- Email: [email protected]
Alpha particles in coincidence with the superdeformed band in 150Tb
1 August 1996
PHYSICS LETTERS B
ELSEVIER
Physics Letters B 382 (1996) 24-28
Alpha particles in coincidence with the superdeformed band in
150Tb G. Viesti a, M. Lunardon a, D. Bazzacco a, R. Burch a, D. Fabris a, S. Lunardi a, N.H. Medina a, G. Nebbia a, C. Rossi Alvarez a G. de Angelis b, M. Cinausero b, E. Famea b, E. Fioretto b, G. Prete b, G. Vedovato b a Dipartimento di Fisica dell'Universitd di Padova, and LN.EN. Sezione di Padova, 1-35131 Padova, Italy b I.N.EN. Laboratori Nazionali di Legnaro, 1-35020 Legnaro (Padova), Italy Received 5 March 1996; revised manuscript received 13 May 1996 Editor: R.H. Siemssen
Abstract
Alpha particle spectra in coincidence both with normal deformed (ND) and superdeformed (SD) bands of ~5°Tb have been measured using the reaction 12°Sn(aTCl,tr3n) at 187 MeV bombarding energy. A clear difference is observed between the two spectra, that in coincidence with the SD states being shifted to lower energies. This effect is understood in terms of different angular momentum regions from which the ND and SD states originate. The standard statistical model fails to describe the angular momentum dependence of the alpha particle energies. PACS: 27.70.+q; 21.10.Re; 25.70.Gh Keywords: Heavy-ion reactions; Superdeformed band; Statistical model; Deformation; Angular momentum
The study of correlations between particle evaporation from highly excited compound nuclei at large angular momenta and the states in the final, cold evaporation residues (ER) is a field of investigation which only has been opened, in the last few years, with the advent of high efficiency detection systems [ 1-5]. With the new large v-ray arrays it is now possible to observe many different bands in the same final nucleus with shapes ranging from spherical to superdeformed (SD) and to correlate them with the evaporation spectra. It is generally accepted that the particle evaporation from the compound nucleus is chaotic (i.e. only the relevant quantities as energy, angular momentum and parity are conserved) and that only in the near-yrast
~/cascade, where the feeding of different classes of states takes place, the ordered motion is restored [6]. Compound nucleus decay is then indicated as an example of chaos-to-order transition. The sensitivity of the particle spectra on the feeding of specific states in the residual nuclei can be taken as an indication that additional degrees of freedom might be important in the evaporation process or that particular regions of the phase space open to the decay populate preferentially some selected structures in the final cold nucleus. This latter point is important for the understanding of the feeding mechanism of SD states. Several experiments performed so far did not find a clear dependence of the shapes of the particle spectra on the excited states having different deformations in
0370-2693/96/$12.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PH S 0 3 7 0 - 2 6 9 3 ( 9 6 ) 0 0 6 1 9 - 3
25
G. Viesti et a l . / Physics Letters B 382 (1996) 24-28
the ER. For example, the proton spectra in coincidence with transitions in the SD bands of 133Nd [4] and IS2Dy nuclei [4,5] were found to be similar to those in coincidence with transitions in the normal deformed (ND) bands. Furthermore, the shapes of the proton spectra in coincidence with different ND structures in a given decay channel are very similar when a defined region of angular momentum is selected. In contrast, there is a strong dependence of the shape and the centroid of the proton spectra on the angular momentum region [ 1-3]. This strong dependence is satisfactorily reproduced by statistical model calculations. Alpha particles have been proposed since long as a sensitive probe of the deformation of the emitting nucleus [7]. In this letter results are presented of an experiment in which we have measured the energy spectra of alpha particles associated with different classes of states (ND and SD) in the 15°Tb nucleus populated in the reaction 37C1(12°Sn,a3ny) 15°Tb. The experiment was performed at the XTU Tandem facility of the Laboratori Nazionali di Legnaro using a beam of 187 MeV 37C1 (intensity ~8 pnA) and a target made of two foils (0.5 mg/cm2+0.4 mg/cm 2) of 12°Sn. Gamma-rays were detected with the GASP spectrometer [8], which consists of an array of 40 large volume Compton suppressed Ge detectors and of an inner ball of 80 Bismuth Germanate (BGO) crystals. Charged particles were detected with the ISIS silicon ball which is made of 40 AE-E telescopes ( 130 /zm and 1000/~m thick, respectively) covering a geometrical solid angle of about 90% of 47r. The event trigger was determined by any three or more Compton suppressed Ge detectors and five or more BGO scintillators firing in coincidence with the charged particle detectors. A total of 5.5x 108 events in coincidence with alpha particles were recorded. The a spectra presented in this work are those measured in the first forward ring of the silicon ball (six telescopes at 0lab ,v 34 ° ) for which the threshold due to the thickness of the AE detector is unimportant. The energy spectra of the telescopes were summed, after gain matching. The data in coincidence with a-particles have been sorted into various 2- and 3-dimension arrays (matrices and cubes), with proper conditions on the fold k and sum energy H measured in the inner ball. The T-ray spectra in coincidence with alpha particles and associated with long T-ray cascades selected in the inner ball (fold k > 10 and sum energy H >
O~ 600
l~rb SD bond 1 Q • •0011
0 tD • Ib •
• •
Z3 400 Q)
•
('-) 200 O' 50(
750
1000
1250
e
Energy (keY)
1500
Fig. 1. The superdeformedband in 150Thobservedin the present experimentin coincidencewith alphaparticles. The spectrumhas been obtained by double gating on all combinationsof clean in-band transitions [9,10] with conditionson the inner ball fold k > 10 and sum energy H > 14 MeV. Transitionsbelongingto the SD band are markedby heavydots. 14 MeV) are very clean and practically only show the residual nuclei 149'150Tb. With the mentioned conditions on fold and sum energy, the total number of events is only 1.6x 108. The spectrum of the known yrast SD band in 15°Tb [9,10] extracted from the y T-Y data in coincidence with c~-particles is shown in Fig. 1. The intensity of the band is ~,0.7% of the 15°Tb total population, a figure which compares well with the data of the (31P,5n) reaction reported in Ref. [ 10]. The t~ particle spectra in coincidence with ND states in 149'150Tbnuclei and with the yrast SD band of 15°Tb are shown in Fig. 2. For comparison, Monte Carlo CASCADE Statistical Model calculations [ 11,12] are presented in the same figure. The spectral shapes of the alpha particles in coincidence with ND states are reproduced by calculations in which standard input parameters [5] are used, with the exception of the emission barrier which is lowered. This is achieved by increasing the radius in the Optical Model potential (r = 1.2xr0, where r0 is the radius of the spherical nucleus). The radius expansion has been introduced often in the past in order to simulate the emission from a deformed nucleus [ 12]. A decrease of the mean alpha particle energy associated with the 149Tb nucleus (a4n decay, (E~) = 25.24 MeV) with respect to ]5°Tb (ot3n decay, (E,,) = 26.90 MeV) is evident from Fig. 2. This effect is well accounted for by the statistical model calculations which give {EC~ ~ac) = 25.6 MeV and (E~ Ic) = 26.8 MeV, respectively. The a-spectrum in coincidence with the yrast SD
26
G. Viesti et al./ Physics Letters B 382 (1996) 24-28
10 8 10 7 10 6 > (l) ~10 5
~'~
,i
~
800
c10
•• •
1000
,,
1200
'49Tb
09
%,
C
o
•
*\\
° ,/'-~
°
•
•/
,
', ,#
10 2
150
0
Tb
L)
,,,(X20)
500 250 800
1000
1200
E.>27 MeV
1000[
i\ I
10
MeV
Fnergy (keV)
4
0103
~-(o 7
/
C \
--~
1
"E600 " • • ~400
',, 1 5 0 T I ~
,,\
CASCADE
/ u SD
750 i 500
•
O.
•
•
•
~0
f"!
250 10
20
30
40
50
60
Energy (MeV) Fig. 2. Alpha particle spectra from the first ring of the ISIS detector in coincidence with transitions in the l~'149Tb nuclei. The spectra relative to the normally deformed states have been obtained by requiring a double coincidence with the y-rays of 786 keV (15/2---ql/2-) and 290 keV (23/2---.19/2-) in 149Thand with the ),-raysof 355 keV ( 18---~16- ) and 276 keV (16----.15-) in 15°Tb.The spectrumin coincidencewith the yrast SD band in 15°Tb has been obtained by double gating on in-band transitions as detailed in the text. In the inset the ),-projection of the ),-Ea matrix is reported. Transitions belonging to the SD band are marked by heavy dots. Alpha particle spectra from the Monte Carlo versionof the code CASCADE are also shown. They are normalized to the experimentalspectra in the region of their maxima. band of 15°Tb has been derived from the y - y - E , , cube by carefully selecting the gates on the transitions of the band in order to avoid contaminations from other structures. This is possible since detailed level schemes of both the t49Tb and 15°Tb nuclei are available [ 13,14]. We have also verified in the y - y - y cube that, by double gating on the selected SD transitions, none of the lines appearing in the resulting y-ray spectrum belong to the 149Tb nucleus. The alpha particle spectrum in coincidence with the 15°Tb yrast SD band was constructed using the following procedure: first a y-E,, matrix was created from the y - y - E , , cube
800
1000
1200
Energy (keY)
Fig. 3. The yrast SD band of 15°Tbin coincidencewith a particles havingenergieslowerand higherthan the averagea-particle energy (Ea} for ND states, respectively. without background subtraction. A y-E,, background matrix was then created selecting proper background regions for each SD transition. This background matrix was subtracted from the previous one. The inset of Fig. 2 shows the y-projection of the resulting y-E,~ matrix. The final spectrum of Fig. 2 was obtained using only the SD band transitions with energies of 954, 1007, 1112, 1166, 1219 and 1272 keV. The average energy of this spectrum is (E,~) -- 25.06-4-0.01 MeV, which is about 2 MeV lower than that derived for the ND states of 15°Tb. As a cross check of this result, two y - y matrices were also created from the y-y-E,~ coincidence data requiring a coincidence with a-particles of energy larger than or lower than the average energy of the spectrum in coincidence with the ND states of 15°Tb. Gates have then been set on the SD transitions in both y - y matrices. The results reported in Fig. 3, confirm that the SD band is preferentially populated (a factor 1.9 larger) by alpha particles having lower energies.
27
G. Viesti et al./ Physics Letters B 382 (1996) 24-28
In order to explain the shift in energy between the alpha particles associated with the ND and SD bands we will next explore their angular momentum dependence and how this is reflected by the average energy
10 ~0 1 50
10 9
'% 26
(E,,). For this purpose, we have extracted the k-fold distributions of the events associated with the spectra of Fig. 2 by double gating on a y-y-k cube. The fold distributions themselves do not exhibit sizeable differences when selecting ND ((kND) = 18.3) and SD ((ksD) = 18.6) transitions in the 15°Tb nucleus. This does not imply a similarity in the associated angular momentum, because the average multipolarity of the gamma-rays cascade in coincidence with ND and SD states is not the same [15]. The feeding of the yrast SD band of 15°Tb is known to occur at spins IER~48-58h [9,13] and this is confirmed by the feeding pattern obtained in the present experiment. Therefore, we may associate to the measured mean fold (ksD) in coincidence with the SD band an angular momentum of at least IER~53h. Taking into account a correction AJN8 h for the angular momentum carded away by the alpha particles [ 16], the average value of the compound nucleus angular momentum correlated with the SD spectrum is estimated to be (JsD)>61 h. On the other hand, the value (kND) = 18.3 for the ND states of 15°Tb nucleus can be associated with a much lower angular momentum value, (JND)~47 h, using an empirical spin-fold calibration for ND states in this mass region [ 17] and the above defined correction for the a-particles evaporation. In order to understand better the role of the angular momentum in the observed effects, we have derived the ~ spectra feeding the ND states in ~5°Tb for three different fold conditions k = 11-15, k = 16-20 and k = 21-25, which correspond roughly [ 17] to JND~35h, 46h and 59h, respectively. As shown in Fig. 4, the spectra exhibit, with increasing fold, a shift toward lower energies becoming also narrower. Qualitatively, the same effect was observed in the proton spectra of Refs. [ 1,2,5] where it was reproduced by statistical model calculations and explained in terms of the reduction of the thermal energy available to the decay chain when increasing the fold k (or equivalently the angular momentum). The correlation between (E,~) and the average angular momentum is reported in the inset of Fig. 4, where the value in coincidence with the SD band is also included. The experimental data
> 28
Tb=27 J~V'
10 8
~
W
25
I-e,
24 20
40
10 7 6
~10
60 '
Spi~ (~) k~
(J)
~10
11-15
5
(35 ~)
(/3
-4--'
4
0 o'o#, \
(--) 10 3
~
°
o\
10 2
e ° \ "~
•
10 1
10
16-20 (4-6 ~)
20
30
",.
40
21-25
(59 ~)
50
Energy (MeV)
60
Fig. 4. Alpha particle spectra in coincidence with the 15°Tb 355 keV (18----.16-) transition for different values of the ),-my fold k measured in the inner ball. The solid lines represent the total a-particle spectrum with no condition in fold. The comparison demonstrates the sensitivity of the spectral shape to the selection in fold. Average energies versus angular momentum are shown in the inset. Stars indicate (F_~) for ND states, the heavy dot that for the SD band. Error bars include also the uncertainty in spin deriving from the response function of the inner ball [17]. The triangles show predictions from CASCADE statistical model calculations.
feature a continuous decrease of the average energy with increasing angular momentum without a distinction between the ND and SD data. Furthermore, from the calculations reported also in the inset of Fig. 4, it appears clearly that the statistical model does not describe correctly the angular momentum dependence of (E~). In fact, the average energy is predicted to increase with the angular momentum suggesting that the reduction in thermal energy is overwhelmed in the model by the so-called spin-off contribution [ 18]. As a conclusion, it seems that the a energy spectra in coincidence with a given decay channel are, as those of protons, affected by the different selection of the ,/-ray fold k and therefore of the angular momentum. In contrast with earlier investigations of the proton
28
G. Viesti et a l . / Physics Letters B 382 (1996) 24-28
spectra, a clear difference in energy is observed between the a spectra in coincidence with states having different deformation in a given decay channel, the SD channel being shifted to lower energies. Despite the uncertainties in deriving the angular momentum from the measured k-fold in the case of the ND and SD structures, the present work strongly suggests that this shift is related to the differences in the angular momenta associated with the two classes of states. The standard statistical model fails in reproducing quantitatively and qualitatively the angular momentum dependence of the tr spectra. A further lowering of the emission barriers, with respect to the Optical Model ones, seems to be required to describe the spectra at the higher angular momenta. The failure of the model predictions was not evidenced in earlier studies because of the lower sensitivity of the energy spectra of protons to angular momentum induced effects (as the spin-off energy and changes in the emission barrier). The modelling of the statistical decay at large angular momenta, especially in the region of competition between evaporation and fission (J:-,70h in the present case) should be further pursued as it is particularly important for the understanding of the feeding mechanism of the SD bands and of the dynamics of the fission process.
We thank the accelerator crew of the Tandem XTU in Legnaro for providing good beam quality and efficient operation during the experiment. Thanks are due also to A. Buscemi, M. Caldogno, R. Isocrate and R. Zanon for skillful technical help in preparing the experiment. References [1] [2] [3] [4] [5] [6l [7]
[8] [9] [ 10] [11] [12] [13] [14] [ 15] [ 16] [17] [18]
D.G. Samntites et ai., Phys. Rev. Lett. 64 (1990) 2129. D.J. Blumenthal et al., Phys. Rev. Lett. 66 (1991) 3121. K.R. Phol et al., Phys. Rev. 49 (1994) 1372. A. Galindo-Uribarri, Prog. Part. Nucl. Phys. 28 (1992) 463. G. Viesti et al., Phys. Rev. C 51 (1995) 2385. T.L. Khoo et al., Nucl. Phys. A 557 (1993) 83. R.G. Stokstadt, Treatise on Heavy-lon Science, ed. D.A. Bmmley (Plenum, New York, 1985) Vol. 3, p. 83 and references therein. D. Bazzacco et al., Phys. Lett. B 309 (1993) 235. M.A. Deleplanque et al., Phys. Rev. C 39 (1989) 1651. P. Fallon et ai., Phys. Rev. C 52 (1995) 93. E Pulhofer, Nucl. Phys. A 280 (1977) 267. R.K. Choudhury et ai., Phys. Lett. B 143 (1984) 74. G. Duchene et al., Z. Phys. A 350 (1994) 39. Z. Meliani et al., Nucl. Phys. A 575 (1994) 221. See for example E Soramei et al., Phys. Lett. B 350 (1995) 173 and references therein. Average value estimated by the statistical model code PACE2 see A. Gavron, Phys. Rev. C 20 (1980) 1230. M. Lops, Thesis, University of Padova 1994, unpublished. N.N. Ajitanand et al., Phys. Rev. C 34 (1986) 877.
PHYSICS LETTERS B
ELSEVIER
Physics Letters B 382 (1996) 24-28
Alpha particles in coincidence with the superdeformed band in
150Tb G. Viesti a, M. Lunardon a, D. Bazzacco a, R. Burch a, D. Fabris a, S. Lunardi a, N.H. Medina a, G. Nebbia a, C. Rossi Alvarez a G. de Angelis b, M. Cinausero b, E. Famea b, E. Fioretto b, G. Prete b, G. Vedovato b a Dipartimento di Fisica dell'Universitd di Padova, and LN.EN. Sezione di Padova, 1-35131 Padova, Italy b I.N.EN. Laboratori Nazionali di Legnaro, 1-35020 Legnaro (Padova), Italy Received 5 March 1996; revised manuscript received 13 May 1996 Editor: R.H. Siemssen
Abstract
Alpha particle spectra in coincidence both with normal deformed (ND) and superdeformed (SD) bands of ~5°Tb have been measured using the reaction 12°Sn(aTCl,tr3n) at 187 MeV bombarding energy. A clear difference is observed between the two spectra, that in coincidence with the SD states being shifted to lower energies. This effect is understood in terms of different angular momentum regions from which the ND and SD states originate. The standard statistical model fails to describe the angular momentum dependence of the alpha particle energies. PACS: 27.70.+q; 21.10.Re; 25.70.Gh Keywords: Heavy-ion reactions; Superdeformed band; Statistical model; Deformation; Angular momentum
The study of correlations between particle evaporation from highly excited compound nuclei at large angular momenta and the states in the final, cold evaporation residues (ER) is a field of investigation which only has been opened, in the last few years, with the advent of high efficiency detection systems [ 1-5]. With the new large v-ray arrays it is now possible to observe many different bands in the same final nucleus with shapes ranging from spherical to superdeformed (SD) and to correlate them with the evaporation spectra. It is generally accepted that the particle evaporation from the compound nucleus is chaotic (i.e. only the relevant quantities as energy, angular momentum and parity are conserved) and that only in the near-yrast
~/cascade, where the feeding of different classes of states takes place, the ordered motion is restored [6]. Compound nucleus decay is then indicated as an example of chaos-to-order transition. The sensitivity of the particle spectra on the feeding of specific states in the residual nuclei can be taken as an indication that additional degrees of freedom might be important in the evaporation process or that particular regions of the phase space open to the decay populate preferentially some selected structures in the final cold nucleus. This latter point is important for the understanding of the feeding mechanism of SD states. Several experiments performed so far did not find a clear dependence of the shapes of the particle spectra on the excited states having different deformations in
0370-2693/96/$12.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PH S 0 3 7 0 - 2 6 9 3 ( 9 6 ) 0 0 6 1 9 - 3
25
G. Viesti et a l . / Physics Letters B 382 (1996) 24-28
the ER. For example, the proton spectra in coincidence with transitions in the SD bands of 133Nd [4] and IS2Dy nuclei [4,5] were found to be similar to those in coincidence with transitions in the normal deformed (ND) bands. Furthermore, the shapes of the proton spectra in coincidence with different ND structures in a given decay channel are very similar when a defined region of angular momentum is selected. In contrast, there is a strong dependence of the shape and the centroid of the proton spectra on the angular momentum region [ 1-3]. This strong dependence is satisfactorily reproduced by statistical model calculations. Alpha particles have been proposed since long as a sensitive probe of the deformation of the emitting nucleus [7]. In this letter results are presented of an experiment in which we have measured the energy spectra of alpha particles associated with different classes of states (ND and SD) in the 15°Tb nucleus populated in the reaction 37C1(12°Sn,a3ny) 15°Tb. The experiment was performed at the XTU Tandem facility of the Laboratori Nazionali di Legnaro using a beam of 187 MeV 37C1 (intensity ~8 pnA) and a target made of two foils (0.5 mg/cm2+0.4 mg/cm 2) of 12°Sn. Gamma-rays were detected with the GASP spectrometer [8], which consists of an array of 40 large volume Compton suppressed Ge detectors and of an inner ball of 80 Bismuth Germanate (BGO) crystals. Charged particles were detected with the ISIS silicon ball which is made of 40 AE-E telescopes ( 130 /zm and 1000/~m thick, respectively) covering a geometrical solid angle of about 90% of 47r. The event trigger was determined by any three or more Compton suppressed Ge detectors and five or more BGO scintillators firing in coincidence with the charged particle detectors. A total of 5.5x 108 events in coincidence with alpha particles were recorded. The a spectra presented in this work are those measured in the first forward ring of the silicon ball (six telescopes at 0lab ,v 34 ° ) for which the threshold due to the thickness of the AE detector is unimportant. The energy spectra of the telescopes were summed, after gain matching. The data in coincidence with a-particles have been sorted into various 2- and 3-dimension arrays (matrices and cubes), with proper conditions on the fold k and sum energy H measured in the inner ball. The T-ray spectra in coincidence with alpha particles and associated with long T-ray cascades selected in the inner ball (fold k > 10 and sum energy H >
O~ 600
l~rb SD bond 1 Q • •0011
0 tD • Ib •
• •
Z3 400 Q)
•
('-) 200 O' 50(
750
1000
1250
e
Energy (keY)
1500
Fig. 1. The superdeformedband in 150Thobservedin the present experimentin coincidencewith alphaparticles. The spectrumhas been obtained by double gating on all combinationsof clean in-band transitions [9,10] with conditionson the inner ball fold k > 10 and sum energy H > 14 MeV. Transitionsbelongingto the SD band are markedby heavydots. 14 MeV) are very clean and practically only show the residual nuclei 149'150Tb. With the mentioned conditions on fold and sum energy, the total number of events is only 1.6x 108. The spectrum of the known yrast SD band in 15°Tb [9,10] extracted from the y T-Y data in coincidence with c~-particles is shown in Fig. 1. The intensity of the band is ~,0.7% of the 15°Tb total population, a figure which compares well with the data of the (31P,5n) reaction reported in Ref. [ 10]. The t~ particle spectra in coincidence with ND states in 149'150Tbnuclei and with the yrast SD band of 15°Tb are shown in Fig. 2. For comparison, Monte Carlo CASCADE Statistical Model calculations [ 11,12] are presented in the same figure. The spectral shapes of the alpha particles in coincidence with ND states are reproduced by calculations in which standard input parameters [5] are used, with the exception of the emission barrier which is lowered. This is achieved by increasing the radius in the Optical Model potential (r = 1.2xr0, where r0 is the radius of the spherical nucleus). The radius expansion has been introduced often in the past in order to simulate the emission from a deformed nucleus [ 12]. A decrease of the mean alpha particle energy associated with the 149Tb nucleus (a4n decay, (E~) = 25.24 MeV) with respect to ]5°Tb (ot3n decay, (E,,) = 26.90 MeV) is evident from Fig. 2. This effect is well accounted for by the statistical model calculations which give {EC~ ~ac) = 25.6 MeV and (E~ Ic) = 26.8 MeV, respectively. The a-spectrum in coincidence with the yrast SD
26
G. Viesti et al./ Physics Letters B 382 (1996) 24-28
10 8 10 7 10 6 > (l) ~10 5
~'~
,i
~
800
c10
•• •
1000
,,
1200
'49Tb
09
%,
C
o
•
*\\
° ,/'-~
°
•
•/
,
', ,#
10 2
150
0
Tb
L)
,,,(X20)
500 250 800
1000
1200
E.>27 MeV
1000[
i\ I
10
MeV
Fnergy (keV)
4
0103
~-(o 7
/
C \
--~
1
"E600 " • • ~400
',, 1 5 0 T I ~
,,\
CASCADE
/ u SD
750 i 500
•
O.
•
•
•
~0
f"!
250 10
20
30
40
50
60
Energy (MeV) Fig. 2. Alpha particle spectra from the first ring of the ISIS detector in coincidence with transitions in the l~'149Tb nuclei. The spectra relative to the normally deformed states have been obtained by requiring a double coincidence with the y-rays of 786 keV (15/2---ql/2-) and 290 keV (23/2---.19/2-) in 149Thand with the ),-raysof 355 keV ( 18---~16- ) and 276 keV (16----.15-) in 15°Tb.The spectrumin coincidencewith the yrast SD band in 15°Tb has been obtained by double gating on in-band transitions as detailed in the text. In the inset the ),-projection of the ),-Ea matrix is reported. Transitions belonging to the SD band are marked by heavy dots. Alpha particle spectra from the Monte Carlo versionof the code CASCADE are also shown. They are normalized to the experimentalspectra in the region of their maxima. band of 15°Tb has been derived from the y - y - E , , cube by carefully selecting the gates on the transitions of the band in order to avoid contaminations from other structures. This is possible since detailed level schemes of both the t49Tb and 15°Tb nuclei are available [ 13,14]. We have also verified in the y - y - y cube that, by double gating on the selected SD transitions, none of the lines appearing in the resulting y-ray spectrum belong to the 149Tb nucleus. The alpha particle spectrum in coincidence with the 15°Tb yrast SD band was constructed using the following procedure: first a y-E,, matrix was created from the y - y - E , , cube
800
1000
1200
Energy (keY)
Fig. 3. The yrast SD band of 15°Tbin coincidencewith a particles havingenergieslowerand higherthan the averagea-particle energy (Ea} for ND states, respectively. without background subtraction. A y-E,, background matrix was then created selecting proper background regions for each SD transition. This background matrix was subtracted from the previous one. The inset of Fig. 2 shows the y-projection of the resulting y-E,~ matrix. The final spectrum of Fig. 2 was obtained using only the SD band transitions with energies of 954, 1007, 1112, 1166, 1219 and 1272 keV. The average energy of this spectrum is (E,~) -- 25.06-4-0.01 MeV, which is about 2 MeV lower than that derived for the ND states of 15°Tb. As a cross check of this result, two y - y matrices were also created from the y-y-E,~ coincidence data requiring a coincidence with a-particles of energy larger than or lower than the average energy of the spectrum in coincidence with the ND states of 15°Tb. Gates have then been set on the SD transitions in both y - y matrices. The results reported in Fig. 3, confirm that the SD band is preferentially populated (a factor 1.9 larger) by alpha particles having lower energies.
27
G. Viesti et al./ Physics Letters B 382 (1996) 24-28
In order to explain the shift in energy between the alpha particles associated with the ND and SD bands we will next explore their angular momentum dependence and how this is reflected by the average energy
10 ~0 1 50
10 9
'% 26
(E,,). For this purpose, we have extracted the k-fold distributions of the events associated with the spectra of Fig. 2 by double gating on a y-y-k cube. The fold distributions themselves do not exhibit sizeable differences when selecting ND ((kND) = 18.3) and SD ((ksD) = 18.6) transitions in the 15°Tb nucleus. This does not imply a similarity in the associated angular momentum, because the average multipolarity of the gamma-rays cascade in coincidence with ND and SD states is not the same [15]. The feeding of the yrast SD band of 15°Tb is known to occur at spins IER~48-58h [9,13] and this is confirmed by the feeding pattern obtained in the present experiment. Therefore, we may associate to the measured mean fold (ksD) in coincidence with the SD band an angular momentum of at least IER~53h. Taking into account a correction AJN8 h for the angular momentum carded away by the alpha particles [ 16], the average value of the compound nucleus angular momentum correlated with the SD spectrum is estimated to be (JsD)>61 h. On the other hand, the value (kND) = 18.3 for the ND states of 15°Tb nucleus can be associated with a much lower angular momentum value, (JND)~47 h, using an empirical spin-fold calibration for ND states in this mass region [ 17] and the above defined correction for the a-particles evaporation. In order to understand better the role of the angular momentum in the observed effects, we have derived the ~ spectra feeding the ND states in ~5°Tb for three different fold conditions k = 11-15, k = 16-20 and k = 21-25, which correspond roughly [ 17] to JND~35h, 46h and 59h, respectively. As shown in Fig. 4, the spectra exhibit, with increasing fold, a shift toward lower energies becoming also narrower. Qualitatively, the same effect was observed in the proton spectra of Refs. [ 1,2,5] where it was reproduced by statistical model calculations and explained in terms of the reduction of the thermal energy available to the decay chain when increasing the fold k (or equivalently the angular momentum). The correlation between (E,~) and the average angular momentum is reported in the inset of Fig. 4, where the value in coincidence with the SD band is also included. The experimental data
> 28
Tb=27 J~V'
10 8
~
W
25
I-e,
24 20
40
10 7 6
~10
60 '
Spi~ (~) k~
(J)
~10
11-15
5
(35 ~)
(/3
-4--'
4
0 o'o#, \
(--) 10 3
~
°
o\
10 2
e ° \ "~
•
10 1
10
16-20 (4-6 ~)
20
30
",.
40
21-25
(59 ~)
50
Energy (MeV)
60
Fig. 4. Alpha particle spectra in coincidence with the 15°Tb 355 keV (18----.16-) transition for different values of the ),-my fold k measured in the inner ball. The solid lines represent the total a-particle spectrum with no condition in fold. The comparison demonstrates the sensitivity of the spectral shape to the selection in fold. Average energies versus angular momentum are shown in the inset. Stars indicate (F_~) for ND states, the heavy dot that for the SD band. Error bars include also the uncertainty in spin deriving from the response function of the inner ball [17]. The triangles show predictions from CASCADE statistical model calculations.
feature a continuous decrease of the average energy with increasing angular momentum without a distinction between the ND and SD data. Furthermore, from the calculations reported also in the inset of Fig. 4, it appears clearly that the statistical model does not describe correctly the angular momentum dependence of (E~). In fact, the average energy is predicted to increase with the angular momentum suggesting that the reduction in thermal energy is overwhelmed in the model by the so-called spin-off contribution [ 18]. As a conclusion, it seems that the a energy spectra in coincidence with a given decay channel are, as those of protons, affected by the different selection of the ,/-ray fold k and therefore of the angular momentum. In contrast with earlier investigations of the proton
28
G. Viesti et a l . / Physics Letters B 382 (1996) 24-28
spectra, a clear difference in energy is observed between the a spectra in coincidence with states having different deformation in a given decay channel, the SD channel being shifted to lower energies. Despite the uncertainties in deriving the angular momentum from the measured k-fold in the case of the ND and SD structures, the present work strongly suggests that this shift is related to the differences in the angular momenta associated with the two classes of states. The standard statistical model fails in reproducing quantitatively and qualitatively the angular momentum dependence of the tr spectra. A further lowering of the emission barriers, with respect to the Optical Model ones, seems to be required to describe the spectra at the higher angular momenta. The failure of the model predictions was not evidenced in earlier studies because of the lower sensitivity of the energy spectra of protons to angular momentum induced effects (as the spin-off energy and changes in the emission barrier). The modelling of the statistical decay at large angular momenta, especially in the region of competition between evaporation and fission (J:-,70h in the present case) should be further pursued as it is particularly important for the understanding of the feeding mechanism of the SD bands and of the dynamics of the fission process.
We thank the accelerator crew of the Tandem XTU in Legnaro for providing good beam quality and efficient operation during the experiment. Thanks are due also to A. Buscemi, M. Caldogno, R. Isocrate and R. Zanon for skillful technical help in preparing the experiment. References [1] [2] [3] [4] [5] [6l [7]
[8] [9] [ 10] [11] [12] [13] [14] [ 15] [ 16] [17] [18]
D.G. Samntites et ai., Phys. Rev. Lett. 64 (1990) 2129. D.J. Blumenthal et al., Phys. Rev. Lett. 66 (1991) 3121. K.R. Phol et al., Phys. Rev. 49 (1994) 1372. A. Galindo-Uribarri, Prog. Part. Nucl. Phys. 28 (1992) 463. G. Viesti et al., Phys. Rev. C 51 (1995) 2385. T.L. Khoo et al., Nucl. Phys. A 557 (1993) 83. R.G. Stokstadt, Treatise on Heavy-lon Science, ed. D.A. Bmmley (Plenum, New York, 1985) Vol. 3, p. 83 and references therein. D. Bazzacco et al., Phys. Lett. B 309 (1993) 235. M.A. Deleplanque et al., Phys. Rev. C 39 (1989) 1651. P. Fallon et ai., Phys. Rev. C 52 (1995) 93. E Pulhofer, Nucl. Phys. A 280 (1977) 267. R.K. Choudhury et ai., Phys. Lett. B 143 (1984) 74. G. Duchene et al., Z. Phys. A 350 (1994) 39. Z. Meliani et al., Nucl. Phys. A 575 (1994) 221. See for example E Soramei et al., Phys. Lett. B 350 (1995) 173 and references therein. Average value estimated by the statistical model code PACE2 see A. Gavron, Phys. Rev. C 20 (1980) 1230. M. Lops, Thesis, University of Padova 1994, unpublished. N.N. Ajitanand et al., Phys. Rev. C 34 (1986) 877.