performed in the middle of the nh,, shell by Hamamoto and Mottelson ‘) has been attempted. The calculation shown as a dashed curve in fig. 6b does not take the \i, alignments effects into account. The theoretical values corresponding to 7 = - IS’ show qualitative agreement. With ;’ = + IS’ almost no signature dependence is obtained. It should be noted that the observed values (averaged over the two signatures to + 0.3 (eh/2Mc)’ below the crossing) are around 4 times lower than the shell-model value for a band built on the nh:, state, which is roughly the value obtained for the r = -: band in the CSM calculations of Hamamoto and Sagawa I’). The ratio Q,/Qo (which is proportional to 6) -could only be obtained for both signatures in “‘Ho. Since values of S are extracted from angular distributions measured in singles, it was not possible to obtain b-values for the transitions from the higher-spin states. The values presented in fig. 7 for 15’Ho below the crossing show a sizeable signature dependence with average values of about 1 and 1.8 in the a = +$ and r = -i bands, respectively. In rs5Ho the value for a = +t is around 0.6. which probably would imply an even larger signature depedence as observed also in the excitation energies (cf. fig. 4) and in the values of B(M I,1 --t I - l)/B(E2.1 -+ l-2) (cf. fig. 5). An indication of such a signature effect is contained in the value of B(M1, 7 + y)/B(E2,? + s) which is considerably lower than neighbouring values in the LX= -f band. The denominator is related to the a = + : rather than the a = - { band due to a level inversion large energy splitting. A Q,, which is greater in the r = + f than

caused by the in the 2 = -$

band would explain the discrepancy for this spin vale (cf. (Qo(a = +i))/(Qo(a as discussed above). Calculations = -$)) = 1.2fO.l below the crossing in “‘Ho of QI/Qo in the triaxial rotor model of ref. “) are also shown in fig. 7, for two different values of y( = f 15”). Qualitatively the trend is reproduced for both signs of 7, but is should be noted that a value of p = + 15O would give no signature dependence in B(M I,1 + I - 1) and therefore disagree strongly with another part of the experimental information. A striking difference between the two nuclei in the B(Ml.1 + 1 -I)/ B(E2,l + l-2) values is apparent from fig. 5. The signature splitting in “‘Ho is very large, and provided that the Q,, is only slightly signature dependent as observed in 15’Ho this large splitting below the crossing is mostly due to the B(M1, 1 -+ I- 1) values. The pronounced rise in the crossing region in

G. B. Hagemann et al. / 155, i57Ho

380

31512

25/z

35/2

45/2

I

Fig. 7. Experimental values of

(see eq. (2)) for ‘55.357Ho as a function of I. Open and closed symbols correspond to transitions from states with c( = -f and a = +f respectively. The full lines connect the two signatures in *“HO. The dashed and dot-dashed curves correspond to triaxiai particle-rotor model calculation for 7 = + IS’ by Hamamoto and Mottelson “) performed in the middle of the zh, i,z shett.

“‘Ho may be obscured for a = -f in 155H~ due to the extremely large splitting at frequencies below the crossing. An intermediate situation between the two Ho nuclei is found ‘) in i5’Tm, in which the B(MI, I -+ I - l)/B(E2, I + I - 2) ratio rises at the crossing to a value of N 2(eh/2_~c)2/e2. b2 which persists for a few transitions above the crossing. The results in i5’Tm have been discussed ‘*16) in terms of the magnetic moment of the aligned pair of i,? neutrons, which qualitatively explains the observed rise in B(Ml,Z -+ Z- 1) values. Such an explanation does not seem suffzcient for the present cases. In “‘Ho, which is very shape unstable (as is also reflected in the poor rotational behaviour with y0 = 10 MeV-’ . h2 below the backbend) and probably triaxial with,a value of y 5 - 30”, i.e. approaching the oblate shape, the rise is hidden in the signature effect. In i5’Ho which is less triaxial, the rise in B(M1) value observed at the vi t5 alignment does not stay constant at higher spins.

G. B. Hagemann et al. 1 ls5* 15’Ho 5.

381

Summary

The two nuclei studied both show, features characteristic of the deformation changes taking place when a pair of iy neutrons align. Before this alignment a large signature dependence is observed in excitation energies and even more markedly in After the alignment a slight signature the I + I- 1 transition probabilities. inversion takes place in the excitation energies, and a large reduction - consistent with no signature dependence - is seen in the splitting in transition probabilities. By means of the lifetime measurements it is demonstrated that in ls7Ho very large B(M1, Z + I- 1) values, increased by up to a factor of 5, connect states of I and I- 1 in the crossing region. In the same region very little effect on the probabilities B(E2, I + Z-2) values is seen. The B(E2, Z + Z - 1) transition measured below the backbend show a large signature dependence in 157H~. The triaxial particle-rotor-model calculations of ref. 6, seem to reproduce these observed signature effects qualitatively, but so far a detailed understanding of the features which would enable a determination of the shape parameters and their changes is lacking. This is especially true for the ratios Q1/Qo which approach a value as high as 2 for u = -r 2 in 157H~ but cannot be reproduced with the current models. Discussions with B. Mottelson, I. Hamamoto, F. May, J. Waddington and A. Larabee are acknowledged. This work has been supported by the Danish Natural Science Research Council, the Nordic Comittee for Accelerator-Based Research. and the UK Science and Engineering Research Council. One of us (B.M.N.) would like to thank the British Council for a visiting fellowship.

References 1) G. B. Hagemann, .I. D. Garrett, B. Herskind, G. Sletten, P. 0. Tjom, A. Henriques, F. Ingebretsen, J. Rekstad, G. Ldvhdiden and T. F. Thorsteinsen, Phys. Rev. C25 (1982) 3224 2) A. J. Larabee and J. C. Waddington, Phys. Rev. C24 (1981) 2367; L. L. Riedinger, L. H. Courteny, A. J. Larabee, J. C. Waddington, M. P. Fewell, N. R. Johnson, I. Y. Lee and F. K. McGowan, abstract to the Conf. on high angular momentum properties of nuclei, Oak Ridge, USA, Nov. 1982, p. 4; and to be published 3) R. Holzmann, J. Kuzminski, M. Loiselet, M. A. van Hove and J. Vervier, Phys. Rev. Lett. 50 (1983) 1834 4) S. Frauendorf and F. R. May, Phys. Lett. 125B (1983) 245 5) R. Bengtsson, H. Frisk, F. R. May and J. A. Pinston, Nucl. Phys. A415 (1984) 189 R. Bengtsson, J. A. Pinston, D. Barntoud, E. Monnand and F. Schussler, Nucl. Phys. A389 (1982) 158 6) I. Hamamoto and B. R. Mottelson, Phys. Lett. 132B (1982) 7 7) M. D. Devous and T. T. Sugihara, Z. Phys. A288 (1978) 79; C. Foin, S. Andre, D. Barntoud, J. Boutet, G. Bastin, M. G. Desthuilliers and J. P. Thibaud, Nucl. Phys. A324 (1979) 182 8) P. J. Nolan and J. O’Gara, Daresbury Laboratory DL/NUC/TM61E (1982) 9) P. Butler, private communication 10) R. Bengtsson and S. Frauendorf, Nucl. Phys. A314 (1979) 28; A327 (1979) 139

382 11) 12) 13) 14) 15) 16)

G. B. Hagemann et al. / 155- l”Ho

S. M. Harris, Phys. Rev. 138 (1965) B509 I. Forsblom, S. A. Hjorth and A. Spalek, Nucl. Phys. A252 (1975) 315 R. Bengtsson, J. de Phys. Colloq. 41 (1980) CIO-84 E. Mtiller and U. Mosel, Nucl. Phys., to be published I. Hamamoto and H. Sagawa, Nucl. Phys. A327 (1979) 99 F. Donau and S. Frauendorf, Proc. Conf. on high angular momentum properties of nuclei, Oak Ridge (1982) ed. N. R. Johnson (Harwood, New York, 1983) p. 143 17) P. J. Twin, P. J. Nolan, R. Aryaeinejad, D. J. G. Love, A. G. Nelson and A. Kirwan, Nucl. Phys. A409 (1983) 343~ 18) R. Aryaeinejad, D. J. G. Love, A. H. Nelson, P. J. Nolan, P. J. Smith, D. M. Todd and P. J. Twin, J. of Phys. G, to be published