Gamma-ray spectroscopy of superdeformed states in the nucleus 152 Dy

J. Phys. G: Nucl. Part. Phys. 17 (1991) 481-510. Printed in the UK

Gamma-ray spectroscopy of superdeformed states in the nucleus ='Dy

M A Bentleyt, A Alderson$, G C Balls, H W Cranmer-Gordonto, P Fallont, B Fantll, P D Forsytht, B Herskindn, D Howet, C A Kalfas*, A R Mokhtart, J D Morrisonto, A H Nelson?, B M Nyak6#, K SchifferO', J F Sharpey-SchaferS, J Simpsont, G Slettenq and P J Twin$ t SERC Daresbury Laboratory, Daresbury, Warrington WA4 4AD, Cheshire, UK t Oliver Lodge Laboratory, University of Liverpool, Liverpool L69 3BX, UK §Chalk River Nuclear Laboratories, Chalk River, Ontario, Canada KOJ IJO I/ University of Helsinki, Siltavuorenpenger 20D, SF-00170 Helsinki, Finland fl Niels Bohr Institute, Ris0, DK-4000 Roskilde, Denmark * Nuclear Research Centre Demokritos, Aghia Paraskevi Attika, Greece #Institute of Nuclear Research of the Hungarian Academy of Sciences, H-4001, Debrecen, Pf51 Hungary

Received 14 September 1990, in final form 13 November 1990

Absmd. A y-ray spectraswpic study of the high spin states of the nucleus '5'Dy has been performed using the reaction '0RPd(dsCa,4n)'"Dy at a bombarding energy of 205 MeV. Gamma rays were detected using the TESSA) multi-detector array. A set of discrete-line States forming a rotational band has been observed in the data and has been shown to extend up to a spin of around 6Ofi and an excitation energy of about 30MeV. The y-ray energy data is consistent with dynamic moment of inertia P of (85 f 3)h2 MeV-', indicating a large quadrupole deformation. A measurement of the collectivity of the band has been made using the Doppler Shift attenuation method, with the data for the lower spin states yielding a qlladrupole moment of e,,= (J813)e b. This is in excellent agreement with the calculated value of 17.6 e b for a superdeformed shape with a major-to-minor axis ratio of 2 : l . The data for the dynamic moment of inertia are consistent with the calculated high-j configuration for the superdeformed band, and the variation of 9''' with frequency is reproduced by both cranked Nilssan and Woods-Saxon models. The intensity pattern for the band indicates that the superdeformed states are populated with an anomalously high intensity at spins close to the fission limit, suggesting that there is some enhanced population mechanism. The hand is observed to de-excite suddenly at around I = 26h, although the linking transitions between these States and the yrast States have not been Observed. Evidence is presented for the existence of non-yrast superdeformed bands in the p ray continuum. The intensity of these bands is measured and compared with the results of Monte Carlo simulations.

NUCLEAR REACnONS "Pd("Ca,4n) E ("Ca) = 205 MeV; measured E,, I,, y-y coincidence and angular correlations. '''Dy; deduced levels, decays; assigned E,, J and n. Superdeformed band; quadrupole moment. *licmscopic structure, comparison with Nilssan and Woods-Saxon models. Feeding mechanisms. Comparison with results of Monte Carlo simulations.

Present address: ICI, Runwrn, Cheshire, UK. Present address: Australian National University, Canberra, ACT2601. Australia.

0954-3899/91/040481+ 30 $03.50 0 191 IOP Publishing Ltd 481

482 M A Bentley et a1

1. Introduction

The idea that nuclei could adopt highly deformed prolate shapes at low tempera- t ~ e s {yras! or near-yras!) origina!ec! with the discn~ery of the deferzed fission isomers in the actinide region (Polikanov et al l962, Specht et a1 1972). These effects were explained (Strutinski 1967) in terms of a low ‘shell energy’ for prolate shapes with a major-to-minor axis ratio of approximately 2 : 1 ; an effect seen clearly in the simplest of nuclear models, the deformed harmonic oscillator. In this heavy mass region the combination of the low Coulomb energy and !ow she!! energy for ‘superdeformed‘ shape allows states associated with a 2 : l axis ratio to be energetically favoured at very low spin and excitation energy. For lighter nuclei (e.g. around A = 150), such shell effects are again expected to occur for large deforma- tions (e.g. Strutinski 1967). However, a large fission barrier is known to exist in this mass region, making highly deformed states unfavoured relative to lower deformed states.

Subsequent calculations (e.g. Neergard and Paskevich 1975, Neergard et ul 1976, Anderson et a1 1976, Bengtsson et al 1975) show that superdeformed shapes in nuclei around A = 150 could become yrast at high spins, with the total energy of the nucleus lowered relative to low-deformation shapes by the collective- rotation, Indeed, several theoretical calculations indicated (Ragnarsson et a1 1980, Aberg er a1 1981, Schutz et a1 1982) that IsZDy is a particularly favourable case in which to see such effects. It was expected, therefore, that prolate rotational bands exhibiting high moments of inertia should be observable in the lsZDy y-ray continuum, corresponding to superdeformed structures at high spins.

The first experimental indication of a 2 : 1 shape at high spin in 15*Dy came with the discovery of ‘ridges’ (Nyak6 et al 1984) in an Ey-Ey correlation matrix, which were interpreted as coincidences between in-band decays of high moment-of-inertia bands (see Andersen et a1 1979, Herskind 1980). The ridge separation energy indicated that the average moment of inertia was around 85h2 MeV-’ (roughly equivalent to a 2 : 1 axis ratio) and it was assumed that the ridges corresponded to many non-yrast rotational bands at high spins with similar in-band moments of inertia. A measurement of the collectivity of the ‘ridge’ decays (Twin er a1 1985) showed that an upper limit of 100 fs could be assigned to the lifetimes of the states, indicating a highly collective (i.e. deformed) structure.

An experiment (described in detail here) to investigate these structures, revealed a discrete line rotational band of 19 y rays (Twin er al 1986) exhibiting a moment of inertia similar to that obtained in the correlation data of Nyak6 ef al (1984). This hand is shown to extend up to a spin of around 60h, and an excitation energy of around 30 MeV. The remarkably constant increase in y-ray energy of 47 keV with increasing spin corresponds to a dynamic moment of inertia 3(’) of (85f 3)h2 MeV-’, implying a quadrupole deformation of eZ = 0.6 (Bz = 0.65). An experiment to measure the collectivity of this superdeformed band (reported in Bentley et a1 1987) was subsequently performed in order to accurately determine the deformation of the nucleus. The data yield a quadrupole moment of Q,) = (18 f 3 ) e b, which agrees well with the value expected for a 2 : 1 axis ratio. This should be compared with a typical value of Qo = 5 e b for a normai deformed proiate rotor (e.g. Oshima et a1 1986). These data therefore confirm that discrete transitions between states of a superdeformed nucleus of high spins have indeed been observed. The detailed results of both these experiments are given in this work.

Gamma-ray spectroscopy of the nucleus I5'Dy 483

A rotational band with similar characteristics had been previously observed in I3*Ce (Nolan et a1 1985b), and a further experiment to measure the collectivity of the nucleus (Kirwan et a1 1987) showed that the band was associated with a highly deformed shape (Qo - 9 e b). The discovery of similar bands very close to A = 130 soon followed (see Nolan and Twin 1988), implying that these structures may only be found in very localized mass regions. The search for other examples in the A = 150 region culminated in the discovery (Haas et a1 1988) of a discrete line superdeformed band in '"Gd showing remarkably similar properties to the lszDy band. Other examples have now been found in this region, for example in lasGd (Deleplanque et a1 1988), isoGd and isiTb (Fallon et a1 1989), ''Tb (Deleplanque 1989), '"Dy (Rathke et a1 1988) and Is3Dy (Waddington 1989). Indeed, calculations (Chasman 1989) and recent experimental results (Moore et a1 1989) show that nuclei in other mass regions, such as those around A = 190, exhibit such phenomena also.

The experimental study of the superdeformed phase in nuclei has significantly extended our knowledge of how a nucleus behaves near the yrast line, and has enabled detailed spectroscopic studies to be made on a nucleus at very high spin and excitation energy. The results of these experiments have therefore raised many intriguing questions regarding the existence of discrete superdeformed states. For example, the superdeformed bands in the mass 150 region are all populated with an anomalously high intensity around 55h, with no significant population of these states below 45-50h. What is the population mechanism behind this enhanced feeding for a superdeformed shape, and what causes the sudden depopulation out of the bands around 30h7 Another question of importance is the underlying microscopic structure for the superdeformed bands, and how effects such as static pairing correlations affect the nucleus at such high spins. These questions and many others have been the subject of much experimental and theoretical effort since the discovery of the superdeformed band in 152Dy, and in this paper we will present the experimental uara wnicn nave leu tu me urvt-iupuieni UL rnaiiy UL tne C U I L ~ I I ~ Liieuicucdi iura>.

Some of the data on IszDy, described in detail in this work, have been published previously in letters (e.g. Twin et nl 1 9 8 C T h e discovery of the superdeformed band, and Bentley er a1 1987-A measurement of the quadrupole moment) and in some conference proceedings. A review of work on superdeformed nuclei, including some of the data presented here, has been published in review articles (Nolan and 1 w,,, l700, a,,'lryGy-aLrlaLr, 'U," O L " 1 p u L 1 "VU,. 1111a yL.pcL p c " c L " " a I"., a,,"

detailed account of the various experiments, the data analysis, and the interpretation of the results. Occasionally there are small differences in derived values due to improved analysis procedures.

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2. Experimental techniques

Several experiments to study the high spin states of 152Dy have been performed at the SERC Daresbury Laboratory, using the tandem Van de Graaff accelerator at the Nuclear Structure Facility. The two experiments described here were performed on the y-ray spectrometer TESSA~ and the details of the experiments are given below.

2.1. Thin target TESSAS experiment In the first experiment, a beam of 48Ca at a bombarding energy of 205 MeV was employed to excite the highest spin states of the nucleus ISZDy with the reaction

-

484 M A Bentley et 41

108Pd(48Ca,4n)'52Dy. The target consisted of two 500 pg cm-2 '"Pd self-supporting foils isotopically enriched to -95%. The reaction and beam energy were chosen such that the angular momentum of the compound system was high enough to populate the higher spin states, with a classical angular momentum limit of 86h.

The "'Dy excited nuclei recoiled into a vacuum and the y decays were detected using the TESSA~ multi-detector array (shown schematically in figure l), consisting of 12 escape suppressed spectrometers (ESS) (Nolan et 4l 1985a, Sharpey-Schafer and Simpson 1988) surrounding a 50-element bismuth germanate (BGO) 'crystal ball' calorimeter (Twin et 41 1983).

The de-exciting y rays were recorded in the BGO ball in the form of the total energy deposited in the BGO elements (sum-energy) and also the number of elements recording an event within a given time interval (fold). The fold (a function of y-ray multiplicity) and sum-energy information can be used to select the exit channel from the compound system. In this reaction the major channels were the 3n, 4n and 5n channels, leading to lS3Dy, lS2Dy and lslDy respectively.

The ESSS used consisted of a hyper-pure n-type germanium detector with an intrinsic energy resolution of 2.0-2.5 keV for the 1.33 MeV y ray from "CO, and a photo-peak efficiency of about 25% with respect to a 76 mm X 76 mm NaI(TI) detector at 25 cm. Each Ge detector is surrounded by a BGo/NaI(TI) anti-Compton shield (Nolan et 41 1985a). The signal from the BGO shield, when measured in coincidence with the germanium signal from the same ESS, is used to veto the event in order to reduce the number of Compton scattered events recorded, and hence reduce the background. The resulting peak-to-total ratio for a "CO source is increased to about 55% (compared with 20% for an unsuppressed Ge detector). The E S S ~ are at angles 35", YO" and 145" to the beam direction with four detectors at each angle, positioned 23 cm from the target.

A gold catcher foil was placed 5cm downstream from the target so that the

U @re 1. The 7ESSA3 multidetector array. The apparatus consists of 12 escape- suppressed spectrometers (Nolan N ai 198%). surrounding a 50-element BOO calorimeter (Twin et al 1983) in order to measure the total y-ray energy and y-ray multiplicity.

Gamma-ray spectroscopy of the nucleus '52Dy

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decays from below the 10ns and 6011s isomers at J " = 21- and 17+ (see e.g. Haas et a1 1979) respectively in 15*Dy and the 18 ns isomer at 9 in Is1Dy would take place whilst the recoiling nucleus was outside the focus of the 12 germanium detectors but still inside the BGO ball. A timing spectrum between a prompt Bco-Ge-Ge coincidence and any subsequent delayed y ray recorded by the BGO ball was generated using a time-to-amplitude converter (TAC). If no decays were measured within 200ns of the prompt event, then the TAC was stopped automatically. The resulting spectrum is shown in figure 2. The shaded part of the spectrum corresponds to cascades which have passed through an isomer, and the associated germanium events measured are from y rays preceding that isomer. The effect of a software 'gate' on this part of the TAC spectrum selects with a 25% efficiency the y rays preceding the 60ns 17+ isomer in "'Dy ('isomer events'). A gate on the sharp peak reduces by 25% the contribution from above that isomer and selects all the events which bypass any isomer ('prompt events').

About 120 million prompt Ge-Ge coincidences were recorded onto magnetic tape along with data for the sum energy and fold. The selection of a 'clean' exit channel from the compound system is vital, and for this purpose a two-dimensional plot of sum energy against fold was created in order to show a separation between the 3n, 4n and 5n channels. A two-dimensional (ZD) software 'window' on such a plot allows one to preferentially select the desired reaction channel. This technique reduced the contribution from the 5n channel ('"Dy) by 42% and the 3n channel (15'Dy) by 35% with very little reduction in 15'Dy. Figures 3(a) and 3(b) show the total y-ray spectrum and a spectrum selected by the ZD 'window' on the sum energy and fold plot. The isomer selection described above also aids channel selection as there are no known isomers in I5'Dy and only a short-lived isomer (-18ns) in 15'Dy. The technique of isomer selection increases the selection of ISZDy relative to '"Dy by about 60%. A spectrum gated by both the ZD window and the isomer selection is shown in figure 3(c), and shows a strong population of 15*Dy states with a reduction in the contribution from 15'Dy. The spectrum in figure 3(c) appears

486 M A Bentley et al

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0 0 200 400 600 800 1000 1200 1400 1600

Energy I keV1

Figure 3. (a) The total y-ray spectrum for the thin target m S A 3 experiment showing all the reaction channels. The major contributions from lS'Dy (182 keV, 9 - y; 377 keV,

- T) are shown by the arrows. (b) Spectrum as in (a) but with a sum-energylfold condition to preferentially select '"Dy. The spectrum shows a substantial reduction of y rays resulting from '%y. (c) As in (b) but with the condition that an isomeric event was rewrded in the BOO ball. The clear reduction in the background comes from the elimination of the 3n channel ("'Dy) where there are no known isomers.

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much 'cleaner', resulting mainly from the elimination of the 3n channel. A timing spectrum was also recorded between the BGO ball prompt signal and the first germanium event measured. This was used to further reduce the background events by identifying and rejecting (by time of flight discrimination) some of the delayed neutron-induced events in the Ge detectors.

The data were sorted offline into four 4096 x 4096 channel matrices with the data preselected using both sum energy/fold and timing conditions. Two matrices of 'isomer' events and two of 'prompt' events were created, with each matrix selected by either a high-fold or a low-fold condition. A 'high-fold' window was used to select high spin events, and corresponds to fold 3 22 (with fold = 22 being the centre of the I5'Dy fold distribution). The high-fold 'isomer' matrix, used in much of the following analysis, contains only events preceding the isomer in "'Dy, with no major contribution from other reaction channels.

Gamma-ray spectroscopy of the nucleus 15'Dy 487

2.2. Thick target T E S S A ~ experiment

A Doppler shift attenuation experiment has been performed with the same reaction and using a similar experimental set-up to the thin target experiment. The target in this case consisted of 1.3 mg cm-2 of "'Pd on a 15 mg cm-' gold foil. The recoiling lszDy nuclei slowed up in the target and gold backing before finally stopping completely in the gold. The subsequent y rays from states with short effective lifetimes (-5Wfs or less) should therefore show some Doppler shift to higher or lower energies for y rays measured at forward or backward angles respectively to _L. L--- .I:---.:-- an--. -c .L- -A:-- 1 5 2 n . ~ J...~~. ... I I - __.. mc ucaiii UILCLLIUII. LVIUSL UL LUC 1uaju1 u y uccays are bnuwn io nave longer lifetimes of the order of a few picoseconds (Haas et a1 1979), and should decay when the nucleus has come to rest in the backing, with these y rays showing no Doppler shift.

The beam of 48Ca at 205 MeV was hunched to 2 ns wide pulses every 150 ns so that the timing information recorded (for the purpose of isomer selection) was less ".."" --tihla tn r~nrln- .-ni-ciAa-oao .,,hieh ---+Ah..+- nn. .o:Aa.mhl.r +- +La k"-L J"JCGp'"".C L" L O L I Y " L . L L".I.CL"CI.CCD " l l L C l l C U L L L l L " U L C C"LL"'YC."".J t" L l l G U"&&-

ground. The isomer TAC (see section 2.1) was started with a BGo-Ge-Ge signal in coincidence with the beam pulse, and stopped by any subsequent decay (measured as three individual EGO elements firing) whilst the beam was 'off. Over 200 million Ge-Ge coincidence events were recorded onto tape with the sum energy and fold data as well as additional timing information. The data were sorted offline into six y-y coincidexe matrices, corresponding to coincidences between y r y s recorded a! the three different detector angles in TESSA~. The events were preselected using a high-fold condition to reduce the "'Dy contribution, with the data also gated by the isomer condition described in the previous section. The gains of the detectors were matched offline such that the y rays exhibiting no Doppler shift were aligned in the same channel for the different angles. For states with short lifetimes, the y-ray enprgies should therefore he shifted and states with lifetimes of less than 1Wfs should show almost a full Doppler shift.

3. Results and interpretation

3.1. Thin target data

The structure of the yrast line in IS*Dy has been well studied and coexistence between two distinct structures has been seen to occur up to high spins. The spectrum of lsZDy is dominated by an oblate (single-particle) structure, see figure 4, which forms the yrast line up to spins S 36fi (see Khoo et a1 1978, Merdinger et al 1979, Howe 1986). In addition, a rotational cascade of y rays corresponding to a

(Styczen et a1 1983) was shown to coexist with the single particle structure up to spin 40h (see the left-hand side of figure 4). This band is suggested by Nyak6 et a1 (1986) to be associated with a four quasi-particle prolate configuration and above spin -20fi the band exhibits a classic rotational behaviour. In this work, we have added three more transitions to this band: the 1341 keV, 1399 keV and 1454 keV

transitions respectively. A further sequence of nineteen y rays exhibiting characteristics of a rotational

Z(I + 1) sequence was discovered in the data from the thin target TEsSA3 experiment

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F i w 4. The '52Dy decay scheme showing the coexistence of three distinct StNCtUTeS. On the left-hand side, a prolate rotational band is built on the ground-state band (Nyak6 er 011986) with a low deformation (&- 0.3, y - 25"). In the Centre of the level scheme, an oblate single particle structure is shown (&-0.1. y = MT) up to spins 336h (Howe 1986). On the right-hand side is the superdeformed band (& -0.6, y = 0") extending up to a spin of 60h. (The values of Bz and yare taken from Dudek 1987.) The link between this band and the known scheme is not observed.

Gamma-ray spectroscopy of the nucleus "'Dy 489

described in section 2.1. The spectrum, showing a band extending from E,,= 602keV to 1449keV is plotted in figure 5(a) and comes from a sum of y-ray coincidence spectra ('gates') taken from the high-fold 'isomer'-gated matrix described in section 2.1. An individual gate on each of the band members shows all the observed y rays in coincidence demonstrating that there is a simple rotational-like sequence of states. Examples of this (after a background subtraction) are shown in figures 6(a) and 6(b) where the spectra of y rays in coincidence with the third and fourth members of the band, the 693 keV and 737 keV transitions, are plotted. This

decay paths in I5'Dy. A detailed analysis of the relative intensities of the superdeformed and oblate yrast transitions shows that relative to the total '"Dy channel, this band is populated with an intensity of 1.4 + 0.1%.

To determine that the observed band is indeed associated with a rotational structure, it is first of all necessary to establish the quadrupole nature of the y-ray

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mgUre 5. (a) A spectrum of the superdeformed band measured in coincidence with the 693, 737, 829, 876, 923 and 1161 keV y rays. The spins shown are taken from the -".....n-.*" A0".-.x-.4 :" "*^.in" 1 1 Re .I i" *Le e..-...-.- -"-L..A ... i*L "1"..." ",LIY,,.C,,," YLaL.,"C" ,,. _._I. &..* , .", '... ..... "y'**..Y... - ....

the oblate yrast transitions between 17* and 25-. The spectrum comes from the high-fold 'isomer' matrix (see text). (b) A similar sum of coincidence gates as (a) but taken from the high-fold 'prompt' matrix (see text). The two y rays marked are the 2+-0+ and 6+-4+ transitions in '''Dy.


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Figure 6. (a) A spectrum measured in coincidence with the 693 keV transition in ihe superdeformed band. All the other members of the band are observed in coincidence, indicating a simple rotational behaviour. (b) A spectrum measured in coincidence with the 737 keV y ray.

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Figure 7. The angular correlation ratios, 1(35")/1(90") (see text) for the members of the superdeformed band (squares). The data are compared with values obtained for known stretched quadrupole transitions (stars) and stretched dipole transitions (circles) in '5'DY.

Gamma-ray spectroscopy of the nucleus I5'Dy 491

transitions. The two detector angles in TESSA~ (35" (= 145") and 90") allow triple angular correlation measurements (Harris et a[ 1965) to be made for the transitions in the band. Spectra are created which are gated by stretched E2 transitions observed in the 35" detectors, and the intensities of the y rays in the resulting spectra are measured for the different angles. The ratio of the intensities of the in-band transitions at 35" to the intensity at 90" is measured and plotted (squares) in figure 7 (the ratio is multiplied by a factor of $ to account for the different numbers of detectors at 35" and 90"). The ratios for three known stretched quadrupole transitions (stars) and stretched dipole transitions (circles) are also plotted. It can be seen from figure I that the angular correlation ratios for the in-band transitions up to 1161 keV are all between 1.6 and 2.0 (consistent with the known stretched quadrupole transitions) and are roughly twice the values measured for the stretched dipole y rays. All the in-band y rays have therefore been assigned as stretched E2.

The measured y-ray energies and relative intensities for the rotational band (calculated after correction for the efficiency of the germanium detectors) are listed in table 1. It can be seen that the difference in y-ray energy as the nucleus de-excites

Table 1. The measured y-ray energies and relative intensities of the transitions in the superdeformed band (the results come from averaging data from the two TESSA3

experiments). The assigned spins are shown, and the relative intensity is quoted relative to the average intensity of the transitions between 693 keV and 1017 keV. In the lower part of the table, the oblate yrast y rays seen in coincidence with the band are listed, along with their relative intensities measured from the spectrum in figure 5(a).

Assigned spin of emitting state ( f i ) y-ray energy (keV) Relative intensity

24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60

602.3 f 0.3 647.2 + 0.2 693.2 f 0.2 737.5 * 0.2 783.5 f 0.3 829.2 f0.2 876.1 -t 0.2 923.1 f 0 . 2 970.0 + 0.2

1017.0 f 0.2 1064.8 f 0.2 1112.7f0.3 l l60.8f0.3 1208.7 f 0.3 1256.6 f 0.3 1304.7 f 0.3 1353.0f0.3 1401.7 f 0 . 4 1449.4 f 0.6

0.17f0.03 0.51 f0 .07 1.01 fO.10 0.93 f 0.11 0.96 f0.11 1.01 f0 .08 1.08 f O . l l 1.04 fO.10 1.00fO.11 0.98f0.12 0.98 f 0.08 0.9tlf0.10 0.87 f 0.06 0.89f0.12 0.75f0.10 0.62f0.07 0.49 f 0.08 0.30 f 0.07 0.16f0.06

18 254 0.24 f 0.04 19 525 0.20 f 0.07 20 770 0.47 f 0.05 21 262 0.05 f 0.03 22 625 0.13f0.03 23 991 0.49f0.12 25 541 0.08 f 0.05


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Spin (fi)

Figure 8. The dynamic (3"') and kinematic @(IJ) moments of inertia for the superdeformed band. 3"' shows a gradual decrease with increasing spin, with a -7% variation in 3'2' over the range of the band. 3"' is calculated from the spin assignments shown in figure 5 and in table 1.

through the band is remarkably constant at around AE, = 47 keV, and it is clear from the y-ray energies and from the number of transitions that a very high spin has been reached. The dynamic moment of inertia X(') can be calculated for each transition from X")=4/AEy. The values for S(') plotted in figure 8 are found to vary from 89h2 MeV-' to 83h' MeV-' with increasing spin, with an average of (85 i 3)hZMeV-'. This compares well with the moment of inertia for the superdeformed continuum ridge observed by Nyak6 er a1 (1984) in their y-y correlation data. This result for 3'" is in excellent agreement with the predicted value for a superdeformed prolate ellipsoid with a quadrupole deformation of & = 0.65 (E' = 0.6).

The intensities of the y-ray transitions are plotted in figure 9 relative to the average intensity of the six transitions from 693 to 1017 keV and as a function of y-ray energy. It is clear that the band is populated at very high spin and excitation

Figure 9. The intensity (after efficiency correc- ,tion) of the individual y-ray transitions in the superdeformed band. The values are shown relative to the average intensity of the y rays between 693 and 1017 keV.

Gamma-ray spectroscopy of the nucleur '''Dy 493

energy, with the feeding taking place over only five to six transitions. The intensity then stays 'in-band' with little or no side-feeding until a sudden de-excitation at a rotational frequency (E,/2) of hw - 0.3 MeV. However, the total intensity of the band, whilst remaining essentially constant below E,, = 1.2MeV, represents only a very small fraction of the total 15*Dy decay intensity.

In order to attempt to determine the spins of the superdeformed states it is necessary to establish where the band feeds in to the known decay scheme. Figure 5(a) shows that several of the major yrast oblate transitions from above the 60 ns isomer are seen strongly in coincidence with the superdeformed y rays. All the y rays shown in the decay scheme between the 17+ isomer and the 25- state are clearly seen, indicating that the major decay intensity is above the 17+ level and passes through the 60 ns 17+ isomer in "'Dy. Figure 5(b) shows a spectrum of the superdeformed band after a sum of gates taken from the 'prompt' matrix (i.e. no isomer decay was recorded). The 614 keV (2+-0+) and the 683 keV (6+-4+) transitions are both seen in coincidence with the band, indicating that there is a decay path depopulating the superdeformed structure bypassing the 60 ns isomer. However, this represents only -10% of the total superdeformed decays, and most of the intensity passes through the 60 ns isomer. From the relative intensities of the oblate yrast transitions in coincidence with the superdeformed band (listed in table I), it is clear that there is direct feeding of the states between 17+ and 25Y. Accurate measurements of the individual transition intensities is made more complicated by the existence of the 10 ns isomer at spin 21-. Only about 15% of the intensity of the 262 keV transition will be observed due to the recoils passing out of the focus of the Ge detectors. However, the intensity of the 525 keV (19--18+) transition is significantly enhanced, and thus the 19- state is clearly fed directly. The state at 23- is also fed directly, but the 328 keV transition will not be seen, as the major decay intensity from that state decays through the 991 keV transition. The 625 keV and 770 keV y rays have been placed in the decay scheme (Haas 1988, Aldenon er a1 1989) and are assigned as the 22+ to 20+ and 20+ to 18+ transitions. These y rays are seen strongly in coincidence with the superdeformed band indicating that the 22+ and 20+ states are also fed directly. Studies of the oblate yrast states, into which the superdeformed band feeds, have subsequently been made (e.g. Zuber et a1 1989, Styczen et a1 1987) and a more detailed scheme of these states can be found in Zuber et a1 (1989). A feeding pattern can now be established as follows: (7 f 4)% to the 25- level, (37f lo)% to the 23- level, (12 f 3)% to the 22+ level, (30 f4)% to the 20+ level and (14 f 6)% to the 19- level. The average spin at which the intensity from the superdeformed band decays into the yrast states can now be estimated as 21.6h. The 21- state does not appear to be fed directly, although the existence of the isomer at this point results in a large error on the measurement of the intensity of the 262keV transition (21--19-). However, any inaccuracy here should not greatly affect the value of the average entry spin.

In order to make a reasonable estimate of the spins of the superdeformed states, it is assumed that the average spin at which the band de-excites (taken here to be the point at which the intensity of the band falls to 50% of its full intensity) must be greater than the average energy spin into the single particle yrast levels (estimated above as 21.6h). If even spins are assumed for the superdeformed band, then an examination of the intensity pattern of figure 9 reveals that the lowest average spin at which the band de-excites must be 22.3h (this assumes a 22+-20+ assignment for the 602 keV y ray). If the entry spin into the oblate states is taken to be 21.6h, then


the average angular momenlum lost in the decays between the superdeformed and normal deformed states would be realistically either 0.7h, 2.71 or 4.7h.

The superdeformed band is initially populated on average when the y-ray energy is around 1.35 !vta'v', auggcsiing that the superdeformed band is yrast at about this point. The intensity pattern shown in figure 9 also demonstrates that below Ey = 1.35 MeV, the nucleus loses 30 units of spin before reaching the de-excitation point. As we know that the oblate single particle states are populated on average at 22.61, this suggests that the superdeformed states are yrast well above spin 50h. In

states are plotted against spin such that the superdeformed states become yrast above spin 50h and above Ey = 1.35 MeV. This clearly shows that the bottom of the superdeformed band must lie 3-4 MeV above the yrast line and it therefore seems most likely that the superdeformed band decays into the normal deformed yrast states over several transitions. The average spin loss in these transitions is therefore taken !e be 2.7k If positi-e pyi ty is assumed fer the sqxrdefermed !eve!. (see calculations of Ragnarsson and Aberg 1986) then the 602 keV y ray is now assigned to be the 24+ to 22+ transition. It can be seen from figure 5(a) that the top y ray of 1449 keV must be the 60+ to 58+ transition (the assigned spins for all the y rays are listed in table 1). These spin assignments are clearly not unambiguous, and we estimate that with the even spin assumption, the uncertainty in these spin assignments is 2h. However, it is unlikely that the spins are less than those quoted, as this would mean that almost no angular momentum is removed by the transitions (spanning 3-4 MeV in excitation energy) between the bottom of the superdeformed band and the single particles states.

In figure 11 the angular momentum of the superdeformed band is plotted along with the low deformation band as a function of rotational frequency. It is interesting to note that with our present spin assignments both the low deformation and superdeformed bands at high spins show a remarkable linearity with frequency, and an extrapolation to zero rotational frequency indicates that at very high spins all the angular momentum is generated by collective rotation. This is the behaviour expected of a 'classical' rigid rotor (e.g. Price et al 1983, Swiatecki 1987).

With the angular momentum assignments, the kinematic moment of inertia, S('),

f _.._ ~ In +La auritn+i-n n-ami-r -f +ha ~...-~~rlnf---~-l I -... -laf----+:-- ..-A ,.l.t--- rrgu.= I" U,= GAL.lLm.LI"II C1LCL&'"D "L L L l C "up1"C'"""cu, L"W UCl"llll'lLl"ll *,,U "UIdtL:

Figure 10. The superdeformed, low deformation and oblate single particle states in '52Dy shown in the excitation energylspin plane. The low deformation band is extrapolated to higher spins, and the decay from the superdeformed band into the oblate states is shown schematically.

Gamma-ray spectroscopy of the nucleus "'Dy

~

495

60 -

50 -

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 8

Rotational frequency - h o (MeV)

Figure 11. The spin of two rotational structures (low deformation band and superdeformed band) shown as a function of frequency. With the present spin assignments, the data for both bands at high spins shows that all the increase in angular momentum comes from classical rotation (see e.g. Price et nl 1983).

can be calculated from the spins and y-ray energies, and is shown in figure 8 as a function of spin. The kinematic moment shows an extremely smooth variation with angular momentum, increasing gradually to a constant value at high spins. Above spin -44h, the kinematic and dynamic moments of inertia are constant and approximately equal around 83h2 MeV-' (this is once again characteristic of rigid rotation). The exact determination of the kinematic moment, however, requires an unambiguous assignment of the angular momentum, and when comparing the respective values of 3(') and 3('), the uncertainty in the spin assignment must be taken into account.

It is necessary to attempt to establish how much of the ridge seen in the y-y correlation matrix (NyakC e: 01 1954) is cailsed by the sliperdeformed band and how much, if any, is due to the existence of non-yrast superdeformed bands in the y-ray quasicontinuum.

As the superdeformed structures form only a small fraction of the "'Dy decay intensity, the ridges in the y-y matrix are not easily resolvable from the background continuum and a measurement of the ridge intensity is therefore difficult. It is also necessary to ensure good channel selection as it would not be possible to distinguish between the continuum contributions from the different reaction channels. To this end, the matrix gated by both the isomer condition and a high-fold condition was used in the analysis to reject the contributions from other reaction channels. Slices were taken across the matrix in a plane perpendicular to the E,,, = E,,> diagonal in the range E, = 600-1500 keV. The widths of the slices were chosen to be 94 keV wide, so as to always include two discrete line coincidences from the superdeformed band. The integrated intensity of the first ridge (corresponding to coincidences where E,, - .Ey2 = 47 keV (= AE,)) was measured for each successive slice.

In lsZDy there are several coincidences between strong oblate yrast transitions where AE, - 47 keV or -94 keV, and these will appear in the first and second ridges respectively. As far as possible, the measurements of ridge intensities were


2 . 0

1 . 5

0.5 ,. Z o 0 , \

l b 6 2 . 5 : - + lil Uo = l .OMeV .. I i i l Uo = 1 .3MeV .- ? 2.0 - - liiil U0 = 1. lMeV + _ _ IivI Ua = 2.0MeV

I v l Uo = 3.0MeV ' 1 . 5

-

-

0 . 5

600 800 IOW imo i c c ~ i 6 w

Energy I KeV I Figure 12. (a) m e intensity of the 'first ridge' (AE7 -47 keVj in the high-fold isomer matrix (squares) plotted relative to the intensity of the known discrete line transitions (circles). The data marked by open squares come from the first ridge intensity measured in 94 keV wide slices across the matrix, and the closed square represents a 2x2 keV wide slice. The data show that, at high spins, only part of the ridge intensity is accounted for by the discrete line transitions. (bj Predicted intensity oi the hrst ridge (curvesj irom the Monte Carlo simulation described in section 4.4. The experimental data without the error bars are shown. The five curves correspond to simulations with values of U. (see text) between 1.0 and 3.0MeV.

corrected for these, although above E., - 1.2 MeV there were no such contaminants. The contribution to the ridges from the discrete-line superdeformed y rays in the range 600-1500 keV is known from the measured intensities shown in figure 9. The total intensity of the first ridge (AE., = 47 keV) is plotted in figure 12(a) relative to the discrete line intensity. Below E., = 1-1.1 MeV, the intensity of the first ridge was impossible to measure due to the existence of discrete-line yrast contaminants, but the data indicate that below this point the discrete lines account for all the ridge inte~sitv i' Ahove E? = L1 MeV, however, the intensity of the first ridge becomes much greater than the known discrete-line contribution. This additional intensity from E., = 1100-1500 keV represents in-band coincidences between y rays in non-yrast superdeformed bands of a similar moment of inertia. The data are reproduced in figure 12(b) along with the results of Monte Carlo decay simulations which will be described in section 4.4. Significant superdeformed ridge intensity has been observed in 152Dy using other reactions (see Macchiavelli et a1 1987 and references therein).

3.2. The DSAM experiment The measured moment of inertia, described in section 3.1, corresponds to a quadrupole deformation parameter of p2=0.65. However, it is known that the

,

Gamma-ray spectroscopy of the nucleus '52Dy 491

moment of inertia can he influenced by other factors apart from the deformation, such as particle alignment coupled to a strong interaction (e.g. Simpson et al 1986, Riley el al 1988). It is therefore possible to have a large and constant moment of inertia, caused by microscopic effects, whilst the overall deformation remains constant. A measurement of the collectivity of the hand is therefore vital to confirm the superdeformed shape. The previous DSAM experiment to establish the collectivity of the ridge structure (Twin et al 1985) could only establish an upper limit of 100 fs on the higher spin decays and could not assign a measure of the collectivity directly. An accurate determination of the deformation, however, requires lifetime measurements of the discrete states. For this purpose a Doppler shift attenuation experiment, described in section 2.2, has been performed to measure the lifetimes and hence the quadrupole moment, Q,,, of the superdeformed hand.

The spectra shown in figure 13 result from a summation of gates of known y rays in the lower spin part of the superdeformed hand, and show the hand recorded at

~

~

101

28 38 48 5.3 1 1 1 1 1

28 I 1

38

800 1000

1 I

I 145'

Energy fkeVI

Figure U. Spectra of the superdeformed band from the DSAM experiment following a sum of y-ray coincidence gates. The spectrum in (a) corresponds to y rays recorded at 35" to the beam direction and (b) y rays recorded at 145" to the beam direction.

498 M A'BentIey et a1

Table 2. The measured Doppler shifts from the DSAM experiment (averaged over the forward and backward angles) for each y-ray transition in the superdeformed band. The measured apparent lifetimes for the decay (including the lifetimes of all the states above) are shown, along with the intrinsic lifetime of each state calculated assuming e.,= 18- b.

Average Doppler shift Spin ( h ) (keV)

28 12.1 i 0.4 30 13.4 i 0.4 32 15.3 -t 0.3 34 16.8 + 0.3 36 18.5 i 0.3 38 19.8 i 0.3 40 21.3 i 0 . 3 42 22.8 i 0.3 44 23.8 i 0.3 46 25.4 i 0.4 48 26.1 + 0.4 50 28.1 i 0.5 52 29.3 i 0.5 54 30.6 + 0.6 56 30.8 i 0.7 58 33.0 i 0.7 60 34.7 -t 0.8

~~

Apparent T (fs)

211i20 43.4 135 i 17 31.6 112*11 23.2 87 i 10 17.6 65 f 9 13.4 54 f 8 10.3 44 i 8 8.0 3 2 i 7 6.3 3 2 i 7 5.0 22 i 8 4.0 29 & 8 3.3 13 f 8 2.6 l l f 7 2.2

22 f 13 1.5 1.3

<10 1.0

Intrinsic z (fs)

7':o 1.8

5-5 +to

35" and 145" to the beam directiont. It is clear from the data in figure 13 that there is a large Doppler shift to higher y-ray energies in the 35" spectrum and to lower energies in the 145" spectrum. The measured y-ray energy shifts are listed in table 2, and the fractional Doppler shift A E J E , = (v/c cos e) is calculated and plotted in the upper part of figure 14 as a function of the spin of the emitting state.

The initial I5*Dy recoil velocity is calculated to vary from (u/c cos e) =2.43% to 2.33% from the front to the back of the target, so the average unattenuated recoil velocity is taken to be 2.38% (consistent with experimental measurements with a thin target). It is clear from the data that the highest spin y rays are fully Doppler shifted, with the shift decreasing gradually with decreasing spin. At the lowest spins, th-Doppler shift is still at -72% of the expected full shift value.

To determine the lifetimes of the superdeformed states, it is first of all necessary to calculate the stopping process in the target and backing for the recoiling 15'Dy nuclei. In these calculations, the stopping power of the palladium target is particularly important as many of the superdeformed transitions will take place whilst the nucleus is still recoiling in the target. The dominant process for the attenuation of the recoiling nuclei in this reaction is electronic stopping, which was calculated using the semi-empirical stopping powers of Northcliffe and Schilling (1970) after normalization t o the alpha-stopping powers of Ziegler and Chu (1974). The small contribution from the nuclear stopping was also taken into account using

t It should be noted that some of the superdeformed y rays have the same energy as some of the major yrast transitions, causing difficulties in the analysis of the thin target TESSA3 data. In the DSAM

experiment, these yrast transitions are shifted to regions of low-intensity background, enabling a more accurate evaluation of the y-ray energies and intensities. I n this work. all the data for y-ray intensities and energies, and hence the moments of inertia, come from combining data from the two TESSA3

experiments.

Gamma-ray spectroscopy of the nucleus '-52Dy

~

499

I

M 40 M 60 spin 1h1

Fire 14. The fraction of full Doppler shift (F = "/U") and thc fractional Doppler shift (AE,,/E, = v / c cos R) for the y-ray energies measured from the spectra in figure 13. The data came from averaging the Doppler shift for both angles. The full Doppler shift, calculated at v l c cos R = 2.38%. is shown by the broken line, and the uncertainty on this value is shown by the hatched area. For the upper part of the figure, calculated values of F with spin are plotted far values of Q, = 5 . 10, 15, 18.2, 20 and 25 e b. In the lower part, curves far Q, = 18 e b are shown assuming feeding times into the top of the band of 10 fs and 20 fs, as well as rhe calculation assuming cascade ieeding only.

the method of Lindhard et a1 (1963) with nuclear scattering corrections (Blaugrund 1966).

The output of these calculations yields the fraction of the full shift, F ( t ) = u/uo (where uo is the initial recoil velocity), as a function of time (or effective lifetime), z. The apparent lifetimes for the superdeformed transitions can therefore be measured directly and these are listed in table 2. The apparent lifetimes quoted have contributions both from the intrinsic lifetime of the state and also from the cumulative feeding times from all the preceding states. The intrinsic lifetime (and hence quadrupolc moment) for cach individual state cannot be measured accurately as the statistics are too poor and the fractional Doppler shift changes only very slightly from state to state. It is necessary to assume a constant deformation and fit the whole hand with a single quadrupole moment, Q,,, from which the intrinsic lifetimes can be calculated. It is also necessary to make some assumption regarding the feeding time into the top of the hand as this will play a major role in the calculation of the quadrupole moment. The intensity distribution of the band (see

500 M A Benfley et a1

figure 9) shows that the band is -50% fed by spin 56h and -80% fed by spin 50h. The changes in Doppler shift from state to state below spin 50h are therefore due only to the intrinsic lifetimes of each successive transition. Above spin 50h, however, there is clearly some side-feeding. but the data in tab!? 2 sh~w :ha: :he effective lifetimes of these states (including side-feeding) are SI0 fs. It was assumed in the first place, therefore, that the effects of side-feeding at the highest spins were negligible (i.e. the total feeding time of a level was assumed to be comparable with the effective lifetime of the state decaying above).

Using the above assumptions, the intrinsic lifetime for each state is calculated for a given Q, and the predicted effective fractional Doppler shift, F (after correction for the feeding from the above states) is plotted in the upper part of figure 14 for values of Q, of 5, 10, 15, 20 and 25 e b.

It is clear from the shape of the data curve in figure 14 that the deformation remains approximately constant at lower spins, and a fit to the bottom nine transitions yields a quadrupole moment of 18.2e b. The major contribution to the error in the quadrupole moment comes from the uncertainties in the stopping processes, estimated at f15%. The measurement therefore gives a Q, of (18f 3) e b, corresponding to an enhanced in-band transition strength, B(E2) of 2390 W U. The intrinsic lifetimes of the superdeformed states, based on a quadrupole moment of 18 e b are quoted in table 2.

The effects of including side-feeding corrections in the analysis are shown in the lower part of figure 14, where the three calculated F(r ) curves assume a constant Qo of 18 e b. The upper curve makes the same assumption as in the above analysis (i.e. effects of side-feeding are neglected), whereas the lower two curves assume a constant side-feeding time of 10 fs and 20 fs respectively for all the states between 50h and 60h. The amount of side-feeding is deduced from the experimental intensities of figure 9, with the assumption that below 50h, the feeding time to each state comes only from the cumulative feeding from all the states above. This analysis shows, as can be seen from figure 14, that the data are consistent with a side-feeding time of less than 10fs, and it is also clear that the effect of including this in the calculations has little effect on the fit to the data at lower spins.

It is clear from the data in figure 14 that below spins 45-50h the value for the quadrupole moment must stay constant at around 18e b. Above these spins, although the fit to the data becomes more ambiguous, the quadrupole moment cannot realistically be less than 15 e b, corresponding to a maximum variation in the deformation, p2(eZ), of -20%. All the data are therefore consistent with the superdeformed band having a constant quadrupole moment of (18 f 3) e b. The

18 e h, in excellent agreement with the experimental data. Because of the fast electronic stopping time, a (calculated to be -500 fs for both

the target and backing), only states with a very short effective lifetime will show a measurable centroid shift for the y-ray energy. All the most intense y rays in 15*Dy should appear as stopped transitions. Thus a subtraction of a total y-ray projection at forward angles to the beam direction from a similar projection at backward angles should show the transitions associated with the superdeformed band with all other y rays cancelling out. Figure 15 shows the 35" projection subtracted from the 145" projection after normalization on the 221 keV (27--25-) y ray. Although there are no coincidence requirements, the resulting spectrum clearly shows the superdeformed band. We can also see from figure 15 that there are no other highly deformed rotational bands of similar intensity as these should also appear.

ca!cG;a:eb va!i;e fG; a si;per&.fc:E-ed st;uct.;;e (P,ag"arsscx and Aberg 1986)

Gamma-ray spectroscopy of the nucleus 15'Dy 501

-1500 600 700 800 900 1000 1100 1200 1300 1400 1500

Energy LkeVl

Figure 15. A spectrum of all y rays measured at 35" in the DSAM experiment subtracted from a simiiar spectrum at 145" after a suitable normalization. The arrows mark the superdeformed y rays, and the spins of the initial level are shown.

One of the most interesting aspects of the spectrum shown in figure 13 is the apparent lack of lineshape effects for the superdeformed y-ray transitions, resulting in a very narrow spectral linewidth. This feature has been shown to be characteristic (Bacelar et al 1986) of cascade feeding down a rotational band with negligible sidefeeding. Figure 16 shows the measured linewidths (open squares) as a function of y-ray energy, compared with those of the stopped transitions (closed squares). Using a simple decay model (Rowley 1988) the recoil velocity distribution was calculated for the decays from each state in order to estimate the contribution to the linewidths from lifetime effects, assuming cascade feeding only.

that the recoils are attenuated only by electronic stopping of the form ~ ( t ) = u0 e-"" where U is the recoil velocity, after time t. Using the measured lifetimes, the RMS

As ;he p,fsc;x,es of Bie kiiWwii io be extieiiie;y. splofL, ii is assllmrd

Energy (keV) 16. The measured widths (RVHM) of the y rays in the DSAM experiment for the

superdeformed band (open squares) and for some 'stopped' transitions (closed squares). The calculated RMS contribution to the lineshape from cumulative lifetime effects is also shown (circles).


deviation in the velocity distribution, and hence the spread in pray energy, is calculated for each transition, and plotted (open circles) in figure 16. It can be seen from this that lifetime effects will not make a measurable contribution to the linewidths, as these are calculated to be much smaller t h a n the combined effect =f Doppler broadening and the experimental resolution of the germanium detectors (typically 2.5 keV at 1 MeV). The effects of the mixing of superdeformed and normal deformed states on the feeding processes and hence on the lineshapes has been discussed by Schiffer et al (1988).

4. Discussion

4.1. Properties of the superdeformed band

The results from sections 3.1 and 3.2 clearly show that decays between discrete superdeformed states have been observed up to 60h and an excitation energy of at least 30MeV. The discovery reveals that there is a rich coexistence of three distinctly different shapes over the spin range 22-42h, as can be seen from the decay scheme in figure 4. The oblate single particle structure forms the yrast line up to high spin, with the low deformation structure lying a few MeV above in excitation energy. The superdeformed band itself extends over a wide range of angular momentum and lies high in energy above the low deformation structure at low spins, becoming closer to yrast at higher spins. This shape coexistence is reproduced by some theoretical calculations: for example, the cranked Woods-Saxon Strutinsky calculation of Dudek (1987) shows coexistence at I = 42h of an oblate single particle structure (p2 = 0.12, y = 60"), a low deformation prolate triaxial structure (pZ = 0.3, y = 25") and a superdeformed structure (b2 = 0.6, y = 0"). The spin ranges over which these shapes are caicuiated to be favourabie agree W+i with the experimentai data. Calculations using a Nilsson model (Ragnarsson and Aberg 1986) also predict a similar coexistence of the three shapes.

It is clear from the data (see, for example, figure 15) that there is only one discrete superdeformed band in "'Dy of any significant intensity, implying that one configuration is lowered in energy relative to the other superdeformed states. The observation of a singie superdeformed band is strong confirmation of caicuiaied single particle structures using both a cranked Nilsson model (Aberg et a[ 1988) and a cranked Woods-Saxon model (Nazarewicz el al 1989). Both these theoretical calculations predict large shell gaps for a 2: 1 axis ratio for both N = 86 and Z = 66 over the entire frequency range of the observed superdeformed band. A second superdeformed band in '"Dy would have a single-particle structure that would

therefore lie significantly higher in energy. The single particle energy gap in the calculations of Nazarewicz er a1 (1989) is 1-2 MeV for both protons and neutrons.

It was not possible to establish the link between the bottom of the superdeformed band and the single particle oblate states into which they decay. It was impossible therefore to determine unambiguously the spin and excitation energy of IIIG ~upGr"cLur,l,c" SLZllG>,.

dynamic moment of inertia 3(2) (= 4h/AE,), the relative intensity pattern of the band and the absolute intensity of the population of the superdeformed states relative to the lower deformation structures. The moment of inertia 3@) yields the

invoive an exc i~d~ ion Bcroyy this gdp (for eiihei proions or iieuiiOnSj and miis;

. . .I. 2 - E _I . I TI... - -I . . -~ -^.-.-" ...~""..-"Lla ,...^"+:tin" m I P l l l C urrry ~ ~ 1 U ' l ~ ~ U U ~ IIIcL1D"Ia"Lc 'I"'.LLLLLCU ".U :he

Gamma-ray spectroscopy of the nucleus '"Dy

~

503

0.14 . , . , 0 I O 20 30 40 50 60

Spin

Figure 17. The intensity of the superdeformed band with spin (squares) plotted relative to the total intensity of the channel ("*Dy). The relative intensities of the lower deformed rotational bands in "Er (Simpson ct al 1987) and '"Yb (Bacelar el 01 1985) are shown by closed circles and open circles respectively.

most nuclear structure information as it is sensitive to both the shape and the details of the single particle structure (including microscopic effects such as band crossings). The dynamic moment of inertia shown in figure 8 is seen to have very little variation with frequency (-7%), showing a gradual and smooth decrease with increasing frequency. The information that this yields with regard to the microscopic structure is described in the next section.

The relative intensity pattern for the superdeformed band (see figure 9) also shows some surprising features. The band appears to be populated only at very high spins (reaching half the full intensity at -55fi), implying that below spin 50h, the superdeformed structure rapidly becomes non-yrast. The fact that the intensity then remains constant down to 28h (fiw = 0.35 MeV) suggests that although the superdeformed band is no longer energetically favourable, there is a significant potential barrier preventing the decay to a more favoured low deformation structure (see, for example, Ragnarsson er al 1980). The sudden and unexpected depopulation around hw = 0.3 MeV suggests a sudden change in the underlying s t ructurethis is discussed in section 4.5.

The absolute intensity of the superdeformed band (measured at -1.4% for I = 30h-50h) is perhaps the most unexpected feature of the band. Figure 17 shows the intensity of the superdeformed band (relative to the total population of "'Dy) along with the high spin 'normal-deformed yrast bands of IMEr (Simpson et al 1987) and "Yb (Bacelar et al 1985). It can be seen from figure 17 that the population mechanism of the superdeformed band is markedly different, and indeed the intensity of the band at the highest spins (50h-60h) exceeds by an order of magnitude the intensity expected for a low deformation structure. Since the discovery of the superdeformed band in "'Dy, there has been much experimental and theoretical interest in the population mechanisms of superdeformed states (e.g. Macchiavelli et a1 1987, Herskind and Schiffer 1987).


4.2. Microscopic structure

In order to gain information about the microscopic structure of the band, it is necessary to study the dynamic moment of inertia, %’). As the moment of inertia i g

dependent on the angular momentum alignment (for a particular orbital v, S!? = di,/dw, where i, is the alignment), it is sensitive to the particular orbital configuration involved. Recent calculations (e.g. Ragnarsson and Aberg 1986, Aberg et a1 1988, Nazarewicz et a1 1989) have consistently shown that the configuration for the superdeformed band should involve the occupation of high-j intruder o r b i t a l s in particular, orbitals from shells which would not be occupied for spherical or low-deformation states. These orbitals appear near the Fermi surface for a superdeformed shape and as they are the lowest energy orbitals in that shell, they typically have a large angular momentum alignment on the rotational axis. It is these orbits therefore that contribute most strongly to the dynamic moment of inertia.

In the case of “‘Dy, this ‘intruder’ configuration has been calculated by both Nilsson (Aberg et a1 1988, Ragnarsson and Aberg 1986) and Woods-Saxon models (Nazarewicz et a1 1989) to have four protons in the lowest orbits of the i,3n shell, and two neutrons in the J,,, shell ( ~ r ( i , ~ , ) ~ v ( j ~ ~ ~ ) ’ ) . These intruder orbitals originate from the N = 6 (protons) and the N = 7 (neutrons) shells, and the configuration is more usually written as ~ 6 ~ ~ 7 ’ . Once the configuration has been established it is possible to calculate the moment of inertia for each orbital (from the differential of the alignment i, with respect to rotational frequency), and sum the contribution to 3(’) for all the proton and neutron orbitals. These calculations have been performed using a cranked Nilsson model (see Bengtsson et al 1988, .&berg et a1 1988, Bengtsson 1988), and some results are shown in figure 18. The experimental 3(’) is plotted (squares) along with the cranked Nilsson model calculations for a fixed deformation, E* = 0.58 (open circles) and for calculations where the deformation is vaned self-consistently (closed circles). Figure 18 shows that the agreement between

Rotational frequency (MeV)

Figure 18. The dynamic moment of inertia for the superdeformed band. The experimental S@) is shown by the squares and the cranking calculations at a wnstant deformation of E%= 0.58 shown by the open circles (Bengtssnn 19%). The closed circles show similar calculations where the deformation is allowed to vary self-consistently.

I Gamma-ray spectroscopy of the nucleus "'Dy 505

both the calculated 3(') and the experimental data is good, and the calculations with the variable deformation reproduce well the gradual decrease in 3(') with frequency.

The calculations show that the change of 3(2) with respect to frequency is critically dependent on the number of h i g h 4 intruder orbitals occupied (see Aberg et a1 1988). In the case of neutrons, the two N = 7 orbitals both have a decreasing, hut positive contribution to the moment of inertia with frequency. For the protons, the first and third N = 6 orbits have an %') showing little variation with frequency. The second orbit in N = 6 , however, has a positive and rapidly decreasing contribution to %'), and the fourth orbit has a negative and rapidly increasing contribution. In 152Dy, therefore, with four N = 6 orbits occupied, the total proton contribution to the moment of inertia shows little variation with frequency, and the slight decrease in the 3(2) comes mostly from the N = 7 neutrons. The virtually constant 3(2) is therefore particular to 152Dy, and a much greater variation with frequency is expected for the neighbours of I5'Dy with different proton configurations. Indeed in "'Gd and '"Tb (n62 and n63 respectively) the experimental 3(') for the superdeformed bands shows a much sharper decrease with frequency (Fallon et a1 1989).

The above calculations have not included static pairing effects, which are generally thought to be unimportant at such high spins. Recent calculations using a cranked Woods-Saxon model and including a self-consistent calculation of the pairing strength (Nazarewicz et a1 1989) have been performed, and also show good agreement with the data. In the work of Nazarewicz et a1 it was suggested that the pairing strength was weak in "'Dy due to the large 2 = 66 and N = 86 shell gaps at bz = 0.62.

4.3. Population mechanisms of the superdeformed states

The anomalously high population intensity for the discrete superdeformed band at high spins (50h-60fI) compared with low deformation bands is demonstrated in figure 17. The fact that the superdeformed decays channel into a single discrete hand (the superdeformed yrast states) so close to the fission limit (generally calculated to lie between 65fI and 70h) implies that the mechanisms by which the nucleus approaches the yrast line are enhanced for a superdeformed shape. Indeed, the transition probability for these 'cooling' decays (presumably statistical E l decays) has to be sufficiently enhanced to compete with the highly collective E2 transitions along superdeformed bands above the yrast line.

In order to explain these effects, it has been proposed (Herskind et a1 1987) that the El transition probability for a superdeformed shape is enhanced by two effects. The first effect is associated with the giant dipole resonance strength function (GDR) which for a prolate shape will have two components corresponding to neutron- proton vibrations along the two principal axes with one component lowered significantly in energy relative Lo the other. For the 2: 1 axis ratio the lower energy component is calculated (see Aberg 1987) to lie at about 8 MeV and significantly alters the shape of the GDR strength function. As a result the E l strength is enhanced several times. The second effect is associated with theolower level density for superdeformed states relative to normal deformed states (Aberg 1987). These calculations showed that the intensity of the superdeformed band at high spins could be reproduced when these effects are taken into account. It was also demonstrated by Herskind et a1 (1987) that there should be a relatively large number of high


energy y rays associated with the population of superdeformed states, although firm experimental evidence to support this has not yet been reported.

4.4. The superdeformed continuum

The measurement of the intensity of the first ‘ridge’ in the y-y correlation data (see section 3 and figure 12(a)) showed that, above E, = 1100keV, there are coincidences observed between y-ray transitions along bands in the superdeformed continuum, indicating that below this point these hands decay into the superdeformed discrete band, or into the normal deformed structures. The latter effect is consistent with the idea that as the spin decreases, the normal deformation level density increases rapidly, making decays to these states statistically favourable.

In order to investigate further the population mechanisms of the superdeformed band and the effect on the superdeformed continuum, a statistical decay simulation has been performed using a Monte Carlo code (described in detail in Herskind and Schiffer 1987, Schiffer et a1 1988). The code simulates the competition between ‘statistical’ E l decays and ‘rotational’ E2 decays in both the superdeformed and normal deformed minima. Tunnelling through the potential barrier between the two structures is taken into account, and the effects described earlier which enhance the E l strength have also been included in the calculations. For full details of the parameters used, see Herskind and Schiffer (1987). A y-y correlation matrix was simulated, and the intensity of the first ‘ridge’ was measured relative to the intensity of the discrete band. The results are plotted in figure 12(h), and the five curves plotted correspond to different values of U , a parameter describing the energy above the yrast line at which rotational damping begins to take place (see Lauritzen ef a1 1986).

The data in figure 12 show that there is a marked similarity between the shape of the experimental ridge intensity with spin and the computer simulation, although the absolute ridge intensity at high spins clearly depends of the magnitude of U,,. The increase in intensity with U,, is expected due to the fact that at an excitation energy helow Uo, the E2 decays take place along single rotational bands with a well defined moment of inertia, and coincidences between these transitions will contribute to the ridge. Above Uo, mixing between the bands occurs, and a spread in the effective dynamic moment of inertia is observed.

A comparison between the simulation and the experimental data in figure 12(a) suggests that a simulation with a value of U,, of around 1.5MeV would closely resemble the experimental ridge intensity although the small ridge intensity observed in the simulation between Ey = 800 and 1000 keV is not seen experimen- tally. In the calculations, the loss in intensity in the continuum ridge is mainly caused by the growing level density of the competing normal deformed states. The point at which this occurs is critically dependent on the relative positions of the normal-deformed and super-deformed yrast lines. It is also dependent on the height of the potential barrier between the two structures (taken from Ragnarsson et a1 1980).

4.5. De-excitation from the superdeformed band

The intensity pattern shown in figure 9 shows that a sudden depopulation of the superdeformed band takes place over two transitions between spins 28fi and 24h.

Gamma-ray spectroscopy of the nucleus lS2Dy 507

This rapid decay out of the superdeformed minimum into the normal deformation structures cannot he due simply to a statistical competition between the E 2 in-hand transitions and the 'cooling' transitions to the yrast line, as this would beexpected to take place over many levels. Indeed calculations (Ragnarsson and Aberg 1986) predict a gradual depopulation of the superdeformed hand over a wide spin range helow 30h. They point out that this is clearly at variance with the experimental data, suggesting that there are some other underlying processes involved.

It has been suggested (Herskind et a1 1987) that an increase in static pairing takes

of low-lying high-j particles. It is proposed that this increase in the pairing interaction causes the sudden depopulation out of the superdeformed hand into the normal deformed structures by increasing the mixing between the two sets of states. The calculations of Herskind et a1 (1987) have indeed shown that when an increase in pairing at hw = 0.3 MeV is assumed, the intensity pattern at low spins can he reproduced extremely well.

If the sudden decay out of the band is due to these effects, then a measurement of the frequency of de-excitation of other superdeformed hands can give important information regarding the underlying structure. For example, recent results on ""Gd and "'Tb (Fallon et a1 1989, Nazarewicz et a1 1989) have shown that the higher frequency of de-excitation in these hands could he a measure of a stronger pairing i-te:actic?n in !!IC SecQnd minim??m.

piace ai the point of ;e-exciiation, possibiy associaie~ with the deaiignriieiit of a pair

5. Summary

The discovery of the superdeformed band in I5'Dy has for the first time enabled a

30 MeV, and since the initial discovery, other examples in the mass 150 region have been discovered. Many aspects of the superdeformed band in '"Dy have been investigated, revealing some remarkable features.

(i) The band is populated at -6Ofi with an intensity of around 0.3%. This is at least an order of magnitude greater than the intensity expected for a normal deformed rotor. This strong population of the yrast states so close to the fission limit is seen as evidence for enhanced transition strengths for the statistical 'cooling' y rays at high spins.

(ii) The population of the superdeformed states occurs at very high spins, with no significant side-feeding of the superdeformed hand below spins 45fi-50h. This is consistent with the predictions that the superdeformed band forms the yrast-line at spins 9 5 3 1 . A rapid de-excitation out of the band takes place at --I = 26h, and this is possibly due to- the onset of pairing in the superdeformed phase. The decays out of the hand are not observed and are assumed to be 'statistical' in nature.

(iii) The dynamic moment of inertia, 3'", is virtually constant with respect to rotational frequency at a value of (85 f 3)hZ MeV-'. The calculated 'intruder' configuration of the hand is ~ r ( i , ~ / ~ ) ~ v ( j ~ ~ / ~ ) ' , and cranking calculations for this high-j configuration reproduce well the slightly downward trend of the moment of inertia. Neighbouring nuclei, such as ""Gd and 'S'Th, are observed to have rapidly decreasing moments of inertia, in agreement with similar calculations for the different high-j configurations. The kinematic moment of inertia, %'), is shown to he constant and approximately equal to X(') at high spins. This behaviour is characteristic of a good, or 'rigid', rotor.

spec.trosmpk stfidy Qf a nucleus at spins up to hnh and an excitation energy up to

508 M A Bentley el a1

(iv) Both the measured quadrupole moment of (18f3)e h and the measured transition probability of -2400 times the single particle value establish the collectivity of the hand and confirm that it is indeed associated with a superdeformed qhape:. The ra!cu!ated vi!=e of the qu~dmp~!c momciit hi a 2 ; i axis ratio is 18 e h which, following the calculations of Bengtsson er al(1988) is also consistent with a n(i,3n)4v(J15n)2 configuration. The data indicate that the superdeformed band is fed rapidly at high spins, with feeding times of only a few femtoseconds.

Acknowledgments

This work has been supported by the United Kingdom Science and Engineering Research Council (SERC) from whom five of us were at the time of the experiments in receipt of post-graduate studentships (MAB, HWCG, PF, ARM and JDM). D Howe acknowledges the receipt of an SERC post-doctoral fellowship. The authors wish to thank those involved in the design, development and maintenance of the apparatus, namely P J Nolan, A J Kirwan, T Burns, G Platt and C Brookes.

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Gamma-ray spectroscopy of superdeformed states in the nucleus 152 Dy

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