Absolute cross sections for scattering of 42 MeV alpha particles from even isotopes of cadmiu

Baron, N.

Leonard, R. F.

Stewart, W. M.

English

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SCATTERING OF 
42-MeV (6.7-pJ) ALPHA PAKTICLES 
FROM EVEN ISOTOPES OF CADMIUM 
Supplement I - Absolute Cross Sections 
by Norton Buron, Regis F. Leonurd, und WiZZium M .  Stedart 
Lewis Reseurch Center 
CZevelund, Ohio 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. DECEMBER 1968 
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NASA T N  D-4948 
SCATTERING OF 42-MeV (6.7-pJ) ALPHA PARTICLES 
FROM EVEN ISOTOPES OF CADMIUM 
SUPPLEMENT I - ABSOLUTE CROSS SECTIONS 
By Norton Baron ,  Reg i s  F. Leonard ,  and Wil l iam M. S tewar t  
Lewis  R e s e a r c h  C e n t e r  
Cleveland, Ohio 
N A T I O N A L  AERONAUTICS AND SPACE ADMINISTRATION 
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ABSTRACT 
Measurements have been performed that permit the determination of absolute 
cross sections for elastic and inelastic scattering of 42-MeV alpha particles from the 
even isotopes of cadmium. 
verted to absolute cross sections because of the presence on the targets of a gold back- 
ing of unknown thickness. The thickness of the backing has been determined by mea- 
suring the yield of elastically scattered alpha particles from a gold foil of known thick- 
ness and comparing this yield with that observed from the gold backing during the cad- 
mium experiment. Optical model and distorted-wave Born approximation calculations 
are carried out and compared with the absolute cross sections. 
Previously reported measurements were unable to be con- 
ii 
SCAl lERlNG OF 42-MeV (6.7-pJ) ALPHA PARTICLES 
FROM N E N  ISOTOPES OF CADMIUM 
SUPPLEMENT I - ABSOLUTE CROSS SECTIONS 
by Nor ton  Baron, Regis F. Leonard, and Wi l l iam M. Stewart  
Lewis Research Center  
SUMMARY 
Auxiliary experiments have been performed to determine the amount of gold backing 
present on targets used in a previously reported experiment. 
possible the determination of absolute cross  sections for the scattering of 42-MeV alpha 
particles from isotopically enriched targets of cadmium 110, 112, 114, and 116. 
parameter Woods -Saxon potential, and excellent fits have been obtained. Inelastic 
scattering has been analyzed using a distored-wave Born approximation (DWBA) calcula- 
tion. The results of these calculations are in excellent agreement with the experimental 
data and with previously reported measurements of deformation parameters for one- 
phonon states. 
These measurements make 
The absolute elastic cross  sections obtained have been analyzed using a four- 
INTRODUCTION 
The present work was performed in order to obtain absolute cross  sections based 
solely on experimental measurement for the scattering of 42-MeV alpha particles from 
the even isotopes of cadmium. In a previous report (ref. l), absolute cross  sections 
were inferred by adjusting their values in order to optimize the quality of f i t  obtainable 
in optical model calculations. This procedure was followed in the analysis of that data 
because of the presence of a gold.backing of unknown thickness on the targets used in that 
work. 
EX PER IMENTAL ARRANGEMENT 
The experimental arrangement for the present work is identical to that described in 
reference 1. Alpha particles were scattered from a gold target of known thickness and 
detected in the same geometrical arrangement as was  employed in reference 1. Com- 
parison of the yield of this scattering with the yield of alpha particles scattered from 
the gold impurity in the cadmium targets then made possible an absolute determination 
of the amount of gold present in each of the cadmium targets. The thicknesses of the 
carbon backings were known so that it was then possible to obtain an absolute value for 
the thickness of the cadmium targets. In addition, it was possible to correct the cad- 
mium elastic yields at forward angles where the gold elastic peak had interfered with 
the cadmium elastic peak. 
EX PER IMENTAL RESULTS 
The four cadmium targets employed in the work of reference 1 were determined to 
have the compositions and thicknesses given in table I. Thicknesses a re  quoted as a 
real density (mg/cm ) and as the energy loss (keV) suffered by an 8.78 MeV alpha 
particle in passing through the target. 
2 
CROSS SECTIONS 
The absolute cross sections for elastic and inelastic scattering of 42-MeV alpha 
particles from the even isotopes of cadmium are listed in tables 11 to V and are plotted 
in figure 1. 
ANALYSIS OF ELASTIC AND INELASTIC SCATTERING 
Both the elastic and inelastic scattering were analyzed in exactly the same way as 
reported in reference 1. The elastic data were fitted with a four-parameter Woods- 
Saxon potential, the parameters of which were automatically optimized by the computer 
code SCAT 4. The inelastic data were treated using the computer code DRC and the 
optical potentials which resulted from the fitting of the elastic scattering. Table VI 
lists the optical potentials that were obtained. Table VII lists the deformation param- 
eters which resulted from fitting the inelastic data. The results of these calculations 
are shown with the data in figure 1. 
2 
CONCLUSIONS 
Because the absolute magnitudes of the cross sections have been changed somewhat, 
the optical model parameters and nuclear deformation parameters reported herein are 
slightly different from those listed in reference 1. Fundamentally, however, the con- 
clusions to be drawn from the earlier work are unchanged. 
Lewis Research Center, 
National Aeronautics and Space Administration, 
Cleveland, Ohio, September 13, 1968, 
129-02 -04 -06 -22. 
REFERENCE 
1 .  Baron, Norton; Leonard, Regis F. ; and Stewart, William M. ; Scattering of 42-MeV 
(6.7-pv) Alpha Particles From Even Isotopes of Cadmium. NASA TN D-4256, 1967. 
3 
TABLE I. - TARGET THICKNESS 
Cadmium I Cadmium thickness 
0.127 
114 1.01 
116 .791 
keV 
29.42 
72.0 
~ 
134 
182 
Gold thickness 
~ 
mg/cm2 
0.045 
.028 
.024 
0 
~ ~ 
keV 
7.32 
4.57 
3.8 
0 
- 
4 
TABLE II. - DLFFERENTIAL CROSS SECTION FOR SCATTERING OF 
42-MeV ALPHA PARTICLES FROM CADMIUM 110 
(a) Elas t ic  scat ter ing 
Center-of -mass  
scat ter ing angle, 
deg 
31.04 
33.11 
35.17 
37.23 
39.28 
41.34 
43.40 
45.45 
31.05 
33.11 
35.18 
37.24 
39.30 
41.35 
43.41 
45.46 
31.06 
33.13 
35.19 
37.25 
39.31 
41.37 
43.42 
45.48 
31.07 
33.13 
35.20 
37.26 
39.32 
41.38 
43.43 
45.49 
Differential 
c r o s s  section, 
do/dQ, 
2 f m  /sr 
26.8iO. 1 
20.9kO.l 
1 2 . b O . l  
5.93k0.02 
3.66k0.02 
3.55iO. 02 
2 . 9 0 4 . 0 2  
1.49*0.01 
Center  -of -mass  
scat ter ing angle, 
'cm' 
deg 
47.50 
49.55 
51.60 
53.64 
55.69 
57.73 
59.77 
61.81 
(b) Inelastic scat ter ing,  0.65 MeV 
0.433*0. 015 
.186iO. 009 
.334*0.011 
.539+0.009 
.368*0.009 
. 123+0.005 
.068*0.005 
.176*0.005 
47.51 
49.56 
51.61 
53.66 
55.70 
57.74 
59.78 
61.82 
(c) Inelastic scattering, 1.48 MeV 
0.088iO. 009 
.030*0.006 
.014+0.005 
.047iO. 002 
.057*0.005 
.030iO. 002 
.019iO. 004 
.014*0.001 
47.53 
49.59 
51.63 
53.68 
55.72 
57.76 
59.80 
61.84 
(d) Inelastic scattering, 2.07 MeV 
0.171iO. 011 
.320iO. 009 
.200*0.009 
.103iO. 004 
.066i00. 005 
.138iO. 005 
. 1 4 4 4 . 0 0 6  
.079-+0.004 
- 
47.54 
49.59 
51.64 
53.69 
55.73 
57.78 
59.82 
61.85 
Differential 
c r o s s  section, 
do/dCZ, 
fm2/s r  
0.670iO. 012 
.647+0.012 
.692iO. 012 
.481*0.011 
.210+0.007 
.087*0.005 
.143*0.006 
.155+0.004 
0.192*0.007 
.110*0.005 
.032+0.002 
.040*0.002 
.061+0.004 
.069*0.004 
.032-+0.002 
.007+0.001 
i 
0.010*0.001 
.031*0.002 
.022*0.002 
.010*0.001 
.006*0.001 
.010*0.001 
.0095*0.0015 
.0079*0.0014 
0.032k0.002 
.041iO. 004 
.0516+0.0035 
.04701t0.0033 
.0179iO. 0021 
.0198*0.0021 
.0108iO. 0016 
.0274iO. 0026 
5 
TABLE III. - DIFFERENTIAL CROSS SECTION FOR SCATTERING OF 
42-MeV ALPHA PARTICLES FROM CADMIUM 112 
31.03 0.374iO. 013 
33.09 . 1 6 0 a .  009 
35.16 .320iO0.O09 
37.21 .596+0.012 
39.27 .351i0.011 
41.33 .101iO. 005 
43.38 .054iO. 004 
45.43 .203iO. 007 
Center -of -mass  
scat ter ing angle, 
*cm, 
deg 
47.49 
49.53 
51.58 
53.63 
55.67 
57.71 
59.75 
61.79 
31.02 
33.09 
35.15 
37.20 
39.26 
41.32 
43.37 
45.42 
0.154iO. 008 
.254iO. 008 
. 169iO. 007 
.070iO. 004 
.0334*0.0052 
.118rto. 004 
.0945*0.0046 
.054OiO. 0039 
~. . 
(a) Elast ic  scat ter ing 
47.51 
49.56 
51.61 
53.66 
55.70 
57.74 
59.78 
61. a2 
Differential 
c ros s  section, 
du/dQ, 
fm2/sr  
26. O i O .  1 
20. o*o. 1 
11.3iO. 1 
5.26*0.03 
3.04*0.03 
3.44iO. 03 
2.64h0.01 
1. 35*0.01 
Center -of -mass  
scat ter ing angle, 
*C” 
deg 
47.47 
49.52 
51.57 
53.62 
55.66 
57.70 
59.74 
61.78 
31.04 
33.10 
35.17 
37.22 
39.28 
41.34 
43.39 
45.45 
31.05 
33.11 
35.18 
37.24 
39.29 
41.35 
43.41 
45.46 
0.0393iO. 0058 
.0300iO. 0054 
.0146iO. 0042 
.0341iO. 0040 
.0303*0.0040 
.0338iO. 0031 
.0127*0.0024 
.0127*0.0023 
47.50 
49.55 
51.60 
53.64 
55.69 
57.73 
59.77 
61.81 
. -  
~ 
Differential 
c r o s s  section, 
du/dfi, 
fm2/sr  
0.653iO. 006 
.755*0.008 
.735*0.008 
.462iO. 005 
.161*0.004 
.010*0.003 
.162+0.004 
. 165*0.003 
~ 
0.209iO. 004 
.072iO. 003 
.015.0.001 
.042iO. 003 
.087*0.003 
.07OiO. 003 
.0264*0.0016 
.0031iO. 0008 
~~ 
0.0186iO. 0015 
.0201iO. 0016 
.0105-10.0013 
.0058iO. 0009 
.005OiO. 0007 
.0080*0.0008 
.0125*0.0009 
.009OiO. 0008 
0.0264i-O. 0017 
.0284iO. 0019 
.0452*0.0023 
.0355*0.0021 
.0186*0.0012 
.0096iO. 0009 
.0168iO. 0012 
.0168iO. 0013 
6 
TABLE IV. - DIFFERENTIAL CROSS SECTION FOR SCATTERING OF 
42-MeV ALPHA PARTICLES FROM CADMIUM 114 
(a) Elastic scat ter ing 
47.48 
49.53 
51.58 
53.63 
55.67 
57.71 
I 59.75 
61.79 
'enter-of-mass 
xa t t e r ing  angle, 
QC,, 
deg 
31.01 
33.07 
35.13 
37.18 
39.24 
41.29 
43.35 
45.40 
31.01 
33.07 
35.13 
37.19 
39.25 
41.30 
43.36 
45.41 
31.02 
33.08 
35.14 
37.20 
39.26 
41.31 
43.37 
45.42 
31.03 
33.09 
35.15 
37.21 
39.27 
41.33 
43.38 
45.43 
Differential 
c r o s s  section, 
du/dfl, 
2 fm /sr 
27.1*0 
18.5*0 
11.3*0 
5.35*0.03 
3.72*0.02 
3.44*0.01 
2.54*0.01 
1.15*0.01 
Center-of-mass 
scat ter ing angle, 
Q c m ?  
deg 
47.45 
49.50 
51.54 
53.59 
55.63 
57.67 
59.71 
61.74 
(b) Inelastic scattering, 0.560 MeV 
0.602*0.008 
.194*0.003 
.436+0.006 
.568*0.007 
.370iO. 005 
.106iO. 003 
.105iO. 003 
.208iO. 004 
47.46 
49.51 
51.55 
53.60 
55.64 
57.68 
59.72 
61.76 
(c) Inelastic scattering, 1 . 2 3  MeV 
0.0458iO. 0038 
.0197iO. 0029 
.0231iO. 0023 
.0298iO. 0023 
.0460iO. 0019 
.0309*0.0016 
.0207*0.0015 
. 0 0 7 0 ~ 0 . 0 0 1 0  
47.47 
49.52 
51.57 
53.61 
55.65 
57.69 
59.73 
61.77 
(d) Inelastic scattering, 1 .93 MeV 
0.206*0.004 
.229*0.005 
.1471*0. 0035 
.0540*0.0023 
.0630iO. 0022 
.0881*0.0026 
.0917*0.0026 
.0365iO. 0018 
Differ entia1 
c r o s s  section, 
du/dS2 , 
2 fm /sr 
0.630*0.004 
.678*0.004 
.670*0.004 
.374iO. 003 
.135*0.002 
.0985iO. 0017 
.151*0.002 
.138iO. 002 
0.160*0.003 
.052&0. 0019 
.0180~0.0010 
.0426*0.0013 
.0770*0.0016 
.0570*0.0014 
.018350.0009 
.0026iO. 0005 
0.0097kO. 0008 
.0155*0.0009 
.0124*0.0008 
.0055+0.0005 
. 0 0 3 0 ~ 0 . 0 0 0 4  
.0072iO. 0005 
.0084iO. 0006 
.0069iO. 0005 
0.0119*0.0010 
.0170iO. 0010 
.0341iO. 0012 
.0251iO. 0010 
. O l l l * O .  0007 
.0057iO. 0005 
.0093*0.0006 
.0105*0.0008 
7 
TABLE v. - DIFFERENTIAL CROSS SECTION FOR SCATTERING OF 42-MeV ALPHA PARTICLES FROM CADMIUM 116 
0.193*0.005 
.175*0.005 
.142+0.004 
.0450*0.0023 
.0674*0.0024 
.0974*0.004 
.079*0.003 
.0344*0.0018 
.0186*0.0008 
.0238*0.0011 
.0318*0.0011 
.02061t0.0011 
8.28 
10.34 
12.41 
14.48 
16.55 
18.61 
20.68 
22.74 
24.80 
28.93 
30.99 
33.05 
35.11 
37.16 
39.22 
41.27 
43.32 
55.64 
57.68 
59.72 
61.76 
63.79 
65.82 
67.85 
69.88 
71.90 
73.93 
75.45 
77.97 
(a) Elastic scattering 
Center -of -mass Differential 
1190110*21 
9250k14 
4770+10 
2360+7.3 
1290*5.4 
67053.9 
330*2.7 
199*2.1 
122. o*o. 10 
31.6*0.053 
26.6*0.045 
21.2*0.038 
11. o*o. 029 
1.52*0.020 
3.88*0.017 
3.31*0.019 
2.44*0.014 
Center-of-mass 
scattering angle, 
‘cm 2 
deg 
45.37 
47.42 
49.47 
51.52 
53.56 
55.60 
57.64 
59.70 
61.71 
63.75 
65.78 
67.81 
69.83 
71.86 
73.88 
Differential 
cross section, 
d a/dQ 
2 fm /sr 
.929*0.010 
.620*0.005 
.693*0.005 
.572*0.004 
.241*0.003 
.101*0.002 
.107t0.002 
.142*0.002 
.0895*0.002 
.0355*0.001 
.0132*0.0005 
.0228~0.0008 
.0299*0.0008 
.0227&0.0009 
.00733*0. 0003 
75.90 I .00255*0.0002 
77.92 .0464*0.0002 
Center-of -mass 
scattering angle, 
31.00 
33.06 
35.11 
37.17 
39.23 
41.28 
43.33 
45.38 
47.43 
49.48 
51.53 
53.57 
(b) Inelastic scattering, 0.513 MeV 
Differential 
cross section, 
du/dS2, 
2 fm /sr 
0.58550.008 
.131*0.004 
.478*0.006 
.593*0.008 
.322*0.005 
.0925*0.004 
.101*0.004 
.244*0.005 
.167*0.003 
.0535*0.003 
.0204*0.0009 
.0659*0.0017 
Center-of-mass 
scattering angle, 
‘cm 9 
deg 
55.61 
57.65 
59.69 
61.72 
63.76 
65.79 
67.82 
69.85 
71.87 
73.89 
75.91 
77.93 
cross section, 
0.0730*0.0016 
.0365iO. 0009 
.0149*0.0007 
.0096*0.0005 
.0254*0.0009 
.0258*0.0008 
.0122&. 0006 
.0020&. 0003 
.0033&. 0004 
.0086iO. 0004 
.0099&. 0005 
.0053&. 0003 
, 
28.94 
31.00 
33.06 
35.12 
37.18 
39.24 
41.29 
43.34 
45.40 
47.45 
49.49 
51.54 
53.58 
(c) Inelastic scattering, 1.21 MeV 
0.0604+0.0024 
.0836*0.0026 
.0260*0.0015 
.0327*0.0016 
.0618*0.0029 
.0466*0.0020 
.0295*0.0020 
.0137+0.0011 
.0151+0.0014 
.0206*0.0008 
.0190*0.0014 
. O l l ? * O .  0006 
.00410~0.00050 
55.63 
57.67 
59.70 
61.74 
63.77 
65.81 
67.84 
69.86 
71.89 
73.91 
75.93 
77.95 
.00523*0.00046 
.00792*0.00043 
.00549+0.00044 
.00174*0.00021 
.00151kO. 00022 
.00233*0.00023 
.00338*0.00033 
.00371~0.00031 
.00153~0.00019 
.00068~0.00010 
.00083~0.00014 
.00124~0.00013 
31.01 
33.07 
35.13 
37.19 
39.25 
41.30 
43.36 
45.41 
47.46 
49.51 
51.55 
53.60 
D.00725*0.0006 
.00590*0.00037 
.00945*0.0005 
.00965iO. 0005 
.005511t0.0005 
.00222*0.00023 
.00249iO. 00029 
.00353*0.00028 
.00434*0.00032 
.00242*0.00018 
.00109~0.00015 
.00056~0.00009 
Cadmium 
isotope 
110 
I12 
114 
116 
0.6324 
.6377 
.6587 
.7048 
TABLE VI. - ELASTIC SCATTERING ANALYSIS 
potential , tical potential, 
MeV MeV 
1.50 
I. 50 
1.50 
1.50 
44.19 
44.09 
39.34 
35.48 
Cadmium 
20.07 
20.89 
21.26 
22.05 
Nuclear deformation parameters 
isotope 
110 
1€2 
114 
116 
p2 p3 
0.20 0. 18 
.19 .I5 
.21 .14 
.23 .15 
Total reaction 
cross section, 
OR' 
2 fm 
180.9 
184.6 
188.3 
197.1 
Goodness 
of fit, 
X2/N 
0.22 
.58 
.16 
2.11 
9 
i 
Excitation energies, 
MeV 
Excitation energies, 
MeV 
L VI 
N- 
E c 
VI- 
c 
u 
VI 
.- 
c 
VI 
u e 
0 Ground state (rat io to 0 Ground state (rat io to 
A 0.651 A 0.621 
0 2.07 0 1.98 
Rutherford) Rutherford) 
---- 
- 
- 
I I I I I I I I  
Center of mass scattering angle, €Icm, deg 
(a) Cadmium 110. (b) Cadmium 112. 
Figure 1. - Differential cross sections for elastic and inelastic scattering of 42-MeV alpha particles. 
10 
Excitation energies, 
101 IO0 ~ ~ ~ d ~ r a t i o  to 
Calculation 
Experimental two-phonon ---- 
distr ibut ion 
10-1 
(c) Cadmium 114. 
E 
Excitation energies, 
MeV 
0 Ground state (rat io to 
A 0.513 
Rutherford) 
0 1. 90 
0- 0 1.21 
Calculation 
Experimental two-phonon 
distr ibut ion 
x10-2 
x 1 ~ - 3  
10 20 30 40 50 60 70 80 
I I I I I I I I I I I I I I I I I  
0 
Center of mass scattering angle, Ocm, deg 
(d) Cadmium 116. 
Figure 1. -Concluded. 
11 
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Scattering of 42 MeV /6.7-pJ/ alpha particles from even isotopes of cadmium. Supplement 1 - Absolute cross sections

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