Decay of superdeformed structures studied with GASP

NUCLEAR PHYSICS A HS~:VLH~

Nuclear Physics A583 (1995) 191-198

Decay of superdeformed structures studied with GASP Dino Bazzacco ~ q.N.F.N, and Dipartimento di Fisica dell'Universit£ di Padova, 1-35131 Padova, Italy Some studies on the subject of superdeformation, performed using the 3' detector array GASP, are presented. The attention is focussed to the problem of the decay of the superdeformed bands. The cases of 133Nd, where the decay proceeds by discrete transitions, and of 194pb, where the decay proceeds in a statistical way, are presented. 1. I N T R O D U C T I O N One of the main topics in present days "),-ray spectroscopy is the study of the atomic nucleus in the second potential energy well where very deformed shapes and high angular momenta are achieved [1-3]. This kind of research has started with the identification of superdeformed structures in rare earth nuclei and has lead to the discovery of many superdeformed (SD) bands in the A=130, A=150 and A=190 mass regions. Despite the big efforts devoted to this subject and the advent of new generations of more and more efficient detectors, the population mechanism of these structures and their decay to less deformed configurations are still arguments of intense investigation [4-8]. In fact, although some recipes have been learned on the combinations of beam, beam energy and target which enhance the population of the SD bands, there is still no accepted model that can describe in details how the decay flux is trapped in the second minimum. On the low energy side of the superdeformed bands, the problem of their connection to the ND states has been solved essentially only for the nuclei of the A=130 region. Here however, the deformations and excitation energies are smaller than in the heavier mass regions and the decay proceeds via a few relatively strong transitions. In the heavier mass regions the decay seems to fragment into many branches and to proceeds through several intermediate steps with the consequence that there is little hope to see anything more than continuous features in the v-ray spectra. Clearly in these conditions definite assignments of spin and parity of the SD bands are much more difficult. In this paper we first present the experimental setup GASP which was used for our investigations on this topics and then we report on some interesting cases we studied with it in its first two years of operation. 2. G A S P GASP [9] is a 4rr detector array of the last generation which has been built for high spin ")'-spectroscopy but is flexible enough to be used as a general purpose high efficiency setup. The detector is sited at the Laboratori Nazionali di Legnaro (LNL) Tandem+Linac 03750474/95/$09.50 © 1995 Elsevier Science B.V. All fights reserved. SSDI 0375-9474(94)00658-X

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D. Bazzacco / Nuclear Physics A583 (1995) 191-198

accelerator and has been built as a joint project of INFN Padova, LNL, Milano and Firenze. The array consists of 40 Compton suppressed high efficiency (83% on the average) HPGe detectors and of a 4~ calorimeter composed of 80 BGO crystals which cover 80% of the solid angle. The detector system has room in its centre for a reaction chamber of 34 cm diameter where the light charged particles detection system ISIS which is composed of 40 Si A E + E telescopes can be installed. Evaporation residues produced in the centre of GASP can be injected into the recoil mass spectrometer CAMEL in use at LNL, without the need to remove any of the gamma detectors. The geometry of GASP is based on a polyhedron with 122 faces: the inner ball uses 80 of these faces while the remaining 42 are used for the beam ports and for the 40 Ge+AC systems. The total solid angle subtended by the germanium detectors, which are positioned at 27 cm from the target, is about 10% corresponding to a measured total absolute photopeak efficiency at 1332 keV of about 3%. For the 6°Co source the Compton suppressed spectra have a P / T ratio of 60-65% confirming that, as planned, GASP has the best response function among the arrays of the last generation. The target-germanium distance can be reduced to about 20 cm if the inner ball is removed, thereby gaining a factor of two in efficiency. This is planned for those cases (like plunger and Transient Field g-factor measurements) where the collected statistics is the critical figure and the decrease of resolving power due to increased doppler broadening can be accepted. By now only a reduced set of parameters is being taken from the BGO ball and namely the fold and the sum energy. However, in a planned improvement of the system we foresee the acquisition of both energy and time for each of the 80 detectors of the inner ball in order to obtain the details of the hit pattern and a better definition of the total energy of the event. In high spin measurements the acquisition rate is typically between 5 and 10 kHz when the singles counting rate in the germanium detectors is about 10 kHz and the trigger is to (Compton suppressed) triples or higher fold coincidences in the germanium detectors and fold larger than 5 in the BGO ball. 3. D I S C R E T E L I N K I N G T R A N S I T I O N S IN 1SaNd In the mass A=130 region the deformation in the second minimum is smaller than in the heavier mass regions and furthermore the so called "normal deformed states" have a sizable deformation fl = 0.20 - 0.25. Because of these two reasons the SD bands are sometime call "highly deformed". At variance with the heavier mass regions, their decay to the ND structures should then proceed by means of a few transitions which should be sufficiently strong to be observed. In fact, the first nucleus where some discrete linking transitions have been seen is 135Nd [10]. In the very first measurement performed with the GASP array, which was a thin target experiment with the l°~Pd +32S reaction at 155 MeV, we identified three transitions connecting the SD band to levels of lower deformation in the nucleus 133Nd [11]. This allowed us to unambiguously fix spins and excitation energies of the SD band states in 133Nd. Only one third of the intensity of the SD band is carried out by the three observed transitions whereas the remaining part of the decay could not be identified in this measurement. In order to understand the decay mechanism of the SD bands ( at least in the mass 130 region), it is important to know their complete decay-out and to find how

D. Bazzacco / Nuclear Physics A583 (1995) 191-198

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they interact with the bands at normal deformation. The fact that only a few levels were known at low energy [12-14] is, most likely, one of the main reasons which prevented the identification of the complete decay-out of the SD band in Z33Nd. Although we obtained a substantial improvement of the level scheme of a33Nd already in the thin target measurement, the real clue to the solution of the problem was a high statistics and high resolution backed target experiment. In fact, as the levels of the SD band below P = 3 3 / 2 + have lifetimes larger than the stopping time of the recoiling ions in gold, the transitions deexciting the lowest levels of the SD band appear as sharp lines in a ~/-ray spectrum. Since the decay-out of the band occurs just below P = 3 3 / 2 + the linking transitions also will not suffer from the Doppler broadening effect. When the lifetimes of the levels of

SD band decay

SD b a n d

[404]7/2

' aNd 73

67/2*

60

[54~]~/2 [53011/'2

,I

6.P_L?2_ _

59/2- ~

57•2-

55/2-

53/2" 118257/2" i092

5 0 ~ ~

61/2+r158

5112" 11594912-108853/.__~029

r53bll/~'-"f-~

15140/2

47/2- 10774512.100649/2-- ~6 Z

[4oo]i/2

43/2" 987 41/2- 92O 45/2' ~04

41/2' 39/2+ 5s8137/2~"~ , [402]5/2 ~. :14[ ,, 75413112+ 3 ......... 0___ -~29/2--=/~5t~ ;

[51419/2 39/2" 885 3712- 841 4112.__:56 760 775 3712__: 62 " ~ 33/2~ ~ 2" 31/2" 637 ~

7781311:35/2 53/2565 2, 2

o

~25/2-, 702

,02 82812 /2 231 19/2~

6

1500 r 1266 [63/2* 61 t24 1225 + 1184 [59/2 57/24 11471 53/2,1107 55/2+ 1712 140011/2 49/2.1056 1072 51/2+ 651Z

~2J3312+ ~

968 1002147/'2*

907 93714312* 41/2' 41/2..+ ~52 879 139/2+ 37/2 821 35/2* 3312' 783/743 31/2+ 7't "1

~72~ 695 27/2*

,5I; .... P_~t23/2:_23~ ..... ,,.-T/T~--~3Y_~ 30'-~) 636 23/2* '1117~+ ~ " ,9/2+174°~ i97"--'I585 19i2+

N--~ ~-1 ~2---/ 2 3 Jl5/2¢72~ 4~ 1312-I~" 349 42 xna.o ~ ' 8 ~1112" 7~2; ~16."-5/2~L235..~ "3/2"~138--170~u_ ns _ _ _'~ 300ns~ 1 7 ~ ,/3~2"-

3--5-8_...x

45/2"

165] 648 15/2+ 7/2+

i8"~ 631 11 ]2. Z45" 519 712+

Figure 1. Level scheme of 13aNd. The SD band is shown only partially. The inset shows the. decay out of the 133Nd SD band.

interest allow it, the high energy resolution achievable in a backed target experiment is as important as high-fold coincidences for the extraction of low intensity transitions from the enormous "),-ray flux emitted in a nut!ear reaction. For this experiment [15] we used the l°4pd +32S reaction at a beam energy of 135 MeV. After unfolding the stored events we had 1.2 giga of triple coincidences availa,ble for the off-line analysis. They were sorted

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D. Bazzacco / Nuclear Physics A583 (1995) 191-198

into (2k) 3 symmetrized cubes from which many matrices could be easily extracted setting gates on the different band structures of 133Nd. The spectra obtained from these gated matrices are very clean allowing for a clear identification of the transitions connecting the various bands. The full SD band intensity has been found to divide into ten different paths which connect the band to levels of different structure at lower spin. A complete level scheme of 133Nd, comprising seven bands built on different Nilsson orbitals, has also been established and is shown in Fig. 1. The SD band is based on the N=6 i13/2 orbital [66011/2 whose occupation drives the nucleus to a larger deformation. Since it is yrast above spin 29/2 +, the band is the most strongly populated discrete structure at high spin ( up to I~=89/2+). Below 29/2 + the band is no more yrast and when it disappears ( at spin 17/2 +) it is the furthest from yrast of all the observed bands of this nucleus. The decay of the SD band to the other nuclear states is occurring in the spin interval (17/2+-29/2 +) where the band is crossing levels of similar spin and parities and can mix with them. If the intensity of the SD band is taken equal to 100 at spin 33/2 +, the sum of the intensities of the linking transitions gives 1014-6 indicating that the full intensity of the band is taken away by the observed connecting transitions. It is clear from Fig. 1 that the three strongest transitions ( 409, 633 and 667 keV) are responsible for almost 70% of the decay-out whereas the other seven are much weaker. This fact can be related to a level mixing phenomenon. In fact the 29/2 + level of the SD band (29/2+D), which decays through the strong 633 keV transition to the 25/2140417/2 + , lies only 39 keV apart from the 29/2~4o417/2. Furthermore a weak transition of 553 keV is observed to decay from the 29/2~40417/2 to the 25/2+D . These facts are a clear indication of a level mixing occurring between levels differing by two major oscillator quantum numbers ( N=6 and N=4). Analogously, the mixing of the 17/2+D with the 17/2140011/2 + (AE=64 keV) can explain the strong transitions linking the 21/2+D to the 17/2~-40o]1/2 (409 keV) and the one from the 17/2+9 to the 13/2~o011/2 ( 667 keV). Also in this case the decay of the [40011/2 band into the SD band is observed ( 21/214oo]1/2-+17/2sD, + + 527 keV). The interaction matrix elements and the mixing amplitudes of the states, have been extracted by means of a two-band mixing calculation [16] assuming a constant interaction V between the interacting bands and a vanishing interband transition strength. For the square of the ratio of the amplitudes one gets:

a__~ AEe,p(I) - AEo(I) a~ AEe=p(I) + AE0(I) (1) where as and a~ are the amplitudes of the SD and of the ND configuration in the superdeformed state. AE0(I), is the difference of the two unperturbed energies, is given by: AEo(I) = CAE~xv(I) 2 - (2 * V) 2. The extracted interaction matrix elements at spin 29/2 + and 17/2 + are 11 keV and 22 keV respectively (see Table1). The corresponding amounts of ND configuration into the SD states are 8.7 % and 15.8 %. The branching ratios of the 33/2 + and 25/2 + states of the SD band can be also calculated and the agreement with the experimental values is remarkable. From this analysis one can also derive the unperturbed energies of the SD band and hence recalculate its dynamic j(2) moment of inertia. With the new energy values (absence of mixing!) the irregular behaviour of j(2), typical of the SD bands in the mass 130 region at the decay-out, disappears indicating that it is likely due to the mixing with the normal deformed states.

D. Bazzacco /Nuclear Physics A583 (1995) 191-198

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Table 1 Experimental branching ratios for the levels relevant for the mixing between SD and normal states in laaNd. In the last column the extracted interaction matrix elements are given, together with the calculated branching ratios of the 33/2+0 and 25/2+D levels.

I[ -+ I'~

E.~ (keV)

Exp. branching ratios (%)

V (keV)

29/2+D --+ 2 5 / 2 + 29/2+D -+ 25/2~4o4F/2

514 633

69(3) 26(3)

11

672

92(1)

29/2[4o417/2 -+ 25/2SD

553

8(1)

21/2+o -+ 17/2+o

345 409

57(4) 43(4)

591

87(2)

527

13(2)

+ + 29/214o417/2 -+ 25/214o417/2 + +

2 1 / 2 % -+ 17/2;0011/2 + + 21/2140011/2 -+

17/214oo]1/2

21/2;oo]1/2 -+ 1 7 / 2 +

22

3 3 / 2 + -+ 2 9 / 2 + + 3 3 / 2 + -+ 29/2[40417/2

604 565

93(2) 7(2)

Calc. branching ratios (%) 94 6

25/2+ -+ 21/2+o 25/2 +o -+ 1/2;04j7/2

441 723

95(1) 5(1)

93 7

The SD band ends at spin 17/2 + although the expected band-head is at spin 13/2 +. We could not see in our spectra any indication of the 17/2+D-+13/2+ n transition which should have an energy of 250-300 keV. A transition in that energy range should have an intensity ~ 5% of that of the 667 keV transition if one takes into account the composition of the 17/2 + state of the SD band and the energy factor in calculating the branchingratios. This gives for the 17/2+o-+13/2+ 9 transition an intensity of ~ 1% of that of the SD band at V=33/2 +. This value is two times smaller than that of the weakest linking transition and explains why the SD band has been observed only from 17/2 + upwards. 4. S T U D Y OF T H E D E C A Y OF T H E S D B A N D IN 194pb

As an example of a different decay mode, the case of 194pb is presented. It is found that also in this case the decay proceeds because of a mixing phenomenon but the mixing amplitudes are much weaker and involve so many normal deformed states that no discrete transition can be identified. Indeed, as shown by M.Carpenter in a different contribution to this conference, in the A=190 mass region the decay is believed to proceed in about three steps, to involve a total energy difference of about 4 MeV and to be essentially of

D. Bazzacco / Nuclear Physics A583 (1995) 191-198

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statistical origin. The decay can be studied considering the lifetimes of the SD band states where the sudden decrease of intensity happens. An advantage of this way to proceed is that one can give quantitative estimates of the involved mixings using only well accepted assumptions on the statistical nature of the decay and on the shape of the barrier between the second minimum and the normal deformed states. The SD band in 194pb was observed several years ago [17-20]; the lifetimes of individual states with spins _> 20 h were determined [21] by means of the DSAM technique supporting the assumption of a constant deformation /3 ~ 0.6 corresponding to a transition quadrupole moment Qt = 20.6 eb for the upper part of the band. We populated the SD states in this nucleus by the reaction 162Dy +36S at 186 MeV using a 1.0 m g / c m 2 162Dy layer evaporated on a 1.4 m g / c m 2 tantalum backing [22]. The recoiling nuclei had a velocity v/c=1.65% and were stopped in a 10 m g / c m 2 gold foil. The Cologne plunger apparatus used in this measurement is described in [23]. An average of 635 million events of two and higher fold coincidences were recorded at five targetto-stopper distances from 15 to 97/~m. The lifetimes of the SD states were determined with the Differential Decay Curve Method [23,24]. Gated spectra with gates on shifted components of the feeding transitions of the SD band were analyzed in order to determine the transition intensities of interest. By this procedure it was possible to determine the

Table 2 Obtained lifetimes, B(E2) values and transition quadrupole moments Qt for the 213 keV, 256 keV and 298 keV transitions•

E~

I

~

B(E2)

Q,

(k~v)

(h)

(p~)

(lO~ w.u.)

(~b)

213 256 298

(10) (12) (14)

8 • 6/+3"2\ \--3.21 3 5 (+2°~ ~-1.5J 2 • 6/+1.s~ ~-1.0]

2 • 0/+l'5x \--0.4)

19• 7/+7"5x (-2.0) +7.3 23.6(_5.0) 19 • 6 (+5.% ~-3.91

•

2 •9 t+ar~ ~-1.2J 2 ' 0t+1.1~ \-0.S}

lifetimes of three low lying SD levels, which are assigned to have spin 10, 12 and 14 respectively according to [19]. The results are presented in Table 2 together with the derived Qt. The constancy of Qt is a well established feature of this SD band which has then/32 = 0.57 corresponding to an axis ratio of c/a=1.7. The total transition probability A -- 1/T is the sum of the partial decay probabilities for an intra band transition Aintra and the decay out of the band Ao~,. The decay probability out of the band at spin I can be expressed as:

~o~,(i) =

n(i) ~(t) (a + n(i) )

(2)

D. Bazzacco / Nuclear Physics A583 (1995) 191-198

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where R = Nout/N~,~tra is the ratio of the "/-ray intensities. With R(10) = 0.23(3) for the I = l(fi SD state, the probability for the decay out is Ao=~(10) = 25(11) ns -1. The decay of the SD band can be treated with the model by Vigezzi et al. [6] which has been previously applied for the discussion of the intensities and lifetimes of the bands in 152Dy and 192H9 [7,8,25,26]. The wave function of the real state at spin I is decomposed into a SD part and a ND part ]q~>= a, lS'D> +a,~IND> with a~2 + a n2 = 1. The mixing amplitudes can be obtained using our results because, assuming vanishing electromagnetic (EM) transition probabilities between SD and ND states, the decay probability out of the band at spin I is given by Aout = a~(I).An. Here An is the EM decay probability in the ND well, for which one should consider statistical E1 and collective E2 and M1 transitions. The E1 decay probability AE1 can be calculated within the statistical model, using Fermigas approximation for the level density of [7,27]. with a pairing gap of 2,Ca0 = 1 M e V and a level density parameter a = 22.4 M e V - I : A~1 = ~E1

£~ p(u - Ew) ~

P-~)

3

" fGDR( Ew) " E'~ " dew

(3)

It is found that calculated E1 decay probability at spin 10 h is three orders of magnitude larger than the collective E2 decay probability. Therefore this last, as well as the M1 which is supposed to be of the same order can be neglected. The I = 10//SD state in 194pb is assumed to have an excitation energy of about 4 MeV above the yrast line [7,8]. For this excitation energy the calculated E1 decay probability is A~ 1 ~ 15ps -1. For the mixing amplitude one gets then a~(10) ~ 2 . 1 0 -3. The striking result is that as A~ is much larger than Ao,,t and Aint~, a very small admixture of ND configurations to the SD band is sufficient to account for the decay to ND states. The admixture between ND and SD states is often explained in a semiclassical tunneling approach where the tunneling width is given by:

hw~ 2roW Vo~, = 5 V e x p { - 7 - g [ - }

(4)

1

here ~hw~ is the zero point energy in the SD well, a;b is the barrier frequency and W is the barrier height. According to [5] the tunneling probability Tts can be expressed in the limit of high level density and large A~ 1 values in the ND well by Tts ~ Ao~t. In our case we obtain Fo~t = hT~s = 16 + 7l~eV. The action of the tunneling process is given by A = (7r • W/liwb)h. Using hw~ = hwb = 0.6 M e V we obtain an action of A = 11.2 :t: 0.3h and a barrier height at spin 10h of W = 2.1 M e V This result is to be compared with a prediction by Shimizu et al. [7] who, before the information on the lifetime at the point of decay was known, obtained a barrier action A = 4.4h for this same nucleus. 5. C O N C L U S I O N S The two examples presented show that the decay of the SD bands is explained by mixing of ND states in the SD ones. If the excitation energy of the SD band is relatively small the, mixing is strong and the decay involves a few transitions which are strong enough to be seen in experiments performed with the present generation of detector arrays. When the excitation energy of the SD band is large the mixings are much smaller; the decay

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D. Bazzacco /Nuclear Physics A583 (1995) 191-198

proceeds through intermediate steps and is fragmented into so many branches that it is unlikely that with the selectivity of the present generation of detectors any individual transition can be seen. In this case one usually has to resort to the very difficult study of continuous features of the spectrum. The efficiency of present detectors is, however, sufficient to measure with good precision the lifetime of the decaying states which can be used to determine, in a quantitative way, some important parameters of the decay. 6. A C K N O W L E D G E M E N T S

The results presented here have been obtained with the effort of all the participants to the GASP collaboration. All of them are warmly acknowledged. I would like to thank E.Maglione for the band mixing calculations in X33Nd. The lifetime experiment in 194pb has been performed by the Cologne group: special thanks are due in particular to R.Kriicken, A.Dewald, P.Sala and P.von Brentano. REFERENCES

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

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