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Correlated intermediate structures in the elastic-inelastic scattering and α-transfer channels of 24Mg + 24Mg
Volume 185, number 3,4
PHYSICS LETTERS B
19 February 1987
CORRELATED INTERMEDIATE STRUCTURES IN THE ELASTIC-INELASTIC AND a-TRANSFER CHANNELS OF z4Mg+24Mg S SAINI’, RR
SCATTERING
BETTS
Argonne Natronal Laboratory2, 9700 South Cass Avenue, IL 60439, USA
R W ZURMljHLE,
P H KUTT
Physzcs Department, Unrversztyof Pennsylvama3, Phtladelphru, PA 19104, USA
and B K. DICHTER4 A W Wrrght Nuclear Structure LaboratoryZ, Yale Umverszty, New Haven, CT 06520, USA Received 7 October 1986
Excitation functions for the u-transfer reaction 24Mg(24Mg~@Ne)*sS1 as well as the elastic and melasoc scattermg of 24Mg+24Mg have been measured m 100 keV steps over the energy range Elab= 89 720 - 95 520 MeV The u-transfer channels show narrow structures of width rCM - 200 keV which are strongly correlated with the structures m the elastic and melastic channels The dlstnbutlon of resonance strength mto vanous modes of decay is deduced from the measured data
The resonance behavior of light heavy-ion (HI) systems has been studied extensively [ 11, raising many interesting questions concerning nulcear structure effects at high excitation energies and angular momenta More recently, narrow resonances of wdth rCM= 100-300 keV have been observed m the elastic and melastlc scattenng of the heavier systems 28S1+28S1 [2,3] and 24Mg+24Mg [4] In particular, the 24Mg+24Mg system shows narrow and well-lsolated resonances that are strongly correlated m the elastic and melastlc excitation functions These narrow states are characterized by excitation energies of E,=50-60 MeV m the compound system 48Cr and angular momenta [ 4,5 ] close to the grazing value m ’ Present address Physics Department, Umverslty of Pennsylvania, Philadelphia, PA 19 104, USA * Work performed under the auspices ofthe Of&e of High Energy and Nuclear Phyacs, Division of Nuclear Physics, US department of Energy 3 Work supported by the National Science Foundation 4 Present address Physics Dlvlslon, Argonne National Laboratory, Argonne, IL 60439, USA
316
the entrance channel One possible interpretation of these structures 1s that they correspond to states of very large deformation m the composite system This interpretation is supported by the results of calculations [ 6,6] of potential energy surfaces which predict the existence of extremely deformed metastable states for the compound systems 56N1and 48Cr m the region of angular momenta and excitation energies relevant to the observed narrow resonances An important aspect of this mterpretatlon 1s that the decay of a well-defined super-deformed configuratlon should proceed not only to the symmetric decay channel but to all open channels, perhaps with enhanced widths to fission-hke decays We may, therefore, expect slmllar narrow structures to appear coherently m decay modes other than elastic and melastlc scattering We also known [ 41 that the elastic and low-lying inelastic transltlons exhaust only 15-20% of the total resonance strength The mappmg of the remaining decay strength to vanous reaction channels 1s of great interest and may help m the
0370-2693/87/$ (North-Holland
03 50 0 Elsevier Science Publishers Physics Pubhshmg Dlvulon)
BV
Volume 185, number 3,4
19 February 1987
PHYSICS LETTERS B
detalled understanding of these states In the present letter, we report the observation of narrow structures m the reaction 24Mg(24Mg, 20Ne)28S1 which are strongly correlated v&h the structures seen m elastic and melastlc scattermg Such correlations among exit channels of different mass dlvlslon have not been observed before m this mass region These observations are in contrast to the results of studies [ 8,9] of the reactlons 24Mg(160,160)24Mg and 24Mg(160,12C)28S~,where no such correlations were observed A 24Mgbeam from the Brookhaven National Laboratory MP tandem was used to bombard a target conslstmg of 15 &cm2 of 24Mg metal evaporated onto a thin 12Cbacking The reaction products were ldentlfied by measurmg their energes and angles (E,, t13, E4, and e,) m a comcldence arrangement consisting of two pontoon-senatlve solid-state detectors placed at 45” on either side of the beam axis The defining detector covered an angular range of A&,, = 25 ’ m the reaction plane with a solid angle of 23 msr The recoil detector was placed close to the target with an opening angle of A&,, = 33’ The comcadence efflclency of this setup is N 100% for Q-values close to elastic events and decreases almost linearly to zero for two-body reaction events with Q- -30 MeV The excitation fun&Ions for elastic and melastlc scattering, and the a-transfer channel 24Mg(24Mg,20Ne)28S1were measured in 100 keV steps over the energy range E,,,=89.720-95 520 MeV The data were normalized to the elastic scattering yields measured m two monitor detectors placed at ? 15’ relative to the beam axis Typical Q-value spectra for the exit channel a nd 24Mg(24Mg,24Mg)24Mgare 24Mg(24Mg,20Ne)28S1 shown m fig 1 The lowest three peaks are unamblguously identified In ldentlfymg the other resolved peaks, It has been assumed that only the collective smgle or mutual excltatlons of the fragments are excited to an appreciable extent It is clear that the atransfer channels are weakly populated compared to the elastic and inelastic channels Excitation functions for the three lowest-lying transitions in the reactions 24Mg(24Mg,2?Ne)28Sland 24Mg(24Mg,24Mg)24Mgare compared m fig 2 The plotted cross sections are averaged over the angular acceptance of the defining detector and corrected for the comcldence efflclency The three strong struc-
60
,
,
,
I ’ I
’
I
’ I
’
I
’ 1 ’
6+0+
24Mq(24Mg,20Ne) 2*S~ , ’ , 40
20 ? 20 2 0 100
0 -28
-24
-20
-16
-8
-12
Q-VALUE
-4
0
4
(MeV)
Fig 1 Q-value spectra for the reactions “‘Mg(“Mg,*~e)‘*Sl and 2“Mg(‘4Mg,*4Mg)2”Mgfor Ebb = 9 1 320 MeV The fall off at lower Q-values reflects m part the decreasing comcldence eficlency The peak labels correspond to lcnown levels m the residual nuclei
44
45
46
47
48
E cm (MeV)
Fig 2 Excitation functions for the three lowest transltlons m the reactions (a) Z4Mg(24Mg,Z4Mg)24Mg and (b) 24Mg(24Mg, 2@Ne)Z8SiThe cross sectlons are averaged over the angular range 32 5”
Volume 185, number 3,4
PHYSICS LETTERS B
tures seen in the 24Mg ( 24Mg, 2°Ne) 2851 reaction (fig 2b) at energies ECM=45 66, 46 64, and 47 25 MeV show clearly visible correlations not only among themselves but also with the structures seen in the elastic and xnelasuc channels (fig 2a) The strong correlations between structures in the two different mass exit channels indicate a c o m m o n non-statistical origin for these structures The a-transfer excitatxon functions also show a weak structure at ECM-----45 40 MeV which does not appear m the entrance channel except the 2-- 0 + transition We have also analyzed the energy dependence o f the cross sectmn In the 2a-transfer channel 24Mg(24Mg,160)325 The cross section for this reaction 1S quite small and the statistical uncertainties in the data preclude any definite conclusion about possible correlations between this channel and the data shown in fig 2 In order to quantify our observations and put them in a better perspective, the data were subjected to tests for statistical fluctuatmns as outhned in ref [ 3 ] The summed deviation function D(E) and the cross-correlation function C(E) were deduced from the experimental data using a sliding gaussian smoothmg function o f F ~ ss = 0 5 MeV The averaging interval was chosen such that the moments o f the D(E) and C(E) distributions do not show large variations with the averaging interval The D(E) and C(E) for the 24Mg(24Mg,2°Ne) 2ss1 and 24Mg(24Mg,24Mg)24Mg reactions were first calculated separately using the excitation function data for the transitions shown m figs. 2a and 2b Except for some minor details, D(E) and C(E) for the two reactions l~oked very similar The D(E) and C(E) for the 24Mg(24Mg,2°Ne)2SS1 reaction are shown in fig 3b The strong peaks or dips in D(E) and peaks i n C(E) signify strong correlations among the excit a t i o n functions of the transitions shown in fig 2b It is clear from fig 3b that the maxima and m l m m a corresponding to the three structures at ECM = 45 66, 46 64, and 47 25 MeV are strongly correlated The same observation was found to be true for the data o f fig 2a for the 24Mg(24Mg,24Mg)24Mg r e a c t i o n Next, to establish that the structures seen m the 24Mg(24Mg,2°Ne)28S1 reaction have strong correlations with the structures in the 24Mg(24Mg, 24Mg)EgMg reaction, D(E) and C(E) were calculated by combining the data of figs 2a and 2b To 318
19 February 1987 3
i
,
i
o -1 7
7
C3
-1 -2
-
44
45
46 P"cm (MeW
47
48
Fig 3 Summed deviation functions D(E) and cross-correlation functions C(E) versus bombarding energy in the center of mass D(E) and C(E) are obtained from (a) the three lowest transitions m the reactions 24Mg(24Mg,2°Ne) 28S1 and 24Mg(24Mg,24Mg)24Mg (data of fig 2a and fig 2b) and, (b) the three lowest transluons m 24Mg(24Mg,2°Ne)2851 (data of fig 2b) The dashed hnes indicate 95% confidence limits for statistical
fluctuattons suppress the contribution to the correlations coming from the transitions within a reaction channel (lntrareaction correlations) and thus accentuate the correlations between the two reaction channels (interreaction correlations), only the cross terms between the two reactions were retained in the calculation of C(E) The functions D(E) and C(E) thus obtained are shown in fig 3a Strong correlations between structures seen in the two reactions are clearly evident in fig 3a The results o f this analysis are summarlzed m table 1 The variance o f the experimental distributions of D ( E ) and C(E) are much larger than the corresponding values expected for statistical fluctuations, indicating a non-statistical ongln for the structures in figs. 2a and 2b The dashed hnes in fig 3 indicate 95% confidence limits on D(E) and C ( E ) calculated for statistical fluctuations [ 3 ]. Clearly, the events corresponding to the structures lie outside these hmlts In order to get an idea about the distribution of the resonance strength into various decay channels, the
V o l u m e 185, n u m b e r 3,4
PHYSICS LETTERS B
19 February 1987
Table 1 Results of fluctuation analysis Mean (/t) and variance (0"2) for the experimental distributions of D ( E ) and C(E) are compared wath that expected for statistical fluctuations Reaction
D(E)
Data set
/./
24Mg(24Mg,24Mg)24Mg 24Mg(24Mg,2°ye)28Sl both reactions
experament a) fluctuations experiment b) fluctuations experiment ~) fluctuations
0 0 0 0 0 0
O0 O0 O0 O0 O0 O0
C(E) 0 -2
~
0 0 0 0 0 0
0 0 0 0 0 0
735 33 658 33 568 167
0-2
602 O0 528 O0 427 O0
0 556 033 0714 0 33 0 464 011
a) Using experimental data of fig 2a b) Using experimental data of fig 2b o U s l n g e x p e r l m e n t a l d a t a o f f i g s 2 a a n d 2 b For detalls see text Table 2 Resonance parameters for the structures at ECM = 45 66, 46 64, and 47 25 MeV for various exit channels ER (MeV)
F (keV) a)
45 66
180+25
46 64
230+30
47 25
195+30
Final state b)
gs 2+0 + 2+2 + 4+0 + 4+2 + 6+0 + 4+4 + 6+4 +
-rF,~/F d) gs 2+0 + 2+2 + 4+0 + 4+2 + 6+0 + 4+4 + 6+4 +
~rF,~/1" a) gs 2+0 + 2+2 + 4+0 + 4+2 + 6+0 + 4+4 + 6+4 +
".~F./F a)
Z4Mg(24Mg,24Mg)24Mg
24Mg(e4Mg,2°Ne)28Sl
F,.IF(XlO -2)
y~/7~p( x 10 -z) c)
F ~ / F ( X 10 -2)
y~/y~p(X 10 -2) ~)
1 75 3 80 4 40 210 2 15 11 00 11 00 6 40 3t 6 1 47 7 40 5 10 2 10 3 50 2 80 2 80 3 60 25 97 139 4 90 2 70 0 65 1 10 5 40 5 40 1 14 1728
140 1 90 1 53 1 11 0 81 1070 4 58 5 90
013 0 53 1 07 107 1 40 1 70 1 70
0094 0 25 0 38 038 0 50 1 60 1 24
483 022 1 10 1 20 1 20 0 93 1 80 1 80
0 10 0 34 0 31 0 31 0 23 1 00 0 80
5 25 019 0 36 0 60 0 60 0 93 3 60 3 60
009 0 12 0 15 0 15 0 24 1 85 1 50
076 2 60 1 28 0 74 0 93 1 70 0 75 1 90 070 1 70 0 70 0 23 0 30 3 00 1 60 0 60
568
") Total width F has been corrected for target thickness effects b) States excited m the residual nuclei c) ?~ =F,~ P / w i t h PI=2kR/(F] +G] ) The R-matrix matching radms R ( f m ) = 1 5(A 1/3 +A4t/3) was used The single-particle Wlgner hmlt y~p is given by 3h2/2#R 2 a) Summation in ~rF~,/1" refers only to the s u m over the states listed in the table 319
Volume 185, number 3,4
PHYSICS LETTERS B
three structures at ECM=45 66, 46 64, and 47 25 MeV were analyzed as isolated resonances supenmposed on a nonresonafit direct-reaction background, using the Brelt-Wagner formula
The resonance spm was taken to be 34fi, based on previously measured angular &stnbutlons [ 4,5] The maximum resonance cross section was obtained by Incoherent subtraction of a smooth nonresonant background The total resonance cross sectlons were then obtained by assummg angular dlstrlbutlons of the type P:( cos 0) and l/sm 6 for the g s and excited state transitions respectively The resulting resonance parameters are shown m table 2 The reduced widths ~2, =r, P, were calculated assuming a maximum value for the Coulomb penetrability PI which occurs for a stretched configuration, e g , l= J-S where J IS the resonance spm and S= S, + S2, S, and S2 being the spins of the residual nuclei The ratios of the reduced wdth (r: ) to the single-partde limit ( y$) were obtained wth a radms parameter ro= 1 50 fm The estimated error on partial wdths and reduced widths is N 20% and is mainly due to errors m background subtraction Although an appreciable fraction of the decay strength goes into the 24Mg(24Mg,20Ne)*‘Si reaction, it is lower by a factor of 4- 10 as compared to elastic and inelastic strength It 1s also clear from table 2 that decay to high spin final states 1s favored m some cases To summanze, we have observed narrow resochannel in the a-transfer nance structures 24Mg(24Mg,20Ne)28S1These structures show strong correlations mth structures m the elastic and melastic channels Such strong correlations between the
320
19 February 1981
entrance and mass rearrangement exit channels have not been observed before m such heavy systems and suggest a resonance mechanism which 1s mdependent of the specific reaction channel The resonances have a slgmficant partial width (30-40% of the total wdth) for decay mto fission-like channels However, the resonance decay strength carried by atransfers 1s small compared v&h the entrance channel decays It may be that these resonances corespond to superdeformed high spm states m 48Cr as predicted by ref. [ 7 ] which because of their special structure, do not mix strongly with the rest of the contmuum states However, much more expenmental as well as theoretlcal work needs to be done m order to firmly establish this type of connection between the resonances and the states m the highly deformed second muuma References [ 1] E Ahnqulst, D A Bromley and J A Kuehner, Phys Rev Lett 4 (1960) 515, K.A Eberhard, ed , Selected contnbutlons m resonances in heavy-ion reactions (Spnnger, Berlin, 1982) [ 21 R R Betts, B B Back and B G Glagola, Phys Rev Lett 47 (1981) 23, R R Betts, S B DiCenzo and J F Petersen, Phys Rev Lett 43 (1979) 253 [ 31 S Sam1 and R R Betts, Phys Rev C 29 (1984) 1769 [4] RW Zurmuhleetal,Phys Lett B 129 (1983) 384 [ 51 R R Betts et al , to be published [ 61 G Leander and S E Larsson, Nucl Phys A 239 (1975) 93, S E Larsson et al , Nucl Phys A 261 (1976) 77, T Bengtsson et al, Phys Scr 24 (1981) 200 [ 71 M E Faber and M PloszaJczak, Phys Scr 24 (1981) 189, pnvate communication [8] M Pauletal,Phys Rev C21 (1980) 1802 [9] SJ Sandersetal,Phys Rev C22(1980) 1914
PHYSICS LETTERS B
19 February 1987
CORRELATED INTERMEDIATE STRUCTURES IN THE ELASTIC-INELASTIC AND a-TRANSFER CHANNELS OF z4Mg+24Mg S SAINI’, RR
SCATTERING
BETTS
Argonne Natronal Laboratory2, 9700 South Cass Avenue, IL 60439, USA
R W ZURMljHLE,
P H KUTT
Physzcs Department, Unrversztyof Pennsylvama3, Phtladelphru, PA 19104, USA
and B K. DICHTER4 A W Wrrght Nuclear Structure LaboratoryZ, Yale Umverszty, New Haven, CT 06520, USA Received 7 October 1986
Excitation functions for the u-transfer reaction 24Mg(24Mg~@Ne)*sS1 as well as the elastic and melasoc scattermg of 24Mg+24Mg have been measured m 100 keV steps over the energy range Elab= 89 720 - 95 520 MeV The u-transfer channels show narrow structures of width rCM - 200 keV which are strongly correlated with the structures m the elastic and melastic channels The dlstnbutlon of resonance strength mto vanous modes of decay is deduced from the measured data
The resonance behavior of light heavy-ion (HI) systems has been studied extensively [ 11, raising many interesting questions concerning nulcear structure effects at high excitation energies and angular momenta More recently, narrow resonances of wdth rCM= 100-300 keV have been observed m the elastic and melastlc scattenng of the heavier systems 28S1+28S1 [2,3] and 24Mg+24Mg [4] In particular, the 24Mg+24Mg system shows narrow and well-lsolated resonances that are strongly correlated m the elastic and melastlc excitation functions These narrow states are characterized by excitation energies of E,=50-60 MeV m the compound system 48Cr and angular momenta [ 4,5 ] close to the grazing value m ’ Present address Physics Department, Umverslty of Pennsylvania, Philadelphia, PA 19 104, USA * Work performed under the auspices ofthe Of&e of High Energy and Nuclear Phyacs, Division of Nuclear Physics, US department of Energy 3 Work supported by the National Science Foundation 4 Present address Physics Dlvlslon, Argonne National Laboratory, Argonne, IL 60439, USA
316
the entrance channel One possible interpretation of these structures 1s that they correspond to states of very large deformation m the composite system This interpretation is supported by the results of calculations [ 6,6] of potential energy surfaces which predict the existence of extremely deformed metastable states for the compound systems 56N1and 48Cr m the region of angular momenta and excitation energies relevant to the observed narrow resonances An important aspect of this mterpretatlon 1s that the decay of a well-defined super-deformed configuratlon should proceed not only to the symmetric decay channel but to all open channels, perhaps with enhanced widths to fission-hke decays We may, therefore, expect slmllar narrow structures to appear coherently m decay modes other than elastic and melastlc scattering We also known [ 41 that the elastic and low-lying inelastic transltlons exhaust only 15-20% of the total resonance strength The mappmg of the remaining decay strength to vanous reaction channels 1s of great interest and may help m the
0370-2693/87/$ (North-Holland
03 50 0 Elsevier Science Publishers Physics Pubhshmg Dlvulon)
BV
Volume 185, number 3,4
19 February 1987
PHYSICS LETTERS B
detalled understanding of these states In the present letter, we report the observation of narrow structures m the reaction 24Mg(24Mg, 20Ne)28S1 which are strongly correlated v&h the structures seen m elastic and melastlc scattermg Such correlations among exit channels of different mass dlvlslon have not been observed before m this mass region These observations are in contrast to the results of studies [ 8,9] of the reactlons 24Mg(160,160)24Mg and 24Mg(160,12C)28S~,where no such correlations were observed A 24Mgbeam from the Brookhaven National Laboratory MP tandem was used to bombard a target conslstmg of 15 &cm2 of 24Mg metal evaporated onto a thin 12Cbacking The reaction products were ldentlfied by measurmg their energes and angles (E,, t13, E4, and e,) m a comcldence arrangement consisting of two pontoon-senatlve solid-state detectors placed at 45” on either side of the beam axis The defining detector covered an angular range of A&,, = 25 ’ m the reaction plane with a solid angle of 23 msr The recoil detector was placed close to the target with an opening angle of A&,, = 33’ The comcadence efflclency of this setup is N 100% for Q-values close to elastic events and decreases almost linearly to zero for two-body reaction events with Q- -30 MeV The excitation fun&Ions for elastic and melastlc scattering, and the a-transfer channel 24Mg(24Mg,20Ne)28S1were measured in 100 keV steps over the energy range E,,,=89.720-95 520 MeV The data were normalized to the elastic scattering yields measured m two monitor detectors placed at ? 15’ relative to the beam axis Typical Q-value spectra for the exit channel a nd 24Mg(24Mg,24Mg)24Mgare 24Mg(24Mg,20Ne)28S1 shown m fig 1 The lowest three peaks are unamblguously identified In ldentlfymg the other resolved peaks, It has been assumed that only the collective smgle or mutual excltatlons of the fragments are excited to an appreciable extent It is clear that the atransfer channels are weakly populated compared to the elastic and inelastic channels Excitation functions for the three lowest-lying transitions in the reactions 24Mg(24Mg,2?Ne)28Sland 24Mg(24Mg,24Mg)24Mgare compared m fig 2 The plotted cross sections are averaged over the angular acceptance of the defining detector and corrected for the comcldence efflclency The three strong struc-
60
,
,
,
I ’ I
’
I
’ I
’
I
’ 1 ’
6+0+
24Mq(24Mg,20Ne) 2*S~ , ’ , 40
20 ? 20 2 0 100
0 -28
-24
-20
-16
-8
-12
Q-VALUE
-4
0
4
(MeV)
Fig 1 Q-value spectra for the reactions “‘Mg(“Mg,*~e)‘*Sl and 2“Mg(‘4Mg,*4Mg)2”Mgfor Ebb = 9 1 320 MeV The fall off at lower Q-values reflects m part the decreasing comcldence eficlency The peak labels correspond to lcnown levels m the residual nuclei
44
45
46
47
48
E cm (MeV)
Fig 2 Excitation functions for the three lowest transltlons m the reactions (a) Z4Mg(24Mg,Z4Mg)24Mg and (b) 24Mg(24Mg, 2@Ne)Z8SiThe cross sectlons are averaged over the angular range 32 5”
Volume 185, number 3,4
PHYSICS LETTERS B
tures seen in the 24Mg ( 24Mg, 2°Ne) 2851 reaction (fig 2b) at energies ECM=45 66, 46 64, and 47 25 MeV show clearly visible correlations not only among themselves but also with the structures seen in the elastic and xnelasuc channels (fig 2a) The strong correlations between structures in the two different mass exit channels indicate a c o m m o n non-statistical origin for these structures The a-transfer excitatxon functions also show a weak structure at ECM-----45 40 MeV which does not appear m the entrance channel except the 2-- 0 + transition We have also analyzed the energy dependence o f the cross sectmn In the 2a-transfer channel 24Mg(24Mg,160)325 The cross section for this reaction 1S quite small and the statistical uncertainties in the data preclude any definite conclusion about possible correlations between this channel and the data shown in fig 2 In order to quantify our observations and put them in a better perspective, the data were subjected to tests for statistical fluctuatmns as outhned in ref [ 3 ] The summed deviation function D(E) and the cross-correlation function C(E) were deduced from the experimental data using a sliding gaussian smoothmg function o f F ~ ss = 0 5 MeV The averaging interval was chosen such that the moments o f the D(E) and C(E) distributions do not show large variations with the averaging interval The D(E) and C(E) for the 24Mg(24Mg,2°Ne) 2ss1 and 24Mg(24Mg,24Mg)24Mg reactions were first calculated separately using the excitation function data for the transitions shown m figs. 2a and 2b Except for some minor details, D(E) and C(E) for the two reactions l~oked very similar The D(E) and C(E) for the 24Mg(24Mg,2°Ne)2SS1 reaction are shown in fig 3b The strong peaks or dips in D(E) and peaks i n C(E) signify strong correlations among the excit a t i o n functions of the transitions shown in fig 2b It is clear from fig 3b that the maxima and m l m m a corresponding to the three structures at ECM = 45 66, 46 64, and 47 25 MeV are strongly correlated The same observation was found to be true for the data o f fig 2a for the 24Mg(24Mg,24Mg)24Mg r e a c t i o n Next, to establish that the structures seen m the 24Mg(24Mg,2°Ne)28S1 reaction have strong correlations with the structures in the 24Mg(24Mg, 24Mg)EgMg reaction, D(E) and C(E) were calculated by combining the data of figs 2a and 2b To 318
19 February 1987 3
i
,
i
o -1 7
7
C3
-1 -2
-
44
45
46 P"cm (MeW
47
48
Fig 3 Summed deviation functions D(E) and cross-correlation functions C(E) versus bombarding energy in the center of mass D(E) and C(E) are obtained from (a) the three lowest transitions m the reactions 24Mg(24Mg,2°Ne) 28S1 and 24Mg(24Mg,24Mg)24Mg (data of fig 2a and fig 2b) and, (b) the three lowest transluons m 24Mg(24Mg,2°Ne)2851 (data of fig 2b) The dashed hnes indicate 95% confidence limits for statistical
fluctuattons suppress the contribution to the correlations coming from the transitions within a reaction channel (lntrareaction correlations) and thus accentuate the correlations between the two reaction channels (interreaction correlations), only the cross terms between the two reactions were retained in the calculation of C(E) The functions D(E) and C(E) thus obtained are shown in fig 3a Strong correlations between structures seen in the two reactions are clearly evident in fig 3a The results o f this analysis are summarlzed m table 1 The variance o f the experimental distributions of D ( E ) and C(E) are much larger than the corresponding values expected for statistical fluctuations, indicating a non-statistical ongln for the structures in figs. 2a and 2b The dashed hnes in fig 3 indicate 95% confidence limits on D(E) and C ( E ) calculated for statistical fluctuations [ 3 ]. Clearly, the events corresponding to the structures lie outside these hmlts In order to get an idea about the distribution of the resonance strength into various decay channels, the
V o l u m e 185, n u m b e r 3,4
PHYSICS LETTERS B
19 February 1987
Table 1 Results of fluctuation analysis Mean (/t) and variance (0"2) for the experimental distributions of D ( E ) and C(E) are compared wath that expected for statistical fluctuations Reaction
D(E)
Data set
/./
24Mg(24Mg,24Mg)24Mg 24Mg(24Mg,2°ye)28Sl both reactions
experament a) fluctuations experiment b) fluctuations experiment ~) fluctuations
0 0 0 0 0 0
O0 O0 O0 O0 O0 O0
C(E) 0 -2
~
0 0 0 0 0 0
0 0 0 0 0 0
735 33 658 33 568 167
0-2
602 O0 528 O0 427 O0
0 556 033 0714 0 33 0 464 011
a) Using experimental data of fig 2a b) Using experimental data of fig 2b o U s l n g e x p e r l m e n t a l d a t a o f f i g s 2 a a n d 2 b For detalls see text Table 2 Resonance parameters for the structures at ECM = 45 66, 46 64, and 47 25 MeV for various exit channels ER (MeV)
F (keV) a)
45 66
180+25
46 64
230+30
47 25
195+30
Final state b)
gs 2+0 + 2+2 + 4+0 + 4+2 + 6+0 + 4+4 + 6+4 +
-rF,~/F d) gs 2+0 + 2+2 + 4+0 + 4+2 + 6+0 + 4+4 + 6+4 +
~rF,~/1" a) gs 2+0 + 2+2 + 4+0 + 4+2 + 6+0 + 4+4 + 6+4 +
".~F./F a)
Z4Mg(24Mg,24Mg)24Mg
24Mg(e4Mg,2°Ne)28Sl
F,.IF(XlO -2)
y~/7~p( x 10 -z) c)
F ~ / F ( X 10 -2)
y~/y~p(X 10 -2) ~)
1 75 3 80 4 40 210 2 15 11 00 11 00 6 40 3t 6 1 47 7 40 5 10 2 10 3 50 2 80 2 80 3 60 25 97 139 4 90 2 70 0 65 1 10 5 40 5 40 1 14 1728
140 1 90 1 53 1 11 0 81 1070 4 58 5 90
013 0 53 1 07 107 1 40 1 70 1 70
0094 0 25 0 38 038 0 50 1 60 1 24
483 022 1 10 1 20 1 20 0 93 1 80 1 80
0 10 0 34 0 31 0 31 0 23 1 00 0 80
5 25 019 0 36 0 60 0 60 0 93 3 60 3 60
009 0 12 0 15 0 15 0 24 1 85 1 50
076 2 60 1 28 0 74 0 93 1 70 0 75 1 90 070 1 70 0 70 0 23 0 30 3 00 1 60 0 60
568
") Total width F has been corrected for target thickness effects b) States excited m the residual nuclei c) ?~ =F,~ P / w i t h PI=2kR/(F] +G] ) The R-matrix matching radms R ( f m ) = 1 5(A 1/3 +A4t/3) was used The single-particle Wlgner hmlt y~p is given by 3h2/2#R 2 a) Summation in ~rF~,/1" refers only to the s u m over the states listed in the table 319
Volume 185, number 3,4
PHYSICS LETTERS B
three structures at ECM=45 66, 46 64, and 47 25 MeV were analyzed as isolated resonances supenmposed on a nonresonafit direct-reaction background, using the Brelt-Wagner formula
The resonance spm was taken to be 34fi, based on previously measured angular &stnbutlons [ 4,5] The maximum resonance cross section was obtained by Incoherent subtraction of a smooth nonresonant background The total resonance cross sectlons were then obtained by assummg angular dlstrlbutlons of the type P:( cos 0) and l/sm 6 for the g s and excited state transitions respectively The resulting resonance parameters are shown m table 2 The reduced widths ~2, =r, P, were calculated assuming a maximum value for the Coulomb penetrability PI which occurs for a stretched configuration, e g , l= J-S where J IS the resonance spm and S= S, + S2, S, and S2 being the spins of the residual nuclei The ratios of the reduced wdth (r: ) to the single-partde limit ( y$) were obtained wth a radms parameter ro= 1 50 fm The estimated error on partial wdths and reduced widths is N 20% and is mainly due to errors m background subtraction Although an appreciable fraction of the decay strength goes into the 24Mg(24Mg,20Ne)*‘Si reaction, it is lower by a factor of 4- 10 as compared to elastic and inelastic strength It 1s also clear from table 2 that decay to high spin final states 1s favored m some cases To summanze, we have observed narrow resochannel in the a-transfer nance structures 24Mg(24Mg,20Ne)28S1These structures show strong correlations mth structures m the elastic and melastic channels Such strong correlations between the
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entrance and mass rearrangement exit channels have not been observed before m such heavy systems and suggest a resonance mechanism which 1s mdependent of the specific reaction channel The resonances have a slgmficant partial width (30-40% of the total wdth) for decay mto fission-like channels However, the resonance decay strength carried by atransfers 1s small compared v&h the entrance channel decays It may be that these resonances corespond to superdeformed high spm states m 48Cr as predicted by ref. [ 7 ] which because of their special structure, do not mix strongly with the rest of the contmuum states However, much more expenmental as well as theoretlcal work needs to be done m order to firmly establish this type of connection between the resonances and the states m the highly deformed second muuma References [ 1] E Ahnqulst, D A Bromley and J A Kuehner, Phys Rev Lett 4 (1960) 515, K.A Eberhard, ed , Selected contnbutlons m resonances in heavy-ion reactions (Spnnger, Berlin, 1982) [ 21 R R Betts, B B Back and B G Glagola, Phys Rev Lett 47 (1981) 23, R R Betts, S B DiCenzo and J F Petersen, Phys Rev Lett 43 (1979) 253 [ 31 S Sam1 and R R Betts, Phys Rev C 29 (1984) 1769 [4] RW Zurmuhleetal,Phys Lett B 129 (1983) 384 [ 51 R R Betts et al , to be published [ 61 G Leander and S E Larsson, Nucl Phys A 239 (1975) 93, S E Larsson et al , Nucl Phys A 261 (1976) 77, T Bengtsson et al, Phys Scr 24 (1981) 200 [ 71 M E Faber and M PloszaJczak, Phys Scr 24 (1981) 189, pnvate communication [8] M Pauletal,Phys Rev C21 (1980) 1802 [9] SJ Sandersetal,Phys Rev C22(1980) 1914