- Email: [email protected]
The (He3, α) reaction on C13
2.B: 2.G
Nuclear Physics 70 (1965) 561--566; (~) North-Holland Pubhshing Co., Amsterdam Not to be reproduced by photoprlnt or mlcrofdm without written permissionfrom the publisher
T H E (He s, ~) R E A C T I O N O N C Is v. K. DESHPANDE t Department of Phystcs and Astronomy ct, University of Rochester, Rochester, New York Recewed 16 December 1964 Abstract: Angular distributions of alpha particles leading to the 0+ ground state and the 2+ first excited state of C1~have been obtained for the bombarding energies of 8.82, 9.44 and 10 3 MeV. Those leading to the 0 + second excited state were obtained in the forward cone up to 80°. The ground state distributions show forward peaks sensitive to the bombarding energy and strong backward peaks at all energies. The first excited state distributions show strong forward and backward peaks at all energies. The seond exoted state distributions are forward-peaked with cross sections changing rapidly with the bombarding energy. Analysis of the data has been made in terms of the neutron pickup process by using the Oak Ridge distorted wave Born approximation programme. General features of the ground state and the first excited state &stnbutlons, including the strong backward peaks and the various secondary maxima, are found to be accounted for by the pickup process alone. The ratio of the spectroscopic factor for the transition to the first excited state to that for the transition to the ground state is found to be 1.29, in agreement with calculations of Macfarlane and French based on the Rosenfeld exchange mixture.
El
NUCLEAR REACTION a3C(3He, ~), E = 8.8-10.3 MeV; measured or(E; E , 0). Enriched target.
1. Introduction Studies of one-particle a n d two-particle transfer reactions with He 3 as the b o m b a r d ing particle have been made in recent years. M a n y o f the cases studied, particularly those involving the transfer o f a single particle, indicate the presence of a direct stripping or p i c k u p process. C o m p e t i n g processes, particularly c o m p o u n d nucleus f o r m a t i o n , are in general also present, b u t if the b o m b a r d i n g energy is r e a s o n a b l y high these usually do n o t obscure the general features o f a n g u l a r distributions expected o n the basis o f the direct process. Thus useful spectroscopic i n f o r m a t i o n is o b t a i n a b l e t h r o u g h the study o f the (He 3, d) reaction, which is equivalent to the experimentally more difficult (d, n) reaction, a n d the (He 3, e) reaction, which gives the same spectroscopic i n f o r m a t i o n as the (p, d) a n d (d, t) reactions. The Rochester cyclotron, which produces a He 3 b e a m u p to 11 MeV in energy, is being used to study (He 3, e) reactions, a m o n g s t others, to determine the extent to which these reactions can be considered as &rect reactions, a n d to o b t a i n spectroscopic i n f o r m a t i o n . I n the present case the relatively high Q value o f the (He 3, e) reaction m a k e s easy the c o u n t i n g of a l p h a particles in the presence o f a variety o f t Now at I. I. T. Kanpur, Kanpur, India. tt This work was supported by the U.S. Atormc Energy Commission. 561
562
v.K.
DESHPANDE
other reaction products. The C13(He 3, ~) reaction has been studied previously 1,z) for energies below 4.5 MeV. Large backward peaks are observed in this reaction at most energies. The angular distributions at 2.0 and 4.5 MeV were analysed by Owen and Madansky 3) in terms of a coherent mixture of pickup and heavy particle stripping in the plane wave approximation. In the present work data are obtained at higher energies, up to 10.3 MeV and the analysis is done in terms of pickup process by using the DWBA programme at Oak Ridge 4, 8). I0000-
C 13 (H~a) I000-
al 2 I00-
I
z
a
o
I0.
o"
2'0
'
Jo
v
'do
do
:bo
CHANNEL NO. Fig. 1. Pulse height spectrum.
2. Experimental Method The target was made by cracking methyl iodide enriched in the C 13 isotope. The target thickness was 200 #g/cm 2 with about equal amounts of C lz and C Ia. Surface barrier type silicon counters were used to detect the reaction products. The spectrum observed at an angle of 60 degrees is shown in fig. 1. The first three alpha groups from C ~3 can be resolved clearly, although for larger angles the second excited state alpha group starts merging with the ground state alpha group from C ~2. Data for this second state group could not, therefore, be obtained for angles larger than 80 degrees. The Q value of the ground state transition is 15.63 MeV, therefore the alpha groups studied had energies between 17.8 and 25.5 MeV at forward angles. Data could be obtained up to a forward angle of 5 degrees by stopping the scattered He a beam in an aluminium absorber. Measurements were made at 5 degree intervals
(He3, ~) REACTION
563
with additional measurements at intermediate angles when they were found necessary for defining the shape of the curve. The limits of error in the absolute cross section are estimated to be about + 20 ~ , due primarily to uncertainties in the beam integration and the target thickness. 6
4
8 82 MeV
3
°
2
ee °°
•
I
°
}, 0
E
3
I0:50 MeV
2 I
0
°
'
•
°
4b
'
do
'
I~'O
i~o
0CM Fig. 2. G r o u n d
state angular dlstrlbutions f o r the C~3(He a, cQ reactlons showing D W B A arbitrarily normahzed.
fit,
3. Analysis of Data The ground state reaction is a ½- ~ 0 + transition, involving the pickup of a p~ neutron. The angular distributions obtained are shown in fig. 2. Except for the relative intensity of the forward peak, the shapes of the angular distributions do not change much with the bombarding energy. The forward peak contributes little to the total cross section, which is found to have about the same value at all three energies. Strong backward peaks were observed at all three energies. Because of the high Q value of this reaction, the zero-degree m o m e n t u m transfer K corresponds to the second m a x i m u m of (jI(KR)) 2 for R = 5 fm. The angular range 0 to 180 degrees contains four secondary maxima of the Bessel function as observed experimentally. The strong backward maximum however cannot be reproduced by a plane wave treatment of the pickup mechanism. For the distorted wave treatment,
564
V. K. DESHPANDE
scattering d a t a are desirable to p r o v i d e the initial guesses for the optical m o d e l p a r a meters. Since the presently available C 13 targets also c o n t a i n C ' z , elastic scattering d a t a c o u l d n o t easily be o b t a i n e d . A l f o r d et al. 5), have o b t a i n e d fits to the ( H e 3, a) d a t a on 016, in the same energy range. Their p a r a m e t e r s , shown in table 1, were used in the present analysis. T h e p a r a m e t e r s are for the S a x o n - W o o d s well for b o t h the real a n d the i m a g i n a r y potential. S p i n - o r b i t terms were used in defining the o p t i c a l channels as well as in genegrating the b o u n d state wave function. N o fits c o u l d be o b t a i n e d w i t h o u t using a cut-off radius. This single p a r a m e t e r R° was used as the one a d j u s t a b l e variable o f the p r o b l e m . T h e D W B A fits are s h o w n in fig. 2. S t r o n g b a c k TABLE 1 Optical parameters
m out
V
W
r0
ro
a
105 110
21 5
1.52 1.4
1.3 1.3
0.65 0.68
Energy 8.84 9.44 10.30
Re
Re*
5.1 4.9 4.7
4.3 4 15 4.0
•
:5
8 8 2 MeV
/
e /
/
2 |
• •
•
•
•
0
3
9 . 4 4 MeV
L
4
3
I 0 3 0 MeV
0
40
80
120
160
eC.M.
Fig. 3. First excited-state angular distributions showing DWBA fit, arbitrarily normahzed.
(He 3, o:) REACTION
565
ward peaks are produced by the pickup mechanism alone when the plane wave approximation is dropped. A shght variation in the cut-off radius with the bombarding energy does produce a rapid change in the intensity of the forward peak. The overall agreement with the data is fairly good.
7 6 8 8 ; ) MeV
5 4 3
o~
~
I
"o
"-. 0 b "o
•
9 4 4 MeV
3 2 I
0 I0 3 0 MeV
I •
e •
•
e
40
80
OeM Fig. 4
Second excited-state angular distributions.
The reaction leading to the first excited state involves a ½- --* 2 + transition 1,1 which a p~ neutron is picked up. The angular distrlbutxons and the D W B A fits are shown in fig. 3. The parameters used for this case are the same as those for the ground state transition except the cut-off radius R*. W]th the variation m only one parameter, D W B A curves are found which fairly well reproduce the general features of these angular distributions. In particular both large forward and backward peaks are reproduced. In this case as well as the previous one the agreement might well be improved by use of more realistic optical model parameters for the reaction. The angular distributions leading to the second excited state are shown in fig. 4. This reaction involves a ½- ~ 0 + transition in which a p~ neutron is picked up. The angular distributions change rapidly with energy. With the optical parameters used for the two lower states, no fits could be obtained for these angular distributions for
566
v.K. DESHPANDE
any value of the cut-off radius. It is known that this 7.656 MeV, 0 + state of C x2 does not have an s4p 8 configuration 6), The transition to this state could therefore be mainly via the compound nucleus process rather than via the pickup processes. The absolute cross section a, in terms of the output of the Oak Ridge programme Julie 4, a) is given by = (C2S)T(C2S)pD~
1 5.1 x 10 30"Jul '
where T and p refer to the target and the projectde assembly, C is the isospin ClebschGordan coefficient, S is the spectroscopic factor and D Ois the strength of the effective zero range interaction. This effective interaction is to represent the actual finite range interaction between the incoming He 3 and the picked up neutron. In the approximation where the n - H e 3 well is assumed to be of zero range, so that the neutron wave function is exponential everywhere, the formula for D O is D~] =
2.38" 1034B//.~ 3,
where B and/~ are the binding energy and the reduced mass of the neutron. By use of the maximum values of the spectroscopic factor 7) the calculated absolute cross sections are found to be smaller than the experimental cross sections by a factor of about ten. In view of the uncertainty in the strength of the zero range interaction, an analysis on the basis of ratios of cross sections was made. A value of the ratio S * / S for the target can be obtained from the experimental cross sections aexp * and O'ex p for the first excited state and ground state transitions, respectively. This ratio is independent of both the interaction strength and the spectroscopic factor for the projectile. The total cross sections were averaged over the three bombarding energies. The value of S * / S was then given by S*/S
-~- ( O ' e*x p / O ' e x p ) ( O ' J u l / O ' J u * l)
=
1.29.
The value of this ratio has been calculated by Macfarlane and French 7) as a function of the spin orbit parameter. They find that with the Rosenfeld exchange mixture S * / S > 1.2. Macfarlane and French's plane wave analysis of the available (p, d) and (d, t) data on C 13 gave values of 0.95 and 0.78 respectively, which were below the expected minimum. The present value of 1.29 obtained by DWBA analysis therefore perhaps represents some improvement.
1) 2) 3) 4) 5) 6) 7) 8)
References H. D. Holmgren, Phys. Rev. 106 (1957) 100 H. D. Holmgren et al, Phys. Rev. 106 (1957) 102 G. E. Owen, L. Madansky and S. Edwards, Phys. Rev. 113 (1959) 1575 R. H. Bassel, R. M. Dnsko and G. R. Satchler, The Distorted-Wave Theory of Direct Nuclear Reactxon, ORNL-324~) W. P. Alford, L. Blau, D. Chne, private commumcatlon J. B. French, Nuclear spectroscopy, Part B (Academic Press, 1960) M. H. Macfarlane and J. B. French, Revs. Mod. Phys. 32 (1960) 567 G. R. Satchler, Nuclear Physics 55 (1964) 1, and prxvate commumcatlon
Nuclear Physics 70 (1965) 561--566; (~) North-Holland Pubhshing Co., Amsterdam Not to be reproduced by photoprlnt or mlcrofdm without written permissionfrom the publisher
T H E (He s, ~) R E A C T I O N O N C Is v. K. DESHPANDE t Department of Phystcs and Astronomy ct, University of Rochester, Rochester, New York Recewed 16 December 1964 Abstract: Angular distributions of alpha particles leading to the 0+ ground state and the 2+ first excited state of C1~have been obtained for the bombarding energies of 8.82, 9.44 and 10 3 MeV. Those leading to the 0 + second excited state were obtained in the forward cone up to 80°. The ground state distributions show forward peaks sensitive to the bombarding energy and strong backward peaks at all energies. The first excited state distributions show strong forward and backward peaks at all energies. The seond exoted state distributions are forward-peaked with cross sections changing rapidly with the bombarding energy. Analysis of the data has been made in terms of the neutron pickup process by using the Oak Ridge distorted wave Born approximation programme. General features of the ground state and the first excited state &stnbutlons, including the strong backward peaks and the various secondary maxima, are found to be accounted for by the pickup process alone. The ratio of the spectroscopic factor for the transition to the first excited state to that for the transition to the ground state is found to be 1.29, in agreement with calculations of Macfarlane and French based on the Rosenfeld exchange mixture.
El
NUCLEAR REACTION a3C(3He, ~), E = 8.8-10.3 MeV; measured or(E; E , 0). Enriched target.
1. Introduction Studies of one-particle a n d two-particle transfer reactions with He 3 as the b o m b a r d ing particle have been made in recent years. M a n y o f the cases studied, particularly those involving the transfer o f a single particle, indicate the presence of a direct stripping or p i c k u p process. C o m p e t i n g processes, particularly c o m p o u n d nucleus f o r m a t i o n , are in general also present, b u t if the b o m b a r d i n g energy is r e a s o n a b l y high these usually do n o t obscure the general features o f a n g u l a r distributions expected o n the basis o f the direct process. Thus useful spectroscopic i n f o r m a t i o n is o b t a i n a b l e t h r o u g h the study o f the (He 3, d) reaction, which is equivalent to the experimentally more difficult (d, n) reaction, a n d the (He 3, e) reaction, which gives the same spectroscopic i n f o r m a t i o n as the (p, d) a n d (d, t) reactions. The Rochester cyclotron, which produces a He 3 b e a m u p to 11 MeV in energy, is being used to study (He 3, e) reactions, a m o n g s t others, to determine the extent to which these reactions can be considered as &rect reactions, a n d to o b t a i n spectroscopic i n f o r m a t i o n . I n the present case the relatively high Q value o f the (He 3, e) reaction m a k e s easy the c o u n t i n g of a l p h a particles in the presence o f a variety o f t Now at I. I. T. Kanpur, Kanpur, India. tt This work was supported by the U.S. Atormc Energy Commission. 561
562
v.K.
DESHPANDE
other reaction products. The C13(He 3, ~) reaction has been studied previously 1,z) for energies below 4.5 MeV. Large backward peaks are observed in this reaction at most energies. The angular distributions at 2.0 and 4.5 MeV were analysed by Owen and Madansky 3) in terms of a coherent mixture of pickup and heavy particle stripping in the plane wave approximation. In the present work data are obtained at higher energies, up to 10.3 MeV and the analysis is done in terms of pickup process by using the DWBA programme at Oak Ridge 4, 8). I0000-
C 13 (H~a) I000-
al 2 I00-
I
z
a
o
I0.
o"
2'0
'
Jo
v
'do
do
:bo
CHANNEL NO. Fig. 1. Pulse height spectrum.
2. Experimental Method The target was made by cracking methyl iodide enriched in the C 13 isotope. The target thickness was 200 #g/cm 2 with about equal amounts of C lz and C Ia. Surface barrier type silicon counters were used to detect the reaction products. The spectrum observed at an angle of 60 degrees is shown in fig. 1. The first three alpha groups from C ~3 can be resolved clearly, although for larger angles the second excited state alpha group starts merging with the ground state alpha group from C ~2. Data for this second state group could not, therefore, be obtained for angles larger than 80 degrees. The Q value of the ground state transition is 15.63 MeV, therefore the alpha groups studied had energies between 17.8 and 25.5 MeV at forward angles. Data could be obtained up to a forward angle of 5 degrees by stopping the scattered He a beam in an aluminium absorber. Measurements were made at 5 degree intervals
(He3, ~) REACTION
563
with additional measurements at intermediate angles when they were found necessary for defining the shape of the curve. The limits of error in the absolute cross section are estimated to be about + 20 ~ , due primarily to uncertainties in the beam integration and the target thickness. 6
4
8 82 MeV
3
°
2
ee °°
•
I
°
}, 0
E
3
I0:50 MeV
2 I
0
°
'
•
°
4b
'
do
'
I~'O
i~o
0CM Fig. 2. G r o u n d
state angular dlstrlbutions f o r the C~3(He a, cQ reactlons showing D W B A arbitrarily normahzed.
fit,
3. Analysis of Data The ground state reaction is a ½- ~ 0 + transition, involving the pickup of a p~ neutron. The angular distributions obtained are shown in fig. 2. Except for the relative intensity of the forward peak, the shapes of the angular distributions do not change much with the bombarding energy. The forward peak contributes little to the total cross section, which is found to have about the same value at all three energies. Strong backward peaks were observed at all three energies. Because of the high Q value of this reaction, the zero-degree m o m e n t u m transfer K corresponds to the second m a x i m u m of (jI(KR)) 2 for R = 5 fm. The angular range 0 to 180 degrees contains four secondary maxima of the Bessel function as observed experimentally. The strong backward maximum however cannot be reproduced by a plane wave treatment of the pickup mechanism. For the distorted wave treatment,
564
V. K. DESHPANDE
scattering d a t a are desirable to p r o v i d e the initial guesses for the optical m o d e l p a r a meters. Since the presently available C 13 targets also c o n t a i n C ' z , elastic scattering d a t a c o u l d n o t easily be o b t a i n e d . A l f o r d et al. 5), have o b t a i n e d fits to the ( H e 3, a) d a t a on 016, in the same energy range. Their p a r a m e t e r s , shown in table 1, were used in the present analysis. T h e p a r a m e t e r s are for the S a x o n - W o o d s well for b o t h the real a n d the i m a g i n a r y potential. S p i n - o r b i t terms were used in defining the o p t i c a l channels as well as in genegrating the b o u n d state wave function. N o fits c o u l d be o b t a i n e d w i t h o u t using a cut-off radius. This single p a r a m e t e r R° was used as the one a d j u s t a b l e variable o f the p r o b l e m . T h e D W B A fits are s h o w n in fig. 2. S t r o n g b a c k TABLE 1 Optical parameters
m out
V
W
r0
ro
a
105 110
21 5
1.52 1.4
1.3 1.3
0.65 0.68
Energy 8.84 9.44 10.30
Re
Re*
5.1 4.9 4.7
4.3 4 15 4.0
•
:5
8 8 2 MeV
/
e /
/
2 |
• •
•
•
•
0
3
9 . 4 4 MeV
L
4
3
I 0 3 0 MeV
0
40
80
120
160
eC.M.
Fig. 3. First excited-state angular distributions showing DWBA fit, arbitrarily normahzed.
(He 3, o:) REACTION
565
ward peaks are produced by the pickup mechanism alone when the plane wave approximation is dropped. A shght variation in the cut-off radius with the bombarding energy does produce a rapid change in the intensity of the forward peak. The overall agreement with the data is fairly good.
7 6 8 8 ; ) MeV
5 4 3
o~
~
I
"o
"-. 0 b "o
•
9 4 4 MeV
3 2 I
0 I0 3 0 MeV
I •
e •
•
e
40
80
OeM Fig. 4
Second excited-state angular distributions.
The reaction leading to the first excited state involves a ½- --* 2 + transition 1,1 which a p~ neutron is picked up. The angular distrlbutxons and the D W B A fits are shown in fig. 3. The parameters used for this case are the same as those for the ground state transition except the cut-off radius R*. W]th the variation m only one parameter, D W B A curves are found which fairly well reproduce the general features of these angular distributions. In particular both large forward and backward peaks are reproduced. In this case as well as the previous one the agreement might well be improved by use of more realistic optical model parameters for the reaction. The angular distributions leading to the second excited state are shown in fig. 4. This reaction involves a ½- ~ 0 + transition in which a p~ neutron is picked up. The angular distributions change rapidly with energy. With the optical parameters used for the two lower states, no fits could be obtained for these angular distributions for
566
v.K. DESHPANDE
any value of the cut-off radius. It is known that this 7.656 MeV, 0 + state of C x2 does not have an s4p 8 configuration 6), The transition to this state could therefore be mainly via the compound nucleus process rather than via the pickup processes. The absolute cross section a, in terms of the output of the Oak Ridge programme Julie 4, a) is given by = (C2S)T(C2S)pD~
1 5.1 x 10 30"Jul '
where T and p refer to the target and the projectde assembly, C is the isospin ClebschGordan coefficient, S is the spectroscopic factor and D Ois the strength of the effective zero range interaction. This effective interaction is to represent the actual finite range interaction between the incoming He 3 and the picked up neutron. In the approximation where the n - H e 3 well is assumed to be of zero range, so that the neutron wave function is exponential everywhere, the formula for D O is D~] =
2.38" 1034B//.~ 3,
where B and/~ are the binding energy and the reduced mass of the neutron. By use of the maximum values of the spectroscopic factor 7) the calculated absolute cross sections are found to be smaller than the experimental cross sections by a factor of about ten. In view of the uncertainty in the strength of the zero range interaction, an analysis on the basis of ratios of cross sections was made. A value of the ratio S * / S for the target can be obtained from the experimental cross sections aexp * and O'ex p for the first excited state and ground state transitions, respectively. This ratio is independent of both the interaction strength and the spectroscopic factor for the projectile. The total cross sections were averaged over the three bombarding energies. The value of S * / S was then given by S*/S
-~- ( O ' e*x p / O ' e x p ) ( O ' J u l / O ' J u * l)
=
1.29.
The value of this ratio has been calculated by Macfarlane and French 7) as a function of the spin orbit parameter. They find that with the Rosenfeld exchange mixture S * / S > 1.2. Macfarlane and French's plane wave analysis of the available (p, d) and (d, t) data on C 13 gave values of 0.95 and 0.78 respectively, which were below the expected minimum. The present value of 1.29 obtained by DWBA analysis therefore perhaps represents some improvement.
1) 2) 3) 4) 5) 6) 7) 8)
References H. D. Holmgren, Phys. Rev. 106 (1957) 100 H. D. Holmgren et al, Phys. Rev. 106 (1957) 102 G. E. Owen, L. Madansky and S. Edwards, Phys. Rev. 113 (1959) 1575 R. H. Bassel, R. M. Dnsko and G. R. Satchler, The Distorted-Wave Theory of Direct Nuclear Reactxon, ORNL-324~) W. P. Alford, L. Blau, D. Chne, private commumcatlon J. B. French, Nuclear spectroscopy, Part B (Academic Press, 1960) M. H. Macfarlane and J. B. French, Revs. Mod. Phys. 32 (1960) 567 G. R. Satchler, Nuclear Physics 55 (1964) 1, and prxvate commumcatlon