Radiat Environ Biophys (2012) 51:469–475 DOI 10.1007/s00411-012-0427-8
ORIGINAL PAPER
Studies on mass attenuation coefficient, effective atomic number and electron density of some vitamins ¨ znu¨lu¨er D. Demir • A. Turs¸ ucu • T. O
Received: 9 March 2012 / Accepted: 9 June 2012 / Published online: 26 June 2012 Ó Springer-Verlag 2012
Abstract Mass attenuation coefficient, lm , atomic crosssection, ri , electronic cross-section, re , effective atomic number, Zeff and effective electron density, Nel , were determined experimentally and theoretically for some vitamins (retinol, beta-carotene, thiamine, riboflavin, niacinamide, pantothenic acid, pyridoxine, biotin, folic acid, cyanocobalamin, ascorbic acid, cholecalciferol, alphatocopherol, ketamine, hesperidin) at 30.82, 59.54, 80.99, 356.61, 661.66 and 1,408.01 keV photon energies using a NaI(Tl) scintillation detector. The theoretical mass attenuation coefficients were estimated using mixture rules. The calculated values were compared with the experimental values for all vitamins. Keywords Mass attenuation coefficient Atomic crosssection Electronic cross-section Effective atomic number Effective electron density
Introduction Mass attenuation coefficients, atomic and the electronic cross-sections, effective atomic numbers and effective electron densities are of great significance in both applied and fundamental science. They are invaluable in many applied fields, such as nuclear diagnostics, radiation protection, nuclear medicine and radiation dosimetry. The D. Demir (&) A. Turs¸ ucu Department of Physics, Faculty of Science, Atatu¨rk University, 25240 Erzurum, Turkey e-mail:
[email protected] ¨ znu¨lu¨er T. O Department of Chemistry, Faculty of Science, Atatu¨rk University, 25240 Erzurum, Turkey
mass attenuation coefficient lm (l/q) is a measure of the average number of interactions between incident photons and matter that occur in a given mass per unit area thickness of the substance under investigation (Hubbell 1999). It tends to increase with increasing atomic number at the same photon energy, so materials with high atomic numbers (and, hence, high mass attenuation coefficients) are normally chosen to shield X- and gamma-radiation. For example, Demir and Keles¸ (2006) measured the radiation transmission of concrete including boron waste for gamma rays, and mass attenuation coefficients have been measured for mono- and di-saccharides at different photon energies by Chitralekha et al. (2005). For photon interaction in composite materials, the atomic number cannot be represented by a single number across the entire energy region, as in the case of pure elements. For composite materials, this quantity is called the effective atomic number (Zeff ) and it varies with energy (Hine 1952). Zeff is a convenient parameter for representing the attenuation of X- and gamma-rays in a complex medium, and particularly for the calculation of the dose in radiation therapy. Investigation of radiation effects on biologically important complex molecules finds important applications in the field of medical physics, radiation biology and radiopharmaceutical research. Complex molecules such as carbohydrates, proteins, lipids, enzymes, vitamins and hormones are involved in a variety of physiological functions of living systems and assist in producing and storing the energy. They have as their basic building blocks sugars, amino acids, fatty acids, etc., which are essentially H-, C-, N- and O-based compounds. The human body needs these vitamins for growth, function, energy, tissues repair and waste removal. Manjunathaguru and Umesh (2009) investigated photon energy absorption coefficients of H-, C-, N-
123
470
Radiat Environ Biophys (2012) 51:469–475
and O-based compounds of biological interest in the energy range from 200 to 1,500 keV. Bhandal et al. (1994) studied energy absorption coefficients for 662 and 1,115 keV gamma rays in some fatty acids. Studies on effective atomic number, electron density and kerma for some fatty acids and carbohydrates were also made by Manohara et al. (2008a). In the present work, the mass attenuation coefficients for some vitamins (retinol, beta-carotene, thiamine, riboflavin, niacinamide, pantothenic acid, pyridoxine, biotin, folic acid, cyanocobalamin, ascorbic acid, cholecalciferol, alphatocopherol, ketamine, hesperidin) at 30.82, 59.54, 80.99, 356.61, 661.66 and 1,408.01 keV photon energies were measured by means of a NaI(Tl) scintillation detector and also determined theoretically. Additionally, atomic and electronic cross-sections, effective atomic numbers and electron densities have been calculated for these vitamins using the measured lm values. Finally, the investigated parameters have been compared using the results of WinXCom calculations.
Materials and methods Theoretical concepts Mass attenuation coefficients for any materials and energies can be determined by radiation transmission. A narrow beam of mono-energetic photons with an incident intensity I0, penetrating a layer of material with mass thickness t (mass per unit area) and density q shows an intensity I given by the exponential attenuation law I ¼ I0 exp½lm t
ð1Þ
where I/I0 is the transmission fraction T and lm ¼ l=q is the mass attenuation coefficient. The cross-section per molecule rs can be written in terms of an effective (average) cross-sections per atom, ra , and an effective (average) cross-section per electron, re , as rs ¼ nra ¼ nZeff re
The effective electron density Nel expressed as the number of electrons per unit mass is closely related to the effective atomic number. The electron density can be generalized for a compound nZeff Zeff Nel ¼ NA P ¼ NA h Ai i n i Ai
ð4Þ
where h Ai is the average atomic mass of the compound (Manohara et al. 2008b). The theoretical lm values for present samples were obtained by the WinXCom code (Gerward et al. 2001). This program depends on the use of the mixture rule to calculate the partial and total mass attenuation coefficients for all elements, compounds and mixtures at standard as well as selected energies. Experimental setup and measurements The experimental arrangement used in the present study is sketched in Fig. 1. The source-sample and sample-detector distance was each set to 25 mm. Kerur et al. (1991) used the transmission range 0.02 \ T \ 0.5 for NaI(Tl) detectors. Samples with a thickness ranging from 0.065 to 0.392 g/cm2 were prepared in the form of cylindrical pellets with a diameter of 13 mm by means of a manually operated hydraulic press at a pressure of 10 tons. In order to irradiate the vitamins at energies 30.82, 59.54, 80.99, 356.61, 661.66 and 1,408.01 keV, polyester-coated 241Am, 133 Ba, 137Cs and 152Eu radiation sources (intensity: 10 lCi) were used, provided by Isotope Products Laboraties, Valancia CA. Photon intensities were measured using a NaI(Tl) scintillation detector (Canberra Model 802). The detector was housed in a 16-mm-thick lead shield with a collimator (diameter, 5 mm). The signals obtained with the NaI(Tl) detector were coupled to a digital spectrum analyzer (DSA-1000), which represented 16K multichannel analyzer on advanced digital signal processing (DSP) techniques, and recorded by the Genie-2000 gamma
ð2Þ NaI (Tl) detector
P
where Zeff is the effective atomic number and n ¼ i ni is the total number of atoms present in a molecule. Essentially, it is assumed that the actual atoms of the molecule can be replaced by the same number of identical (average) atoms, each having Zeff electrons. Zeff is given by P ni Ai ðl=qÞi i P Zeff ¼ ð3Þ ni Ai =Zi ðl=qÞi
Pb collimators Amplifier
Sample
i
where Zi and Ai are the atomic number and the atomic weight of the ith element present in a molecule, respectively.
123
Radiactive source HV
Fig. 1 Experimental arrangement
MCA
Radiat Environ Biophys (2012) 51:469–475
471
spectroscopy software. The Genie-2000 software included peak searching, peak evaluation, energy/efficiency calculation and nuclide identification. The NaI(Tl) detector was calibrated using energies of the 241Am, 133Ba, 137Cs and 152 Eu radiation sources. The pulse height spectra of the photons that passed the vitamin samples were acquired for a period of 180–300 s. The data were collected into 1,024 channels of the DSA1000. The counting electronics included a pile-up rejection circuit and a live-time clock that was used for dead time correction. Since there were no escape peaks, satellites or unwanted effects contributing to the spectrum, the mean of ten channels at each side of the coherent peaks was used to calculate the background and to define the peak region. It was assumed that a linear background function could be used to quantify the background contribution below the Xand gamma-ray peaks. The resulting background count rate was subtracted from the measured peak area. X- and gamma-ray peaks were fitted into one Gaussian. A typical spectrum of 80.99 keV gamma ray transmissions through vitamin B3 is shown in Fig. 2. The maximum errors in the measurement of the mass attenuation coefficients were calculated from errors in intensities I0 (without sample), I (with sample) and densities using the following relation Dðlm Þ ¼ Dðl=qÞ ¼ ( " #)1=2 1 DI 0 2 DI 2 I0 2 Dq 2 Ds 2 þ þ ln þ qs I q s I0 I ð5Þ where DI 0 , DI, Ds and Dq are the errors in the intensities I0 and I, thickness s and density q, respectively. In this experiment, the intensities I0 and I were obtained for the same time and under the same experimental conditions.
6000
Counts/Channel
5000
Results and discussion The mean atomic numbers and the chemical formulas of the vitamins studied in the present work are given in Table 1, while the experimental and theoretical results for the mass attenuation coefficients of are shown in Table 2. It is clearly seen that the mass attenuation coefficient depends on the photon energy and chemical content, and that the lm values of the vitamins decrease with increasing photon energy. The atomic cross-sections, the electronic cross-sections and the effective atomic numbers of the investigated vitamins are listed in Tables 3, 4 and 5, respectively. As can be seen from Table 4, the electronic cross-sections of the vitamins decrease with increasing photon energy. The similarity of the effective atomic numbers of those samples containing the elements H, C, N and O in the energy region 30.82–1,408.01 keV (Table 5) implies that the number of electrons per atom participating in the process of photon interaction with the sample is roughly constant. This indicates that compounds containing H, C, N and O behave as incoherent scatterers. The Nel values of the vitamins are listed in Table 6. It is clearly seen that Nel depends on the photon energy and chemical content. Also, the ratio Zeff =h Ai was 0.533 for the investigated vitamins in the energy region 30.82–1,408.01 keV. In order to study the global reproducibility of the measurements, five vitamin B3 samples were prepared and measured under the same experimental conditions. Calculated relative standard deviations (RSD) are given in Table 1 Mean atomic numbers of the investigated vitamins Vitamins
Chemical name
Chemical formula
Mean atomic number, Z
Vitamin A
Retinol
C20H30O
3.10
Provitamin A
Beta-carotene
C40H56
3.08
Vitamin B1
Thiamine
C12H17N5O4S
4.41
Vitamin B2 Vitamin B3
Riboflavin Niacinamide
C17H20N4O6 C6H5NO2
4.21 4.57 3.69
Vitamin B5
Pantothenic acid
C9H17NO5
4000
Vitamin B6
Pyridoxine
C8H12N2O2
3.75
3000
Vitamin B7
Biotin
C10H16N2O3S
4.06
Vitamin B9
Folic acid
C19H19N7O6
4.51
Vitamin B12
Cyanocobalamin
C63H88CoN14O14P
3.97
Vitamin C
Ascorbic acid
C3H4O3
4.60
Vitamin D3
Cholecalciferol
C27H44O
2.97
Vitamin E
Alphatocopherol
C29H50O2
2.96
2000 1000 0 250
260
270
280
290
300
310
320
Channel Fig. 2 Spectrum of 80.99 gamma rays obtained with absorber (vitamin B3)
Vitamin K
Ketamine
C13H16ClNO
3.94
Vitamin P
Hesperidin
C28H34O15
4.18
123
123
0.560 ± 0.028
0.290 ± 0.015
Vitamin K
Vitamin P
0.455
0.300
0.566
0.271
0.267
0.316
0.662
0.289
0.509
0.287
0.302
0.289
0.291
0.206 ± 0.010
0.195 ± 0.010
0.232 ± 0.012
0.195 ± 0.010
0.192 ± 0.010
0.211 ± 0.011
0.265 ± 0.013
0.197 ± 0.010
0.225 ± 0.011
0.173 ± 0.009
0.172 ± 0.009
0.192 ± 0.010
0.187 ± 0.009
0.219 ± 0.011
0.181 ± 0.009
0.190
0.228
0.195
0.194
0.191
0.244
0.187
0.220
0.191
0.194
0.187
0.189
0.211
0.192
0.193
Theo.
111.805 ± 5.590
74.600 ± 3.730
215.902 ± 10.795
Vitamin B5
Vitamin B6
Vitamin B7
47.102 ± 2.355
166.124 ± 8.306
201.761 ± 10.088
317.386 ± 15.869
294.124 ± 14.706
Vitamin C
Vitamin D3
Vitamin E
Vitamin K
Vitamin P
203.103 ± 10.155
54.193 ± 2.710
Vitamin B3
1,502.844 ± 75.142
170.679 ± 8.534
Vitamin B2
Vitamin B12
242.529 ± 12.126
Vitamin B1
Vitamin B9
124.672 ± 6.234
228.308 ± 11.415
Provitamin A
304.266
320.787
193.891
170.596
46.224
1,491.58
211.901
206.568
80.188
109.984
59.101
181.933
247.423
232.767
127.051
197.773 ± 9.889
131.489 ± 6.574
139.516 ± 6.976
122.676 ± 6.134
30.865 ± 1.543
597.082 ± 29.854
144.445 ± 7.222
91.312 ± 4.566
48.337 ± 2.417
62.640 ± 3.132
39.264 ± 1.963
116.912 ± 5.846
119.089 ± 5.954
161.421 ± 8.071
98.025 ± 4.901
Exp.
Exp.
Theo.
59.54 keV
30.82 keV
Vitamin A
Vitamins
192.702
129.222
139.516
123.954
27.939
549.766
137.113
89.283
53.366
70.652
38.242
118.163
114.739
171.231
91.839
Theo.
0.154 ± 0.008
0.192 ± 0.010
0.178 ± 0.009
0.166 ± 0.008
0.165 ± 0.008
0.203 ± 0.010
0.166 ± 0.008
0.182 ± 0.009
0.191 ± 0.010
0.175 ± 0.009
0.189 ± 0.009
0.170 ± 0.009
0.189 ± 0.009
0.180 ± 0.009
0.181 ± 0.009
Exp.
80.99 keV
156.190 ± 7.809
108.818 ± 5.441
127.353 ± 6.368
106.064 ± 5.303
24.136 ± 1.207
457.387 ± 22.869
121.715 ± 6.086
73.861 ± 3.693
53.366 ± 2.668
63.733 ± 3.187
38.651 ± 1.933
106.284 ± 5.314
102.776 ± 5.139
160.529 ± 8.026
86.128 ± 4.306
Exp.
80.99 keV
Table 3 Atomic cross-sections (barn/molecule) of the investigated vitamins
0.260 ± 0.013
0.282 ± 0.014
Vitamin D3
Vitamin E
0.667 ± 0.033
0.322 ± 0.016
Vitamin B12
0.277 ± 0.014
Vitamin B9
Vitamin C
0.267 ± 0.013
0.532 ± 0.027
Vitamin B6
Vitamin B7
0.265 ± 0.013
0.307 ± 0.015
Vitamin B3
Vitamin B5
0.446 ± 0.022
0.273 ± 0.014
Vitamin B1
Vitamin B2
0.261
0.267
0.262 ± 0.013
0.256 ± 0.013
Exp.
Theo.
Exp.
Vitamin A
59.54 keV
30.82 keV
Provitamin A
Vitamins
Table 2 Mass attenuation coefficients (cm2/g) of the investigated vitamins
173.431
105.984
127.352
113.730
25.0137
434.855
123.914
74.672
48.336
63.732
34.560
106.283
97.3379
142.692
83.7491
Theo.
0.171
0.187
0.178
0.178
0.171
0.193
0.169
0.184
0.173
0.175
0.169
0.170
0.179
0.160
0.176
Theo.
103.450 ± 5.173
56.676 ± 2.834
86.571 ± 4.329
77.311 ± 3.866
14.628 ± 0.731
225.314 ± 11.266
106.493
60.077
79.417
70.922
15.213
238.83
76.255
43.423
49.105 ± 2.455 83.587 ± 4.179
29.896
39.332
21.268
65.645
57.097
98.101
52.343
Theo.
0.105
0.106
0.111
0.111
0.104
0.106
0.104
0.107
0.107
0.108
0.104
0.105
0.105
0.110
0.110
Theo.
32.690 ± 1.635
44.067 ± 2.203
25.358 ± 1.268
75.649 ± 3.782
62.536 ± 3.127
107.019 ± 5.351
57.102 ± 2.855
Exp.
356.61 keV
0.102 ± 0.006
0.100 ± 0.006
0.121 ± 0.006
0.121 ± 0.006
0.100 ± 0.006
0.100 ± 0.006
0.114 ± 0.006
0.121 ± 0.006
0.117 ± 0.006
0.121 ± 0.006
0.124 ± 0.006
0.121 ± 0.006
0.115 ± 0.006
0.120 ± 0.006
0.120 ± 0.006
Exp.
356.61 keV
87.527 ± 4.376
46.418 ± 2.321
63.748 ± 3.187
56.801 ± 2.840
11.805 ± 0.590
190.390 ± 9.520
59.024 ± 2.951
34.212 ± 1.711
23.302 ± 1.165
30.300 ± 1.515
16.790 ± 0.839
51.204 ± 2.560
44.156 ± 2.208
75.270 ± 3.764
39.590 ± 1.980
Exp.
661.66 keV
0.086 ± 0.004
0.082 ± 0.004
0.089 ± 0.004
0.089 ± 0.004
0.081 ± 0.004
0.085 ± 0.004
0.081 ± 0.004
0.084 ± 0.004
0.083 ± 0.004
0.083 ± 0.004
0.082 ± 0.004
0.082 ± 0.004
0.081 ± 0.004
0.084 ± 0.004
0.083 ± 0.004
Exp.
661.66 keV
82.659
46.418
61.602
54.884
11.804
184.75
59.024
33.399
23.106
30.300
16.421
50.828
44.155
75.983
40.542
Theo.
0.082
0.082
0.086
0.086
0.081
0.082
0.081
0.082
0.083
0.083
0.080
0.081
0.081
0.085
0.085
Theo.
52.131 ± 2.607
30.265 ± 1.513
36.703 ± 1.835
38.081 ± 1.904
7.811 ± 0.391
132.485 ± 6.624
39.154 ± 1.958
22.929 ± 1.146
15.172 ± 0.759
21.014 ± 1.051
10.920 ± 0.546
34.073 ± 1.704
30.615 ± 1.531
52.707 ± 2.635
24.792 ± 1.240
Exp.
1,408.01 keV
0.051 ± 0.003
0.053 ± 0.003
0.051 ± 0.003
0.060 ± 0.003
0.053 ± 0.003
0.059 ± 0.003
0.053 ± 0.003
0.057 ± 0.003
0.054 ± 0.003
0.058 ± 0.003
0.053 ± 0.003
0.055 ± 0.003
0.056 ± 0.003
0.059 ± 0.003
0.052 ± 0.003
Exp.
1,408.01 keV
57.303
32.192
42.713
38.080
8.192
127.978
40.913
23.132
16.009
21.013
11.390
35.261
30.615
52.706
28.122
Theo.
0.056
0.057
0.059
0.060
0.056
0.057
0.056
0.057
0.057
0.058
0.056
0.056
0.056
0.059
0.059
Theo.
472 Radiat Environ Biophys (2012) 51:469–475
45.488 ± 2.274
338.028 ± 16.901
10.568 ± 0.528
67.475 ± 3.374
76.256 ± 3.813
88.986 ± 4.449
67.682 ± 3.384
Vitamin B9
Vitamin B12
Vitamin C
Vitamin D3
Vitamin E
Vitamin K
Vitamin P
53.800
70.662
80.384
71.762
62.864
9.494
372.595
44.463
50.182
21.514
30.304
12.171
41.814
36.833 ± 1.842
46.464 ± 2.323
37.957 ± 1.898
56.794 ± 2.840
46.342 ± 2.317
6.762 ± 0.338
168.973 ± 8.449
33.233 ± 1.662
20.646 ± 1.032
12.907 ± 0.645
17.086 ± 0.854
8.209 ± 0.410
24.984 ± 1.249
25.008 ± 1.250
58.212 ± 2.911
44.916
32.434
51.188
45.285
5.778
137.567
28.953
21.743
14.315
19.449
7.929
27.264
25.084
59.387
31.678
Theo.
3.56 ± 0.17
4.34 ± 0.21
Vitamin K
Vitamin P
2.46 ± 0.12
2.64 ± 0.13
Vitamin D3
Vitamin E
4.44 ± 0.22
4.45 ± 0.22
4.46 ± 0.22
Vitamin B9
Vitamin B12
4.11 ± 0.20
Vitamin B7
Vitamin C
3.66 ± 0.18
3.46 ± 0.17
Vitamin B5
Vitamin B6
4.64 ± 0.23
4.56 ± 0.22
Vitamin B2
Vitamin B3
2.75 ± 0.13
4.67 ± 0.23
Provitamin A
Vitamin B1
2.65 ± 0.13
4.30
3.99
2.70
2.71
4.86
4.00
4.76
4.11
3.72
3.62
4.85
4.35
4.59
2.86
2.87
4.25 ± 0.21
3.46 ± 0.17
2.45 ± 0.12
2.64 ± 0.13
4.56 ± 0.22
3.53 ± 0.17
4.34 ± 0.21
4.42 ± 0.22
3.74 ± 0.18
3.66 ± 0.18
4.78 ± 0.23
4.67 ± 0.23
4.76 ± 0.23
2.77 ± 0.13
2.66 ± 0.13
Exp.
Exp.
Theo.
59.54 keV
30.82 keV
Vitamin A
Vitamins
4.29
3.98
2.72
2.73
4.83
3.99
4.73
4.10
3.72
3.63
4.82
4.33
4.57
2.88
2.89
Theo.
Table 5 Effective atomic numbers (Zeff ) of the investigated vitamins
21.513 ± 1.076
52.450 ± 2.622
Vitamin B6
Vitamin B7
11.872 ± 0.594
30.507 ± 1.525
Vitamin B3
Vitamin B5
51.867 ± 2.593
36.729 ± 1.836
Vitamin B1
Vitamin B2
81.312
44.134
46.982 ± 2.349
82.820 ± 4.141
Exp.
Theo.
Exp.
Vitamin A
59.54 keV
30.82 keV
Provitamin A
Vitamins
4.38 ± 0.21
3.88 ± 0.19
2.74 ± 0.13
2.75 ± 0.13
4.83 ± 0.24
3.93 ± 0.19
4.73 ± 0.23
4.11 ± 0.20
3.44 ± 0.17
3.45 ± 0.17
4.87 ± 0.24
4.78 ± 0.23
4.77 ± 0.23
2.77 ± 0.13
2.97 ± 0.14
Exp.
80.99 keV
35.636 ± 1.781
28.038 ± 1.401
46.366 ± 2.318
38.495 ± 1.924
4.993 ± 0.249
116.290 ± 5.814
25.715 ± 1.285
17.964 ± 0.898
15.499 ± 0.774
18.455 ± 0.922
7.924 ± 0.396
22.235 ± 1.111
21.516 ± 1.075
57.890 ± 2.894
28.924 ± 1.446
Exp.
80.99 keV
Table 4 Electronic cross-sections (barn/molecule) of the investigated vitamins
4.28
3.98
2.73
2.74
4.82
3.99
4.72
4.10
3.72
3.63
4.80
4.32
4.56
2.89
2.90
Theo.
40.493
26.622
46.535
41.383
5.190
108.900
26.244
18.206
12.965
17.537
7.189
24.569
21.333
49.323
28.793
Theo.
4.34 ± 0.21
3.66 ± 0.18
2.59 ± 0.13
2.60 ± 0.13
4.72 ± 0.23
3.87 ± 0.19
4.85 ± 0.24
4.77 ± 0.23
3.63 ± 0.18
3.54 ± 0.17
4.79 ± 0.24
4.29 ± 0.21
4.45 ± 0.22
2.57 ± 0.12
2.55 ± 0.12
Exp.
356.61 keV
23.793 ± 1.189
15.457 ± 0.772
33.411 ± 1.670
29.711 ± 1.485
3.098 ± 0.154
58.102 ± 2.905
17.218 ± 0.860
10.275 ± 0.513
9.006 ± 0.450
12.443 ± 0.622
5.289 ± 0.264
17.601 ± 0.880
14.029 ± 0.701
41.636 ± 2.081
22.347 ± 1.117
Exp.
356.61 keV
4.24
3.96
2.79
2.80
4.74
3.97
4.65
4.07
3.73
3.64
4.73
4.28
4.50
2.94
2.95
Theo.
25.069
15.145
28.454
25.310
3.206
60.040
16.382
10.645
8.015
10.801
4.493
15.309
12.667
33.364
17.712
Theo.
4.57 ± 0.22
3.67 ± 0.18
2.66 ± 0.13
2.66 ± 0.13
4.88 ± 0.24
3.24 ± 0.16
4.11 ± 0.20
4.13 ± 0.20
3.23 ± 0.16
3.34 ± 0.16
4.44 ± 0.22
4.44 ± 0.22
4.44 ± 0.22
2.13 ± 0.10
2.34 ± 0.11
Exp.
661.66 keV
19.126 ± 0.956
12.646 ± 0.632
23.929 ± 1.196
21.315 ± 1.066
2.417 ± 0.121
58.735 ± 2.937
14.336 ± 0.717
8.284 ± 0.414
7.213 ± 0.361
9.059 ± 0.453
3.778 ± 0.189
11.526 ± 0.576
9.934 ± 0.497
35.334 ± 1.767
16.884 ± 0.844
Exp.
661.66 keV
4.23
3.96
2.81
2.82
4.71
3.97
4.62
4.07
3.73
3.64
4.70
4.27
4.48
2.96
2.97
Theo.
19.525
11.720
21.891
19.429
2.504
46.521
12.756
8.207
6.194
8.314
3.491
11.897
9.845
25.668
13.628
Theo.
4.20 ± 0.21
3.55 ± 0.17
2.77 ± 0.13
2.43 ± 0.12
4.55 ± 0.22
3.33 ± 0.16
4.33 ± 0.21
3.95 ± 0.19
3.21 ± 0.16
3.44 ± 0.17
4.22 ± 0.21
4.33 ± 0.21
4.55 ± 0.22
2.95 ± 0.14
3.09 ± 0.15
Exp.
1,408.01 keV
12.395 ± 0.620
8.518 ± 0.426
13.239 ± 0.662
15.672 ± 0.784
1.714 ± 0.086
39.740 ± 1.987
9.035 ± 0.452
5.793 ± 0.290
4.724 ± 0.236
6.094 ± 0.305
2.587 ± 0.129
7.863 ± 0.393
6.718 ± 0.336
17.831 ± 0.892
8.000 ± 0.400
Exp.
1,408.01 keV
4.21
3.95
2.84
2.85
4.67
3.96
4.59
4.05
3.73
3.64
4.66
4.25
4.45
2.98
2.99
Theo.
13.592
8.143
15.027
13.348
1.751
32.287
8.907
5.700
4.290
5.760
2.441
8.291
6.869
17.658
9.377
Theo.
Radiat Environ Biophys (2012) 51:469–475 473
123
123
0.320
0.320
0.288 ± 0.014
0.319 ± 0.016
0.321
0.321
0.297 ± 0.015 0.321
0.322 0.330 ± 0.017
0.297 ± 0.015 0.322
0.325 0.333 ± 0.017
0.314 ± 0.016 0.322
0.325
0.289 ± 0.014
0.330 ± 0.016
Vitamin K
Vitamin P
0.323 ± 0.016
0.323
0.326
0.299 ± 0.015
0.281 ± 0.014
0.347 ± 0.017
0.321
0.321
0.274 ± 0.014
0.314 ± 0.016
0.318
0.318 0.301 ± 0.015
0.300 ± 0.015 0.315
0.315 0.293 ± 0.015
0.293 ± 0.015 0.309
0.30 0.311 ± 0.016
0.311 ± 0.016 0.308
0.308
0.278 ± 0.014 Vitamin D3
Vitamin E
0.298 ± 0.015 0.305
0.305
0.305 ± 0.015
0.278 ± 0.014
0.320
0.319
0.269 ± 0.013
0.311 ± 0.016
0.320
0.322 0.334 ± 0.017
0.262 ± 0.013 0.321
0.324 0.323 ± 0.016
0.313 ± 0.016 0.322
0.329 0.330 ± 0.017
0.318 ± 0.016 0.322
0.330
0.323
0.332
0.359 ± 0.018 Vitamin B12
Vitamin C
0.286 ± 0.014
0.302 ± 0.015 0.322 0.323 0.338 ± 0.017 0.328 0.329 ± 0.016 0.329 0.331 0.311 ± 0.016 Vitamin B9
0.302 ± 0.015
0.320
0.325
0.298 ± 0.015
0.325 ± 0.016
0.312 ± 0.016
0.320
0.312
0.312 ± 0.016
0.287 ± 0.014
0.320 0.276 ± 0.014
0.321 0.326 ± 0.016
0.320 0.320
0.321 0.377 ± 0.019
0.312 ± 0.016 0.320
0.323 0.324 ± 0.016
0.296 ± 0.015 0.320
0.323
30.82
Vitamin B6
0.322 ± 0.016
Table 7 Relative standard deviations (RSD) of vitamin B3
Vitamin B7
0.349 ± 0.017
0.278 ± 0.014
0.319
0.320
0.289 ± 0.014
0.303 ± 0.015
0.322
0.320
0.304 ± 0.015
0.294 ± 0.015 0.320
0.324 0.328 ± 0.016
0.311 ± 0.016 0.319
0.329 0.334 ± 0.017
0.303 ± 0.015 0.319
0.330 0.328 ± 0.016
0.322 ± 0.016
0.333
0.319
0.313 ± 0.016
0.322 ± 0.016
Vitamin B3
Vitamin B5
0.319
0.320
0.327 ± 0.016
0.326 ± 0.016
0.323
0.321
0.319 ± 0.016
0.334 ± 0.017 0.322
0.323 0.320 ± 0.016
0.323 ± 0.016 0.325
0.327 0.343 ± 0.017
0.360 ± 0.018 0.326
0.328 0.342 ± 0.017
0.352 ± 0.018
0.330
0.327
0.336 ± 0.017
0.350 ± 0.017
Vitamin B1
Vitamin B2
0.321
0.321
0.332 ± 0.017
0.318 ± 0.016
0.318
0.315
0.251 ± 0.013
0.229 ± 0.011 0.316
0.316 0.274 ± 0.014
0.277 ± 0.014 0.311
0.311 0.319 ± 0.016
0.299 ± 0.015 0.310
0.310 0.285 ± 0.014
0.299 ± 0.015
0.309
0.309
0.284 ± 0.014
0.297 ± 0.015
Vitamin A
Provitamin A
Theo. Exp. Exp. Exp. Exp. Theo. Exp.
Exp.
Theo.
80.99 keV 59.54 keV 30.82 keV Vitamins
Table 6 Effective electron densities (1024 electrons/g) of the investigated vitamins
Theo.
356.61 keV
Theo.
661.66 keV
Theo.
Radiat Environ Biophys (2012) 51:469–475
1,408.01 keV
474
Line (coherent peak) [keV]
(a) 5 samples/1 measurement RSD (%)
(b) 1 sample/5 measurements RSD (%)
0.89
0.24
59.54
0.91
0.26
80.99 356.61
0.99 0.93
0.28 0.32
661.66
0.85
0.31
1,408.01
0.92
0.34
Table 7 (a). Keeping in mind that the values obtained following this procedure also include the uncertainty due to sample preparation, and instrument and counting statistics, the RSD values are satisfactory. Additionally, one of the sample was measured five times and the RSD associated was also calculated [Table 7 (b)]. Note that the RSD values obtained using the five samples prepared under the same conditions are higher than those obtained for the same sample measured five times [Table 7 (a), (b)]. Because the same sample was measured for five times, the relative standard deviation was very small; therefore, it is concluded that the spectrometry sensitivity was very good. Manual errors might occur when the samples were weighed. However, from the data obtained, it could be deduced that the uncertainty introduced by sample preparation [comparing Table 7 (a), (b)] is acceptable. The overall error in the measured mass attenuation coefficients is estimated to be B5 %. This error represents the sum of the uncertainties in the different parameters used to calculate the experimental values, namely, the area under the X- and gamma-ray peaks, the mass thickness of the samples and the counting statistics of the measurements. The errors in the evaluation of the area under the gamma ray peaks include two main sources, that is, errors in the elimination of the background and those in the peak fitting procedures. The present theoretical calculations are based on photon–atom interaction cross-sections. Therefore, the experimental values obtained in the present work are in good agreement, within the experimental uncertainties, with the calculated theoretical predictions as is demonstrated in Tables 2, 3, 4, 5 and 6.
Conclusions The present study has been undertaken to get correct values of lm ; ri ; re ; Zeff and Nel in the photon energy range 30.82–1,408.01 keV. Values of lm ; ri ; re ; Zeff and Nel depend on photon energy and chemical content of the investigated vitamins. The relation between Zeff and h Ai for vitamins containing the elements H, C, N and O turned
Radiat Environ Biophys (2012) 51:469–475
out to be almost a constant, in the energy region 30.82–1,408.01 keV. More sensitive experiments would be required to study any possible effects of matrix environments and chemical bonding on the physical parameters of the investigated biomolecules.
References Bhandal GS, Singh K, Rani R, Kumar V (1994) Energy absorption coefficients for 662 and 1,115 keV gamma rays in some fatty acids. Appl Radiat Isot 45:379–381 Chitralekha B, Kerur R, Lagare MT, Nathuram R, Sharma DN (2005) Mass attenuation coefficients of saccharides for low-energy X-rays. Radiat Phys Chem 72:1–5 Demir D, Keles¸ G (2006) Radiation transmission of concrete including boron waste for 59.54 and 80.99 keV gamma rays. Nucl Instrum Methods B 245:501–504 Gerward L, Guilbert N, Jensen KB, Levring H (2001) X-ray absorption in matter reengineering XCOM. Radiat Phys Chem 60:23–24
475 Hine GJ (1952) The effective atomic numbers of materials for various gamma interactions. Phys Rev 85:725–728 Hubbell JH (1999) Review of photon interaction cross section data in the medical and biological context. Phys Med Biol 44:R1–R22 Kerur BR, Thontadarya SR, Hanumaiah B (1991) A novel method for the determination of X-ray mass attenuation coefficients. Appl Radiat Isot 42:571–576 Manjunathaguru V, Umesh TK (2009) Simple parametrization of photon mass energy absorption coefficients of H-, C-, N- and O-based samples of biological interest in the energy range 200–1500 keV. Pramana J Phys 72:375–387 Manohara SR, Hanagodimath SM, Gerward L (2008a) Energy dependence of effective atomic numbers for photon energy absorption and photon interaction: studies of some biological molecules in the energy range 1 keV–20 MeV. Med Phys 35:388–402 Manohara SR, Hanagodimath SM, Thind KS, Gerward L (2008b) On the effective atomic number and electron density: a comprehensive set of formulas for all types of materials and energies above 1 keV. Nucl Instrum Methods B 266:3906–3912
123
