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Investigations of the mechanism of the 40Ca(d, p)41 Ca reaction at the bombarding energies Ed = 1.9–2.0 MeV
2.B:2.G [
Nuclear Physics 73 (1965) 155--160; ( ~ North-Holland Publishin9 Co.. Amsterdam
I
Not to be reproduced by
photoprint or
microfilm without written permission from the publisher
INVESTIGATIONS OF T H E MECHANISM OF T H E 4°Ca(d, p)41Ca REACTION AT T H E BOMBARDING ENERGIES Ed ---- 1.9-2.0 MeV I L O N A F O D O R , 1. SZENTPI~'TERY a n d J. Z I M , ~ N Y i
Central Research Institute for Physics, Budapest, Hungary Received 25 M a y 1965 Abstract: T h e absolute differential cross sections for the 4°Ca(d. p p t C a reaction lcading to the g r o u n d a n d first excited states have been m e a s u r e d at b o m b a r d i n g deuteron energies Ed ~ 1.9 and 2.0 MeV. T h e results are discussed in terms of the D W B A model o f stripping reactions. E
NUCLEAR
R E A C T I O N 4°Ca(d, pL E = 1.8.-2.0 MeV; m e a s u r e d a(E; Ep). Natural target.
I I
1. Introduction
At intermediate deuteron bombarding energies the DWBA model presents a satisfactory description of the (d, p) stripping reactions. Many measurements have been interpreted in this way. Recently an exhaustive investigation was made to check the predictions of the DWBA model i). The 4°Ca(d, p)4'Ca reaction was studied in the deuteron energy range Eo = 7-12 MeV and a very good agreement was found between the experimental facts and the theoretical predictions. It remains to be seen, however, what is the limit for the applicability of the DWBA model when the incident deuteron energies are lowered. Another problem arising in connection with this question is, what are the optical model parameters for deuterons - if they have a meaning in this case at all - when the deuteron energies are far below the Coulomb barrier. These parameters, in fact, cannot be obtained from elastic scattering since this is almost pure Rutherford scattering, thus essentially insensitive to nuclear distortions. The stripping matrix element, on the other hand, is insensitive to nuclear distortions only if proton energies are also far below the Coulomb barrier, i.e. in the case of low bombarding energies and low reactions Q values (the case of pure Coulomb stripping). However, if the energy of the protons is high enough, the stripping matrix element is very sensitive to the nuclear distortions of the deuteron waves, in spite of the low deuteron kinetic energy 2). The aim of the present work is to contribute to the investigation of these problems. The 4°Ca(d, p ) g t c a reaction is particularly suitable for such investigations, since the spectroscopic factors are known and the level density of the 42Sc compound nucleus is high enough to keep the fluctuations small. 155
156
i. FODOR et al.
2. Experimental Method and Results The deuteron beam was provided by the 2 MeV Van de Graaff accelerator of the Central Research Institute for Physics. The target was natural Ca metal evaporated on gold and silver backings. The thickness of the Ca target was about 150 l~g/cm 2. The analysed deuteron current was about 0.5/tA. The reaction protons were detected by a CsI(TI) scintillation counter, the proton groups of lower energies (up to 6 MeV) were also detected by a silicon surface barrier detector. The angular distribution was measured in 10 ~ steps from 20 to 150 degrees relative to a monitor detector tixed at 150:'. The spectrum of both the measuring and the monitor detector was analysed by a 128-channel analyser at each angular position. A typical proton spectrum obtained with the scintillation detector is shown in fig. 1. Although the proton group leading ~000
-
CoUld,p1/
~0
50
~0
70
60
SO : ~0 c h a s t e ! r,o,"nlzc,
Fig. 1. T y p i c a l p r o t o n s p e c t r u m o b t a i n e d w i t h a s c i n t i l l a t i o n c o u n t e r at E,~ = 2.00 MeV.
to the 1.95 MeV state (p~) could not be separated at the given resolution from protons leading to the 2.01 MeV level (P2), the contribution from the P2 group is assumed to be negligible owing to its very low relative yield ~). There was no indication of an appreciable presence of these protons in our semiconductor detector spectra. For the determination of the absolute cross section the elastically scattered deuterons were also detected at 135 ° by means of a silicon surface barrier detector and a multichannel analyser. The elastic scattering of deuterons in this energy range is known to be pure Rutherford scattering 3). The absolute value of the (d, p) cross section was determined therefore relative to this known cross section. A typical spectrum of the elastically scattered deuterons is shown in fig. 2. The result of this measurement at E d = 2.00 MeV was in agreement with the cross section value reported by Lee and Schiffer 4) within the estimated error, for the P0 proton group. On the basis of this agreement we have adopted the excitation function reported in ref. 4) for the further evaluation of our measurements.
40000
30000
10000
]1
•
~
Chonnel rtumber Fig. 2. Typical spectrum o f the elastically scattered deuterons obtained with a Si surface barrier detector. d£2
025 *
T
, < T
o
T
I
0.20
0.~
0.40
Fig. 3. Measured differential cross section at ,~'~l = 1.90 MeV ( × ) and E~ = 2.00 MeV (o) for protons leading to the first excited state in *~Ca. The solid line is the D W B A cross section calculated with the parameters given in table 1.
O.
20
0
0.45
-
0.40
0.05
0.0"I
20"
~0°
gC"
¢20"
¢5c"
Fig. 4. M e a s u r e d d i f f e r e n t i a l c r o s s s e c t i o n at Eo ~ 1.90 M e V ( × ) a n d / : h t o n s l e a d i n g to the g r o u n d s t a t e in *~Ca.
- -
l
,,,9",0
2.00 M e V (o) for pro-
i
! 0.2-
0.4
0.04
48O'3
4900
2000
E d keV
Fig. 5. Measured excitation function at ~p = 904 for protons ]eading to the first excited state, The c u r v e is m e a n t as a g u i d e to the eye a n d is w i t h o u t a n y t h e o r e t i c a l significance.
159
4°Ca(d, p)41Ca REACTION
The differential cross sections measured at Ed = 1.90 MeV and Ed = 2.00 MeV are shown in figs. 3 and 4. The statistical errors are given there. The normalization of the absolute value to the results reported in ref. 4) was made at 90 °. To evaluate the excitation function for the Pl group, the relative yield of p~ to Po protons at ,gp = 90 ~ was measured between 1.80 and 2.00 MeV in 20 keV steps. The excitation function for the pt group is shown in fig. 5.
3. Discussion For the theoretical interpretation of the measured data by means of the DWBA model one needs the parameters of the optical potentials. These are usually obtained from the fit of the elastic scattering cross section. However, in the present case it is impossible to get the deuteron parameters in this way because the elastic scattering of the deuterons is almost purely Rutherford scattering. An attempt was made therefore to fit the experimental data with extrapolated potentials. Both volume and surface absorption optical potentials were used but no spin-orbit term, thus we have
U ( r ) = U c o ~ , ( r ) + v l (I +e -~ +i
1 W + 4 W o dd~) ~+eX
where
X = (r-roA~)/a,
x' = (r-roA~)/a ',
and Ucouz is the Coulomb potential for the uniform charge of the radius rc A*. In the calculations one of the parameters W and Wt~ was taken to be zero. The neutron wave function was taken to be the eigenfunction of a real Saxon well without a spinorbit potential. TABLE 1
Parameters used in the DWBA calculation
Deuteron Proton
V
ro
a
110
1.2
0.9
0
1.25
0.65
7.5
56.2
W
Wf~
r' o
a'
rc
20
1.55
0.47
1.3
0
1.25
0.65
1.3
The proton parameters were those given by Hodgson -~) except for the shape of the imaginary part where a volume absorption term was used (see table 1). First, the Ed = 2.00 MeV Pt data were fitted. Several calculations were made with different deuteron potentials. Volume absorption type deuteron potentials yielded incorrect shapes for the differential cross section. The potential used by Satchler 6) for 7 MeV deuteron elastic scattering o n 4 3 C a has given better results. This potential was used therefore in a one-parameter search code t. t This code was written for a National Eliott 803 B computer by J. Zimfinyi and G. N6mcth.
160
i. FODOR et al.
The best fit was obtained (see fig. 4) when r o was searched. The neutron parameters were ro, = 1.3 fro, a, = 0.65 fm. The spectroscopic factor was obtained as 1.16. The parameters of the best fit mentioned above are listed in table 1. In order to see to what extent this description for the reaction is physically reasonable or only a meaningless mathematical fit, the calculations must be repeated with the same potential parameters at a different energy. The characteristic width of the fluctuations in this reaction is 4) about 30 keV. Therefore, at bombarding energy Ed = 1.90 a contribution from quite different levels is expected than at 2.00 MeV. Thus, if the differential cross section is determined by some fluctuation effect, it will change its shape and absolute value to become different from that predicted by the DWBA model. The D W B A calculation, performed with Ed = 1.90 MeV and the same potential parameters as for E d = 2.00 MeV, shows this is not the case (see fig. 3). The change in magnitude is satisfying and the change in shape is qualitatively reproduced. The situation is quite different for the ground state proton group. Different potentials with and without cut-off have been used, but the measured forward peaking angular distribution could not be reproduced in any case, although the correct order of magnitude of the cross section was obtained in the backward hemisphere. it should be also noted, that even at Ed = 11 MeV the contribution from the compound processes was estimated 1) to be about five times higher for transitions to the ground state than for the Pt transitions.
4. Conclusions Investigation of the mechanism of the 4°Ca(d, p)4~Ca reaction at E d = 2.00 and 1.90 MeV indicated that the reaction leading to the tirst excited state can be attributed to an overwhelmingly direct stripping process as described by the D W B A model. The optical potentials parameters for these low energy deuterons were found to be very similar to the parameters obtained at higher deuteron energies. The only difference is the wider real potential due, perhaps, to the internal structure of the deuterons. For the ground state transition no DWBA interpretation could be given.
References 1) 2) 31 41 5~ 61
L. L. L. J. A. Z. L. L. P. E. J. H.
Lee et al., Phys. Rev. 136B (1964) 971 B. Goldfarb, to be published El-Bchay, M. A. Farouk, M. tl. N a s s e f a n d 1. I. Zaloubovsky, Nuclear Physics 61 (1965) 282 Lee a n d J. P. Schiffer, Phys. Rev. 107 (19571 1340 Hodgson, in Proc. P a d u a Conf., 1962 ( G o r d o n a n d Breach, New York, 19631 Bjerregaard et aL, Phys. Rev., to be published
Nuclear Physics 73 (1965) 155--160; ( ~ North-Holland Publishin9 Co.. Amsterdam
I
Not to be reproduced by
photoprint or
microfilm without written permission from the publisher
INVESTIGATIONS OF T H E MECHANISM OF T H E 4°Ca(d, p)41Ca REACTION AT T H E BOMBARDING ENERGIES Ed ---- 1.9-2.0 MeV I L O N A F O D O R , 1. SZENTPI~'TERY a n d J. Z I M , ~ N Y i
Central Research Institute for Physics, Budapest, Hungary Received 25 M a y 1965 Abstract: T h e absolute differential cross sections for the 4°Ca(d. p p t C a reaction lcading to the g r o u n d a n d first excited states have been m e a s u r e d at b o m b a r d i n g deuteron energies Ed ~ 1.9 and 2.0 MeV. T h e results are discussed in terms of the D W B A model o f stripping reactions. E
NUCLEAR
R E A C T I O N 4°Ca(d, pL E = 1.8.-2.0 MeV; m e a s u r e d a(E; Ep). Natural target.
I I
1. Introduction
At intermediate deuteron bombarding energies the DWBA model presents a satisfactory description of the (d, p) stripping reactions. Many measurements have been interpreted in this way. Recently an exhaustive investigation was made to check the predictions of the DWBA model i). The 4°Ca(d, p)4'Ca reaction was studied in the deuteron energy range Eo = 7-12 MeV and a very good agreement was found between the experimental facts and the theoretical predictions. It remains to be seen, however, what is the limit for the applicability of the DWBA model when the incident deuteron energies are lowered. Another problem arising in connection with this question is, what are the optical model parameters for deuterons - if they have a meaning in this case at all - when the deuteron energies are far below the Coulomb barrier. These parameters, in fact, cannot be obtained from elastic scattering since this is almost pure Rutherford scattering, thus essentially insensitive to nuclear distortions. The stripping matrix element, on the other hand, is insensitive to nuclear distortions only if proton energies are also far below the Coulomb barrier, i.e. in the case of low bombarding energies and low reactions Q values (the case of pure Coulomb stripping). However, if the energy of the protons is high enough, the stripping matrix element is very sensitive to the nuclear distortions of the deuteron waves, in spite of the low deuteron kinetic energy 2). The aim of the present work is to contribute to the investigation of these problems. The 4°Ca(d, p ) g t c a reaction is particularly suitable for such investigations, since the spectroscopic factors are known and the level density of the 42Sc compound nucleus is high enough to keep the fluctuations small. 155
156
i. FODOR et al.
2. Experimental Method and Results The deuteron beam was provided by the 2 MeV Van de Graaff accelerator of the Central Research Institute for Physics. The target was natural Ca metal evaporated on gold and silver backings. The thickness of the Ca target was about 150 l~g/cm 2. The analysed deuteron current was about 0.5/tA. The reaction protons were detected by a CsI(TI) scintillation counter, the proton groups of lower energies (up to 6 MeV) were also detected by a silicon surface barrier detector. The angular distribution was measured in 10 ~ steps from 20 to 150 degrees relative to a monitor detector tixed at 150:'. The spectrum of both the measuring and the monitor detector was analysed by a 128-channel analyser at each angular position. A typical proton spectrum obtained with the scintillation detector is shown in fig. 1. Although the proton group leading ~000
-
CoUld,p1/
~0
50
~0
70
60
SO : ~0 c h a s t e ! r,o,"nlzc,
Fig. 1. T y p i c a l p r o t o n s p e c t r u m o b t a i n e d w i t h a s c i n t i l l a t i o n c o u n t e r at E,~ = 2.00 MeV.
to the 1.95 MeV state (p~) could not be separated at the given resolution from protons leading to the 2.01 MeV level (P2), the contribution from the P2 group is assumed to be negligible owing to its very low relative yield ~). There was no indication of an appreciable presence of these protons in our semiconductor detector spectra. For the determination of the absolute cross section the elastically scattered deuterons were also detected at 135 ° by means of a silicon surface barrier detector and a multichannel analyser. The elastic scattering of deuterons in this energy range is known to be pure Rutherford scattering 3). The absolute value of the (d, p) cross section was determined therefore relative to this known cross section. A typical spectrum of the elastically scattered deuterons is shown in fig. 2. The result of this measurement at E d = 2.00 MeV was in agreement with the cross section value reported by Lee and Schiffer 4) within the estimated error, for the P0 proton group. On the basis of this agreement we have adopted the excitation function reported in ref. 4) for the further evaluation of our measurements.
40000
30000
10000
]1
•
~
Chonnel rtumber Fig. 2. Typical spectrum o f the elastically scattered deuterons obtained with a Si surface barrier detector. d£2
025 *
T
, < T
o
T
I
0.20
0.~
0.40
Fig. 3. Measured differential cross section at ,~'~l = 1.90 MeV ( × ) and E~ = 2.00 MeV (o) for protons leading to the first excited state in *~Ca. The solid line is the D W B A cross section calculated with the parameters given in table 1.
O.
20
0
0.45
-
0.40
0.05
0.0"I
20"
~0°
gC"
¢20"
¢5c"
Fig. 4. M e a s u r e d d i f f e r e n t i a l c r o s s s e c t i o n at Eo ~ 1.90 M e V ( × ) a n d / : h t o n s l e a d i n g to the g r o u n d s t a t e in *~Ca.
- -
l
,,,9",0
2.00 M e V (o) for pro-
i
! 0.2-
0.4
0.04
48O'3
4900
2000
E d keV
Fig. 5. Measured excitation function at ~p = 904 for protons ]eading to the first excited state, The c u r v e is m e a n t as a g u i d e to the eye a n d is w i t h o u t a n y t h e o r e t i c a l significance.
159
4°Ca(d, p)41Ca REACTION
The differential cross sections measured at Ed = 1.90 MeV and Ed = 2.00 MeV are shown in figs. 3 and 4. The statistical errors are given there. The normalization of the absolute value to the results reported in ref. 4) was made at 90 °. To evaluate the excitation function for the Pl group, the relative yield of p~ to Po protons at ,gp = 90 ~ was measured between 1.80 and 2.00 MeV in 20 keV steps. The excitation function for the pt group is shown in fig. 5.
3. Discussion For the theoretical interpretation of the measured data by means of the DWBA model one needs the parameters of the optical potentials. These are usually obtained from the fit of the elastic scattering cross section. However, in the present case it is impossible to get the deuteron parameters in this way because the elastic scattering of the deuterons is almost purely Rutherford scattering. An attempt was made therefore to fit the experimental data with extrapolated potentials. Both volume and surface absorption optical potentials were used but no spin-orbit term, thus we have
U ( r ) = U c o ~ , ( r ) + v l (I +e -~ +i
1 W + 4 W o dd~) ~+eX
where
X = (r-roA~)/a,
x' = (r-roA~)/a ',
and Ucouz is the Coulomb potential for the uniform charge of the radius rc A*. In the calculations one of the parameters W and Wt~ was taken to be zero. The neutron wave function was taken to be the eigenfunction of a real Saxon well without a spinorbit potential. TABLE 1
Parameters used in the DWBA calculation
Deuteron Proton
V
ro
a
110
1.2
0.9
0
1.25
0.65
7.5
56.2
W
Wf~
r' o
a'
rc
20
1.55
0.47
1.3
0
1.25
0.65
1.3
The proton parameters were those given by Hodgson -~) except for the shape of the imaginary part where a volume absorption term was used (see table 1). First, the Ed = 2.00 MeV Pt data were fitted. Several calculations were made with different deuteron potentials. Volume absorption type deuteron potentials yielded incorrect shapes for the differential cross section. The potential used by Satchler 6) for 7 MeV deuteron elastic scattering o n 4 3 C a has given better results. This potential was used therefore in a one-parameter search code t. t This code was written for a National Eliott 803 B computer by J. Zimfinyi and G. N6mcth.
160
i. FODOR et al.
The best fit was obtained (see fig. 4) when r o was searched. The neutron parameters were ro, = 1.3 fro, a, = 0.65 fm. The spectroscopic factor was obtained as 1.16. The parameters of the best fit mentioned above are listed in table 1. In order to see to what extent this description for the reaction is physically reasonable or only a meaningless mathematical fit, the calculations must be repeated with the same potential parameters at a different energy. The characteristic width of the fluctuations in this reaction is 4) about 30 keV. Therefore, at bombarding energy Ed = 1.90 a contribution from quite different levels is expected than at 2.00 MeV. Thus, if the differential cross section is determined by some fluctuation effect, it will change its shape and absolute value to become different from that predicted by the DWBA model. The D W B A calculation, performed with Ed = 1.90 MeV and the same potential parameters as for E d = 2.00 MeV, shows this is not the case (see fig. 3). The change in magnitude is satisfying and the change in shape is qualitatively reproduced. The situation is quite different for the ground state proton group. Different potentials with and without cut-off have been used, but the measured forward peaking angular distribution could not be reproduced in any case, although the correct order of magnitude of the cross section was obtained in the backward hemisphere. it should be also noted, that even at Ed = 11 MeV the contribution from the compound processes was estimated 1) to be about five times higher for transitions to the ground state than for the Pt transitions.
4. Conclusions Investigation of the mechanism of the 4°Ca(d, p)4~Ca reaction at E d = 2.00 and 1.90 MeV indicated that the reaction leading to the tirst excited state can be attributed to an overwhelmingly direct stripping process as described by the D W B A model. The optical potentials parameters for these low energy deuterons were found to be very similar to the parameters obtained at higher deuteron energies. The only difference is the wider real potential due, perhaps, to the internal structure of the deuterons. For the ground state transition no DWBA interpretation could be given.
References 1) 2) 31 41 5~ 61
L. L. L. J. A. Z. L. L. P. E. J. H.
Lee et al., Phys. Rev. 136B (1964) 971 B. Goldfarb, to be published El-Bchay, M. A. Farouk, M. tl. N a s s e f a n d 1. I. Zaloubovsky, Nuclear Physics 61 (1965) 282 Lee a n d J. P. Schiffer, Phys. Rev. 107 (19571 1340 Hodgson, in Proc. P a d u a Conf., 1962 ( G o r d o n a n d Breach, New York, 19631 Bjerregaard et aL, Phys. Rev., to be published