Magnetic moments at backbending and spectroscopy of 134Ce

Nuclear Physics A38:î (1982) 16188 © North-Holland Publishing Company

MAGNETIC MOMENTS AT BACKBENDING AND SPECTROSCOPY OF '3'Ce A. ZEMEL, C. BROUDE, E. DAFNI, A. GELBERG fand M. B. GOLDBERG The Weinmann Institute ojScience, Rehonot, Israel J. GERBER Centre de Recherches Nucléaires, Strasbourg, France and

G. J. KUMBARTZKI and K.-H. SPEIDEL Institut für Strahlen- und Kernphysik, Bonn, Germany Received 28 August 1981 (Revised 23 December 1981)

Abstract : Employing the static hyperfine fields at cerium nuclei in magnetized Fe and Gd hosts, the g-factor ofthe "4 Ce(10 + ) stateat backbending (E, = 3719.3 keV) has been determined as g = -0 .30 (25) . The coexistence of this neutron-dominated state with the (vh~r 10 + isomer (Ez = 3208 .5 keV, g = -0 .19(1)) is unexpected. A comprehensive spectroscopic study following the "~Sn(' 60, 4n) reaction, including y-angular distributions, prompt and delayed yy coincidence and recoil~istance measurements has yielded new information on quasi~ollective bands of both parities. The properties of the low-lying positive-parity states are well described by the interacting boson model.

E

NUCLEAR REACTION '=~Sn(' 60, 4nßE = 75, 80 MeV;measured I,(E), y(B~ y(t), yy-coin, recoil, internal-field (Ce in Fe, Gd) precessions. '~ 4Ce deducod levels, l`, b, T,i~, 9~

1. Introdactioo The anomalous behaviour ofhigh-spin rotational states, known as "backbending», characterizes the spectra of a large number of medium and heavy nuclei . This phenomenon manifests itself mainly in the irregular dependence of excitation energy versus spin along the yrast line ; in some cases there is also considerable reduction of the E2 rates at the backbend relative to those of the in-band transitions. Various mechanisms have been suggested to explain these phenomena but it is generally believed that they result from band crossing and reflect the interplay between collective and valence-particle properties at high spin values. Magnetic moment measurements can play a decisive role in clarifying these questions, since this quantity is in many cases a clear signature of the particles involved . Previous attempts to f On kaue from Institut für Kernphysik, K31n, Germany. 165

166

A. Zeme! et al. / Magnetic moments

determine magnetic moments near backbending were hampered by experimental difficulties . The level schemes of many nuclei around A = 130 show similar structures, such as collective bands with enhanced E2 transitions 1-6) and sequences built on 5 - states [refs, s - a )]. The collective bands have been classified in terms of moderately prolate or triaxial y) shapes ; the general features of the low-lying positive-parity states in the even-even isotopes have been reproduced recently io, i i) with the interacting boson model (IBM). The even Ba and Ce nuclei in this region exhibit strong backbending patterns above the 8+ states a' 6). For the lighter of these (A 5 130), the effect has been attributed to rotation-aligned proton pairs, since the isotonic odd-Z neighbours 'Z' . iaeLa do not backbend nZ ). As the h~ neutron shell approaches half closure (N = 76) at ' 32 Ba and ' 3aCe, the identity of the valence particles involved becomes less clear. Moreover, 10 + isomers appear in a number of N = 78, 80 nuclei i 3 -'e) . The negative magnetic moments observed for some of these isomers are a clear indication of (ham)" neutron configurations 1 s . ' e). In 13aCe, an assignment of 10+ had been tentatively proposed for an isomeric state at 3208.5 keV [ref. ")], presumed to be similar in structure to the isomers in the heavier isotopes . The possible coexistence of such an isomer with the nearby 10 + level at backbending raised questions concerning the identity of the valence particles responsible for backbending in this nucleus and its relationship to the neutron-dominated isomers. The current project [refs.l8 ~' 9) and present work] was undertaken to resolve these questions by establishing the assignment of the isomer in ' 3aCe and determining the magnetic moments of both 10+ states . Such measurements can indeed provide direct evidence since the magnetic moments of protons and neutrons in the respective valence configurations have opposite signs. In the following, a detailed account of extensive spectroscopic measurements on 13aCe is given. This information, in conjunction with internal-field precession measurements, enabled the determination of the g-factor of the 10+ state at backbending (Ex = 3719 .3 keV) . In this nucleus, the combined reduction in transition energies and E2 rates in the backbending region ~~ s) gives rise to relatively long mean lives ( x 10 ps) for the 10 + and 12+ states . This feature has been exploited to observe their precession in the static hyperfine field acting on dilute Ce impurities implanted into magnetized Fe and Gd hosts. The observed precession in such a field is proportional to the nuclear mean life with consequent high sensitivity to the magnetic moments of these levels . A brief description of the results has been previously communicated ~e . 19) and some of their implications discussed ' 9~ a °). The lifetime and g-factor measurements of the 10+ isomer [E_ = 3208.5 keV ; T = 485(20) ns ; g = -0.19(1)] have already been reported '9) and will be discussed here only in the overall nuclear structure context.

A . Zemel et al. / Magnetic moments

l67

2. Spectroscopic studies 2 .1 . EXPERIMENTAL

In these measurements, 134Ce levels were populated in the'zzSn(160, 4n) reaction with 75 MeV '60 beams from the Weizmann Institute 14UD Pelletron accelerator. Isotopically enriched tin targets, 1 mg/cmz thick, were rolled onto thin gold (x 2 mg/cmz) or thick lead (x 100 mg/cmz) backings. The series of measurements included (a) Singles y-ray anisotropies employing the logarithmic slope technique z') . Two rigidly coupled Ge(Li) detectors were set up in the geometry of fig. 1 . Data were accumulated at the two angle settings I and II, with frequent alternations to reduce systematic errors . The automatic drive and control system ensured angle reproducibility of 0.05° for a displacement of d B = 8° around a mean detection angle
N t (I)

N,(II)

Nz(I)I Nz(II)

is a measure of the anisotropy of the angular distribution .

Fig . 1 . Rigidly coupled two-detector setup for measuring y-anisotropies . Detxtors 1 and 2 were frequently alternated between angle settings I and II, which represent an angular displacement of dB = 8° around a mean detection angle of (ei = 125° .

168

.f . Zemel et al . / Magnetic moments T~st,e 1

"`Ce y-rays following the `zzSn(` 60, 4n) reaction at 75 MeV E ') (kéV) 189 .5 191 .3 206 .7

zls.a

233 .1 262 .2 288 .3 299.2 309 .1 330.1 332.2 340 °) 347 .3 347 .3 384.1 °) 391 .7 397 .5 `) 403 .1 409.1 417 .3 417 422 .E 429.2 446 .4 451 .7 464.3 532 .3 536.8 556 .1 560.9 561 .0 594 .4 594.7 639 .5 644.E 660 .5 668 °) 677 .8 702.1 713 .7 724 .E °) 730.7 755 .9 763 .1 764

r

b)

7 4 6 a.5 4 4 1 4 3 .5 5 4 .5 5 2 1 .5 5 6 16 .5 3 100 1 .5 3 7 .5 3 .5 4 .5 10 .5 17 13 .5 3 8 1 1 .5 3 .5 8 .5 89 4 .5 11 10 10.5 2 .5 5 .5 11 1 9 7 1

Az °) -0 .60(7) -0 .68 (9) <0 -0.66 (6) -0.7 (2) -0.25 (11) 0.0E (6) -0.43 (12) 0.0E (6) 0.10 (3) -0.86 (13) 0.229(7) 0 .7

(1)

0 .34 0.19 0 .27 0 .24 0.34 0 .01

(10) (5) (3) (4) (15) (5)

0 .18 (12) 0 .20 (7) 0 .28 (1) -0 .16 (12) 0 .30 (5) 0 .22 (5) 0 .21 (5) > 0 0 .09 (9) > 0.1 <~ 0 0 .3E (6)

Transition Ei ~e~

Er (keV)

2896.1 3208.5 2566.0 2027.1 2706.E 3158.3

Spin and parity Ji

Ji

2706.E 3017 .2 2359 .3 1811 .7 2473 .5 28% .1

810+ (6, 7) -

78+ 6-

79-

68-

3208.5 `) 2473 .5 1691 .E 2896.1 2359.3 4345 2706 .E 3158 .3 2027 .1 2566.0 3208 .5 2706.E 409 .1 1382 .5 4762 .2 `) 28% .1 1811 .7 2473 .5 3158 .3 4183 .E 2706 .E 28%.1 965 .2 2920.2 ~ 3719 .3 1643 .0 3753 .0 1048 .E 2027 .1 2303 .5 2359 .3 1643 .0 3719 .3 3017 .2 4908 .2 5492 .9

2920 .2 2174 .3 1382 .5 2566 .0 2027 .1 4006 .3 2359 .3 2811 .0 1643 .0 2174 .3 2811 .0 2303 .5 0 %5.2 4345 2473.5 1382 .5 2027 .1 2706 .E 3719 .3 2174.3 2359.3 409.1 2359 .3 3158.3 1048 .E 3158.3 409.1 1382.5 1643 .0 1691 .E %5.2 3017.2 2303.5 4183 .E 4762.2

10+ 6(4) 8(6 - )

4762 .2 1811 .7

4006.3 1048.E 3208 .5 r)

(a-)

79(4 - ) (6, 7) 10 + 72+ (3+) (14 + ) 86912 + 7' 82+ 10 + 4+ 4+ (4 - ) 6+ (6 - ) 4+ 10 + 8+ 14+ (15) (14 + )

5(3+) (6, 7) (4 - ) (12+) (6 - ) 8+ 4+ 58+ 6+ 0+ 2+ 6(3 + ) (4') 710+ S(6 - ) 2+ (6 ) 94+ 92+ (3 + ) 4+ (4) 2+ 8+ 6+ 12 + (14+ ) (12 + ) 4+ 10 +

169

A. Zemel et al. / Magnetic moments TABLE 1 (continued) Er .)

b)

(keV)

r

789.5 797 .8 814.4 817 .7 872 °) 908 .3 948 .0 955 .8 965 .2 973 .4 978 .5 1005 1103 1125 .7 1197 1233 .9

6 13 .5 48 11 7 19.5 39 2.5 8 5 .5 2.5 2.5 1 .5 23 3 .5 1 .5

A s `)

0 .04 (9) 0.11 (4) 0 .27 (2) 0 .30 (7) 0.28 (5) 0.25 (2) 0.31 (7) 0.30 (7) 0.60 (17) -0.28 (3)

Transition Ei (keV)

Ei (keV)

4542.5 4006.3 1863 .0 5725.9 6598 .1 3719 .3 2811 .0 5498 .3 965 .2 1382 .5 2027 .1

3753 .0 3208 .5 1048 .E 4908 .2 5726 .9 2811 .0 1863 .0 4542.5 0 409.1 1048.E 2811 .0 ~) 4762.2 `) 1048 .E 1048 .6') 409 .1

2174 .3 1643 .0

Spin and parity J;

J~

(12 + ) 6+ 16 + 18 + 10 + 8+

10 + 4+ 14 + 16 + 8+ 6+

2+ (3*) (4 - )

0+ 2+ 4+ 8+ (14+) 4+ 4+ 2+

54+

') Transition energies are accurate to 1 unit of the last quoted digit . b) Intensities are accurate to 1 ~ of the 409 .1 keV 2+ y 0+ transition . °) Values deduced from measured logarithmic slope, assuming A 4 = 0 . °) Composite line in " 4Ce . `) Contaminated by line from competing (' 6 0, 3n) or (' 6 0, Sn) channels. Results quoted refer to net 134 component. Transition between unidentified levels .

For small angular displacements DR z 1 +4(ZdB)

W

dB ,

where (1/W~W/dB is the logarithmic derivative ofthe angular distribution at B =
170

A . Zemel et al. / Magnetic moments

are based on the recoil-distance results of ref. 3) and the present work, in conjunction with the updated spectroscopic information. (c) Prompt y-y coincidence. The targets were rolled on thick lead backings and two Ge(Li) detectors were positioned at ± 130°. Data were accumulated event-byevent and recorded on magnetic tape . The overall statistics permitted identification of y-rays with intensities as low as 2 ~ of the 2+--~0+ transition . Off-line sorting was performed with narrow windows set on photopeaks, subtracting coincidences with appropriate nearby background windows. Fig. 4 shows examples of backgroundcorrected spectra obtained by gating on selected transitions in the major bands observed . (d) Delayed y-y coincidence in the recoil-shadowing geometry t9) . When studying isomers with mean lives longer than x 10 ns, this arrangement suppresses prompt radiation seen by the stopper detector by more than an order of magnitude, thus reducing random coincidence contributions considerably . Fig. 2 shows a delayed y-spectrum of the stopper detector, from which the decay modes of the 3208.5 keV isomer were identified (see level scheme). The transitions feeding it were identified from the corresponding target-detector spectrum . 2 .2 . CONSTRUCTION OF LEVEL SCHEME

The spectroscopic information on 134Ce available prior to the present work can be summarized as follows : A positive-parity band was identified up to ~ 1~ = 16+

Fig . 2. Random-subtracted otFprompt coincidence energy spectrum of the stopper detector in reooilshadowing geometry 1 ~, showing y-rays which deexcite the 3208 .5 keV isomer.

A. Zerre! et al. / Magnetic moments

171

1B'T- 6598 .1

16'

5725 .9 54983

14'

*

4908 .2 4542.5 4183 .6 719.3

3753D --

Fig . 3 . Updated level scheme of' 3 `Ce. Dashed arrows represent feeding transitions from unidentified levels .

[refs. '" Z)] . Strong backhanding accompanied by retarded E2 rates occurs around the 10+ state at 3719.3 keV [ref. s)] . A long-lived isomer at 3208.5 keV, tentatively assigned as I` = 10+ [ref. ")] was known to decay to the ground state band 8+ member. A partial level scheme up to Ex = 2.5 MeV was proposed on the basis of y-rays observed following the decay of t34Pr [ref. ZZ)] . The updated level scheme resulting from the present work is shown in fig. 3 . This scheme was constructed on the basis of prompt and delayed coincidence spectra, energy consistency and photon intensity balance. It also accounts for the transitions and coincidence spectra observed following the decay of 13`Pr [ref. ZZ)] . The spin and parity assignments are based on gamma anisotropies, branching ratios and

172

A. Zemel et al. / Magnetic moments

systematics of neighbouring nuclei . The levels can be classified into five major sequences, which will be referred to as the g.s.b. (2+ through 8+ ground state band members), the "superband" (10 + through 18+ ), a 10+ isomer and levels feeding it, a quasi-y-band (q.y.b.) and a complex negative-parity sequence (n.p.s.). A justification of the updated level scheme is given below using this classification. (a) The g.s.b. members are linked by collective E2 transitions of 20-80 W.u. [ref. s)] . The anisotropies of these transitions obtained in the present work (see table 1) are in agreement with those ofref. z). Forall levels except the 6+ , the interband transitions responsible for the side-feeding intensities have been identified . No branching out of this band has been observed . (b) The pattern of transition energies and E2 probabilities 3) in the g.s.b. suggest that the 10+ state at 3719 .3 keV is not a natural extension of the band but rather the head of a new quasi-rotational band (the "superband") . Moreover, unlike the states in the g.s.b., this state is found to decay also to the 8+ q.y.b. member via a 702.1 keV y-ray. From the branching ratio I(702.1)/I(908.3) = 0.13 (table 1) and mean life T = 8 ps (table 3~ the E2 decay rates to the g.s.b. and q.y.b. 8+ members are 4 and 2 W.u. respectively . A weaker 561 .0 keV branch into the 9- member of the n.p .s. has also been observed. The E2 rates among the superband members are comparable to those in the g.s.b [ref. s)]. The prompt coincidence spectrum gated by the 872.2 keV y-ray (fig. 4a) implies a level at 6598.1 keV which decays to the 16+ state. The anisotropy (table 1) favours an 18+ assignment to the new level . (c) The three strongest lines observed in the target-detector spectrum in the recoilshadowing geometry of ref. 19) form a cascade above the isomer. On the basis of anisotropies, the more intense 755 .9, 797 .8 keV lines are probably stretched E2 transitions, favouring 12+ and 14+ assignments to the 4006 .3 and 4762 .2 keV levels respectively . The latter is fed by a weaker 730.7 keV y-ray with negative anisotropy, favouring a spin 15 assignment to the 5492 .9 keV level . The feeding pattern of the 10+ isomer in' 36Ce is very similar' 3). The ordering of the 339, 417 keV cascade and thus the position of the 4345 keV level is tentative. In the isomer decay spectrum, the 397.5 keV line and the four transitions below it in the g.s.b. are the strongest lines observed (fig. 2). (d) A quintet of weaker lines, (191 .3, 660.5, 677.8, 713.7 and 965.2 keV), observed in the isomer decay (fig . 2) are all in prompt coincidence with each other. Moreover, the sum of these transition energies is equal to the isomer excitation energy, implying that they form a cascade parallel to the g.s.b. decay mode . The 965 .2 and 677.8 keV transitions were previously assigned to levels at965.2 and 1643.0 keV respectively zZ) . This level ordering is supported by the 556.1 and 594.4 keV transitions to the g.s.b., which fulfil the necessary coincidence conditions and are also observed in the isomer decay. The singles intensities of the remaining 3 transitions in this cascade establish their order as 660.5, 713 .7 and 191 .3 keV, and thus the positions of the 2303 .5 and 3017.2 keV levels . Further evidence in favour of a level at 2303 .5 keV is furnished by transitions to and from the n.p.s. The existence of a level at 3017.2 keV is supported

A. Zeme1 et s1. / Magnetic moments

173

Fz O CJ

CHANNEL

NUMBER

Fig. 4. Prompt yy coincidence spectra gated by selected transitions in different bands of "4 Ce. The gating transitions are : (a) the 872.2 keV 18*~16* transition, showing the subsequent superband and g.s.b . cascades, (b) the union of the 556.1, 660.5, 677.8, 713.7 and %5 .2 keVy-rays deexciting the q.y.b . members. The feeding of this band from both 10* states is clearly scen and (c) the 1125 .7 keV 5 - y4 ; transition, showing most of the n.p.s. lines and the two lowest g.s .b. transitions.

by the observation in coincidence of the 702.1 keV feed from the 3719 .3 keV 10 + state and the superband transitions above it. The spin of the isomer, the multiplicity of5 for the cascade below it and the positive anisotropy of the individual transitions identify the 965 .2, 1643.0, 2303 .5 and 3017.2 keV levels as having spin-parities of

174

A . Zemel et al. / Magnetic moments TABLE 2

Interbandfm-band E2 branching ratios Transitions

Ezp

Theory')

22 -~ Oi 22 ~ 2i

0.06 (2)

0.02

3+--2+i i ~ z

0.05 (3)

0.03

0.007(3)

0.002

0.6

0.8

3+

2+

+ 2+ 4z ~ , + 2+ 4z -" z + 4+ 4z -" , + 2+ 4z -" z 4+ 6+z 6+ -4+ ~ z z + 6+ 8z +-,6+ 8z z 10 ; -_ 82 10~ -+ 8i 102 ~ 82 102 -+ 8 ; 102 -+ 10 ; 102 ~

8;

(3)

< 0 .004 ") < 0 .02 b) 12 0 .5

(3) `) (2)

< 1 ")

') Ref.'°). n) An upper limit of 1 % of the intensity of the 2+ -. 0+ transition is taken for unobserved y-rays . `) Corrected for internal conversion .

2+, 4+, 6 + and 8+ respectively . Fig. 4b displays the prompt coincidence spectrum gated by the union of the lines in this cascade (except the 191.3 keV line) and the 556.1 keV 22 ~2i transition . The feeding modes from both 10+ states are clearly seen. No other feeding into the 8+ member has been identified . The assignment of this sequence to a new collective band is based on the B(E2) ratios extracted from branching ratios of in-band y-rays and transitions into the g.s.b. [present work and ref. 22)] assuming pure E2 multipolarities. The derived B(E2) ratios are listed in table 2, together with the IBM predictions t°) which will be discussed later. These ratios, and the non-observation of any transitions to the g.s.b. above the 4+ state imply a retardation of the interband transitions by at least two orders of magnitude relative to the corresponding in-band E2 rates. This property and the nearly equal energy spacings between the members of this band compared

A. Zemelet al. J Magnetic moments

17 5

to those in the g.s.b. identify it as the quasi-y-band 4). By comparing the anisotropies of the 556.1 and 965.2 keV y-rays depopulating the q.y.b. 2+ state a value of S = 9±i4 has been derived for the E2/M1 mixing ratio of the former transition . The predominant E2 nature is in agreement with the systematics found a" zs . za ) for a number ofTe, Xe and Ba isotopes with similar neutron numbers. The existence of a level at 1382.5 keV, proposed in ref. zz), is established by the observation of the decay y-rays (into the 2 + states of the g.s.b. and the q.y.b.) in coincidence with a few feeding lines from the n.p.s. On the basis of the positive anisotropy ofthe 973.4 keV transition to the g.s.b. 2+ state, the absence of a transition a" s" Za. zs)~ we to the ground state and the systematics of neighbouring nuclei 5" '" tentatively assign 1* = 3+ to this level . No other odd-spin members of the q.y.b. have been observed . (e) Most of the intensity difference between the 6+->4+ and 4+->2+ transitions in the g.s.b. is accounted for by the 1125 .7 keV line (see table 1). The two lowest transitions in the g.s.b. are indeed the strongest lines observed in the prompt coincidence spectrum gated by the 1125 .7 keV line (fig . 4c), while the higher g.s.b. transitions are suppressed . Since no other line of comparable intensity appears in this spectrum, it is concluded that this feed into the 4 + state comes from a level at 2174.3 keV, as tentatively proposed in ref. zz). The negative anisotropy of this transition is consistent with dipole character. Since no other decay mode of the new level is observed, the most likely spin assignment is 5. We propose negative parity, in line with assignments to similar states observed in neighbouring Xe, Ba, Ce and Nd isotopes s s) . In all these nuclei such states are the band-heads of 5 - , 7-, 9 - , . . ., sequences linked by stretched E2 transitions. Indeed, the 532.3 and 451 .7 keV lines (fig. 4c), which are in prompt coincidence with each other, form such a cascade as evident from their anisotropies (table 1). The corresponding 7- (at 2706 .6 keV) and 9 - (at 3158.3 keV) levels are supported by the observation in coincidence of a number of additional feeding and decay modes. The 594.7 keV line, also seen in fig. 4c and in coincidence with these two y-rays, may well be the continuation of this E2 cascade;judging by the anisotropy of the 594.4-594 .7 keV doublet. However, the 3753.0 keV level is only tentative since the order of the 594.7-789 .5 keV cascade y-rays is determined only by their relative intensities. Most of the discrete lines below 400 keV (see table 1 and fig. 4c) are associated with the 5- , 7- , 9- sequence and levels at 2359 .3, 2473 .5, 2566 .0 and 2896 .1 keV on the basis ofcoincidence spectra and energy consistency. A number of them exhibit large negative anisotropies, characteristic of mined E2/M1 transitions, which determines the parity of the above quartet to be negative . It is plausible that these mixed multipole transitions contribute to the negative anisotropy of low-energy feeding into the yrast line reported recently ze).

17 6

A. Zemel et al. / Magnetic moments

3. Internal-field precession measurements 3 .1 . GENERAL

In these measurements, performed with the Strasbourg MP Tandem accelerator, the 1 safe recoils following 1ZZSn(160, 4n) were implanted into magnetized Fe and Gd backings. The excited nuclei thus experience the transient magnetic fields 2') while slowing down in the ferromagnet and subsequently the static magnetic hyperfine field ze) once the recoils have come to rest. Since the nuclear feeding times to the g.s.b. and superband members below the 14+ state'are long s) compared to the ion stopping time of about 1 ps, the transient fields act exclusively on the states above the yrast line . The associated precessions are inherited by the discrete states on and near the yrast line, which precess further under the influence of the static field. Since the static field precession is proportional to the nuclear lifetime, the relatively long mean lives of the 10+ and 12+ states at backbending in this nucleus (table 3) ensure high experimental sensitivity to their magnetic moments. The independent precession measurements in the two ferromagnetic hosts served as a precaution against effects associated with backing-induced y-radiation. The PAC technique was employed using four Ge(Li) counters (active volume ? 100 cm3) at f 55°, ± 125° to the beam direction, close to the maximum of the logarithmic slope of the stretched E2 angular distributions. The targets were magnetized in a transverse field of a single polepiece electromagnet, thè field direction being frequently reversed . The use of a single polepiece is not optimal with respect to beam-turning effects, but was required to enable the use of the antiooincidence device (see below) . Singles spectra were accumulated for applied field up and down . Peak intensities were extracted with narrow windows set on photopeaks, subtracting background estimated from appropriate nearby windows. Double ratios were evaluated in similar fashion to the anisotropy measurement (subsect. 2.1a) and averaged for the detector pairs. It was verified that the double-ratios associated with the background windows behave regularly with energy, so that the values derived for the net photopeaks were not affected by local fluctuations of the background precession. The cross ratios 2') were found to be consistent with unity, indicating that the counting system was free of systematic bias. The measured double ratios for both ferromagnetic hosts are presented in table 3, along with the spectroscopic quantities relevant to the analysis of the precessions. 3 .2. RECOIL INTO IRON

Isotopically enriched 1 zzSn layers, about 1 mg/cm2 thick, were rolled onto vacuumdeposited and annealed 1 .2 mg/cm2 thick iron foils. In the experiment, the targets were magnetized in a field of0.01 Twhich was found in magnetometer measurements to suffice for saturation . They were bombarded with 75 MeV 160 beams of about 2nA (particles) intensity.

l77

A . Zemel et al. / Magnetic moments TABLE 3 Spectroscopic data on ' 3 °Ce transitions for the analysis of precessions in Fe') and Gd e)

Level

Er (keV)

2* 4*

h Fe

Gd

409.1

100

100

33

639.s

89

89

s

sl

6+

814.4

48

39

44

lo+

908.3

19 .s

zz

l4+

724.6

I1

16

8+

12'

16 *

r(Ps)`)

948.0

464.3 817.7

17 11

s 1

g

22

1s.9

I1

2.2

1.7

Feeding components I(Fe) I(Gd) 2 9

2.s 8.s

T(ps)

48s000 °)

-2.0 (2)

0.79

0.7s

-s.2(2)

- l .s

4s

0.66

0.61

-1 .4(2)

-0 .4 (2)

a

l .oo

l .o0

2

1 .00

1.00 1 .00

20 2

48s000 4s

6

6

4

5

Gd

-s .7(3)

16 .s 3 2.s

Fe

0.7s

2.s 12.5 23 7

C,(Fe) C,(Gd)

DR-1 (~)

0.79

2 16 23 9

Scale factor

48s000

ls

`)

O.sB

1 .00 1 .00

O.ss

1 .00

-0.3(3)

1 .4(s>

0.6(6)

I .1(14)

0.6(14)

(1)

0.04(s0) 1 .7 (s)

0.9 (4)

3.8 (13) 1 .2 (11)

') For the (' 60, 4n) reaction at 7s McV [ref. a) and present work] . b) For the (' 60, 4n) reaction at 80 MeV (present work). `) Errors on level mean lives of ref. a) have been adopted. °) Contribution taken from measured prcoession of the 22 -. 0' 96s.2 keV line and applied to the 22 -. 2; transition (see subsect. 3.4). `) Contribution taken from measured precession of the s - -. 4; 112s .7 keV line (see subsect. 3.4).

Radiation from 16 0-induced reactions with the iron backing was responsible for some 70 ~ ofthe total singles y-counting rate. However, it waspossible to discriminate strongly against this radiation, since most of it is generated in reaction channels involving the emission of at least one light charged particle, e.g. s6Fe(160, p2n) or 56F~16O~ an), whereas only neutrons are evaporated in the reaction leading to 134 Ce. `'l To this end, the target was surrounded by a plastic scintillator assembly (see fig. 5) subtending a solid angle of about 85 ~ of 4n, with most of the remaining surface taken up by the entrance collimator, polepiece with target holder and beam stop . The interior surface of the scintillator was lined with lead and aluminium layers thick enough to mask it from elastically scattered beam projectiles. The NE 111 scintillator shell, 2 mm thick, was embedded at the bottom of a long vertical plastic light guide coupled to a photomultiplier. This arrangement ensured effective shielding of the photomultiplier from the magnetic fringe field. The spectrum from the scintillator exhibited a very intense low pulse-height region, due predominantly to y-rays, betas and neutrons, and a continuum of higher pulses, due to light charged nuclear reaction products (p, d, a). By operating the Ge(Li) detectors in fast anticoincidence with the scintillator, which was triggered just above the y-ray edge, it was possible to reject most of the prompt, iron-induced

17 8

A. Zeme! et a1. / Magnetic moments

Fig. 5 . Schematic vertical cross section of the scintillator assembly for discriminating against prompt ironinduced radiation.

radiation, but not activity lines. The peak-to-background ratios were improved (over singles counting) by typically a factor of2. By bombarding an iron foil separately at the same effective beam energy, it was verified that none of the contaminant lines overlapped the 134C e peaks of interest. Sections of the resulting anticoincidence spectra are displayed in fig. 6a . Since the intensity of annihilation radiation and other activity lines tended to build up considerably over some 24 hours of bombardment, five dif%rent targets were used over the total measuring period of about one week. 3.3 . RECOIL INTO GADOLINIUM

Measurements using Gd as a magnetic environment require both care iii target preparation and efficient cooling under bombardment to ensure proper magnetization z9) . The total radiation from Gd was considerably weaker than that generated by Fe, since the effective bombarding energy at the backing was barely above the

A . Zeme! et al. / Magnetic moments

x10°

179

xl0 a

30 15

25 20 m f z

ô 15 U

10

10 l'~I~ i I I I

I

I

5 m v o,

ô mI

I (b) I

I I I I

I

I I

W~~~~n~~~n~~~n ~J. .L !u_Lul ~L ' . .1 . . . .1 . . . .1 . . 350 400 460 500 900 1050 1250 1300 1450 1500 1550 CHANNEL NUMBER

Fig. 6. Sections of y-ray spectra showing transitions involved in the fit to the precession data from '6 0+'22 Sn : (a) With Fe backing at 75 MeV and anticoincidence condition and (b) With's 6Gd backing at 80 MeV. Backing-induced lines are also indicated.

Coulomb tamer. The resulting singles spectra (fig . 6b) were thus cleaner than the corresponding anticoincidence Fe spectra. Of all stable Gd isotopes, only's 6 Gd was found to give rise to a spectrum with no discrete y-rays at all t3aCe transition energies of interest . In preparing the target backings, isotopica.lly enriched tseGd203 was reduced to metal by heating it with thorium, and purified by two-fold vacuum distillation . The metal foil was then hotrolled to 3 mg/cm 2 thickness. By subsequently annealing the samples at 550°C in an argon atmosphere for a few hours, about 80 ~ of the saturation magnetization was achieved with an applied field of 0.03 T. After lightly rolling the Sn and Gd layers

180

A . Zerre! et ai. / Magnetic moments

together, a thin layer of natural Pb was evaporated on the Gd surface . This enabled the attachment of the target by light rolling to a thick Pb layer which ensured efficient heat conduction away from the beam spot . The multilayer target was pressed with indium into a copper block which was in good contact with the iron polepiece. The whole assembly was incorporated into a cryostat cooled to liquid nitrogen temperature . Over the total measuring time of four days, data were accumulated with applied fields of 0.05 and 0.1 T and the beam intensity was varied up to 4 nA (particles) to check against loss of magnetization due to beam heating. No significant trends in the precession data were observed . For recoil into Gd, the beam energy was increased to 80 MeV to reduce the yield of the competing izzSn(ie0, 3n) reaction . This implied slight differences in the relative intensities of the feeding lines compared to the spectroscopic information derived at 75 MeV (table 3). 3 .4 . PRECESSION DATA ANALYSIS

In the analysis of the precession data, the following procedure has been adopted (the exact formalism is presented in an appendix) : (i) The unperturbed anisotropies for all transitions in the g.s.b, and superband were taken to have a common value, since the loss of nuclear alignment observed for some transitions (table 1) is dominated by perturbations of the isomer . The value adopted, AZ = 0.28, is the average of experimental anisotropies for all transitions which have no delayed component. (ü) The g-factors of all g.s.b. and superband members (except for the 10+ and 12+ states at backhanding) and the feeding states have been assigned a common collective value
A . Zemel et al. / Magnetic moments

18 1

fields in both media and the g-factor of the 10+ state at backbending. Three different hypotheses concerning the magnetic moments have been tested [cf. assumption (ü)] (a) all g-factors have the same value
0

u

-40

U d 0.

Fig. 7. Scaled precessions of "`Ce levels plotted versus effective precession time (see text) on recoil in Fe and Gd . Note the different scales corresponding to the two ma~etic hosts. T'he curves represent results of best fits with the following three hypotheses : (a) all g-factors have the same value (gi = 0.35 (dashed line, g 2 = 46~(b) g(10+) _ -0.2 ; g(12*) _
182

A. Zemel et al. / Magnetic moments

from the assumed particle-dominated value at I = 10 back to the collective value with increasing spin. No attempt has been made to extend the search for a systematic trend in the magnetic moments to other states, because the short mean lives and complex feeding pattern imply low sensitivity to the corresponding g-factors. ' 34Ce has the spectroscopic property (see table 3) that all level mean lives and feeding times are shorter than 100 ps, with the exception of the 10+ isomer for which T = 485 ns. Consequently, the internal-field precessions are (to a good approximation) either small enough to be linearized, or so large as to generate an isotropic feeding component. As shown in the appendix, the precessions, when divided by a scaling factor CS (representing the attenuation due to feeding from the isomer), have a simple linear dependence on an effective precession time i~rr when all g-factors are equal [hypothesis (a)] . The quantities Cs and Tere are derived from the experimental intensities, mean lives and feeding times (see table 3). Since the static and transient fields at Ce nuclei in both Fe and Gd are antiparallel za), cancellation occurs in the precession at i~rr = -(~TF/g)~/gNH [eq. (A.12)], where 4i.,.F./g is the transient field precession angle per unit g and H is the static internal field. The experimental scaled precession angles ~d4i)/C, are displayed versus the effective precession time Terc in fig. 7 along with best fits for hypotheses (a), (b) and (c). It should be noted that the calculations were performed using the exact formalism (cf. appendix), and the results discussed below do not depend on the values of i~rr and Cs nor on the various assumption implied in their definition . As is evident from fig. 7, hypothesis (a) (with constant g, Xs = 46) cannot account for the experimental trends, whereas the others follow them more closely. In particular, the deviation in precession observed in both ferromagnetic media for the 10+ state relative to the corresponding value for the 12+ state is better reproduced . Both hypotheses (b) and (c) require negative values (-0.2 and -0.3 respectively) for g(10+) in order to describe this variation. The simple relationship between g(10+) and the difference in precessions of the 10+ and 12+ states is independent of spectroscopic uncertainties due to the absence of appreciable side-feeding into the 10+ state. The consistent observation of this difference in both Fe and Gd renders unlikely the possibility that it is due to some background-related contaminant. Judging by the x2 values, hypothesis (c) (with reduced g(12+), Xs = 29) yields a better fit than hypothesis (b) (with g(12+ ) _
A . Zemel et al . / Magnetic moments

18 3

The best XZ obtained substantially exceeds the statistical expectation value.lfiis is hardly surprising in view of the simplifying assumptions invoked in the fit. Furthermore, only the experimental errors on the double ratios were included, but not the uncertainties in the spectroscopic input information. For example, the precessions of the intense 409.1 and 639.5 keV transitions are very accurately determined in the measurement, but it is not possible to take into account in a precise manner the contributions of all the numerous weak lines feeding them. This situation implies higher uncertainty in the derived values of the dif%rent parameters and was taken into account in the final error assignment in the following way : The (1 standard deviation) error on each parameter was determined as the variation required to increase Xz by an increment dx2 = dxôXm, lF [where F is the numberofdegrees of freedom and dXô is the conventional statistical estimate sz )]. Fig. 8 shows Xz versus g(10+) curves obtained by varying g(10*) while : (i) leaving all other parameters unconstrained (solid line), and (ü) keeping all the other parameters fixed at their best-fit values (dashed line). The adopted error which was derived from curve (i) includes correlations with all other parameters and is about three times larger than that which would be obtained from curve (ü). We obtain the following best-fit values and total errors of:

Fig. 8. X' versus g(10*) curves from the fitting using hypothesis (c) (sce text and fig . 7) . The curves were obtained by varying g(10*) while : (i) leaving all other parameters unconstrained (solid line) and (ü) keeping all other parameters fixed at theù best-fit values (dashed line) . Also shown are the increments in Xs and g(10 * ) corresponding to I standard deviation . The adopted error, derived from curve (I), includes correlations with the other parameters .

18 4

A . Zemel et al. / Magnetic moments

for the 10+ state at backbending and H(Ce in Fe) _ -35(7) T, H(Ce in Gd) _ -24(5) T for the static internal fields . The reduction in the in-beam static field value in Gd compared to a radioactivity measurement on an annealed sample sa) at the same temperature has been observed for other impurities in the same host a9) . Because of strong correlations with g(12+ ~ the beam-turning effect (which enters as a constant additive term to the measured precessions) and the large errors on the measured precessions of the higher discrete states, the transient fields were poorly determined . The best fit values (not corrected for beam turning) : ~TF/g(Fe) = 7(13) mrad and ~.rF./g (Gd) = 17(9) mrad are rather small. This may be related to the low average velocity at which the recoils enter the magnetized foils ss), since the Sn target thickness constitutes a large fraction of their range. However, the main conclusions regarding g(10 + ) are not very sensitive to these values . 4. Discussion In the present work the magnetic moment of a high-spin state at backbending was shown, for the first time, to deviate significantly from the collective value. The result g(10 + ) _ -0.30(25) demonstrates that valence h neutrons play a dominant role a°) in the structure of the states near backben~ing in 134Ce . It is therefore unlikely that backbending in this nucleus is associated with a shape transition of the type proposed in ref. s4) . An indication for reduction in g-factors of discrete collective high-spin states has also been observed recently ss) for ieoDy and ~,o, tia Yb . A recent application of the Hartree-Fock-Bogoljubov cranking model to some rare earth nuclei 2°~ ae) attributes this reduction to rotation-alignment of i,~ neutrons. A considerable amount of new spectroscopic information on 134Ce was accumulated in this work. In particular, the superband was extended up to I~ = 18+ and the quasi-gamma-band and a negative-parity sequence were established. The collective properties of these bands suggest that the IBM might provide a good description and indeed, the proton-neutron version of this model has been rather successful in describing collective positive parity states up to I~ = 8+ in Xe, Ba and Ce isotopes lo ' l t) . In particular for ' 3°Ce, the excitation energies of the g.s.b. and q.y.b. members are reproduced reasonably well. Moreover, the strong retardation of the E2 interband transitions relative to the corresponding in-band transitions also agrees with the IBM predictions, as can be seen from table 2. The gradual decrease of B(E2) with increasing spin in the g.s.b. s) can be explained by the IBM as a consequence of the boson cutoff. Furthermore, backbending in the Ce isotopes has been incorporated into the IBM framework s' " 3e) by coupling two h,~ quasiparticles to the A-2 boson core . No existing .model calculation is capable of reproducing the most striking feature of this nucleus, namely, the existence of two neutron-dominated 10 + states . Only the

A. Zemel et al . / Magnetic moments

18 5

isomeric state at 3208 .5 keV can be unequivocally identified with the (h~)" neutron configuration. One possible explanation considers the mixing of the two 10+ states of the collective bands of 134Ce with those formed by coupling two h~ neutrons to the lowest-spin members of the g.s.b. and q.y.b. of the 132C e core. Since the lowest neutron-dominated 10+ states resulting from this mixing have collective components in common, there should be a transition between them with collective E2 strength . Such a transition is not observed experimentally, rendering this hypothesis rather unlikely . Alternative explanations might involve coexistence of weakly deformed and spherical nuclear shapes, or formation of a four-particle 10+ state, lowered in energy by a degree of collectivity . Both these hypotheses can account for the huge difference in B(E2) for transitions deexciting the two 10+ states . A related problem is the location of the 10+ continuations of the g.s.b. and q.y.b. These states could not be definitely identified in this work, although a weak 1005 keV feed into the 8 + g.s.b. member has been observed . This transition energy agrees with the g.s.b. systematics. It appears that the higher 10+ states are very weakly populated in the reaction employed . The authors would like to express their thanks to Professor I . Talmi for many illuminating discussions and sustained interest throughout this project.The assistance of Dr. Y. Niv with some of the measurements is gratefully acknowledged . We are particularly indebted to Eng. B. Feldman for invaluable help with the mechanical setups and to Mr. M. Sidi for designing the electronic control systems. The expertise of Mrs. A. Meens in making the intricate targets was a major contribution to the success of the internal-field precession measurements . We would also like to thank the accelerator personnel of the Rehovot Pelletron and the Strasbourg MP Tandem for their cooperation. Four of us (A.G ., M.B.G ., G.J.K . and K.-H.S.) are indebted to the Minerva Foundation for generous support. Appendix The effect of a classical transverse magnetic field on the angular distribution of decay y-rays from an excited nuclear level is more conveniently described when the unperturbed angular distribution is written as

rather than as the usual Legendre polynomial expansion. For a single level, the field gives rise to a simple rotation of the angular distribution : where co = -g~cNHlh is the corresponding Iranmor frequency. This is also valid for measurements involving ferromagnetic hosts because both the transient and the static internal fields can be treated as classical quantities .

186

A. Zemel et al. / Maynetic moments

In a time-integal measurement on a single level with mean life T one has to average over all nuclear decay times 1 °° WP(B, ao) _ - ~ exp(-t/T)WP(B, tklt = ~ B~,G,~cos(mB-a~), where

r

o

a,~

= arctg(mcor),

(A .3)

(A.4)

For high-spin state population following (HI, xn) reactions two limiting cases are relevant (a) Very small precessions, urc ~ 1 . In this case a,~ x m~ and the attenuation coefficients G~, approach unity so that the net effect is a small precession through an angle
in analogy to the anisotropy measurements using the logarithmic slope technique described in subsect . 2.1a. This situation is realized for all levels with mean lives in the ps range. (b) Very large precessions, an ~ 1 . In this limit the attenuation coeffcients become very small and the angular distribution approaches isotropy . This limit applies to isomers such as the 3208.5 keV level. The generalization of eqs. (A .3)-(A.5) to the perturbed angular distribution of a transition following a cascade of levels with dif%rent mean lives and g-factors is straightforward. The resulting expressions for a single cascade are

where a~, and G~, are the precession angles and attenuation coefficients corresponding to the individual levels i along the cascade. It follows that when all levels obey the small precession limit, the resulting effect is the sum of the time-integral contributions of all levels along the cascade. If, however, an isomer is present in the cascade, the corresponding attenuation coefficient wipes out the angular distribution and no of%ct can be observed for all levels below it. When several parallel cascades merge at a certain level, the contributions of the individual cascades add, weighted by the relative feeding intensities. By way ofillustrating the relationship between the dif%rent parameters, consider a case in which the g-factors of all levels have a common value
A . Zemel et al. / Magnetic moments

18 7

that the mean lives of the levels are either in the ps range or very long ( ~ 100 ns), so that one or the other of the limiting cases considered above is realized for every level. Under these conditions the precession due to any single prompt cascade can be described as a combination of static and transient terms (A.9) where (~TF/g) is the transient precession per unit g and Tjj are the mean lives of the different levels i along the jth cascade. The total precession associated with a level superposes the contributions of all the prompt feeds into that level and that of the level itself : where C~ are the relative intensities of the feeds . Introducing an effective precession time : Teff

where Cs

= ~

= Cs ~, ClTi!' i, j

JCJ, eq. (A.10) becomes :

(A .12)

The factor C, represents the attenuation due to the presence of isomer feeding. The scaled precession
(1975) 13

5) J. Gizon, A . Gizon and D . J. Horch, Nucl . Phys . A252 (1975) 509 6) C . Flaum, D . Cline, A . W. Sunyar, O . C . Kistner, Y. K. Lee and J . S 291, and refs. therein 7) N. Yoshikawa, Nud . Phys . A243 (1975) 143

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Zemel et al. / Magnetic moments

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