- Email: [email protected]
l determinations for 12C + 12C
Volume 108B, number 2
PHYSICS LETTERS
14 January 1982
i DETERMINATIONS FOR 12C + 12C ~ H.T. FORTUNE, S.C. HEADLEY 1, A. SPADAFORA 2 , J. SWEET, S. LaFRANCE 3, M.E. COBERN 4 , G.E. MOORE s, M. NEWCOMER, E. WALLASH, L. BLAND, J. GILFOYLE, R. GILMAN, M. CARCHIDI and G.S. STEPHANS Physics Department, University of Pennsylvania, Philadelphia, PA 19104, USA and L.R. GREENWOOD 6, j.R. ERSKINE 7, R.E. SEGEL 8, T.H. BRAID 9 and K. RAGHUNATHAN lo Argonne National Laboratory, Argonne, 1L 60439, USA Received 22 May 1981
Detailed angular-distribution measurements and Legendre-polynomial fits for 12C(12C, C~o)2°Ne(g.s.)in the bombarding energy region of the so-called "12 ÷" bump in 12C ÷ 12C inelastic scattering show conclusively that l = 10 dominates the a o exit channel throughout the range, except near the narrow 12÷ resonance that was previously known.
Excitation functions of the total cross section for inelastic scattering of 12C from 12C exhibit [1] grossstructure bumps, which have been suggested as being characterized by specific l values. The concept of such a rotational-like sequence of "states" is intriguing, but to date, though several have tried, no experiments have succeeded in identifying the l values that characterized the bumps. In fact, there is no evidence that the cross section at each bump is dominated by a single l value, or that the bumps correspond to resonances [2]. We report here on detailed measurements of the 12C(12C, a)20Ne reaction at bombarding energies that comprise the so-called "12 +" bump in inelastic scat-
":~Work supported by the National Science Foundation. ! Present address: Computervision Corp. of Bedford, MA 01730, USA. 2 Present address: Department of Physics, University of Illinois, Urbana, IL 61801, USA. 3 Present address: 69 Princeton Drive, Delran, NJ 08075, USA. 4 Present address: Teleco Oilfields Services, Middletown, CN 06457, USA. s Present address: 3203 ttolly Hill Drive, Falls Church, VA 22042, USA.
tering, which covers the energy range 3 3 - 4 0 MeV (lab). It is already known [ 3 - 5 ] that at least one 12 + and one 10 + resonances exist in this energy range in the a channel. It is not clear, however, to what extent the a and inelastic final channels sample the same resonances. But the cross section for 12C(12C, o0 is not negligible compared to that for inelastic scattering, so one might expect similar effects for the two. Measurements were performed with a 12C beam from the University of Pennsylvania tandem Van de Graaff accelerator and self-supporting isotropically enriched (99.99%) 12C targets having areal density of about 25/~g/cm 2. Beam currents averaged 2 - 6 / a A .
6 Present address: Chemical Engineering Division, Argonne National Laboratory, Argonne, IL 60439, USA 7 Present address: Division of High Energy and Nuclear Physics, Department of Energy, Washington, DC 20545, USA. 8 Present address: Department of Physics, Northwestern University, Evansville,IL 60201, USA. 9 Present address: RAS, Argonne National Laboratory, Argonne, IL 60439, USA. 10 Present address: Systems and Applied Science Corp., Riverdale, MD 20840, USA. 95
Volume 108B, number 2
PHYSICS LETTERS
Excitation functions were measured at four laboratory angles (6 °, 21 ° , 36 °, and 51°), and detailed angular distributions were obtained for 26 bombarding energies. These extended from either 3 ° or 6 ° (lab) to 90 ° (cm) and contained 2 3 - 6 0 points. Monitor detectors at lab angles of -+10 ° allowed a continuous check on the condition of the target and the position o f the beam spot. Angular-distribution data were corrected for carbon buildup (almost always less than 10%) during the course of the run. Each angular distribution was normalized to the excitation function, for which the data were acquired fast enough that carbon buildup was negligible. The absolute cross section scale was obtained I0:
.
.
.
.
.
.
.
.
.
• ,,ili /I~ " , I
t¢
~7
]
1776
\'f%
,
from comparison with the data o f Greenwood et al. [61. The angular distributions are displayed in fig. 1 for the reaction leading to the ground state o f 20Ne. These include also some previously published data from Argonne for which the experimental details are those of ref. [6]. The data have been fitted with the expression (fig. 2) 2L
,~(~, o)
where in the present case, only even rs contribute. Throughout this paper, we use L to denote the maximum value of l. Presence o f resonances would be more apparent in a sum of the foml
..,
--~/{
/.
o.,aAA;: + ,i... %
,.'~ ,v++
u.+,. ...,
= Z) m(E)el(cos o ) , l=O
o(E, o) °°! i.
14 January 1982
.
?
bl(E)h(cos O)
:
i
(again, l is even), but for a given set o f a l ' s , there exists a multiplicity o f sets o f bl'S that produce identical angular distributions. It is usually not possible to iso-
.
2
1.0 ~.",
o
,"
mC(mC,ao)ZONe (g s.)
O0I" , W ~ ' , "" .L [ ~ . .'% ," +, sos o,I ~. ~ ~ x ' " u i ~ Tg
"~
+&,7 V
0.~
•,. ,...,.
o.L
v-,V
,o~
,816
~,J
-~i,
~
1.o
i
-17
~t%
,&+ • /~
" ,+~o'~ ~,J !: o,.L~ '\df~/h fv2 / ',,/ V + U
.-.
~,
/'
~
+7 7 +W!
O.Oh
:
+.-
•
i
~'/
it
,.o~-
2
,,
li/l
I", 4~,~
1.o
0.0 ,._~__"...~,L'..~,..~ 0.0
0
.
.
.
.
.
30
.
.
.
©.©1L
60
(9Cm(deg)
90
0
,
I
30
.
.
.
.
.
1.o ~- ; .
6
,
,
18
1.o~-
L~-#.
-
,
", % 0.0 ~-*,,,,T.,,~--',,,,~-.'. ~
0.0 " L ~ ' , w #"~ " ",''"
i.O~ .
,.O~f;
8
, ",, ,
o.o ~ - : ~ . . - , . -
o.o L + 2 . ~
1.o
1.o .'. "~--
."
20
.,,',.., j.
.t
0.0
r
.
60
@c m (deg)
Fig. 1. Angular distributions for 12C(12C, ao)2°Ne(g.s.) incasured at the c.m. b o m b a r d ! ~ energies listed. They have been fitted to a sum a(E, 0) = Zi=~al(E)Pl(cos 0), and the resulting afs are plotted versusE in fig. 2.
96
,
0
0.0 .
~4
o oP, ".'r" C,"- ~-oo~,-'~---,-
!: "i/ lF
!
,
/
I
I 0 ~,"
o'(8)~a~o%.P,(cosS)
90
o o "k~F~:..,..,,,~,.'~. . . . i
w
I
m
I
19
r_
20
Ec.m.(MeV)
. .
. i
. i
.
. l
i
20 Ecm.(MeV)
iv
~e
19
Fig. 2. Plot o f a / ' s versus c.m. bombarding energy for / = 0 - 2 4 .
Volume 108B, number 2
PHYSICS LETTERS
late a single set of bl'S as being correct, especially when L is large. However, some information about the bfs can be obtained from the aL's. The al's are real, o f course, whereas all but (an arbitrary) one o f the bl'S are complex. If we choose b L to be real, then a2L arises only from b L and vice versa, i.e. b 2 ~ a2L. Hence, b L is unique. At all bombarding energies investigated in the present work, L = 24 is sufficient to fit the data, i.e. there is no evidence for l > 12. Thus, 13 parameters are enough to characterize the data. Since our angular distributions all contain at least 23 points (roughly evenly spaced), the data provide quite accurate values of these 13 al's. At all energies, some l = 12 is required to fit the data, i.e. a24 4 : 0 in this energy region. However, except for the previously known 12 + resonance, at an energy o f 18.5 MeV (cm), no evidence is found for any additional resonant behavior of I = 12. Furthermore, throughout the energy range, a20 and a22 are significantly larger than a24. And there are resonancelike structures for the al's except for a24. Now, i f / = 12,a22 in the linear sum can arise only from b l 0 and b12 in the coherent sum. Thus any resonance structures in a22 must be due to resonances in bl0 and/or b12. The absence of resonances in a24 (except the one mentioned above) and their presence in a22 strongly suggests resonances characterized by l = 10. Contributions to a20 arise only from terms in
14 January !982
the coherent sum containing b8, b l 0 , b12 (again for l <~ 12). The smallness of a24 relative to a22 makes it unlikely that I = 12 makes a significant contribution to a20. Hence we would expect the energy dependence of a20 to also exhibit any l = 10 resonances that may be present. We thus conclude that in the laboratory energy range 3 3 - 4 0 MeV, the c~0 channel is dominated by l = 10 and there is no hint for any l = 12 resonances except the one reported earlier. Thue either the c~0 and inelastic channels are characterized by different l values or the "12 ÷" bump has been incorrectly labeled. It would be of interest to investigate more carefully the micro structure in the inelastic data in order to ascertain whether it correlates with that of c~0. We already know that considerable correlation exists between the c~ + 2°Ne and 8Be + 12C channels.
References [ 1] T.M. Cormier et al., Phys. Rev. Lett. 38 (1977) 940; 40 (1978) 924. [2] L.E. Cannell, R.W. Zurmuhle and D.P. Balamuth, Phys, Rev. Lett. 43 (1979) 837, [3] H.T. Fortune, T.H. Braid, R.E. Segel and K. Raghunathan, Phys. Lett. 63B (1976) 403. [4] H.T. Fortune et al., Phys, Rev. C14 (1976) 1271. [5] N.R. Fletcher et al., Phys, Rev. C13 (1976) 1173. [6] L.R. Greenwood et al., Phys. Rev. C12 (1975) 156.
97
PHYSICS LETTERS
14 January 1982
i DETERMINATIONS FOR 12C + 12C ~ H.T. FORTUNE, S.C. HEADLEY 1, A. SPADAFORA 2 , J. SWEET, S. LaFRANCE 3, M.E. COBERN 4 , G.E. MOORE s, M. NEWCOMER, E. WALLASH, L. BLAND, J. GILFOYLE, R. GILMAN, M. CARCHIDI and G.S. STEPHANS Physics Department, University of Pennsylvania, Philadelphia, PA 19104, USA and L.R. GREENWOOD 6, j.R. ERSKINE 7, R.E. SEGEL 8, T.H. BRAID 9 and K. RAGHUNATHAN lo Argonne National Laboratory, Argonne, 1L 60439, USA Received 22 May 1981
Detailed angular-distribution measurements and Legendre-polynomial fits for 12C(12C, C~o)2°Ne(g.s.)in the bombarding energy region of the so-called "12 ÷" bump in 12C ÷ 12C inelastic scattering show conclusively that l = 10 dominates the a o exit channel throughout the range, except near the narrow 12÷ resonance that was previously known.
Excitation functions of the total cross section for inelastic scattering of 12C from 12C exhibit [1] grossstructure bumps, which have been suggested as being characterized by specific l values. The concept of such a rotational-like sequence of "states" is intriguing, but to date, though several have tried, no experiments have succeeded in identifying the l values that characterized the bumps. In fact, there is no evidence that the cross section at each bump is dominated by a single l value, or that the bumps correspond to resonances [2]. We report here on detailed measurements of the 12C(12C, a)20Ne reaction at bombarding energies that comprise the so-called "12 +" bump in inelastic scat-
":~Work supported by the National Science Foundation. ! Present address: Computervision Corp. of Bedford, MA 01730, USA. 2 Present address: Department of Physics, University of Illinois, Urbana, IL 61801, USA. 3 Present address: 69 Princeton Drive, Delran, NJ 08075, USA. 4 Present address: Teleco Oilfields Services, Middletown, CN 06457, USA. s Present address: 3203 ttolly Hill Drive, Falls Church, VA 22042, USA.
tering, which covers the energy range 3 3 - 4 0 MeV (lab). It is already known [ 3 - 5 ] that at least one 12 + and one 10 + resonances exist in this energy range in the a channel. It is not clear, however, to what extent the a and inelastic final channels sample the same resonances. But the cross section for 12C(12C, o0 is not negligible compared to that for inelastic scattering, so one might expect similar effects for the two. Measurements were performed with a 12C beam from the University of Pennsylvania tandem Van de Graaff accelerator and self-supporting isotropically enriched (99.99%) 12C targets having areal density of about 25/~g/cm 2. Beam currents averaged 2 - 6 / a A .
6 Present address: Chemical Engineering Division, Argonne National Laboratory, Argonne, IL 60439, USA 7 Present address: Division of High Energy and Nuclear Physics, Department of Energy, Washington, DC 20545, USA. 8 Present address: Department of Physics, Northwestern University, Evansville,IL 60201, USA. 9 Present address: RAS, Argonne National Laboratory, Argonne, IL 60439, USA. 10 Present address: Systems and Applied Science Corp., Riverdale, MD 20840, USA. 95
Volume 108B, number 2
PHYSICS LETTERS
Excitation functions were measured at four laboratory angles (6 °, 21 ° , 36 °, and 51°), and detailed angular distributions were obtained for 26 bombarding energies. These extended from either 3 ° or 6 ° (lab) to 90 ° (cm) and contained 2 3 - 6 0 points. Monitor detectors at lab angles of -+10 ° allowed a continuous check on the condition of the target and the position o f the beam spot. Angular-distribution data were corrected for carbon buildup (almost always less than 10%) during the course of the run. Each angular distribution was normalized to the excitation function, for which the data were acquired fast enough that carbon buildup was negligible. The absolute cross section scale was obtained I0:
.
.
.
.
.
.
.
.
.
• ,,ili /I~ " , I
t¢
~7
]
1776
\'f%
,
from comparison with the data o f Greenwood et al. [61. The angular distributions are displayed in fig. 1 for the reaction leading to the ground state o f 20Ne. These include also some previously published data from Argonne for which the experimental details are those of ref. [6]. The data have been fitted with the expression (fig. 2) 2L
,~(~, o)
where in the present case, only even rs contribute. Throughout this paper, we use L to denote the maximum value of l. Presence o f resonances would be more apparent in a sum of the foml
..,
--~/{
/.
o.,aAA;: + ,i... %
,.'~ ,v++
u.+,. ...,
= Z) m(E)el(cos o ) , l=O
o(E, o) °°! i.
14 January 1982
.
?
bl(E)h(cos O)
:
i
(again, l is even), but for a given set o f a l ' s , there exists a multiplicity o f sets o f bl'S that produce identical angular distributions. It is usually not possible to iso-
.
2
1.0 ~.",
o
,"
mC(mC,ao)ZONe (g s.)
O0I" , W ~ ' , "" .L [ ~ . .'% ," +, sos o,I ~. ~ ~ x ' " u i ~ Tg
"~
+&,7 V
0.~
•,. ,...,.
o.L
v-,V
,o~
,816
~,J
-~i,
~
1.o
i
-17
~t%
,&+ • /~
" ,+~o'~ ~,J !: o,.L~ '\df~/h fv2 / ',,/ V + U
.-.
~,
/'
~
+7 7 +W!
O.Oh
:
+.-
•
i
~'/
it
,.o~-
2
,,
li/l
I", 4~,~
1.o
0.0 ,._~__"...~,L'..~,..~ 0.0
0
.
.
.
.
.
30
.
.
.
©.©1L
60
(9Cm(deg)
90
0
,
I
30
.
.
.
.
.
1.o ~- ; .
6
,
,
18
1.o~-
L~-#.
-
,
", % 0.0 ~-*,,,,T.,,~--',,,,~-.'. ~
0.0 " L ~ ' , w #"~ " ",''"
i.O~ .
,.O~f;
8
, ",, ,
o.o ~ - : ~ . . - , . -
o.o L + 2 . ~
1.o
1.o .'. "~--
."
20
.,,',.., j.
.t
0.0
r
.
60
@c m (deg)
Fig. 1. Angular distributions for 12C(12C, ao)2°Ne(g.s.) incasured at the c.m. b o m b a r d ! ~ energies listed. They have been fitted to a sum a(E, 0) = Zi=~al(E)Pl(cos 0), and the resulting afs are plotted versusE in fig. 2.
96
,
0
0.0 .
~4
o oP, ".'r" C,"- ~-oo~,-'~---,-
!: "i/ lF
!
,
/
I
I 0 ~,"
o'(8)~a~o%.P,(cosS)
90
o o "k~F~:..,..,,,~,.'~. . . . i
w
I
m
I
19
r_
20
Ec.m.(MeV)
. .
. i
. i
.
. l
i
20 Ecm.(MeV)
iv
~e
19
Fig. 2. Plot o f a / ' s versus c.m. bombarding energy for / = 0 - 2 4 .
Volume 108B, number 2
PHYSICS LETTERS
late a single set of bl'S as being correct, especially when L is large. However, some information about the bfs can be obtained from the aL's. The al's are real, o f course, whereas all but (an arbitrary) one o f the bl'S are complex. If we choose b L to be real, then a2L arises only from b L and vice versa, i.e. b 2 ~ a2L. Hence, b L is unique. At all bombarding energies investigated in the present work, L = 24 is sufficient to fit the data, i.e. there is no evidence for l > 12. Thus, 13 parameters are enough to characterize the data. Since our angular distributions all contain at least 23 points (roughly evenly spaced), the data provide quite accurate values of these 13 al's. At all energies, some l = 12 is required to fit the data, i.e. a24 4 : 0 in this energy region. However, except for the previously known 12 + resonance, at an energy o f 18.5 MeV (cm), no evidence is found for any additional resonant behavior of I = 12. Furthermore, throughout the energy range, a20 and a22 are significantly larger than a24. And there are resonancelike structures for the al's except for a24. Now, i f / = 12,a22 in the linear sum can arise only from b l 0 and b12 in the coherent sum. Thus any resonance structures in a22 must be due to resonances in bl0 and/or b12. The absence of resonances in a24 (except the one mentioned above) and their presence in a22 strongly suggests resonances characterized by l = 10. Contributions to a20 arise only from terms in
14 January !982
the coherent sum containing b8, b l 0 , b12 (again for l <~ 12). The smallness of a24 relative to a22 makes it unlikely that I = 12 makes a significant contribution to a20. Hence we would expect the energy dependence of a20 to also exhibit any l = 10 resonances that may be present. We thus conclude that in the laboratory energy range 3 3 - 4 0 MeV, the c~0 channel is dominated by l = 10 and there is no hint for any l = 12 resonances except the one reported earlier. Thue either the c~0 and inelastic channels are characterized by different l values or the "12 ÷" bump has been incorrectly labeled. It would be of interest to investigate more carefully the micro structure in the inelastic data in order to ascertain whether it correlates with that of c~0. We already know that considerable correlation exists between the c~ + 2°Ne and 8Be + 12C channels.
References [ 1] T.M. Cormier et al., Phys. Rev. Lett. 38 (1977) 940; 40 (1978) 924. [2] L.E. Cannell, R.W. Zurmuhle and D.P. Balamuth, Phys, Rev. Lett. 43 (1979) 837, [3] H.T. Fortune, T.H. Braid, R.E. Segel and K. Raghunathan, Phys. Lett. 63B (1976) 403. [4] H.T. Fortune et al., Phys, Rev. C14 (1976) 1271. [5] N.R. Fletcher et al., Phys, Rev. C13 (1976) 1173. [6] L.R. Greenwood et al., Phys. Rev. C12 (1975) 156.
97