Burde, J.

Diamond, R.M.

Macchiavelli, A.O.

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Lawrence Berkeley National LaboratoryRecent WorkTitleSUPERDEF0RMATION IN [SUP]104,105 PDPermalinkhttps://escholarship.org/uc/item/7jx112k4AuthorsMacchiavelli, A.O.Burde, J.Diamond, R.M.Publication Date1988-07-01eScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaLBL-2SS97 .... ~ Preprint Lawrence Berkeley Laboratory UNIVERSITY OF CALIFORNIA Submitted to Physical Review C Superdeformation in l04,lOSPd :-:. " ~ -: I '. _ L '.,~ .... >f~~ -.... _. #' ' "'r'" I 198" ",.101- b A.O. Macchiavelli, J. Surde, R.M. Diamond, C.W. Beausang, M.A. Deleplanque, R.J. McDonald, F.S. Stephens, and J.E. Draper July 1988 TWO-WEEK LOAN COpy This is a Library Circulating Copy which may be borrowed for two weeks. Prepared for tbe U.S. Department of Energy under Contract Number DE-AC03-76SF00098. DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California. , j '. LBL-25597 SUPERDEFORMATION IN 104.105Pd A.O.Macchiavelli., J.Burde--, R.M.Diamond, C.W.Beausang, M.A.Deleplanque R.J.McDonald, F.S.Stephens and J.E.Draper---Nuclear Science Division Lawrence Berkeley Laboratory University of California Berkeley, California 94720 In the _present communication we report the discovery of ~ rotational band in I04Pd and one in IOSPd that can be interpreted as arising from superdeformed shapes. The moments of inertia, J(I) and J(2), of these bands are similar to those measured in the Ce-Nd region, once the A5/ 3 mass dependence is removed. This implies a deformation E - 0.35-0.4. This is the third mass region where superdeformed bands have been found at high spins. This work was supported by the Director, Office of Energy Research, Division of Nuclear Physics of the Office of High Energy and Nuclear Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098. 1 The understanding of the nuclear shape requires a knowledge of macroscopic prop-erties, determined by the interplay of Coulomb, surface and rotational energies, and of microscopic properties associated with the detailed motion of the nucleons near the Fermi surface. Of special interest are those shapes known as "superdeformed" (SD) where the nucleus acquires a very elongated shape that can be approximately represented by an ellipsoid where the ratio of the long to short axis is considerably larger than that of nor-mal deformation,... 1.3:1. Within the framework of the anisotropic harmonic oscillator modeP one can expect the existence of favorable shell gaps that appear regularly as a function of deformation and nucleon number. They are predicted to occur for particular "superdeformed magic numbers" and at deformations corresponding to integer ratios of the lengths of the axes (e.g., .E = 0.6 corresponds to a ratio of 2:1). More realistic cal-culations provide a better prediction of regions of superdeformation2 and these simple regularities are largely lost. Nevertheless, superdeformed shapes are predicted to occur, and their observation and systematic study will result in a better understanding of the interplay between the macroscopic and microscopic aspects of the nuclear motion. The .first observation of SD nuclei goes back to the discovery of fission isomers3 and the identification of the rotational bands built on them4 • This interesting topic of nuclear structure had to wait 15 years until other discrete superdeformed bands were discovered at high spins in the 150 and 130 mass regionss. This was possible only when large arrays of Compton-suppressed Ge detectors became operational and were able to extract these bands from the complex background that occurs in the spin region where they are found. Not much is yet known about the actual properties of these bands, such as their single-particle configuration, pairing correlations and their population and decay mechanisms. It is important, at this stage, to determine experimentally the regions where superdeformation occurs. In the present communication we report the discovery of rotational bands in l04Pd and losPd that can be interpreted as originating from a second minimum in the potential energy surface of these nuclei at high spin and large deformation. This is a new mass region where discrete superdeformed bands have been 2 ( "'-found at high spins, the other known regions being around 152Dy and in the light Ce-N d nuclei. The experiment was carried out at the Lawrence Berkeley Laboratory SS-inch Cy-.. clotron. Two stacked 64Ni, self-supporting targets 0.5 mg/cm2 thick, were bombarded with a 200 MeV 48Ca beam. The emitted -y-rays were detected in 20 Compton-suppressed ... -.~ Ge detectors from the HERA array at an event rate for triple and higher fold coincidences of approximately 2000 S-1. A total of 70 million events were recorded event-by-event on magnetic tapes for subsequent off-line analysis. A "doubles" sort, in which the events were broken into independent pairs showed the existence of a very strong ridge structure in the -y--y correlation matrix 6. The observed energy spacing is consistent with that from a strongly deformed shape. A more detailed inspection revealed the presence of two discrete bands that were associated with l04Pd and 105Pd , the a4n and the a3n products, respectively. Figure 1a shows a backgroWld-substracted spectrum obtained by summing spectra having gates within the band assigned to losPd. These transitions are also clearly seen in the spectrum in Fig. Ib, which corresponds to a gate on the known 306 keV ground-state transition in lOSPd 7 ... A summed spectrum derived from gates in the band assigned to lO4Pd is shown in Fig. lc. A partial decay scheme is shown in Fig. 2 for the_two nuclei. .105Pd : In an attempt to find links between the SD band and the yrast states, a "triples" sort was performed, requiring two -y-ray gates in the SD band or one gate in the band and the other in the ground state ( g7/2) band before incrementing a spectrum wi th the third -y. As in previous cases, no obvious links could be found. However, the -y-ray intensities deduced from the triples sort of the data, summarized in Table 1, show that the band deexcites both to the g7/2 and the hU/2 bands with roughly equal J intensity. The feeding of the g7/2 band seems to take place at a spin of 39/2 and therefore the deexcitation pattern suggests a spin of 43/2 for the first observed level of the new rotational band, with an uncertainty of ± 2 units. Angular correlations with gates on the band members or on the 306 keV (61=1) transition established that the transitions are 3 consistent with stretched quadrupole characterS, thus extending the spin sequence up to 83/2 for the top transition. With the branching derived from the triples sort, the relative intensities from a gate in the 306 keY transition and its known intensity, the population of this band was determined to be ,..., 30% of the total events leading to 105 Pd. _l04Pd : In contrast with I05Pd , the data from the triples sort were insufficient to provide additional useful information, but consistent with the doubles sort analysis (perhaps due to the relatively lower intensity of this product and of its band). From the single-gated spectra it was possible to conclude that the band feeds the yrast states at around spin 22, and therefore a spin 24 ± 2 could be assigned for the lowest state of the band. The population of this band represents,..., 15% of the events in I04Pd , as obtained from gates in low-.spin members of the yrast band 9. Relative intensities are also given in Table 1. It can be argued that these bands should be populated when they are in the yrast region, i.e., close to the highest spins observed. Therefore, due to their large moment of inertia they would deexcite at -2-3MeV above the yrast line. The moments of inertia J(I) and J(2), shown in Fig. 3, are similar to those measured in the mass 130 region, once the A 5/3 dependence is removed, suggesting a deformation of f ,...,. 0.35-0.4 for these bands. The gradual decrease in J(2) can be qualitatively understood by the gradual alignment of the valence nucleons' angular momentum with the rotation axis, as the rotational frequency inCI'eases. Therefore, the generation of angular momentum becomes energetically more expensive and the nucleus approaches the "band termination" that will occur when all the angular momentum available for that configuration is aligned. In comparison with 152Dy, it is expected10 that in the spin range observed a bigger proportion of this maximun angular momentwn is exhausted for these lighter systems, and therefore the reduction of J(2) is faster. Both l04Pd and l05Pd can be interpreted as soft, slightly deformed, prolate rotors in the nonnal (low frequency) regime7•9 • The observation of SD bands indicates the existence of a second minimwn in the potential-energy surface of these nuclei. As mentioned before, 4 these minima are likely at E - 0.35-0.4 and become yrast (lowest in energy) at a spin of about 40. The increase in J(2) in lO5Pd at 1iw - 1 MeV is quite interesting and may ... be caused by a band crossing. It is the first time such a crossing has been seen in a. SD band. \ ".} The structure of these bands can be discussed in terms of the cranked shell model 11 • We have calculated the single-particle routhians at a deformation of E=O.4 and, at the frequencies where the SD bands are observed, a plausible configuration involves lev-els from the N=4 and 5 shells for both neutrons and protons, i.e. 1r(N=4)"(N=5)2 v(N=4)14(N=5)4. The deformation-driving effect of the 1r and v N=5(hu /2) high-j or-bitals will favor the stabilization of the second minima in the potential-energy surface of these nuclei. Furthermore, the calculations suggests that the increase of J(2) in l05Pd at the highest frequencies can be attributed to the alignment of a pair of neutrons in the. N =6 h3/2 level. The crossing is predicted to occur at 1iw - l.lMe V, very close to the observed frequency. Amore general calculation, regarding the existence of SD gaps in a realistic Wood-. Saxon potential has been presented by Dudek et al. 2. An inspection of single-particle levels as a function of deformation reveals the presence of gaps at large quadrupole deformation for Z=46 and N =58. These predictions are consistent with our observations, altough a quantitative comparison is beyond the scope of this work. It is interesting to note that the neutron number of N =58,59 for the present cases can be related to the proton number Z=58,60 in th Ce-Nd region. In conclusion, we have observed bands in l04Pd and l05Pd consisting of stretched E2 transitions. Their regularity and measured moments of inertia suggest that these bands are based on a superdeformed configuration having E - 0.35-0.4, similar to those observed in the Ce-Nd region. The sudden increase in J(2) in the SD band of l 05Pd at the highest spins may be due to the alignment of a pair of i13/2 neutrons. 5 References a Permanent Address: Comision Nacional de Energ{a AtOmica, Buenos Aires, Argentina. aa Permanent Address: Racah Institute of Physics, Hebrew University, Jerusalem, Israel. aaa Permanent Address: University of California, Davis,California 95611 1 A.Bohr and B.Mottelson, Nuclear Structure Vol. 2, (W.A.Benjamin Inc.,1975). 2 V.M.Strutinsky, Nucl. Phys. A95, 420 (1967). V.M.Strutinsky, Nucl. Phys. A122, 1 (1968). K.Neergaard, V.V.Pashkevich and S.Frauendorf, Nucl. Phys. 262, 61 (1976) I.Ragnarsson, T.Bengtsson, G.Leander and S.Aberg, Nucl. Phys. A347, 287 (1980). J.Dudek and W.Nazarewicz, Phys~ Rev. C31, 298 (1985). J.Dudek et al., Phys. Rev. Let~. 59, 1405 (1987). 3 S.M. Polikanov et al., Sov. Phys. JETP 1,5, 1016 (1962). 4H.J.Specht, J.Weber, E.Konecny and D.Heunemann,Phys. Lett. 41B, 2182 (1972). 5 P.J.Twin etal., Phys. Rev. Lett. 57, 811 (1986). P.J.Nolan et al., J. Phys. GIl, L17 (1985). E.M.Beck et al., Phys. Rev. Lett. 58, 2182 (1987), Phys. Lett. B195, 531 (1987). B.Hass et al., Phys. Rev. Lett. 60, 503 (1988). M.A.Deleplanque et aI., Phys. Rev. Lett. in press. 6 O.Andersen et al., Phys. Rev. Lett. 43, 687 (1979). 7 F.A.Rickey, J.A.Grau, L.E.Samuelson and P.C.Simms, Phys. Rev. CIS, 1530 (1977). 8 J.E.Draper, Nucl. Inst. Meth. A247, 481 (1986). 9 J.A.Grau et aI., Phys. Rev. C15, 2302 (1976). 10 I.Ragnarsson, Phys. Lett. B199, 317 (1987). 11 R.Bengtsson and S.Frauendorf, Nucl. Phys. A327, 139 (1979). 6 Table 1 Gamma-ray energies, relative intensities and initial spin of transitions seen in the decay of the SD band. Intensities were derived from "doubles" and "triples" sorts of the data (see text). E., Intensity 1., CI 1'1' E., (keV) % (keV) 556 . 100 2+ 306 768 96 4+ 706 926 1426 6+, 16+ 891 971 87 8+ 854 802 1756 10+, 14+ 539 612 89 12+ 578 1064 100 18+ 795 1194 100 20+ 1014 1178 1263 127c 22+ ,(26) 1381 78 (28) 481 1511 93 (30) 772 1638 79 (32) 958 1763 92 (34) 1919 78 (36) 1208 2079 64 (38) 1282 1379 1488 1597 1720 1846 2007 2141 2240 a : Intensities have an uncertainty of ± 10% . b : Sum of transitions in the yrast sequence. Intensity 1., CI % 50 50 51 45 41 41 35 35 24 50 52 53 51 47 96 105 110 100 60 55 30 12 c : Includes the 1257keV transition in the yrast band. 7 I'" 7/2+ 11/2+ 15/2+ 19/2+ 23/2+ 27/2+ 31/2+ 35/2+ 39/2+ 15/2-19/2-23/2-(47/2) (51/2) (55/2) (59/2) (63/2) (67/2) (71/2) (75/2) (79/2) (83/2) .. ~ Figure Captions Fig.I. a) Spectrum in coincidence with gates within the members of the SD band assigned to losPd ; 'Y -ray transitions are labeled by their energy in keY. b) Spectrum in coincidence with the 306keV transition in lO5Pd. The lines show the position of SD transitions. Transitions in the yrast band are labeled by their initial spin (See Fig. 2). c) Same as a) for the band assigned to l04Pd. Yrast transitions are labeled by their initial spin. Fig. 2. Partial decay schemes of the SD bands in I04Pd and lO5Pd . Fig 3. Moments of inertia for the observed rotational bands. The dotted area represents J(I) with an uncertainty of ± 2 in the spin assignment. Open circles are for I04Pd and full circles for l05Pd . For comparison, the dynamic moment of inertia (scaled by A 5/3) in the SD band in 132Ce is shown as a dotted line. The right-hand scale is in units of the .rigid sphere. 8 1000 .) N 0'1 co _ co ,... co ,... co N "" 0'1 0 o - ~ It') N ~ ~ <Q ." - ~ - co C ,... :J 500 0 0 -0 N ~ 0 0 ~ N N N -\'." 0 800 NN NN ~~ :;,.~ "" "" ~. b' ." .00 I~I I It') I - I c I :J 0 0 200 ~ . .,.~ .. .:~ 0 1000 "" c) <Q • N co -- • + o. NN co ." N ~ ~ - co C ~ ~ :J 500 <Q <Q 0 ~ 0'1 0 0'1 ~ ,... 0 N o~~~~~~~~~~~~~ww~ 1000 1500 2000 2500 Energy (keV) DL '''-1204 Figure 1 9 20 15 10 5, o E (MeV) l04pd -,-(38) 2079 +(36) 1919 +()4) 1763 +(32) 1638 +(30) 1511 +(28) 1381 (8312)'1 (2240) (7912)+ 2141 (7512)+ 2007 (7112)+ 1846 (6712)+ 1720 (63/2)+ 1597 (S912) + 105 Pd +(26) 1263 ~(26+> -j-(24) 1470 '/ 1488 (5512)+ 1379 (5112)+ +(24+) 1.364 -+- (22+) 1251 -+-(20+) 1194 ~18+ 1064 + --l--16 926 + --1..-14 797 2+ --L.-l ~10+ ~8+ ~6+ 926 + --L-4 768 .,+ 556 0+ 1282 (4712) ~ (5112 +)--,-1208 1435 (4312)7\(4712 +)+ 1313 (431iS {4312\_+ _ 1 17 1267 {3912 > (39/2 +) t - 1120 1178 {35/2 )-4- 3512+-+-• 1120 1014 (31/2 >-+- 3112+-+-- 1153 2712+~ 2712 -t- 2312+ 578 - 1100 912+ S~9 2312 -.f- I 854 - 958 1512+-+-1912 --L- 891 1512- 772 1112+-+--4tr + 706 1112 -183 712+~ --""'5122!2r XBL 884-1203 Figure 2 10 , '.' \ .. -' 50 ......-. 40 20 0.8 '. . ~··tg) ! ."" .. '" ~ , , , , .... ". CD • f 0.8 1 h:J(MeV) Figure 3 11 1.2 1.4 1.2 ~ Q. • • at -1.0 ~ ... '" .., 0.8 XBL 884-1205 LA WRENCE BERKELEY LABORA TORY TECHNICAL INFORMATION DEPARTMENT UNIVERSITY OF CALIFORNIA BERKELEY, CALIFORNIA 94720 -

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SUPERDEF0RMATION IN [SUP]104,105 PD

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SUPERDEF0RMATION IN [SUP]104,105 PD

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