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A simple method of determining the photoeffect cross sections of elements for gamma rays
472
Nuclear Instruments and Methods in Physics Research B5 (1984) 472-475 North-Holland, Amsterdam
A SIMPLE METHOD OF DETERMINING ELEMENTS FOR GAMMA RAYS T.K. UMESH
THE PHOTOEFFECT
CROSS SECTIONS
OF
and C. ~NGANATHAIA~
Department of Post -Graduate Studies and Research in Physics, University of Mysore, Manma Gangotri, Mysore 570 006, India
Received 16 May 1984
A simple relation between the total photoeffect cross section of an element and the total attenuation cross section of its compound has been derived. Total attenuation cross sections of some: 15 simple compounds have been measured by performing transmission experiments in a good geometry set up. Using these values and with the aid of the present relation, total photoeffect cross sections of elements of 2 2 47 at 514.0, 661.6, 1115.5, 1173.2 and 1332.5 keV gamma ray energies have been determined and compared with Scofield’s theoretical cross sections.
1. Introduction The atomic photoeffect is one of the major ways by which the gamma rays interact with matter at low photon energies and in high Z elements, Owing to its importance in radiation physics, nuclear physics and transport calculations, the photoeffect process has been the subject of considerable interest over the years. Among the various theoretical calculations of photoeffeet cross sections, the numerical data of Scofield [l] on the total and subshell photoeffect cross sections are considered to be the most accurate theoretical data. These data cover elements of Z = 1 to 101 in the energy region 1 to 1500 keV. A survey of literature on the experimental investigations of the photoeffect reveals that quite a good amount of experimental results exist. In obtaining these results generally two types of experiments [2] have been performed. These are (i) the direct method and (ii) the indirect method or the subtraction technique. The direct method involves the detection of the ejected photoelectrons using an efficient electron detector. Though this is a precise method, it cannot yield accurate results as far as the total photoeffect cross sections are concerned particularly at photon energies above a few hundred keV. The subtraction technique yields accurate results in the energy region where the photoeffect is predominant, say, less than a few hundred keV. A critical study of the results obtained by the above two methods indicates that the major part of these data is confined to elements which are available in their elemental form (i.e., foils), such as C, Al, Cu, Zr, Ag, Sn, Ta, Au, Pb, Th and U. It is also indicative of the fact that for elements of Z = 51 to 73 which includes the lanthanum group, data are practically non-existent [3]. In recent years, there have been efforts to derive the
0168-583X/84/$03.00 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
cross sections of elements particularly in the case of lanthanum group elements from the experimentally measured total attenuation cross sections of their compounds with the aid of a mixture rule 14-61. This procedure is rather tedious as it involves the following steps: (1) measurement of the compound cross section; (2) derivation of the elemental cross section using the mixture rule; (3) interpolation of the “to be subtracted” theoretical scattering cross sections to the desired energy; (4) derivation of photoeffect cross section of the element by subtraction technique. Therefore, it was felt worthwhile to suitably simplify this technique so as to enable speedier determination of the total photoeffect cross section of an element from the experimentally measured total attenuation cross section of its compound. With this end in view, we have obtained a simple relation between the photoeffect cross section of an element and the total attenuation cross section of its compound. This relation yields results which are found to be in good agreement with Scofield’s cross sections for elements Z 2 47 in the energy region 500 to 1500 keV.
2. Experimental procedure Although Sauter’s [7] relation predicts a uniform Z-dependence of photoeffect cross sections, it can be noticed that the Z-dependence varies strongly as the energy increases, A preliminary check revealed the fact that for energies above 500 keV, cross sections show a uniform Z-dependence. Based on this we selected five energies 514.0, 661.6, 1115.5, 1173.2 and 1332.5 keV for
T. K. Umesh, C. Ranganaihaiah / Determination of photoeffect cross sections
473
Table 1 Total attenuation cross sections in compounds (barns per molecule) Compound
AaCl Ki BaO LazOj CeO, Pro, Nd,Gs Sm 203 Gd
203
Dy2°3 Ho203 Er203 Ta 2%
(HCOO),Pb Bi,O,
Molecular weight M
Element
143.32 166.01 153.34 325.82 172.12 172.91 336.48 348.70 362.50 373.00 317.86 382.56 441.89 297.25 465.96
AR
I-
Ba La Ce Pr Nd Sm Gd DY Ho Er Ta Pb Bi
Atomic number z
Atomic weight
47 53 56 57 58 59 60 62 64 66 61 68 73 82 83
107.87 126.90 137.34 138.91 140.12 140.907 144.24 150.35 157.25 162.50 164.93 167.26 180.948 207.19 208.98
M,
the present investigation. The elements were chosen such that the atomic number was greater than 47. In total, fifteen simple compounds of these elements were used. A list of all the compounds used is given in table 1. For the monoenergetic gamma sources 85Sr (514 keV), 13’Cs (661.6 keV), and 65Zn (1115.5 keV), a (1” x 11/4”) NaI(Tl) scintillation detector was used. In the case of 6oCo (1173.2 and 1332.5 keV) a hyperpure germanium detector (23210 ORTEC model) was used in order to separate the two peaks. The total attenuation cross sections of the compounds at these energies were measured by performing transmission experiments in a good geometry set up. Details of the experimental procedure, error calculation and the various corrections applied can be found in our earlier papers [4-61. The overall error on the measured total attenuation cross sections of compounds is less than 2% in all the cases. These are tabulated in table 1.
3. Results and discussion From the cross sections of the compounds so obtained (table l), the cross sections for the individual elements were derived with the aid of the mixture rule [4-61. From these cross sections, the photoeffect cross sections were derived by subtracting the theoretical scattering cross sections [8]. This was done for all elements and at all energies of interest. Now, a parameter X was calculated according to
x=
uPhoto OccnnpMi/M
’
0)
Energy in keV 514.0
661.6
1115.5
1332.5
20.70&0.46 24.31 f0.46 23.27 kO.51 52.07 kO.33 28.08 + 0.20 29.02kO.19 57.41*0.35 60.61*0.39 64.49 f 0.42 68.73 f 0.43 70.73 f 0.48 72.51 f 0.41 89.53 f 0.56 65.78kO.40 116.49kO.73
17.80 f 0.41 21.00f0.38 19.86 f 0.42 42.36 f 0.32 22.98 +0.18 23.42 50.19 45.82 f 0.32 48.28 f 0.36 50.48 +0.39 53.12+0.42 54.56 f 0.41 55.70 f 0.42 68.28 f 0.54 49.27 f0.31 83.54 f 0.61
13.24+0.46 15.43 !i 0.25 14.52 f 0.29 30.68 kO.26 16.44f0.15 16.66*0.14 32.40 rtO.26 33.70 f 0.28 34.92 50.30 36.28 + 0.32 37.06iO.32 31.88 f 0.33 45.00+0.36 31.92*0.27 51.34+0.46
12.20 +0.24 13.84 f 0.22 12.69 f 0.26 27.50 f 0.23 14.82+0.14 15.01*0.13 29.12 f 0.23 30.24 f 0.25 31.28kO.27 32.46 +0.29 33.12 f 0.29 35.14*0.31 39.96 + 0.25 28.65 f 0.24 44.74 f 0.40
is the total photoeffect cross section of the uPhoto element, ucomP the total attenuation cross section of its compound, Mi the atomic weight of the element and M the molecular weight of its compound. The form of this expression is based on a preliminary check that the product of ucCompand the ratio (MJM) nearly gave total photoeffect cross sections in lanthanum group elements at a lower photon energy. As such the parameter X was calculated for the elements Z = 47, 53, 56, 57, 58, 59, 60, 62, 64, 66, 67, 68, 73, 82 and 83, at the energies of interest. These values are listed in table 2. It is clear from the values of X that it varies with energy of where
Table 2 Values of the parameter X from eq. (1) Atomic number Z
Energy in keV 514.0
661.6
1115.5
1332.5
47 53 56 57 58 59 60 62 64 66 67 68 73 82 83
0.1463 0.2040 0.2404 0.2478 0.2699 0.2795 0.2877 0.3077 0.3335 0.3580 0.3893 0.3792 0.4528 0.5939 0.5520
0.1067 0.1330 0.1546 0.1672 0.1812 0.1860 0.1980 0.2099 0.2288 0.2485 0.2716 0.2714 0.3301 0.4458 0.4329
0.0502 0.0676 0.0769
0.0348 0.0528 0.0633 0.0665 0.0696 0.0744 0.0758 0.0874 0.0965 0.1068 0.1190 0.1120 0.1448 0.2008 0.2108
0.0807 0.0847 0.0907 0.0998 0.1122 0.1208 0.1366 0.1334 0.1639 0.2279 0.2358
T.K. Umesh, C. Ranganathaiah
414
/ Determination
Table 3 Values of M and C from eq, (2)
of photoeffect cross sections
values are listed in table 3. Again straight form
Energy in keV
Slope m
Intercept C
514.0 661.6 1115.5 1332.5
2.3164 2.6162 2.8314 3.1342
-
ln m = ml ln E-l- C,
(3)
and
10.9967 12.3501 13.9612 15.3836
C=m,InE+C,
(4)
fitted by the method of least squares, using the values of m, C and energy in table 3. The values of m,, C,, m z and C, so obtained were subjected to a chi-square test [9]. The values of these parameters for which chisquare was minimum were found to be 0.2576, - 0.7328, -4.2442 and 15.4193, respectively. Substituting these values in eq. (2) through (3) and (4), a relation of the form were
the photon and atomic number Z of the element. It is assumed that the relation for X could be of the form lnX=mlnZ+C.
lines of the
(2)
Here m and C vary with energy. Using the values of X and Z in table 2, the values of the slope m and the intercept Cwere obtained at energies 514.0,661.6,1115.5 and 1332.5 keV, by the method of least squares. These
(5) was obtained.
Therefore,
now the expression
(1) can be
Table 4 Total photoeffect cross sections of elements in barns/atom Atomic number Z 41 53 56 57 58 59 60 62 64 66 67 68 73 82 83
Energy in keV 514.0 2.49 a’ 2.28 3.97 3.80 5.06 5.01 5.63 5.50 6.04 6.17 6.51 6.61 7.06 7.08 8.11 8.04 9.36 9.33 10.79 10.72 11.53 11.35 12.27 12.02 16.83 16.60 27.81 21.23 32.63 30.84
661.6 1.36 1.43 2.23 2.14 2.83 2.75 3.01 3.02 3.26 3.39 3.47 3.55 3.73 3.89 4.30 4.37 4.91 5.01 5.61 5.75 6.00 6.31 6.38 6.61 8.78 9.23 14.52 15.31 16.34 16.22
1115.5
1173.2
1332.5
0.457 0.500 0.771 0.800 0.996 1.000 1.06 0.98 1.14 1.08 1.21 1.15 1.30 1.26 1.50 1.45 1.71 1.70 1.96 1.91 2.09 2.00 2.24 2.21 3.07 3.02 5.21 5.07 5.58 5.43
0.419 0.410 0.695 0.708 0.884 0.906 0.958 0.970 1.04 1.07 1.11 1.13 1.19 1.24 1.37 1.44 1.58 1.66 1.80 1.90 1.92 1.98 2.10 2.16 2.82 3.00 4.89 5.00 5.12 5.27
0.336 0.320 0.561 0.560 0.711 0.719 0.774 0.780 0.841 0.840 0.898 0.910 0.965 0.980 1.12 1.14 1.28 1.31 1.46 1.51 1.57 1.61 1 .I4 1.12 2.31 2.37 4.02 4.01 4.20 4.23
a) In each case the first line gives the value obtained using the present formula and the second line Scofield’s theoretical results.
T.K. Umesh, C. Ranganathaiah / Determination of photoeffect cross sections
written
using eq. (5) as
From this expression it is clear that only ucCompis to be measured to determine the ePho,,, of the element. The Photoeffect cross sections obtained using the relation (6) are compared with Scofield’s results in table 4, for all the energies of interest. As it can be seen from the table there is a good agreement between the formula values and Scofield’s values for elements Z 2 47
4. Conclusions It can be concluded that the present formula depicts a novel method to determine the photoeffect cross sections of elements from the experimentally measured total attenuation cross section of its compound. This formula yields fairly accurate results since the compound cross section can be determined to less than 2% accuracy in a good geometry transmission experiment. Also this method substantially reduces the theoretical dependence and the calculation time as compared to the conventional subtraction technique. As such, it serves as a simple technique by which a speedier filling of the
475
existing gaps in the experimental total photoeffect cross section data can be done just by measuring the compound cross section in the energy region 500 to 1500 keV and Z > 47. For low Z elements the present formula gives results which deviate much from Scofield’s results.
References 111 J.H. Scofield UCRL Report No. 15326 (1973). [21 R.H. Pratt, A. Ron and H.K. Tseng, Rev. Mod. Phys. 45 (1973) 273. 131 J.H. Hubbell and Wm.J. Veigele, NBS Report No. TN-901 (1976). Ramakrishna Gowda, KS. 141 T.K. Umesh, C. Ranganathaiah, Puttaswamy and B. Sanjeevaiah, Phys. Rev. A23 (1981) 2365. Gowda and B. Sanjeevaiah, 151T.K. Umesh, Ramakrishna Phys. Rev. A 25 (1982) 1986. and B. Sanjeevaiah, Phys. (61 T.K. Umesh, C. Ranganathaiah Rev. A 29 (1984) 387. 171 F. Sauter, Ann. Physik 9, (1931) 217. PI J.H. Hubbell, Wm.J. Veigele, E.A. Briggs, R.T. Brown, D.T. Cromer and R.J. Howerton, J. Phys. Chem. Ref. Data 4 (1975) 471. and B. Sanjeevaiah, Nucl. [91 T.K. Umesh, C. Ranganathaiah Sci. & Eng. 85 (1983) 426.
Nuclear Instruments and Methods in Physics Research B5 (1984) 472-475 North-Holland, Amsterdam
A SIMPLE METHOD OF DETERMINING ELEMENTS FOR GAMMA RAYS T.K. UMESH
THE PHOTOEFFECT
CROSS SECTIONS
OF
and C. ~NGANATHAIA~
Department of Post -Graduate Studies and Research in Physics, University of Mysore, Manma Gangotri, Mysore 570 006, India
Received 16 May 1984
A simple relation between the total photoeffect cross section of an element and the total attenuation cross section of its compound has been derived. Total attenuation cross sections of some: 15 simple compounds have been measured by performing transmission experiments in a good geometry set up. Using these values and with the aid of the present relation, total photoeffect cross sections of elements of 2 2 47 at 514.0, 661.6, 1115.5, 1173.2 and 1332.5 keV gamma ray energies have been determined and compared with Scofield’s theoretical cross sections.
1. Introduction The atomic photoeffect is one of the major ways by which the gamma rays interact with matter at low photon energies and in high Z elements, Owing to its importance in radiation physics, nuclear physics and transport calculations, the photoeffect process has been the subject of considerable interest over the years. Among the various theoretical calculations of photoeffeet cross sections, the numerical data of Scofield [l] on the total and subshell photoeffect cross sections are considered to be the most accurate theoretical data. These data cover elements of Z = 1 to 101 in the energy region 1 to 1500 keV. A survey of literature on the experimental investigations of the photoeffect reveals that quite a good amount of experimental results exist. In obtaining these results generally two types of experiments [2] have been performed. These are (i) the direct method and (ii) the indirect method or the subtraction technique. The direct method involves the detection of the ejected photoelectrons using an efficient electron detector. Though this is a precise method, it cannot yield accurate results as far as the total photoeffect cross sections are concerned particularly at photon energies above a few hundred keV. The subtraction technique yields accurate results in the energy region where the photoeffect is predominant, say, less than a few hundred keV. A critical study of the results obtained by the above two methods indicates that the major part of these data is confined to elements which are available in their elemental form (i.e., foils), such as C, Al, Cu, Zr, Ag, Sn, Ta, Au, Pb, Th and U. It is also indicative of the fact that for elements of Z = 51 to 73 which includes the lanthanum group, data are practically non-existent [3]. In recent years, there have been efforts to derive the
0168-583X/84/$03.00 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
cross sections of elements particularly in the case of lanthanum group elements from the experimentally measured total attenuation cross sections of their compounds with the aid of a mixture rule 14-61. This procedure is rather tedious as it involves the following steps: (1) measurement of the compound cross section; (2) derivation of the elemental cross section using the mixture rule; (3) interpolation of the “to be subtracted” theoretical scattering cross sections to the desired energy; (4) derivation of photoeffect cross section of the element by subtraction technique. Therefore, it was felt worthwhile to suitably simplify this technique so as to enable speedier determination of the total photoeffect cross section of an element from the experimentally measured total attenuation cross section of its compound. With this end in view, we have obtained a simple relation between the photoeffect cross section of an element and the total attenuation cross section of its compound. This relation yields results which are found to be in good agreement with Scofield’s cross sections for elements Z 2 47 in the energy region 500 to 1500 keV.
2. Experimental procedure Although Sauter’s [7] relation predicts a uniform Z-dependence of photoeffect cross sections, it can be noticed that the Z-dependence varies strongly as the energy increases, A preliminary check revealed the fact that for energies above 500 keV, cross sections show a uniform Z-dependence. Based on this we selected five energies 514.0, 661.6, 1115.5, 1173.2 and 1332.5 keV for
T. K. Umesh, C. Ranganaihaiah / Determination of photoeffect cross sections
473
Table 1 Total attenuation cross sections in compounds (barns per molecule) Compound
AaCl Ki BaO LazOj CeO, Pro, Nd,Gs Sm 203 Gd
203
Dy2°3 Ho203 Er203 Ta 2%
(HCOO),Pb Bi,O,
Molecular weight M
Element
143.32 166.01 153.34 325.82 172.12 172.91 336.48 348.70 362.50 373.00 317.86 382.56 441.89 297.25 465.96
AR
I-
Ba La Ce Pr Nd Sm Gd DY Ho Er Ta Pb Bi
Atomic number z
Atomic weight
47 53 56 57 58 59 60 62 64 66 61 68 73 82 83
107.87 126.90 137.34 138.91 140.12 140.907 144.24 150.35 157.25 162.50 164.93 167.26 180.948 207.19 208.98
M,
the present investigation. The elements were chosen such that the atomic number was greater than 47. In total, fifteen simple compounds of these elements were used. A list of all the compounds used is given in table 1. For the monoenergetic gamma sources 85Sr (514 keV), 13’Cs (661.6 keV), and 65Zn (1115.5 keV), a (1” x 11/4”) NaI(Tl) scintillation detector was used. In the case of 6oCo (1173.2 and 1332.5 keV) a hyperpure germanium detector (23210 ORTEC model) was used in order to separate the two peaks. The total attenuation cross sections of the compounds at these energies were measured by performing transmission experiments in a good geometry set up. Details of the experimental procedure, error calculation and the various corrections applied can be found in our earlier papers [4-61. The overall error on the measured total attenuation cross sections of compounds is less than 2% in all the cases. These are tabulated in table 1.
3. Results and discussion From the cross sections of the compounds so obtained (table l), the cross sections for the individual elements were derived with the aid of the mixture rule [4-61. From these cross sections, the photoeffect cross sections were derived by subtracting the theoretical scattering cross sections [8]. This was done for all elements and at all energies of interest. Now, a parameter X was calculated according to
x=
uPhoto OccnnpMi/M
’
0)
Energy in keV 514.0
661.6
1115.5
1332.5
20.70&0.46 24.31 f0.46 23.27 kO.51 52.07 kO.33 28.08 + 0.20 29.02kO.19 57.41*0.35 60.61*0.39 64.49 f 0.42 68.73 f 0.43 70.73 f 0.48 72.51 f 0.41 89.53 f 0.56 65.78kO.40 116.49kO.73
17.80 f 0.41 21.00f0.38 19.86 f 0.42 42.36 f 0.32 22.98 +0.18 23.42 50.19 45.82 f 0.32 48.28 f 0.36 50.48 +0.39 53.12+0.42 54.56 f 0.41 55.70 f 0.42 68.28 f 0.54 49.27 f0.31 83.54 f 0.61
13.24+0.46 15.43 !i 0.25 14.52 f 0.29 30.68 kO.26 16.44f0.15 16.66*0.14 32.40 rtO.26 33.70 f 0.28 34.92 50.30 36.28 + 0.32 37.06iO.32 31.88 f 0.33 45.00+0.36 31.92*0.27 51.34+0.46
12.20 +0.24 13.84 f 0.22 12.69 f 0.26 27.50 f 0.23 14.82+0.14 15.01*0.13 29.12 f 0.23 30.24 f 0.25 31.28kO.27 32.46 +0.29 33.12 f 0.29 35.14*0.31 39.96 + 0.25 28.65 f 0.24 44.74 f 0.40
is the total photoeffect cross section of the uPhoto element, ucomP the total attenuation cross section of its compound, Mi the atomic weight of the element and M the molecular weight of its compound. The form of this expression is based on a preliminary check that the product of ucCompand the ratio (MJM) nearly gave total photoeffect cross sections in lanthanum group elements at a lower photon energy. As such the parameter X was calculated for the elements Z = 47, 53, 56, 57, 58, 59, 60, 62, 64, 66, 67, 68, 73, 82 and 83, at the energies of interest. These values are listed in table 2. It is clear from the values of X that it varies with energy of where
Table 2 Values of the parameter X from eq. (1) Atomic number Z
Energy in keV 514.0
661.6
1115.5
1332.5
47 53 56 57 58 59 60 62 64 66 67 68 73 82 83
0.1463 0.2040 0.2404 0.2478 0.2699 0.2795 0.2877 0.3077 0.3335 0.3580 0.3893 0.3792 0.4528 0.5939 0.5520
0.1067 0.1330 0.1546 0.1672 0.1812 0.1860 0.1980 0.2099 0.2288 0.2485 0.2716 0.2714 0.3301 0.4458 0.4329
0.0502 0.0676 0.0769
0.0348 0.0528 0.0633 0.0665 0.0696 0.0744 0.0758 0.0874 0.0965 0.1068 0.1190 0.1120 0.1448 0.2008 0.2108
0.0807 0.0847 0.0907 0.0998 0.1122 0.1208 0.1366 0.1334 0.1639 0.2279 0.2358
T.K. Umesh, C. Ranganathaiah
414
/ Determination
Table 3 Values of M and C from eq, (2)
of photoeffect cross sections
values are listed in table 3. Again straight form
Energy in keV
Slope m
Intercept C
514.0 661.6 1115.5 1332.5
2.3164 2.6162 2.8314 3.1342
-
ln m = ml ln E-l- C,
(3)
and
10.9967 12.3501 13.9612 15.3836
C=m,InE+C,
(4)
fitted by the method of least squares, using the values of m, C and energy in table 3. The values of m,, C,, m z and C, so obtained were subjected to a chi-square test [9]. The values of these parameters for which chisquare was minimum were found to be 0.2576, - 0.7328, -4.2442 and 15.4193, respectively. Substituting these values in eq. (2) through (3) and (4), a relation of the form were
the photon and atomic number Z of the element. It is assumed that the relation for X could be of the form lnX=mlnZ+C.
lines of the
(2)
Here m and C vary with energy. Using the values of X and Z in table 2, the values of the slope m and the intercept Cwere obtained at energies 514.0,661.6,1115.5 and 1332.5 keV, by the method of least squares. These
(5) was obtained.
Therefore,
now the expression
(1) can be
Table 4 Total photoeffect cross sections of elements in barns/atom Atomic number Z 41 53 56 57 58 59 60 62 64 66 67 68 73 82 83
Energy in keV 514.0 2.49 a’ 2.28 3.97 3.80 5.06 5.01 5.63 5.50 6.04 6.17 6.51 6.61 7.06 7.08 8.11 8.04 9.36 9.33 10.79 10.72 11.53 11.35 12.27 12.02 16.83 16.60 27.81 21.23 32.63 30.84
661.6 1.36 1.43 2.23 2.14 2.83 2.75 3.01 3.02 3.26 3.39 3.47 3.55 3.73 3.89 4.30 4.37 4.91 5.01 5.61 5.75 6.00 6.31 6.38 6.61 8.78 9.23 14.52 15.31 16.34 16.22
1115.5
1173.2
1332.5
0.457 0.500 0.771 0.800 0.996 1.000 1.06 0.98 1.14 1.08 1.21 1.15 1.30 1.26 1.50 1.45 1.71 1.70 1.96 1.91 2.09 2.00 2.24 2.21 3.07 3.02 5.21 5.07 5.58 5.43
0.419 0.410 0.695 0.708 0.884 0.906 0.958 0.970 1.04 1.07 1.11 1.13 1.19 1.24 1.37 1.44 1.58 1.66 1.80 1.90 1.92 1.98 2.10 2.16 2.82 3.00 4.89 5.00 5.12 5.27
0.336 0.320 0.561 0.560 0.711 0.719 0.774 0.780 0.841 0.840 0.898 0.910 0.965 0.980 1.12 1.14 1.28 1.31 1.46 1.51 1.57 1.61 1 .I4 1.12 2.31 2.37 4.02 4.01 4.20 4.23
a) In each case the first line gives the value obtained using the present formula and the second line Scofield’s theoretical results.
T.K. Umesh, C. Ranganathaiah / Determination of photoeffect cross sections
written
using eq. (5) as
From this expression it is clear that only ucCompis to be measured to determine the ePho,,, of the element. The Photoeffect cross sections obtained using the relation (6) are compared with Scofield’s results in table 4, for all the energies of interest. As it can be seen from the table there is a good agreement between the formula values and Scofield’s values for elements Z 2 47
4. Conclusions It can be concluded that the present formula depicts a novel method to determine the photoeffect cross sections of elements from the experimentally measured total attenuation cross section of its compound. This formula yields fairly accurate results since the compound cross section can be determined to less than 2% accuracy in a good geometry transmission experiment. Also this method substantially reduces the theoretical dependence and the calculation time as compared to the conventional subtraction technique. As such, it serves as a simple technique by which a speedier filling of the
475
existing gaps in the experimental total photoeffect cross section data can be done just by measuring the compound cross section in the energy region 500 to 1500 keV and Z > 47. For low Z elements the present formula gives results which deviate much from Scofield’s results.
References 111 J.H. Scofield UCRL Report No. 15326 (1973). [21 R.H. Pratt, A. Ron and H.K. Tseng, Rev. Mod. Phys. 45 (1973) 273. 131 J.H. Hubbell and Wm.J. Veigele, NBS Report No. TN-901 (1976). Ramakrishna Gowda, KS. 141 T.K. Umesh, C. Ranganathaiah, Puttaswamy and B. Sanjeevaiah, Phys. Rev. A23 (1981) 2365. Gowda and B. Sanjeevaiah, 151T.K. Umesh, Ramakrishna Phys. Rev. A 25 (1982) 1986. and B. Sanjeevaiah, Phys. (61 T.K. Umesh, C. Ranganathaiah Rev. A 29 (1984) 387. 171 F. Sauter, Ann. Physik 9, (1931) 217. PI J.H. Hubbell, Wm.J. Veigele, E.A. Briggs, R.T. Brown, D.T. Cromer and R.J. Howerton, J. Phys. Chem. Ref. Data 4 (1975) 471. and B. Sanjeevaiah, Nucl. [91 T.K. Umesh, C. Ranganathaiah Sci. & Eng. 85 (1983) 426.