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Photon cross section measurements in compounds and elements in the energy range 30–660 keV
Physica 124C (1984) 96-104 North-Holland, Amsterdam
P H O T O N CROSS SECTION M E A S U R E M E N T S IN C O M P O U N D S A N D E L E M E N T S IN THE E N E R G Y R A N G E 3 0 - 6 6 0 keV A.S. N A G E S W A R A R A O , A. P E R U M A L L U * and G. K R I S H N A R A O Department of Physics, Kakatiya University, Warangal, 506 009, India Received 29 August 1983 Revised 28 October 1983 Total photon attenuation coefficientshave been measured at seven energies in the range 30-660 keV for 18 elements and 29 compounds. From the results obtained on compounds, the total photon cross sections for certain elements are obtained applying the mixture rule. Direct measurements could be obtained on 18 elements. Atomic photo effect cross sections in medium and high Z elements in the energy range 30-280 keV are derived from all data by subtracting the relatively small scattering (coherent + incoherent) cross sections from the total atomic cross sections. They are compared with theoretical values.
1. Introduction The knowledge of accurate photon attenuation cross sections is important in such diverse fields as medicine, industry, agriculture, etc. Significant photon attenuation measurements, calculations and compilations in elements have been published [1-8]. Fairly accurate theoretical cross sections of partial gamma ray interaction processes have also been made available [9-11]. However, the data on g a m m a ray attenuation measurements in compounds and mixtures seem to be very limited [12-16]. The mass attenuation and mass absorption coefficients in some compounds and mixtures of dosimetric and biological importance have been compiled by Hubbell [11] for the energy range l k e V - 2 0 M e V . These parameters are widely used for the calculation of photon penetration and energy-deposition in biological, shielding and other materials. The mass attenuation and energy absorption coefficients are defined in the I C R U R e p o r t - 3 3 [17] and are also discussed by Hubbell [11]. Jackson and Hawkes [18] have reviewed mass attenuation coefficients in elements and mixtures, and developed parametric fits for in* Present address: S.R. and B.G.N.R. Govt. College, Khammam, 507 002, India.
dividual collision processes, with particular emphasis on the photon energy range 3 0 150 keV. In the recent review papers of Veigele [8] and Hubbell and Veigele [19] it is pointed out that the data on attenuation measurements in certain elements are meagre; they advocated further measurements in elements and in energy regions which could afford a more critical test of the present theory and would reduce the uncertainties in present photon cross section tabulations. It is therefore considered worthwhile to undertake a systematic study of photon interaction cross sections in elements and compounds. The present report deals with the photon attenuation measurements on 18 elements and 29 compounds (biological, dosimetric, semiconductor and related materials) in the energy range 30-660 keV. From the results obtained on compounds, the total photon cross sections for elements, difficult to obtain in proper form to be used as target foils, were extracted using the mixture rule. From these data and the results of direct measurements on 18 elements, the atomic photo effect cross sections in medium and high Z elements in the energy range 3 0 - 2 8 0 k e V have been derived by subtracting relatively small scattering (coherent + incoherent) cross sections [9] from the total atomic cross sections. A corn-
0378-4363/84/$03.00 O Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
A . S . Nageswara R a o et al. / Photon cross section measurements
parison is made with recent theoretical values of Scofield [10].
2. Experimental details The total attenuation coefficients were determined by performing transmission experiments in a narrow beam geometry similar to the one used previously [20]. Radioactive sources of strength 1 0 - 2 0 m C i obtained from B A R C , Bombay (India) were used in the present work; the details of the sources are given in table I. Depending on the photon energy, two types of NaI(TI) crystals (5.1 × 5.1 cm/5.1 × 0.4 cm) covered by aluminium foils of appropriate thickness, mounted on R C A 8055/9656 photomultiplier tubes were used. The output pulses were amplified and fed to a preset timer through a single channel analyser. The experiments were conducted in an air-conditioned room to avoid possible shift of the photopeaks. The procedure adopted in the transmission experiment is similar to the one used in earlier experiments [20]. Metal foils of dimensions 2 × 2 cm 2 of suitable thickness were used and in the case of mercury, cylindrical cavities of 1 cm radius with varying thickness were made in perspex. In the actual experiment the cavities with and without material were exposed to the beam at several points and the respective intensities were utilized for the calculation of attenuation coefficients. For compounds and a few elements, which are in
Table I Radioactive isotopes used in the present work Radioisotope
Half-life
Energy of photons selected in keV a X-rays
137Cs 2°3Hg t4tCe tT°Tm
30.17 46.8 32.55 128.6
years days days days
v-rays
32.1 (BaK,) 661.6 73.0 (I~"-~) 279.2 145.4 52.0 (K,,~) 84.2
aC.M. Lederer and V.S. Shirley: Tables of Isotopes, Wiley, New York.
97
powder form, pellets of suitable thickness were prepared. In a few cases, where preparation of pellets was not possible, the powder was packed in a perspex holder with 1 cm inner radius and covered with thin mylar foils. The count rates were taken with and without material always keeping the mylar foil on the perspex container. All the metal foils, the pellets and the powders were weighed on a microbalance. Dimensions of foils, pellets and perspex holders were measured using a travelling microscope, and the thickness t of the sample was expressed in gm/cm 2. If I and I0 are the count rates with and without absorber of thickness t, the total atomic cross section is given by the relation
[In(/o//~1 t J'
A tr = ~- [
(1)
where N and A are Avogadro's number and the atomic weight, respectively, while the factor in brackets represents the mass attenuation coefficient (i.t/p). In the case of a compound the total molecular cross section is given by the relation Orc°mP= p N ~ niAi,
(2)
i
where ni is the number of atoms and Ai is the atomic mass of the ith element in a molecule. The errors in the present investigations are mainly due to counting statistics, non-uniformity of the absorber, the impurity content and the scattered photons reaching the detector within the accepted maximum angle of scattering. In the present investigations this angle is less than 2 ° and the error due to this factor is about 0.2%. The statistical errors were always less than 1%. The fractional error due to non-uniformity of the foil was estimated to be (At)2/2, where At is the relative fractional variation of the "thickness"; it is found to be of the order of 0.5%. As the materials are of a high purity the errors due to the presence of impurities is negligible. The overall error thus introduced on the total attenuation cross sections is estimated to be around 2%.
98
A.S. Nageswara R a o et al. / Photon cross section measurements
3. Results and discussion
The measured total mass attenuation coefficients for compounds were converted into total cross sections and are given in table II. Using the tables of Storm and Israel [9] for individual elements, the cross sections for compounds were evaluated using the mixture rule [21] and these theoretical cross sections are given in brackets below the experimental cross sections. One observes a good agreement between experimental and theoretical cross sections. It is difficult to obtain certain elements in a suitable form for cross section measurements; in such cases, applying the mixture rule, the total cross section of the element was extracted from the measured cross section of the compound. This method is claimed [14-17] to be useful especially if the element is in the gaseous form, where a direct measurement needs an elaborate experimental arrangment. It is also suitable in such cases where the elements are difficult to obtain in the free state to be used as target foils. In the present investigation the atomic cross sections in O, Na, CI, K, Ca, Ti, Cr, Mn, Fe, Co, Cu, Zn, Br, Sr, Cd, Te, Ba, W, Bi, Th and U were obtained in this way. In table III the total atomic cross sections of all the elements studied are given for various energies. The figures in the first row for a given element represent cross sections from direct measurements on foils, the second row corresponds to the cross sections obtained from the compounds; and the third row corresponds to the theoretical cross sections of Storm and Israel [9]. The total photon cross sections for Cu, Zn, Cd, T e and Bi have been obtained from measurements both on elements and compounds. A comparison between these two sets of values shows a good agreement within the range of the experimental error. Thus, it may be concluded that the method of extracting the total cross sections in elements, where direct measurement is rather difficult (especially in gases/elements not available in the free state), from the measurements on compounds works out satisfactorily in the present energy range. Since the accuracy as well as the reliability of the results will
increase when the subtracted contribution from other elements decreases for such a measurement, compounds (in powder form) with elements of lower atomic number than the element of interest seem to be preferable. The comparison of the measured cross sections in elements (direct or by subtraction from compound) with the theoretical values of Storm and Israel [9] shows general agreement within the range of the experimental error. The atomic photo effect cross sections were obtained by subtracting the scattering ( c o h e r e n t + incoherent) cross sections reported by Storm and Israel [9]. The subtracting procedure was restricted to only those cases where the scattering contribution does not exceed 20% (in a few cases it is around 30%) of the total photon cross section in a given element. The errors associated with the measured total cross section are carried on to the derived cross sections. As the theoretical scattering cross sections are known to an accuracy of 3%, the theoretical uncertainty entails an error of around 1% in the subtraction procedure. Hence, the error in the derived value of the total cross section for the element (obtained from the compound) is estimated to be
ao. = ___~,a L.,~ + E ,a~,
(3)
i
where A ¢ornpis the root mean square error in the result for the compound and Ai is the error on the subtracted cross section of the ith element. The error on the atomic photo effect cross sections is then estimated by the relation
,,tph = ___',,/A ~. + A~,
(4)
where A~c is the error on the subtracted value of the scattering cross section ( c o h e r e n t + incoherent). In the present case, the overall error on atomic photo effect cross sections for elements is around 3% for direct measurements and in other elements (extracted from compounds) it is 4 - 5 % . In table IV the derived atomic photo effect cross sections appear in the upper rows belonging to each element, while the cor-
99
A.S. Nageswara Rao et al. / Photon cross section measurements
Table II Total photon cross sections of compounds (barn/molecule) (error ~-2%) keV) 32.1 H20 NaCI CaF2 TiO2 NI-hNO3 ZnO NaNO3 KNO3 KH2PO4 GaAs CaTe KBrO3 MnSOd-I20 CdCl2 ZnTe Sr(NO3)2 InSb (CH3COO)2CO4H20 CuSO45H20 Ba(NO3)2 ThO2 FeSO47H20 CoSO47H20 K2Cr207
122.0 (126.0) 256.0 (248.0) 350.0 (357.0) 40.4 (41.7) 1066.0 (1069.0) 54.6 (54.9) 192.0 (207.0) 283.0 (283.0) 2671.0 (2750.0) 2153.0 (2200.0) 662.0 (679.0) 6317.0 (6408.0) 2419.0 (2525.0) 873.0 (847.0) 1096.0 (1119.0) 12312.0 (12617.0) 897.0 (874.0) 949.0 (944.0) 1361.0 (1329.0)
52.0 6.5 (6.6) 44.5 (44.5) 73.0 (74.4) 97.1 (97.9) 26.8 (27.6) 288.0 (295.0) 32.1 (30.9) 71.1 (70.9) 92.2 (95.9) 643.0 (660.0) 2269.0 (2191.0) 563.0 (576.0) 189.0 (196.0) 1655.0 (1699.0) 2419.0 (2420.0) 708.0 (736.0) 3645.0 (3760.0) 242.0 (246.0) 317.0 (328.0) 2852.0 (2851.0) 3565.0 3610.0 243.0 (251.0) 272.0 (276.0) 372.0 (374.0)
73.0 5.6 (5.6) 25.4 (25.8) 40.6 (39.8) 46.9 (47.7) 23.4 (23.7) 123.0 (124.0) 24.0 (25.0) 41.7 (42.2) 55.7 (57.2) 274.0 (284.0) 900.0 (9O4.O) 238.0 (243.0) 100.0 (98.2) 697.0 (707.0) 967.0 (995.0) 312.0 (308.0) 1456.0 (1520.0) 142.0 (137.0) 154.0 (157.0) 1160.0 (1205.0) 1469.0 (1469.0) 144.0 (146.0) 145.0 (153.0) 183.0 (183.0)
84.2
145.4
5.3 (5.4) 21.1 (21.5) 31.2 (31.8) 36.0 (37.2) 23.1 (22.7) 85.1 (84.4) 22.9 (23.6) 35.7 (35.8) 49.0 (48.8) 213.0 (208.0) 614.0 (612.0) 162.0 (172.0) 77.9 (79.3) 467.0 (489.0) 652.0 (670.0) 223.0 (222.0) 1035.0 (1025.0) 109.0 (109.0) 126.0 (130.0) 804.0 (823.0) 1076.0 (1068.0) 111.0 (115.0) 121.0 (122.0) 144.0 (144.0)
4.5 (4.5) 14.0 (14.1) 19.2 (19.6) 20.7 (20.7) 19.0 (19.0) 30.5 (31.4) 19.7 (19.3) 24.1 (24.6) 33.1 (33.4) 62.5 (63.0) 167.0 (158.0) 62.6 (61.9) 45.6 (45.0) 127.0 (128.0) 182.0 (175.0) 80.9 (78.2) 252.0 (260.0) 65.6 (66.8) 69.1 (70.3) 226.0 (228.0) 984.0 (1007.0) 74.4 (72.9) 74.3 (74.8) 81.1 (78.5)
279.2 3.6 (3.6) 9.8 (10.5) 14.1 (14.2) 13.9 (14.4) 14.9 (15.3) 16.3 (16.3) 15.3 (15.3) 18.5 (18.6) 24.8 (25.3) 30.5 (30.2) 47.4 (47.7) 32.6 (32.8) 32.0 (31.7) 45.5 (44.9) 52.7 (53.4) 40.3 (41.6) 71.9 (72.0) 48.4 (47.9) 47.2 (48.3) 71.1 (73.1) 250.0 (250.0) 53.7 (53.8) 52.9 (54.0) 54.3 (54.2)
661.6 2.5 (2.5) 7.3 (7.2) 9.7 (9.7) 9.7 (9.8) 10.5 (10.7) 10.0 (10.1) 10.7 (10.7) 12.7 (12.7) 17.0 (17.5) 17.0 (17.1) 20.7 (2O.5) 19.9 (20.6) 21.0 (21.2) 22.4 (22.9) 23.5 (23.4) 26.8 (26.3) 29.8 (29.4) 31.7 (33.0) 31.8 (32.7) 32.8 (32.6) 51.9 (52.1) 35.9 (36.7) 36.5 (36.9) 37.2 (36.9)
100
A.S. Nageswara Rao et ai. / Photon cross section measurements
Table II (Contd.)
NaWO42H20 Na2B4OT10H20
uo~(cooh3H20
32.1
52.0
73.0
84.2
145.4
5861.0 (6099.0) 222.0 (219.0) 12997.0 (13492.0)
1632.0 (1695.0) 133.0 (136.0) 3959.0 (4010.0)
2967.0 (3044.0) 115.0 (114.0) 1680.0 (1671.0)
2093.0 (2141.0) 111.0 (108.0) 1207.0 (1218.0)
536.0 (544.0)
138.0 (142.0)
49.1 (49.3)
6611.0 (6810.0) 2570.0 (2620.0)
2667.0 (2755.0) 125 1.0 (1231.0)
3866.0 (3965.0) -
90.1 (91.0) 1138.0 (1141.0) 980.0 (1025.0)
71.9 (72.2) 301.0 (302.0) 224.0 (234.0)
'49!8 (50.7) 73.5 (73.6) 62.3 (63.4)
831.0 (825.0)
230.0 (227.0)
79.1 (78.7)
-
HgI2
-
Bi(NO3~SH20
9038.0 (9148.0)
279.2
661.6
Table III Total cross sections of elements (barn/atom) keV) 32.1
Ca
4.74
Ob
4.78 .
Na b
. 21.75 22.00
52.0
73.0
3.66
3.31
3.65 .
84.2
3.14
3.30 .
5.44 5.47
. 4.59 4.60
3.16 .
11.25 10.00
6.20 7.30
4.33 4.38 . 6.09 6.70
.
.
145.4
.
279.2
2.72
661.6
2.19
1.54
2.18
1.54
2.91 2.92
2.06 2.06
5.63 5.17
3.99 4.04
2.83 2.83
2.73 .
. 3.65 3.65
.
.
AP
43.95
16.04
9.14
8.65
6.54
4.75
3.28
Sa
43.80 87.89
15.50 28.81
9.70 15.52
8.60 12.97
6.30 8.00
4.80 6.11
3.35 3.95
6.03
4.10
5.74 6.45
4.54 4.41
7.19 7.30
4.77 4.94
7.52 7.70
5.18 5.15
8.13 8.60
5.59 5.70
9.64 9.60
6.49 6.30
CIb
Kb
Ca b
Ti b
Cr b
89.00 . 100.00 104.00 .
159.00 174.00 . 232.00 225.00 . 332.00 340.00 . 475.00 460.00
28.40 .
15.70 .
34.50 34.50 .
. 18.12 18.50
.
50.25 50.00 .
.
24.05 24.50 .
59.58 61.00 .
. 29.79 29.00
. 86.14 87.00
.
. 37.74 38.50
. 116.00 118.00
. 51.06 51.00
12.90 . 14.40 14.80 .
18.84 18.95 . 21.34 22.00 . 27.42 28.50 . 37.92 38.00
8.00 .
. 8.81 8.95
.
.
9.98 10.50 .
. 10.87 11.30
.
. 13.44 13.40
.
. 17.27 16.00
A.S. Nageswara R a o et al. / Photon cross section measurements
101
Table III (Contd.) 32.1
52.0
73.0
84.2
528.00 545.00
131.00 139.00
61.16 58.50
42.17 43.50
18.51 17.90
10.70 10.40
6.31 6.50
703.00 680.00
147.00 155.00
70.56 72.50
43.36 47.00
20.10 18.60
10.53 10.60
5.84 6.70
775.00 750.00
176.00 180.00
85.00 80.00
54.08 54.50
19.30 20.50
11.29 10.75
5.67 6.90
Ni ~
835.00
211.00
90.50
61.79
22.42
11.89
7.38
860.00
217.00
90.00
62.00
22.50
11.90
7.40
Cu
924.00~ 922.00b 945.00
243.00 234.00 245.00
92.00 91.80 95.00
73.75 69.00 73.00
24.68 23.85 25.00
12.34 11.32 12.40
7.77 6.91 7.80
Zn
1055.00" 1057.00 b 1060.00
290.00 282.00 290.00
120.00 118.00 120.00
80.50 80.70 80.00
27.89 26.83 27.80
13.35 13.43 13.40
8.04 7.96 8.05
Se"
1838.00
405.00
178.00
121.00
37.07
15.92
8.60
1870.00
408.00
180.00
122.00
37.00
16.00
8.60
1953.00 2000.00
496.00 510.00
200.00 205.00
130.00 140.00
41.20 40.50
16.52 16.75
8.84 9.50
2305.00 2460.00
671.0 691.00
277.00 272.00
189.00 188.00
51.70 50.00
17.74 19.00
10.41 9.97
3536.00
1003.00
350.00
278.00
72.00
23.26
11.91
rgy (keV)
145.4
279.2
661.6
Mn b
Fe b
Co b
Br b
Sr b
Mo a
3575.00
1010.00
380.00
280.00
73.00
24.20
12.00
Ag"
5475.00
1536.00
598.00
419.00
99.50
29.73
13.57
5480.00
1540.00
600.00
420.00
100.00
30.00
13.50
Cd
6214.00" 6109.00b 6200.00
1639.00 1586.00 1630.00
656.00 660.00 670.00
455.00 437.00 460.00
109.00 109.00 110.00
31.90 32.63 32.00
14.10 13.63 14.10
In"
6625.00
1778.00
710.00
479.00
120.00
33.70
14.50
6640.00
1780.00
710.00
480.00
120.00
34.00
14.60
6740.00
1870.00
748.00
506.00
129.00
35.95
14.59
6820.00
1880.00
760.00
510.00
130.00
36.00
14.80
1961.00
806.00
534.00
138.00
37.66
15.01
1980.00 2083.00a 2208.00I' 2130.00
810.00 871.00 871.00 875.00
545.00 588.00 592.00 590.00
140.00 144.00 156.00 147.00
38.00 39.88 39.74 40.00
15.00 15.48 15.56 15.41
Sn"
Sb'
Te
102
A.S. Nageswara R a o et al. / Photon cross section measurements
Table III(Contd.)
•"-..•nergy
52.0
73.0
84.2
145.4
Ia
2247.00
923.00
641.00
158.00
Bab
2280.00 .
645.00 .
160.00 .
770.00 790.00
198.00 200.00
(keV) 32.1
279.2
661.6
Element
wb
2810.00 2810.00
.
Hg °
Pb"
Bi
Th b
940.00 .
.
. 1125.00 1170.00
.
.
.
.
41.89
15.70
42.00
15.70
48.56 50.50
16.89 16.70
.
.
5762.00 6000.00
1577.00 1640.00
2923.00 3000.00
2051.00 2100.00
502.00 510.00
111.00 115.00
30.11 30.33
8138.00
2228.00
832.00
2668.00
709.00
143.00
30.98
8200.00
2250.00
875.00
2675.00
705.00
150.00
32.00
8667.00
2514.00
1094.00
749.00
715.00
154.00
37.10
8700.00
2490.00
1070.00
725.00
720.00
160.00
37.00
8812.00 a 8890.00 b 9000.00 . 12294.00 12600.00
2497.00 2474.00 2525.00 . 3554.00 3600.00
1155.00 1170.00 1150.00
697.00 720.00 . 1067.00 1060.00
754.00 766.00 760.00
174.00 178.00 175.00
41.99 42.41 42.00
244.00 245.00
47.83 48.00
268.00 270.00
50.46 50.50
L lb
.
.
12905.00 13400.00
.
. 1460.00 1460.00
.
3899.00 3950.00
.
.
.
1629.00 1620.00
.
977.00 1000.00 .
1158.00 1170.00
1097.00 1100.00
.
"Experimental cross sections of elements derived from direct measurements (error ~ 2%). b Experimental cross sections of elements derived from compounds (error ~-3 to 4%). c The figures, in the third row corresponding to a given element represent the theoretical cross sections obtained from the tables of Storm and Israel [9].
Table IV Atomic photo effect cross sections of elements (barn/atom) 32.1
52.0
73.0
Cr b
443.0 427.0
98.9 100.0
35.4 35.3
Mn b
486.0 503.0
111.0 118.0
44.7 42.1
Fe b
613.0 589.0 709.0 684.0
132.0 139.0 159.0 163.0
47.8 49.8 63.4 58.4
~'~'~nergy Element
Co b
(keV)
84.2
37.4 37.8
145.4
279.2
A.S. Nageswara R a o et al. / Photon cross section measurements
103
Table IV (Contd.) ~ n e r g y (keV) , 32.1 Element ~ . ~ . ~
52.0
73.0
84.2
765.0 790.0 885.0 905.0
184.0 189.0 217.0 219.0
68.6 68.1 75.9 78.9
43.9 44.1 52.0 51.2
1029.0 1034.0 1638.0 1669.0
252.0 251.0 363.0 366.0
91.5 91.0 150.0 152.0
59.6 59.1 99.8 100.0
Br b
1812.0 1859.0
453.0 467.0
167.0 172.0
103.0 112.0
Srb
2223.0 2300.0
624.0 645.0
245.0 240.0
159.0 158.0
Mo a
3386.0 3425.0
943.0 949.0
329.0 358.0
235.0 237.0
Ag"
5365.0 5370.0 5770.0 5756.0 6162.0 6177.0 6580.0 6620.0
1445.0 1449.0 1575.0 1566.0 1686.0 1688.0 1807.0 1817.0
554.0 556.0 589.0 603.0 654.0 653.0 694.0 706.0
369.0 370.0 397.0 402.0 435.0 436.0 468.0 471.0
-
1934.0 1953.0 2049.0 2096.0
757.0 761.0 815.0 819.0
499.0 509.0 547.0 549.0
-
2213.0 2246.0
864.0 880.0
587.0 590.0
5204.0 5442.0
2731.0 2731.0 1385.0 1448.0
1036.0 1081.0 2919.0 2896.0
709.0 728.0 1939.0 1987.0
7429.0 7491.0 8249.0 8282.0
2004.0 2026.0 2278.0 2254.0
755.0 797.0 914.0 890.0
2594.0 2601.0 625.0 601.0
8508.0 8696.0 11727.0 12033.0 12626.0 13121.0
2346.0 2374.0 3312.0 3358.0 3634.0 3685.0
945.0 939.0 1347.0 1347.0 1494.0 1484.0
612.0 635.0 923.0 915.0 999.0 1011.0
Ni" Cu a Zn a Se"
Cd' In a Sna Sb" Te" P Bab Wb
Hg" Pba Bi"
Th b ub
-
145.4
279.2
75.7 76.2 82.9 83.2 90.6 90.5 97.9 98.4 105.0 106.7 113.0 115.0 123.0 124.0 154.0 155.0 455.0 463.0 623.0 618.0 672.0 677.0 702.0 707.0 919.0 942.0 1012.0 1015.0
76.8 80.1 103.0 110.0 115.0 121.0 126.0 127.0 176.0 176.0 190.0 192.0
" Experimental cross sections of elements derived from direct measurements (error ~ 3%). b Experimental cross sections of elements derived from compounds (error,~ 4 to 5%). T h e f i g u r e s in the second row belonging to a given element represent theoretical photo etTect cross sections from the Scofield report [10].
j104
A.S. Nageswara R a o et al. / Photon cross section measurements
r e s p o n d i n g t h e o r e t i c a l v a l u e s f r o m t h e Scofield r e p o r t [10] a r e given in t h e l o w e r rows. It is s e e n that t h e cross s e c t i o n s of T e a n d H g m e a s u r e d in t h e e n e r g y r a n g e 52 k e V to 279 k e V a g r e e with t h e Scofield v a l u e s n o less t h a n t h o s e for o t h e r e l e m e n t s . O n t h e o t h e r h a n d , t h e v a l u e s for T e o b t a i n e d b y W r e d e in t h e r a n g e 1.3 k e V to 97 k e V [22] a r e s y s t e m a t i c a l l y 1 0 30% h i g h e r t h a n t h e v a l u e s given b y Scofield [10], while t h e cross s e c t i o n s for H g o b t a i n e d b e t w e e n 140 a n d 660 k e V b y Q u i v y [23] a n d b e t w e e n 510 a n d 1 2 5 0 k e V by M u r t h y [24] a r e c o n s i s t e n t l y low. T o t h e best of t h e a u t h o r ' s k n o w l e d g e t h e cross s e c t i o n m e a s u r e m e n t s on s t r o n t i u m w e r e m a d e for t h e first t i m e ; t h e results a r e c o n s i s t e n t with t h e t h e o r e t i c a l v a l u e s
[10]. Acknowledgements
T h e a u t h o r s wish t o e x p r e s s t h e i r t h a n k s to Prof. J . H . H u b b e l l , N B S , W a s h i n g t o n , for encouragement and kindly providing the latest l i t e r a t u r e . T h a n k s a r e also d u e to Prof. D . B . S i r d e s h m u k h , H e a d , D e p a r t m e n t of Physics, K a k a t i y a U n i v e r s i t y , for s p a r i n g t h e m e t a l foils. O n e of us ( A . S . N . R . ) w o u l d like t o t h a n k t h e C S I R , N e w D e l h i , for t h e a w a r d of a J u n i o r Research Fellowship. References
[1] J.H. Hubbell, NSRDS-NBS Circular 29 (1969). [2] J.H. Hubbell, Atomic Data 3 (1971) 241.
[3] M. Wiedenbeck, Phys. Rev. 126 (1962) 1009. [4] J.H. McCrary, E.H. Piassmann, J.M. Puckett, A.L. Conner and G.W. Zimmermann, Phys. Rev. 153 (1967) 307. [5] A.L. Conner, H.F. Atwater, E.H. Plassmann and J.H. McCrary, Phys. Rev. (A) 1 (1970) 539. [6] G.W. Grodstein, NBS Circular 583 (1957). [7] R.H. Pratt, A. Ron and H.K. Tseng, Rev. Mod. Phys. 45 (1973) 273. [8] Wm.J. Veigele, Atomic Data Tables 5 (1973) 51. [9] E. Storm and H.I. Israel, Nuclear Data Tables A7 (1970) 565. [10] J.H. Scofield, Report UCRL-51326 (1973). [11] J.H. Hubbell, Int. J. of Appl. Radiation and Isotopes 33 (1982) 1269. [12] J. Rama Rao, K. Parthasaradhi, A. Lakshmana Rao and P.V. Ramana Rao, Ind. J. Phys. 43 (1969) 298. [13] K. Siva Shankara Rao, G. Aruna Prasad, B.V. Tirumala Rao, P.V. Ramana Rao and K. Parthasaradhi, Ind. J. Phys. 48 (1974) 763. [14] T.K. Umesh, K.S. Puttaswamy and B. Sanjeevaiah, Phys. Rev. (A) 23 (1981) 2365. [15] T.K. Umesh, Ramakrishna Gowda and B. Sanjeevaiah, Phys. Rev. (A)25 (1982) 1986. [16] K.S.R. Sarma, K.L. Narasimham, K. Premchand, S. Bhuloka ReAdy, K. Parthasaradhi and V. Lakshminarayana, Pramana 18 (1982) 485. [17] Int. Comm. on Radiation Units and Measurements (ICRU) Report 33, Washington D.C. (1980). [18] D.F. Jackson and D.J. Hawkes, Phys. Reports 70 (1981) 169. [19] J.H. Hubbell and Wm.J. Veigele, NBS Technical Note 901 (1976). [20] A. Perumallu, A.S. Nageswara Rao and G. Krishna Rao, submitted to Can. J. Phys. [21] R.H. Miller and J.R. Greening, J. Phys. B: At. Mol. Phys. 7 (1974) 2332. [22] W. Wrede, Ann. Physik 36 (1939) 681. [23] R. Quivy, J. Physique. 27 (1966) 94. [24] R.C. Murtby, Proc. Phys. Soc. 84 (1964) 1032.
P H O T O N CROSS SECTION M E A S U R E M E N T S IN C O M P O U N D S A N D E L E M E N T S IN THE E N E R G Y R A N G E 3 0 - 6 6 0 keV A.S. N A G E S W A R A R A O , A. P E R U M A L L U * and G. K R I S H N A R A O Department of Physics, Kakatiya University, Warangal, 506 009, India Received 29 August 1983 Revised 28 October 1983 Total photon attenuation coefficientshave been measured at seven energies in the range 30-660 keV for 18 elements and 29 compounds. From the results obtained on compounds, the total photon cross sections for certain elements are obtained applying the mixture rule. Direct measurements could be obtained on 18 elements. Atomic photo effect cross sections in medium and high Z elements in the energy range 30-280 keV are derived from all data by subtracting the relatively small scattering (coherent + incoherent) cross sections from the total atomic cross sections. They are compared with theoretical values.
1. Introduction The knowledge of accurate photon attenuation cross sections is important in such diverse fields as medicine, industry, agriculture, etc. Significant photon attenuation measurements, calculations and compilations in elements have been published [1-8]. Fairly accurate theoretical cross sections of partial gamma ray interaction processes have also been made available [9-11]. However, the data on g a m m a ray attenuation measurements in compounds and mixtures seem to be very limited [12-16]. The mass attenuation and mass absorption coefficients in some compounds and mixtures of dosimetric and biological importance have been compiled by Hubbell [11] for the energy range l k e V - 2 0 M e V . These parameters are widely used for the calculation of photon penetration and energy-deposition in biological, shielding and other materials. The mass attenuation and energy absorption coefficients are defined in the I C R U R e p o r t - 3 3 [17] and are also discussed by Hubbell [11]. Jackson and Hawkes [18] have reviewed mass attenuation coefficients in elements and mixtures, and developed parametric fits for in* Present address: S.R. and B.G.N.R. Govt. College, Khammam, 507 002, India.
dividual collision processes, with particular emphasis on the photon energy range 3 0 150 keV. In the recent review papers of Veigele [8] and Hubbell and Veigele [19] it is pointed out that the data on attenuation measurements in certain elements are meagre; they advocated further measurements in elements and in energy regions which could afford a more critical test of the present theory and would reduce the uncertainties in present photon cross section tabulations. It is therefore considered worthwhile to undertake a systematic study of photon interaction cross sections in elements and compounds. The present report deals with the photon attenuation measurements on 18 elements and 29 compounds (biological, dosimetric, semiconductor and related materials) in the energy range 30-660 keV. From the results obtained on compounds, the total photon cross sections for elements, difficult to obtain in proper form to be used as target foils, were extracted using the mixture rule. From these data and the results of direct measurements on 18 elements, the atomic photo effect cross sections in medium and high Z elements in the energy range 3 0 - 2 8 0 k e V have been derived by subtracting relatively small scattering (coherent + incoherent) cross sections [9] from the total atomic cross sections. A corn-
0378-4363/84/$03.00 O Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
A . S . Nageswara R a o et al. / Photon cross section measurements
parison is made with recent theoretical values of Scofield [10].
2. Experimental details The total attenuation coefficients were determined by performing transmission experiments in a narrow beam geometry similar to the one used previously [20]. Radioactive sources of strength 1 0 - 2 0 m C i obtained from B A R C , Bombay (India) were used in the present work; the details of the sources are given in table I. Depending on the photon energy, two types of NaI(TI) crystals (5.1 × 5.1 cm/5.1 × 0.4 cm) covered by aluminium foils of appropriate thickness, mounted on R C A 8055/9656 photomultiplier tubes were used. The output pulses were amplified and fed to a preset timer through a single channel analyser. The experiments were conducted in an air-conditioned room to avoid possible shift of the photopeaks. The procedure adopted in the transmission experiment is similar to the one used in earlier experiments [20]. Metal foils of dimensions 2 × 2 cm 2 of suitable thickness were used and in the case of mercury, cylindrical cavities of 1 cm radius with varying thickness were made in perspex. In the actual experiment the cavities with and without material were exposed to the beam at several points and the respective intensities were utilized for the calculation of attenuation coefficients. For compounds and a few elements, which are in
Table I Radioactive isotopes used in the present work Radioisotope
Half-life
Energy of photons selected in keV a X-rays
137Cs 2°3Hg t4tCe tT°Tm
30.17 46.8 32.55 128.6
years days days days
v-rays
32.1 (BaK,) 661.6 73.0 (I~"-~) 279.2 145.4 52.0 (K,,~) 84.2
aC.M. Lederer and V.S. Shirley: Tables of Isotopes, Wiley, New York.
97
powder form, pellets of suitable thickness were prepared. In a few cases, where preparation of pellets was not possible, the powder was packed in a perspex holder with 1 cm inner radius and covered with thin mylar foils. The count rates were taken with and without material always keeping the mylar foil on the perspex container. All the metal foils, the pellets and the powders were weighed on a microbalance. Dimensions of foils, pellets and perspex holders were measured using a travelling microscope, and the thickness t of the sample was expressed in gm/cm 2. If I and I0 are the count rates with and without absorber of thickness t, the total atomic cross section is given by the relation
[In(/o//~1 t J'
A tr = ~- [
(1)
where N and A are Avogadro's number and the atomic weight, respectively, while the factor in brackets represents the mass attenuation coefficient (i.t/p). In the case of a compound the total molecular cross section is given by the relation Orc°mP= p N ~ niAi,
(2)
i
where ni is the number of atoms and Ai is the atomic mass of the ith element in a molecule. The errors in the present investigations are mainly due to counting statistics, non-uniformity of the absorber, the impurity content and the scattered photons reaching the detector within the accepted maximum angle of scattering. In the present investigations this angle is less than 2 ° and the error due to this factor is about 0.2%. The statistical errors were always less than 1%. The fractional error due to non-uniformity of the foil was estimated to be (At)2/2, where At is the relative fractional variation of the "thickness"; it is found to be of the order of 0.5%. As the materials are of a high purity the errors due to the presence of impurities is negligible. The overall error thus introduced on the total attenuation cross sections is estimated to be around 2%.
98
A.S. Nageswara R a o et al. / Photon cross section measurements
3. Results and discussion
The measured total mass attenuation coefficients for compounds were converted into total cross sections and are given in table II. Using the tables of Storm and Israel [9] for individual elements, the cross sections for compounds were evaluated using the mixture rule [21] and these theoretical cross sections are given in brackets below the experimental cross sections. One observes a good agreement between experimental and theoretical cross sections. It is difficult to obtain certain elements in a suitable form for cross section measurements; in such cases, applying the mixture rule, the total cross section of the element was extracted from the measured cross section of the compound. This method is claimed [14-17] to be useful especially if the element is in the gaseous form, where a direct measurement needs an elaborate experimental arrangment. It is also suitable in such cases where the elements are difficult to obtain in the free state to be used as target foils. In the present investigation the atomic cross sections in O, Na, CI, K, Ca, Ti, Cr, Mn, Fe, Co, Cu, Zn, Br, Sr, Cd, Te, Ba, W, Bi, Th and U were obtained in this way. In table III the total atomic cross sections of all the elements studied are given for various energies. The figures in the first row for a given element represent cross sections from direct measurements on foils, the second row corresponds to the cross sections obtained from the compounds; and the third row corresponds to the theoretical cross sections of Storm and Israel [9]. The total photon cross sections for Cu, Zn, Cd, T e and Bi have been obtained from measurements both on elements and compounds. A comparison between these two sets of values shows a good agreement within the range of the experimental error. Thus, it may be concluded that the method of extracting the total cross sections in elements, where direct measurement is rather difficult (especially in gases/elements not available in the free state), from the measurements on compounds works out satisfactorily in the present energy range. Since the accuracy as well as the reliability of the results will
increase when the subtracted contribution from other elements decreases for such a measurement, compounds (in powder form) with elements of lower atomic number than the element of interest seem to be preferable. The comparison of the measured cross sections in elements (direct or by subtraction from compound) with the theoretical values of Storm and Israel [9] shows general agreement within the range of the experimental error. The atomic photo effect cross sections were obtained by subtracting the scattering ( c o h e r e n t + incoherent) cross sections reported by Storm and Israel [9]. The subtracting procedure was restricted to only those cases where the scattering contribution does not exceed 20% (in a few cases it is around 30%) of the total photon cross section in a given element. The errors associated with the measured total cross section are carried on to the derived cross sections. As the theoretical scattering cross sections are known to an accuracy of 3%, the theoretical uncertainty entails an error of around 1% in the subtraction procedure. Hence, the error in the derived value of the total cross section for the element (obtained from the compound) is estimated to be
ao. = ___~,a L.,~ + E ,a~,
(3)
i
where A ¢ornpis the root mean square error in the result for the compound and Ai is the error on the subtracted cross section of the ith element. The error on the atomic photo effect cross sections is then estimated by the relation
,,tph = ___',,/A ~. + A~,
(4)
where A~c is the error on the subtracted value of the scattering cross section ( c o h e r e n t + incoherent). In the present case, the overall error on atomic photo effect cross sections for elements is around 3% for direct measurements and in other elements (extracted from compounds) it is 4 - 5 % . In table IV the derived atomic photo effect cross sections appear in the upper rows belonging to each element, while the cor-
99
A.S. Nageswara Rao et al. / Photon cross section measurements
Table II Total photon cross sections of compounds (barn/molecule) (error ~-2%) keV) 32.1 H20 NaCI CaF2 TiO2 NI-hNO3 ZnO NaNO3 KNO3 KH2PO4 GaAs CaTe KBrO3 MnSOd-I20 CdCl2 ZnTe Sr(NO3)2 InSb (CH3COO)2CO4H20 CuSO45H20 Ba(NO3)2 ThO2 FeSO47H20 CoSO47H20 K2Cr207
122.0 (126.0) 256.0 (248.0) 350.0 (357.0) 40.4 (41.7) 1066.0 (1069.0) 54.6 (54.9) 192.0 (207.0) 283.0 (283.0) 2671.0 (2750.0) 2153.0 (2200.0) 662.0 (679.0) 6317.0 (6408.0) 2419.0 (2525.0) 873.0 (847.0) 1096.0 (1119.0) 12312.0 (12617.0) 897.0 (874.0) 949.0 (944.0) 1361.0 (1329.0)
52.0 6.5 (6.6) 44.5 (44.5) 73.0 (74.4) 97.1 (97.9) 26.8 (27.6) 288.0 (295.0) 32.1 (30.9) 71.1 (70.9) 92.2 (95.9) 643.0 (660.0) 2269.0 (2191.0) 563.0 (576.0) 189.0 (196.0) 1655.0 (1699.0) 2419.0 (2420.0) 708.0 (736.0) 3645.0 (3760.0) 242.0 (246.0) 317.0 (328.0) 2852.0 (2851.0) 3565.0 3610.0 243.0 (251.0) 272.0 (276.0) 372.0 (374.0)
73.0 5.6 (5.6) 25.4 (25.8) 40.6 (39.8) 46.9 (47.7) 23.4 (23.7) 123.0 (124.0) 24.0 (25.0) 41.7 (42.2) 55.7 (57.2) 274.0 (284.0) 900.0 (9O4.O) 238.0 (243.0) 100.0 (98.2) 697.0 (707.0) 967.0 (995.0) 312.0 (308.0) 1456.0 (1520.0) 142.0 (137.0) 154.0 (157.0) 1160.0 (1205.0) 1469.0 (1469.0) 144.0 (146.0) 145.0 (153.0) 183.0 (183.0)
84.2
145.4
5.3 (5.4) 21.1 (21.5) 31.2 (31.8) 36.0 (37.2) 23.1 (22.7) 85.1 (84.4) 22.9 (23.6) 35.7 (35.8) 49.0 (48.8) 213.0 (208.0) 614.0 (612.0) 162.0 (172.0) 77.9 (79.3) 467.0 (489.0) 652.0 (670.0) 223.0 (222.0) 1035.0 (1025.0) 109.0 (109.0) 126.0 (130.0) 804.0 (823.0) 1076.0 (1068.0) 111.0 (115.0) 121.0 (122.0) 144.0 (144.0)
4.5 (4.5) 14.0 (14.1) 19.2 (19.6) 20.7 (20.7) 19.0 (19.0) 30.5 (31.4) 19.7 (19.3) 24.1 (24.6) 33.1 (33.4) 62.5 (63.0) 167.0 (158.0) 62.6 (61.9) 45.6 (45.0) 127.0 (128.0) 182.0 (175.0) 80.9 (78.2) 252.0 (260.0) 65.6 (66.8) 69.1 (70.3) 226.0 (228.0) 984.0 (1007.0) 74.4 (72.9) 74.3 (74.8) 81.1 (78.5)
279.2 3.6 (3.6) 9.8 (10.5) 14.1 (14.2) 13.9 (14.4) 14.9 (15.3) 16.3 (16.3) 15.3 (15.3) 18.5 (18.6) 24.8 (25.3) 30.5 (30.2) 47.4 (47.7) 32.6 (32.8) 32.0 (31.7) 45.5 (44.9) 52.7 (53.4) 40.3 (41.6) 71.9 (72.0) 48.4 (47.9) 47.2 (48.3) 71.1 (73.1) 250.0 (250.0) 53.7 (53.8) 52.9 (54.0) 54.3 (54.2)
661.6 2.5 (2.5) 7.3 (7.2) 9.7 (9.7) 9.7 (9.8) 10.5 (10.7) 10.0 (10.1) 10.7 (10.7) 12.7 (12.7) 17.0 (17.5) 17.0 (17.1) 20.7 (2O.5) 19.9 (20.6) 21.0 (21.2) 22.4 (22.9) 23.5 (23.4) 26.8 (26.3) 29.8 (29.4) 31.7 (33.0) 31.8 (32.7) 32.8 (32.6) 51.9 (52.1) 35.9 (36.7) 36.5 (36.9) 37.2 (36.9)
100
A.S. Nageswara Rao et ai. / Photon cross section measurements
Table II (Contd.)
NaWO42H20 Na2B4OT10H20
uo~(cooh3H20
32.1
52.0
73.0
84.2
145.4
5861.0 (6099.0) 222.0 (219.0) 12997.0 (13492.0)
1632.0 (1695.0) 133.0 (136.0) 3959.0 (4010.0)
2967.0 (3044.0) 115.0 (114.0) 1680.0 (1671.0)
2093.0 (2141.0) 111.0 (108.0) 1207.0 (1218.0)
536.0 (544.0)
138.0 (142.0)
49.1 (49.3)
6611.0 (6810.0) 2570.0 (2620.0)
2667.0 (2755.0) 125 1.0 (1231.0)
3866.0 (3965.0) -
90.1 (91.0) 1138.0 (1141.0) 980.0 (1025.0)
71.9 (72.2) 301.0 (302.0) 224.0 (234.0)
'49!8 (50.7) 73.5 (73.6) 62.3 (63.4)
831.0 (825.0)
230.0 (227.0)
79.1 (78.7)
-
HgI2
-
Bi(NO3~SH20
9038.0 (9148.0)
279.2
661.6
Table III Total cross sections of elements (barn/atom) keV) 32.1
Ca
4.74
Ob
4.78 .
Na b
. 21.75 22.00
52.0
73.0
3.66
3.31
3.65 .
84.2
3.14
3.30 .
5.44 5.47
. 4.59 4.60
3.16 .
11.25 10.00
6.20 7.30
4.33 4.38 . 6.09 6.70
.
.
145.4
.
279.2
2.72
661.6
2.19
1.54
2.18
1.54
2.91 2.92
2.06 2.06
5.63 5.17
3.99 4.04
2.83 2.83
2.73 .
. 3.65 3.65
.
.
AP
43.95
16.04
9.14
8.65
6.54
4.75
3.28
Sa
43.80 87.89
15.50 28.81
9.70 15.52
8.60 12.97
6.30 8.00
4.80 6.11
3.35 3.95
6.03
4.10
5.74 6.45
4.54 4.41
7.19 7.30
4.77 4.94
7.52 7.70
5.18 5.15
8.13 8.60
5.59 5.70
9.64 9.60
6.49 6.30
CIb
Kb
Ca b
Ti b
Cr b
89.00 . 100.00 104.00 .
159.00 174.00 . 232.00 225.00 . 332.00 340.00 . 475.00 460.00
28.40 .
15.70 .
34.50 34.50 .
. 18.12 18.50
.
50.25 50.00 .
.
24.05 24.50 .
59.58 61.00 .
. 29.79 29.00
. 86.14 87.00
.
. 37.74 38.50
. 116.00 118.00
. 51.06 51.00
12.90 . 14.40 14.80 .
18.84 18.95 . 21.34 22.00 . 27.42 28.50 . 37.92 38.00
8.00 .
. 8.81 8.95
.
.
9.98 10.50 .
. 10.87 11.30
.
. 13.44 13.40
.
. 17.27 16.00
A.S. Nageswara R a o et al. / Photon cross section measurements
101
Table III (Contd.) 32.1
52.0
73.0
84.2
528.00 545.00
131.00 139.00
61.16 58.50
42.17 43.50
18.51 17.90
10.70 10.40
6.31 6.50
703.00 680.00
147.00 155.00
70.56 72.50
43.36 47.00
20.10 18.60
10.53 10.60
5.84 6.70
775.00 750.00
176.00 180.00
85.00 80.00
54.08 54.50
19.30 20.50
11.29 10.75
5.67 6.90
Ni ~
835.00
211.00
90.50
61.79
22.42
11.89
7.38
860.00
217.00
90.00
62.00
22.50
11.90
7.40
Cu
924.00~ 922.00b 945.00
243.00 234.00 245.00
92.00 91.80 95.00
73.75 69.00 73.00
24.68 23.85 25.00
12.34 11.32 12.40
7.77 6.91 7.80
Zn
1055.00" 1057.00 b 1060.00
290.00 282.00 290.00
120.00 118.00 120.00
80.50 80.70 80.00
27.89 26.83 27.80
13.35 13.43 13.40
8.04 7.96 8.05
Se"
1838.00
405.00
178.00
121.00
37.07
15.92
8.60
1870.00
408.00
180.00
122.00
37.00
16.00
8.60
1953.00 2000.00
496.00 510.00
200.00 205.00
130.00 140.00
41.20 40.50
16.52 16.75
8.84 9.50
2305.00 2460.00
671.0 691.00
277.00 272.00
189.00 188.00
51.70 50.00
17.74 19.00
10.41 9.97
3536.00
1003.00
350.00
278.00
72.00
23.26
11.91
rgy (keV)
145.4
279.2
661.6
Mn b
Fe b
Co b
Br b
Sr b
Mo a
3575.00
1010.00
380.00
280.00
73.00
24.20
12.00
Ag"
5475.00
1536.00
598.00
419.00
99.50
29.73
13.57
5480.00
1540.00
600.00
420.00
100.00
30.00
13.50
Cd
6214.00" 6109.00b 6200.00
1639.00 1586.00 1630.00
656.00 660.00 670.00
455.00 437.00 460.00
109.00 109.00 110.00
31.90 32.63 32.00
14.10 13.63 14.10
In"
6625.00
1778.00
710.00
479.00
120.00
33.70
14.50
6640.00
1780.00
710.00
480.00
120.00
34.00
14.60
6740.00
1870.00
748.00
506.00
129.00
35.95
14.59
6820.00
1880.00
760.00
510.00
130.00
36.00
14.80
1961.00
806.00
534.00
138.00
37.66
15.01
1980.00 2083.00a 2208.00I' 2130.00
810.00 871.00 871.00 875.00
545.00 588.00 592.00 590.00
140.00 144.00 156.00 147.00
38.00 39.88 39.74 40.00
15.00 15.48 15.56 15.41
Sn"
Sb'
Te
102
A.S. Nageswara R a o et al. / Photon cross section measurements
Table III(Contd.)
•"-..•nergy
52.0
73.0
84.2
145.4
Ia
2247.00
923.00
641.00
158.00
Bab
2280.00 .
645.00 .
160.00 .
770.00 790.00
198.00 200.00
(keV) 32.1
279.2
661.6
Element
wb
2810.00 2810.00
.
Hg °
Pb"
Bi
Th b
940.00 .
.
. 1125.00 1170.00
.
.
.
.
41.89
15.70
42.00
15.70
48.56 50.50
16.89 16.70
.
.
5762.00 6000.00
1577.00 1640.00
2923.00 3000.00
2051.00 2100.00
502.00 510.00
111.00 115.00
30.11 30.33
8138.00
2228.00
832.00
2668.00
709.00
143.00
30.98
8200.00
2250.00
875.00
2675.00
705.00
150.00
32.00
8667.00
2514.00
1094.00
749.00
715.00
154.00
37.10
8700.00
2490.00
1070.00
725.00
720.00
160.00
37.00
8812.00 a 8890.00 b 9000.00 . 12294.00 12600.00
2497.00 2474.00 2525.00 . 3554.00 3600.00
1155.00 1170.00 1150.00
697.00 720.00 . 1067.00 1060.00
754.00 766.00 760.00
174.00 178.00 175.00
41.99 42.41 42.00
244.00 245.00
47.83 48.00
268.00 270.00
50.46 50.50
L lb
.
.
12905.00 13400.00
.
. 1460.00 1460.00
.
3899.00 3950.00
.
.
.
1629.00 1620.00
.
977.00 1000.00 .
1158.00 1170.00
1097.00 1100.00
.
"Experimental cross sections of elements derived from direct measurements (error ~ 2%). b Experimental cross sections of elements derived from compounds (error ~-3 to 4%). c The figures, in the third row corresponding to a given element represent the theoretical cross sections obtained from the tables of Storm and Israel [9].
Table IV Atomic photo effect cross sections of elements (barn/atom) 32.1
52.0
73.0
Cr b
443.0 427.0
98.9 100.0
35.4 35.3
Mn b
486.0 503.0
111.0 118.0
44.7 42.1
Fe b
613.0 589.0 709.0 684.0
132.0 139.0 159.0 163.0
47.8 49.8 63.4 58.4
~'~'~nergy Element
Co b
(keV)
84.2
37.4 37.8
145.4
279.2
A.S. Nageswara R a o et al. / Photon cross section measurements
103
Table IV (Contd.) ~ n e r g y (keV) , 32.1 Element ~ . ~ . ~
52.0
73.0
84.2
765.0 790.0 885.0 905.0
184.0 189.0 217.0 219.0
68.6 68.1 75.9 78.9
43.9 44.1 52.0 51.2
1029.0 1034.0 1638.0 1669.0
252.0 251.0 363.0 366.0
91.5 91.0 150.0 152.0
59.6 59.1 99.8 100.0
Br b
1812.0 1859.0
453.0 467.0
167.0 172.0
103.0 112.0
Srb
2223.0 2300.0
624.0 645.0
245.0 240.0
159.0 158.0
Mo a
3386.0 3425.0
943.0 949.0
329.0 358.0
235.0 237.0
Ag"
5365.0 5370.0 5770.0 5756.0 6162.0 6177.0 6580.0 6620.0
1445.0 1449.0 1575.0 1566.0 1686.0 1688.0 1807.0 1817.0
554.0 556.0 589.0 603.0 654.0 653.0 694.0 706.0
369.0 370.0 397.0 402.0 435.0 436.0 468.0 471.0
-
1934.0 1953.0 2049.0 2096.0
757.0 761.0 815.0 819.0
499.0 509.0 547.0 549.0
-
2213.0 2246.0
864.0 880.0
587.0 590.0
5204.0 5442.0
2731.0 2731.0 1385.0 1448.0
1036.0 1081.0 2919.0 2896.0
709.0 728.0 1939.0 1987.0
7429.0 7491.0 8249.0 8282.0
2004.0 2026.0 2278.0 2254.0
755.0 797.0 914.0 890.0
2594.0 2601.0 625.0 601.0
8508.0 8696.0 11727.0 12033.0 12626.0 13121.0
2346.0 2374.0 3312.0 3358.0 3634.0 3685.0
945.0 939.0 1347.0 1347.0 1494.0 1484.0
612.0 635.0 923.0 915.0 999.0 1011.0
Ni" Cu a Zn a Se"
Cd' In a Sna Sb" Te" P Bab Wb
Hg" Pba Bi"
Th b ub
-
145.4
279.2
75.7 76.2 82.9 83.2 90.6 90.5 97.9 98.4 105.0 106.7 113.0 115.0 123.0 124.0 154.0 155.0 455.0 463.0 623.0 618.0 672.0 677.0 702.0 707.0 919.0 942.0 1012.0 1015.0
76.8 80.1 103.0 110.0 115.0 121.0 126.0 127.0 176.0 176.0 190.0 192.0
" Experimental cross sections of elements derived from direct measurements (error ~ 3%). b Experimental cross sections of elements derived from compounds (error,~ 4 to 5%). T h e f i g u r e s in the second row belonging to a given element represent theoretical photo etTect cross sections from the Scofield report [10].
j104
A.S. Nageswara R a o et al. / Photon cross section measurements
r e s p o n d i n g t h e o r e t i c a l v a l u e s f r o m t h e Scofield r e p o r t [10] a r e given in t h e l o w e r rows. It is s e e n that t h e cross s e c t i o n s of T e a n d H g m e a s u r e d in t h e e n e r g y r a n g e 52 k e V to 279 k e V a g r e e with t h e Scofield v a l u e s n o less t h a n t h o s e for o t h e r e l e m e n t s . O n t h e o t h e r h a n d , t h e v a l u e s for T e o b t a i n e d b y W r e d e in t h e r a n g e 1.3 k e V to 97 k e V [22] a r e s y s t e m a t i c a l l y 1 0 30% h i g h e r t h a n t h e v a l u e s given b y Scofield [10], while t h e cross s e c t i o n s for H g o b t a i n e d b e t w e e n 140 a n d 660 k e V b y Q u i v y [23] a n d b e t w e e n 510 a n d 1 2 5 0 k e V by M u r t h y [24] a r e c o n s i s t e n t l y low. T o t h e best of t h e a u t h o r ' s k n o w l e d g e t h e cross s e c t i o n m e a s u r e m e n t s on s t r o n t i u m w e r e m a d e for t h e first t i m e ; t h e results a r e c o n s i s t e n t with t h e t h e o r e t i c a l v a l u e s
[10]. Acknowledgements
T h e a u t h o r s wish t o e x p r e s s t h e i r t h a n k s to Prof. J . H . H u b b e l l , N B S , W a s h i n g t o n , for encouragement and kindly providing the latest l i t e r a t u r e . T h a n k s a r e also d u e to Prof. D . B . S i r d e s h m u k h , H e a d , D e p a r t m e n t of Physics, K a k a t i y a U n i v e r s i t y , for s p a r i n g t h e m e t a l foils. O n e of us ( A . S . N . R . ) w o u l d like t o t h a n k t h e C S I R , N e w D e l h i , for t h e a w a r d of a J u n i o r Research Fellowship. References
[1] J.H. Hubbell, NSRDS-NBS Circular 29 (1969). [2] J.H. Hubbell, Atomic Data 3 (1971) 241.
[3] M. Wiedenbeck, Phys. Rev. 126 (1962) 1009. [4] J.H. McCrary, E.H. Piassmann, J.M. Puckett, A.L. Conner and G.W. Zimmermann, Phys. Rev. 153 (1967) 307. [5] A.L. Conner, H.F. Atwater, E.H. Plassmann and J.H. McCrary, Phys. Rev. (A) 1 (1970) 539. [6] G.W. Grodstein, NBS Circular 583 (1957). [7] R.H. Pratt, A. Ron and H.K. Tseng, Rev. Mod. Phys. 45 (1973) 273. [8] Wm.J. Veigele, Atomic Data Tables 5 (1973) 51. [9] E. Storm and H.I. Israel, Nuclear Data Tables A7 (1970) 565. [10] J.H. Scofield, Report UCRL-51326 (1973). [11] J.H. Hubbell, Int. J. of Appl. Radiation and Isotopes 33 (1982) 1269. [12] J. Rama Rao, K. Parthasaradhi, A. Lakshmana Rao and P.V. Ramana Rao, Ind. J. Phys. 43 (1969) 298. [13] K. Siva Shankara Rao, G. Aruna Prasad, B.V. Tirumala Rao, P.V. Ramana Rao and K. Parthasaradhi, Ind. J. Phys. 48 (1974) 763. [14] T.K. Umesh, K.S. Puttaswamy and B. Sanjeevaiah, Phys. Rev. (A) 23 (1981) 2365. [15] T.K. Umesh, Ramakrishna Gowda and B. Sanjeevaiah, Phys. Rev. (A)25 (1982) 1986. [16] K.S.R. Sarma, K.L. Narasimham, K. Premchand, S. Bhuloka ReAdy, K. Parthasaradhi and V. Lakshminarayana, Pramana 18 (1982) 485. [17] Int. Comm. on Radiation Units and Measurements (ICRU) Report 33, Washington D.C. (1980). [18] D.F. Jackson and D.J. Hawkes, Phys. Reports 70 (1981) 169. [19] J.H. Hubbell and Wm.J. Veigele, NBS Technical Note 901 (1976). [20] A. Perumallu, A.S. Nageswara Rao and G. Krishna Rao, submitted to Can. J. Phys. [21] R.H. Miller and J.R. Greening, J. Phys. B: At. Mol. Phys. 7 (1974) 2332. [22] W. Wrede, Ann. Physik 36 (1939) 681. [23] R. Quivy, J. Physique. 27 (1966) 94. [24] R.C. Murtby, Proc. Phys. Soc. 84 (1964) 1032.