Ridge lifetimes in 167,168Yb

Volume 219, number 1

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9 March 1989

RIDGE LIFETIMES IN 167'168yb K. S C H I F F E R , G.B. H A G E M A N N , B. H E R S K I N D The Niels Bohr lnsitute, Riso, DK-4000 Roskilde, Denmark

K. THEINE, W. SCHMITZ, H. H O B E L lnstitut fiir Strahlen- und Kernphysik, Universitiit Bonn, D-5300 Bonn, Fed. Rep. Germany

R. CHAPMAN, D. CLARKE, F. KHAZAIE, J.C. LISLE and J.N. MO Schuster Laboratoo,, University of Manchester, Manchester M I 3 9PL, UK

Received 16 August 1988; revised manuscript received 10 December 1988

A Doppler shift attenuation technique has been applied lo the quasi continuum ridge structure of the deformed nuclei 16vA68Yb populated by the reaction ~24Sn+4SCa.The Doppler shift of the ridge is analysed and compared to a simple rotational model for the feeding transitions and to more detailed Monte Carlo simulations. The data show a reduction of the rotational strength compared to the low spin E2 decay and point to strong alignment effects around spin 40h.

1. Introduction The detailed investigation o f the 7-decay of high spin states in nuclei has in the past been restricted to excitations close to the yrast line. In the spin region 30h-40h the discrete line intensities d r o p to the order o f 1% o f the intensities o f the low spin yrast transitions for well-deformed nuclei [ 1 ]. Thus it is experimentally difficult to observe and analyze the D o p p l e r shift o f discrete lines above this spin region, unless special structural effects such as s u p e r d e f o r m a t i o n strongly favour the population o f specific rotational bands. The m a i n decay intensity at high spins is believed to pass through a region above the yrast line where the level density is high [ 2 - 4 ] . In o r d e r to learn about nuclear structure in this region o f high spin and excitation energy it is therefore necessary to investigate the ?,-ray quasi-continuum. F r o m the large a m o u n t o f experimental data on the "/-decay from the entry point in an e v a p o r a t i o n residue to the ground state it is known that the decay proceeds mainly via statistical E 1 transitions and collective E2 transitions [5]. F o r excitation energies in excess o f a few h u n d r e d keV above the yrast line the increased level density produces a "/-ray quasi-con52

t i n u u m which, due to the rotational nature o f the decay, displays characteristic correlations. Such correlations have been subject to various investigations in recent years [ 4 - 8 ]. The most striking manifestation o f these rotational correlations in the two-dimensional Ey~ versus Er2 spectra is the occurrence o f a valley along the diagonal defined by Er~ =Er2 and p r o n o u n c e d ridges parallel to the diagonal. The innermost ridge stems from two consecutive transitons in the m a n y rotational cascades. However, only a small fraction o f the cont i n u u m intensity is found to contribute to the ridge structure [4,9]. At excitations o f more than a few MeV above the yrast line the level density has increased and mixing effects due to residual interactions become important. This effect, c o m m o n l y denoted as d a m p i n g of the rotational decay strength [ 10 ] leads to reduction o f the redge structure and a partial filling o f the valley. The ridge structure provides an i m p o r t a n t signal for probing the u n d a m p e d collective E2 correlations in the region close above the yrast line. The time dependence o f nuclear 7-decay is very sensitive to collective as well as to microscopic structural effects. In this letter we present an investigation

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of the ridge structure of 167"16sYband an interpretation of the observed Doppler effects in terms of B(E2) values of the rotational decay and possible alignment effects in the feeding high spin cascades.

2. Experiment High spin states in ~6 7 y b and 1 6 s y b w e r e populated using the ~248n (48Ca, x n ) reaction at 201 MeV beam energy. The 4SCa beam was obtained from the 20 MV tandem accelerator at the SERC Daresbury Laboratory. The target consisted o f a 1 m g / c m 2 layer of tin, highly enriched in ~24Sn, on a 15 m g / c m 2 gold backing, which served as a stopper for the recoiling nuclei. The ~,-rays emitted were detected by means of the ESSA30 european multi-detector array, which contained thirty escape-suppressed germanium detectors. The detectors were positioned at six different angles with respect to the beam axis, namely 37 °, 63 o, 79 °, 101 °, 117 ° and 143 °. Data were also taken using a thin ~248n target without stopper in order to obtain fully shifted coincidence spectra. Approximately 5 × 10s 7-7 coincidence events were recorded with the backed target and about 1 × 108 in the thin target experiment. Calibrations from various radioactive sources were used for gain matching spectra from backed and unbacked targets.

9 March 1989

Nco,(i,j)=N(i,j)- •,N(i,j).•,N(i,j) Ei4N(i,j)

(1)

Spectra projected from the two-dimensional spectra perpendicular to the diagonal, such that 0.5(Ev~ +Ey2) is constant, for a range of values of 0.5(Ev~ +Er2), are shown in fig. 1. The ridge structures in the projected spectra from the backed and the unbacked target data were fitted with gaussian shapes. Dynamical moments of inertia .~¢~2)= 8 h / W were determined as a function of "cut energy", 0.5(Ev~ +Ey2), from the mean separation, W, of the main gaussian component of the inner ridges on either side of the valley. Since the intensity of the ridge drops drastically above 1200 keV the value of.j{2) in this region is determined by the shape (edges) of the valley and therefore represents a lower limit. The extracted moments j~2) are presented in fig. 2a. The average recoil velocity of the 167.~6Syb nuclei was determined to be v/c=2.61%. The fractional Doppler shifts, fD, shown in figs. 2b and 2c, were obtained as the ratio of centroid shifts from backed target data with those obtained from the unbacked target data.

250

1160 keY

200 150

3. Data analysis 7-~' coincidence data obtained from the backed target experiment were sorted into three different twodimensional (Ev, versus Ey2) spectra each specified by a particular combination of detector angles. The sets chosen, specified by the detector angles corresponding to the x- and y-coordinate axes, were (37 °, 143 °), (63 °, 117 °) and (79 ° , 101 °). In addition a fully Doppler-shifted two-dimensional spectrum was prepared from the unbacked data. In order to enhance the correlated structures in twodimensional 7-7 spectra, N(i, j), relative to the smooth background, a background subtraction procedure ("COR" treatment [ 3,9 ] ) specified by eq. ( 1 ) was employed:

200 I-Z :D 0 (.9

0

500

200

0

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Fig. 1. Cuts perpendicular t o the diagonal in the forward-backward (37 °, 143 ° ) spectrum at cut energies of 700 keV, 900 keV and 1160 keV and a width of 40 keV. The position of the stopped and fully shifted ridges are marked by full and dashed lines, respectively. The two-dimensional spectra have been COR (eq. ( 1 ) ) treated before generating the cuts.

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9 March 1989

Spin I (E 7) 20 25 30 55 40 45

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Fig. 2. Part (a) shows mean moments of inertia .g~2) versus 3,-ray energy as extracted from the mean separation of the ridges. Shown with dots and full lines are the .¢(2) moments of inertia as observed from discrete bands in L67yb and ~68yb. A spin scale corresponding to a constant .¢t2) of 65 h2/MeV and i= 0 in eq. (2) is shown at the top. In parts (b) and (c) the fraction fD of the full Doppler shift of the first ridges as observed from the main ridge components in the cuts perpendicular to the diagonal is plotted versus mean 3,-ray energy, 0.5 (Ev~+Ev2). The full lines in part (b) indicate the shift predicted by the one-cascade model for B(E2 ) values of 100, 200, 400 and 800 WU. The dotted lines are the result of a Monte Carlo calculation using an E2 strength of 100 and 800 WU (see also the text). In part (c) the experimental values offD are compared to the mean Doppler shift of discrete lines in the (Tr, c~)= ( - , 1)-band in ]68yb. In addition the result of the one-cascade model assuming an alignment of 1Oh above spin 1= 40h, an entry spin of lo = 50h and a collectivity of 300 WU is superimposed. A s i m i l a r analysis on the raw d a t a gave c o n s i s t e n t results.

4. C a s c a d e m o d e l

T h e o b s e r v e d D o p p l e r shifts c o r r e s p o n d to effect i v e d e c a y t i m e s o f t w o c o n s e c u t i v e transitions. T h e e f f e c t i v e d e c a y t i m e s t e m s f r o m the history o f decays f r o m the e n t r y p o i n t to the o b s e r v e d transtions. In o r d e r to d e s c r i b e the D o p p l e r shifts o f the ridges a s i m p l e o n e - c a s c a d e m o d e l is used. A fixed e n t r y spin Io is a s s u m e d . T h e d e - e x c i t a t i o n o f states with I
~(2), In the d e c a y f r o m the state o f s p i n / t o the state o f spin I - 2 the c o r r e s p o n d i g n T-ray energy is related tO ~.~(2) t h r o u g h the s i m p l e relation: E~ ( 1 - - , 1 - 2 ) = 2 ( l - i ) / J

(2),

(2)

w h e r e i is the aligned a n g u l a r m o m e n t u m . T h e m e a n intrinsic l i f e t i m e o f a state o f spin I is related to Ev a n d B ( E 2 ) in the following way:

r,(1)= ( 6.V2× l O'°.B(E2 ).E~ )-~ s ,

(3)

w h e r e the T-ray energy, E~, is in units o f M e V a n d the B ( E 2 ) in W U . In the m o d e l the e f f e c t i v e l i f e t i m e z o f the state o f spin I is the s u m o f the m e a n l i f e t i m e s r, o f the r o t a t i o n a l states with spin >/I. It s h o u l d be e m p h a s i z e d here that in the e s t i m a t e o f the delay due to all u n o b s e r v e d p r e c e e d i n g t r a n s i t i o n s the alignm e n t plays a p r o m i n e n t role t h r o u g h the E 5 d e p e n -

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dence of the y-decay probability (see eqs. (2) and (3)). To relate the measured mean Doppler shift to the effective lifetimes calculated in the model a knowledge of the time dependence of the velocity of the recoiling nucleus, v(t), is necessary. Calculations using the Monte Carlo code of Bacelar [ 11 ], in which both nuclear and elestronic stopping powers [ 12 ] are taken into account and correlations made for the atomic shell structure of the stopping material [13 ], were used to evaluate v(t) for the recoiling Yb nuclei. The effects of slowing down of the incident 48Ca ions before fusion occurred were also included in the calculations. The results of this simple model are shown in comparison to the data in fig. 2b. In this figure the full lines show the expected fractional Doppler shift for rotational cascades starting at an entry spin Io = 50 and B(E2) values of 100, 200, 400 and 800 WU. A fixed dynamical moment of inertia of J~2~=65h/ MeV was used. For a justification of the use of this one cascade model, a simulation calculation was performed for the decay paths on the basis of the Monte Carlo method. In this model the entry spin, Io, and the energy above the yrast line, U, as well as the moment of inertia, j~2 ~, were chosen randomly from gaussian distributions. The decay of the states from the entry point down to the ground state was determined stepwise by the competition between the statistical E1 decay probability and the collective E2 decay. In the high level density regime at large excitation energies U above yrast the formalism of the damping picture was applied [ 10 ]. One- and two-dimensional spectra were updated from the decay simulation and were processed in the same way as the experimental spectra. Examples of fractional Doppler shifts from such calculations are shown in fig. 2b as dotted lines for B(E2) values of 100 WU and 800 WU. The main part of the deviation originates from the inclusion of E 1 transitions which is only slightly compensated by the increased rates from the rotational damping. The differences between the results of the two models is systematic but rather small. In order to investigate the influence of alignment the one-cascade model was used.

9 March 1989

5. Results and discussion The average moment of inertia j(2) was extracted from the data up to a `/-ray energy of 1360 keV. The value decreases above the 113/2 .2 neutron crossing around 500 keV and approaches a value of about 65h2/MeV. From 700 to 1000 keV the ridge is well pronounced and the value of ,¢t2~ is rather stable. Above this point the average ,¢ ~2~ increases again to approximately 80h2/MeV at around 1100 keV and then stabilizes at values ~<70h2/MeV. The ridge also contains considerable contribution from discrete bands at lower spins and indeed the extracted average moments are in agreement with the .j(2~ of the strongest populated discrete line bands in ~67yb and ~68yb [ 14,15 ], as can be seen in fig. 2a. In the lower parts of fig. 2 the observed fractional Doppler shift, fD, of the main components of the ridges as extracted from the DSAM measurement is shown. The shift can be verified at specific energies by analyzing the shift of the discrete transitions in the bands. The fractional Doppler shifts for the high-spin transitions of the ( - , 1 ) - b a n d in ~6Syb [15] are in good agreement with the corresponding ridge values and are shown in fig. 2c in comparison with the fractional ridge shifts. From Coulomb excitation of the low spin states in t6Syb the B(E2) value of the 2 + ~ 0 + transition is known [ 16 ]. It corresponds to a transition strength at high spins of about 390 WU. From fig. 2b it can be seen that the observedfD values do not correspond to a constant rotational strength over the whole energy region. For ,/-ray energies lower than 900 keV the data are consistent with a B(E2 ) value of around 300 WU. At higher energies the measured points show a fine structure which deviates considerably from a pure rotational decay. The full shift is already observed for transitions around 1200 keV. This feature and the fact that for Ev < 1200 keV the mean fD value drops very sharply towards the line corresponding to model calculations with B(E2 ) = 200 WU can be accounted for by alignment effects. Alignment disturbs the linear relationship between spin and 7-ray energy. The entry point may thereby be shifted towards lower "/-ray energies. The data can be approximately described by a gain in quasiparticle alignment of 1Oh-15h which takes place within 2-3 transitions at around 40h and a B(E2) of 55

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300 WU. The result of the one-cascade model using the latter assumptions describes the data well over the full energy range including the region near Ev = 1100 keV as shown in fig. 2c by the full drawn curve. However the observed shifts could alternatively be explained by assuming different decay patterns in coexistence and/or a series of changes in collectivity from entry point to the discrete line regime. The introduction of alignment to account for the observed timestructure in the ridge decay also is supported by the observed relationship between the maximum E2 transition energies and input angular momenta in the same nuclei [ 17 ]. By inserting the maximum angular momentum of the reaction I ..... =60,5, the extracted moment of inertia ,£c2~=70h2/MeV and the E~aX=l.4MeV determined from the edge of the rotational bump into eq. (2) an average alignment ( i ) ~ 1Oh for the high-spin region is suggested. Theoretically these results and the observed variation in average moment of inertia can be understood from the estimates of Bengtsson and Ragnarsson [ 18 ] and Dossing [ 19]. For spins around 40h or rotational frequencies between h~o=0.5-0.6 MeV several particle rearrangement effects mainly involving the h,~/e and the i, 3/2 proton subshells are predicted [18]. The three lowest calculated bands, for instance, are predicted to gain 14fi, 10fi and 9fi of aligned angular momentum, respectively. The observed reduction of the rotational strength in the ridge structure ( B ( E 2 ) ~ 3 0 0 WU) is indeed also predicted by the calculations of ref. [ 18 ] through a reduction of the e2 deformation from about 0.275 to 0.245 corresponding to a drop in B(E2) from about 430 WU to 330 WU. This can be understood as an effect of the deoccupation of orbitals in which the neutrons or protons are moving in the direction opposite to the rotation [20]. It is predicted to start at fio)..~ 0.4 MeV for the yrast band in 166yb and should occur at a slightly higher rotational frequency in '6SYb. However, the fact that higher excited bands mainly contribute to the ridge intensity may change the onset of the deoccupation effect. The decay structure at higher excitation energies which according to ref. [ 19 ] is also influenced by changes in alignment also may contribute to the time dependent feeding of the ridge structure. We may conclude from the discussion above that 56

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the introduction of an increase of alignment of 1015 units together with a reduction of the B(E2 ) value from 400 WU to 300 WU can explain the main component ~ in the decay flow through the quasi-continuum. It leads to a consistent description of the data both with respect to effective lifetimes and the relationship between 7-ray energy, moment of inertia and multiplicity. The present attempt to analyse the quasi-continuum ridges in a DSAM measurement clearly shows the possibility of extending lifetime results towards higher spins and rotational frequencies, and secondly points to a way of extracting average lifetime properties for a specific region of excitation close to the yrast line. For a further investigation, especially of the Doppler shift of the valley in comparison with that of the ridge structures, more refined ways of analysis need to be developed. Furthermore, systematic studies of the shifts can provide insight into the development of shape and alignment effects at very high spins. The use of multiple coincidences (triples) [21] is particularly promising; the Doppler shift of such enhanced structures in three or more dimensional spectra will give more precise results.

Acknowledgement We would like to thank J.D. Garrett for very fruitful discussions. Financial support from the United Kingdom Science and Engineering Research Council, the Danish Nature Science Research Council and the Nordic Committee for Accelerator based Research is acknowledged. One of the authors (K.S.) would like to acknowledge the support of a FeodorLynen-Fellowship via the Alexander-von-Humboldt Stiftung. D.C. acknowledges receipt of an SERC studentship. This work was partly supported by the Bundesminister f'tir Forschung und Technologic (Fed. Rep. Germany).

"~ It should be noted that in the present analysis of the ridge structure we measure mean effective lifetimes and are therefore unable to identify slowcomponents.

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References [ 1 ] J.N. Mo, S. Sergiwa, R. Chapman, J.C. Lisle, E. Paul, J.C. Willmott, J. Hatula, M. J~i~iskel~iinen, J. Simpson, P.M. Walker, J.D. Garrett, G.B. Hagemann, B. Herskind, M.A. Riley and G. Sletten, Nucl. Phys. A 472 (1987) 295. [ 2] D.L. Hillis, J.D. Garrett, O. Christensen, B. Fernendez, G.B. Hagemann, B. Herskind, B.B. Back and F. Folkmann, Nucl. Phys. A 325 (1979) 216. [3] B. Herskind, J. Phys. (Paris) C 10 (1980) 106. [4] B. Herskind, Proc. Intern. School Physics "Enrico Fermi" (Societa Italiana Di Fisica, Bologna, 1984). [5] R.M. Diamond and F.S. Stephens, Ann. Rev. Nucl. Part. Sci. 30 (1980) 85. [6] J.D. Garrett, G.B. Hagemann and B. Herskind, Ann. Rev. Nucl. Part. Sci B 6 (1987) 419. [7] J.C. Bacelar, G.B. Hagemann, B. Herskind, B. Lauritzen, A. Holm, J.C. Lisle and P.O. Tjom, Phys. Rev. Lett. 55 ( 1985 ) 1858, and references therein. [8] F.S. Stephens, J.E. Draper, J.L. Egido, J.C. Bacelar, E.M. Beck, M.A. Deleplanque and R.M. Diamond, Phys. Rev. Lett 57 ( 1986 ) 2912, and references therein. [9] O. Anderson, J.D. Garrett, G.B. Hagemann, B. Herskind, D.L. Hillis and L.L. Riedinger, Phys. Rev. Lett. 43 (1979) 687. [ 10] B. Lauritzen, T. Dossing and R.A. Broglia, Nucl Phys. A 457 (1986) 61. [11] J.C. Bacelar, A. Holm, R.M. Diamond, E.M. Beck, M.A. Deleplanque, J. Draper, B. Herskind and F.S. Stephens, Phys. Rev. Lett 57 (1986) 3019; J.C. Bacelar, Nucl. Instrum. Methods, to be published.

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[12]L.C. Northcliff and R.F. Shilling, Nucl. Data Tables 7 (1970) 233. [13] F.J. Ziegler and W.K. Chu, Nucl. Data Tables 13 (1974) 463. [14] J.C. Bacelar, M. Diebel, C. Ellegaard, J.D. Garrett, G.B. Hagemann, B. Herskind, A. Holm, C.-X. Yang, J.Y. Zhang, P.O. Tjom and J.C. Lisle, Nucl. Phys. A 442 ( 1985 ) 509. [ 15 ] D. Clarke et al., private communication; and to be published. [16]R.M. Ronningen, R.B. Piercey, J.H. Hamilton, C.F. Maguire, A.V. Ramayya, H. Kawakami, B. van Nooijen, R.S. Grantham, W.K. Dagenhart and L.L. Riedinger, Phys. Rev. C 16 (1977) 2218. [ 17] K. Schiffer, J.D. Garrett, G.B. Hagemann, B. Herskind, B. Lauritzen, R. Chapman, D. Clarke, F. Khazaie, J.L. Lisle and J.N. Mo, to be published. [18] T. Bengtson and I. Ragnarsson, Nucl. Phys. A 436 (1985) 14. [ 19 ] T. D~ssing, private communication; S. Vydrug-Vlasenko, R.A. Broglia, T. Dossing and W.E. Ormand, Proc. Conf. on High-spin structure and novel nuclear shpaes (Argonne National Laboratory, Argone, IL, 1988). [20] J.D. Garrett, J. Nyberg, C.-H. Yu, J.M. Espino and M.J. Godfrey, in: Proc. Conf. on Contemporary topics in nuclear structure physics (Cocoyoc, Mexico, 1988 ), eds. R.F. Casten et al. (World Scientific, Singapore, 1988), to be published. [21 ] B. Herskind, J.J. Gaardhoje and K. Shifter, Proc. Conf. on High-spin structure and novel shapes (Argonne National Laboratory, Argone, IL, 1988 ).

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