The radiative vacancy transfer probabilities of K to L2, L3, M2, M3 sub-shells were calculated using the
experimental K level widths and theoretical partial radiative transitions. The targets were irradiated with
photons of 0.0208 nm wavelength. It has been observed that the obtained values in the present study agree
with theoretical results, theoretical predictions and the other available experimental values.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3544

Ates, A.

Durak, R.

Saglam, M.

Turhan, M.F.

Electronic Sumy State University Institutional Repository

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE NANOMATERIALS: APPLICATIONS AND PROPERTIES Vol. 1 No 4, 04RES10(2pp) (2012)   2304-1862/2012/1(4)04RES10(2) 04RES10-1  2012 Sumy State University Measurements of Radiative Vacancy Transfer Probabilities for Some Elements Irradiated with Photons of 0.0208 Nanometer Wavelengths  R. Durak1,*, M.F. Turhan1,†, M. Sağlam1,‡, A. Ateş2,§  1 Physics Department, science Faculty, Atatürk University, 25240 Erzurum, Turkey 2 Materials Engineering Department, Faculty of Engineering and Natural Sciences,  Yıldırım Bayezıt University, Ankara, Turkey  (Received 22 June 2012; published online 13 August 2012)  The radiative vacancy transfer probabilities of K to L2, L3, M2, M3 sub-shells were calculated using the experimental K level widths and theoretical partial radiative transitions. The targets were irradiated with photons of 0.0208 nm wavelength. It has been observed that the obtained values in the present study agree with theoretical results, theoretical predictions and the other available experimental values.  Keywords: Vacancy transfer probabilities, Level width.    PACS numbers: 61.80. – x, 61.72. jd                                                             * rdurak@atauni.edu.tr † m.f.turhan@hotmail.com  ‡ msaglam@atauni.edu.tr  § aates@ybu.edu.tr 1. INRODUCTION  The knowledge obtained from experimental results of the fluorescence yields, the vacancy transfer proba-bilities, the level and line widths for different elements is very important in the study of some basic phenome-na such as in atomic, molecular and radiation physics and in non-destructive trace element analysis of vari-ous sample using the energy dispersive X-ray fluores-cence method. Both some nuclear process like orbital electron capture or internal conversion and interaction of photons or charged particles such as heavy ions and protons are create primer vacancies in the inner shells /sub-shells of the atoms. In this study, vacancies in atomic shells/sub-shells were created by using a pho-toionization method. In the K shell, one of the higher shell electrons will fall into the vacated orbital followed by the emission of either a K X-ray photon or an Auger electron from one of the higher shells. In the radiative transfer process, a vacancy in the shell is filled by the jump of an electron from the higher shell and the dif-ference in energy of two shells/sub-shells is emitted in the form of characteristic X-ray. These radiation transi-tions, which obey a definite set of selection rules, are called allowed lines.  Ertuğral et al. [1] determined K to L shell vacancy transfer probabilities for 25 elements in the atomic range 58 ≤ Z≤ 92 by measuring the K X-ray yields from targets excited by 123.6 keV photons and using IK  /IK  intensity ratios. Santra et al. [2] measured K to L shell vacancy transfer probabilities ( KL) of Mo, Pd, and Cd by successively exciting them with the K X-rays of Ni and Sn induced by the bremsstrahlung emanating from an X-ray tube. The radiative vacancy transfer probabil-ities from L3 to M shell, 3( )L M R  and L3 to N shell, 3( )L N R , have been determined for W, Re and Pb using synchrotron radiation by Bonzi [3]. The vacancy trans-fer probabilities of K to L1, L2 and L3 shells measured for Ho and Er using L X-ray yields at 59.54 keV inci-dent photons by Ertuğrul [4].  In this study, we determined K to L2, L3, M2, M3 sub-shells radiative vacancy transfer probabilities for some elements (V, Co, Zn, Se) by using the experi-mental K level widths and theoretical partial radiative transitions. The determined probabilities are compared with theoretical predictions, theoretical values and the other available experimental values.   2. EXPERIMENTAL AND CALCULATION PRO-CEDURES   2.1 Experimental Procedure For K X-Ray Fluo-rescence Cross Sections  The values of experimental K X-ray fluorescence cross-sections were calculated using the following equa-tion:  0iii iKKK KNI G t  (I = α, β) (2.1) where iKN is the number of counts per second under the corresponding Ki X-ray photopeak, I0 is the intensi-ty of the exciting radiation, G is the geometrical factor dependent on the source-sample-detector geometry, iK is the detector efficiency for Ki X-rays, t is the thickness of target in g/cm2 unit and iK is the self-absorption correction factor for the target material and is given by:   1 exp cos coscos cosii i e eKi i e ett (2.2)   where i and e are the total mass absorption coeffi-cients of the target material at the incident photon (nano-wavelenght 0.0208 nm) and emitted Ki X-ray energies, respectively. The values of i and e were taken from WinXCom program [6]. The angles of i and e which correspond to incident and emission angles with sample surface were set to 45 , respectively.   R. DURAK, M.F. TURHAN, M. SAĞLAM, A. ATEŞ PROC. NAP 1, 04RES10 (2012)   04RES10-2 2.2 Experimental procedure for K shell fluores-cence yields and K shell level widths and radiative vacancy transition probabilities  The experimental K shell fluorescence yields were calculated from using the following expression:  ( )iKKK E(i = α,β)  (2.3) where iK is the total K X-ray fluorescence cross-section obtained experimentally, K(E) is the theoreti-cal K-shell photoionization cross-section of a given element for the excitation energy taken from Scofield [7]. The experimental values of K shell level widths were evaluated from the following equation:   ( )KKKR, (2.4)  where ( )K R  is radiative transition rate [8], K is the K shell fluorescence yield obtained experimentally.  Some experimental radiative vacancy transition probabilities ( ( )i tX YR  X = (K), Y = (L2, L3 M2, M3) and  t = (1, 2, 3, …) from K shell to L, M sub-shells were evaluated from following equation:   ( )( ) i ti tiX YX YXRR ,  (2.5)  ( )i tX YR  is the partial radiative transition rate and taken from Scofield [8], iX is the level width obtained experimentally.   3. RESULT AND DISCUSSIONS  The experimental Kα, Kβ and Kt X-ray fluorescence cross sections, K shell fluorescence yields, K shell level widths and K to L2, L3, M2, M3, sub-shells vacancy transfer probabilities were measured for some ele-ments. The measured values of X-ray fluorescence cross sections, X-ray fluorescence yields and ГK level widths values were listed in Table 1. For the measured and calculated radiative vacancy transfer probabilities, eqs. (5) were used to include partial radiative transition rates [8] and level widths from Table 1.   The measured values of K to L2,3, M2,3 radiative vacancy transfer probabilities were listed in Table 2 with the calculated values. The present results are generally in the good agreement with theoretical prediction and other exper-imental results can be obtained from literature.  Table 1 –  Experimental and theoretical Ki (i = α, β, t) X-ray fluorescence cross sections (barn/atom), X-ray fluorescence yields and ГK level widths (eV) values   Ele-ment σKα σKβ σKtotal ωK ГK  Experi-mental Theoreti-cal Experi-mental Theoreti-cal Experi-mental Theoreti-cal Experi-mental Theoreti-cal Experi-mental Theoreti-cal 23V 11.54±0.70 10.87 1.48±0.09 1.26 13.01±1.1 12.13 0.260±0.023 0.243[9] 0.88±0.08 1.01[10] 27Co 35.12±1.99 32.46 4.73±0.28 3.95 39.85±3.21 36.41 0.408±0.033 0.373[9] 1.15±0.09 1.33[10] 30Zn 62.18±3.53 63.39 8.70±0.52 7.87 70.88±5.77 71.26 0.471±0.038 0.474[9] 1.59±0.13 1.67[10] 34Se 126.90±7.23 128.08 19.49±1.17 18.25 146.38±11.91 146.33 0.589±0.048 0.589[9] 2.22±0.18 2.33[10]  Table 2 –  Experimental and theoretical K shell to L2, L3, M2, M3 sub-shells radiative vacancy transfer probability   Element ηKL2 (R) ηKL3 (R) ηKM2 (R) ηKM3 (R)  Experi- mental Theore- tical Experi- mental Theore- tical Experi-mental Theore- tical Experi-mental Theore- tical 23V 0.079±0.007 0.068a 0.076[11] 0.154±0.014 0.134a 0.151[11] 0.0091±0.0008 0.0079a  0.0179±0.0016 0.0156a 27Co 0.123±0.010 0.106a 0.116[11] 0.241±0.019 0.0208a 0.228[11] 0.0149±0.0012 0.0129a  0.0293±0.0024 0.0253a  30Zn 0.142±0.012 0.135a 0.142[11] 0.277±0.022 0.263a 0.278[11] 0.0176±0.0014 0.0167a  0.0344±0.0028 0.0326a 34Se 0.176±0.014 0.167a 0.173[11] 0.340±0.028 0.323a 0.336[11] 0.0237±0.0019 0.0226a  0.0464±0.0038 0.0441a  a Theoretical calculation of radiative vacancy transfer probability from eq. (5) obtained theoretical level widths from Krause [10].  REFERENCES  1. B. Ertuğral, G. Apaydın, H. Baltaş, U. Çevik, A.I. Kobya, M. Ertuğrul, Spectrochim. Acta B 60, 519 (2005).  2. S. Santra, A.C. Mandal, D. Mitra, M. Sarkar, D.B. Bhattacharya, Radiat. Phys. Chem. 74, 282 (2005). 3. E.V. Bonzi, Nucl. Instrum. Meth. B 245, 363 (2006). 4. M. Ertuğrul, Spectrochim. Acta B 57, 63 (2002). 5. L. Gerward, N. Guilbert, K.B. Jensen, H. Levring, Radiat. Phys. Chem. 60, 23 (2001). 6. J.H. Scofield. Theoretical photoionization cross-section from 1 to 1500 keV. Theoretical Report No. UCRL 51326 1973; Lawrance Livermore Laboratory, Livermore, CA. 7. J.H. Scofield, Relativistic Hartree-Slater values for K and L X-ray emission rates. At Data Nucl Data Tables 1974;14:121. 8. M.O. Krause, J. Phys. Chem. 8, 307 (1979).  9. M.O. Krause, J.H. Oliver, J. Phys. Chem.8, 329 (1979). 10. P.V. Rao, M.H. Chen, B. Crasemann, Phys. Rev. A 5, 997 (1972). 

Measurements of Radiative Vacancy Transfer Probabilities for Some Elements Irradiated with Photons of 0.0208 Nanometer Wavelengths

SocioEconomic Challenges Journal (Sumy State University)

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE NANOMATERIALS: APPLICATIONS AND PROPERTIES 
Vol. 1 No 4, 04RES10(2pp) (2012) 
 
 
2304-1862/2012/1(4)04RES10(2) 04RES10-1  2012 Sumy State University 
Measurements of Radiative Vacancy Transfer Probabilities for Some Elements Irradiated 
with Photons of 0.0208 Nanometer Wavelengths 
 
R. Durak1,*, M.F. Turhan1,†, M. Sağlam1,‡, A. Ateş2,§ 
 
1 Physics Department, science Faculty, Atatürk University, 25240 Erzurum, Turkey 
2 Materials Engineering Department, Faculty of Engineering and Natural Sciences,  
Yıldırım Bayezıt University, Ankara, Turkey 
 
(Received 22 June 2012; published online 13 August 2012) 
 
The radiative vacancy transfer probabilities of K to L2, L3, M2, M3 sub-shells were calculated using the 
experimental K level widths and theoretical partial radiative transitions. The targets were irradiated with 
photons of 0.0208 nm wavelength. It has been observed that the obtained values in the present study agree 
with theoretical results, theoretical predictions and the other available experimental values. 
 
Keywords: Vacancy transfer probabilities, Level width. 
 
  PACS numbers: 61.80. – x, 61.72. jd 
 
 
                                                          
* rdurak@atauni.edu.tr 
† m.f.turhan@hotmail.com  
‡ msaglam@atauni.edu.tr  
§ aates@ybu.edu.tr 
1. INRODUCTION 
 
The knowledge obtained from experimental results 
of the fluorescence yields, the vacancy transfer proba-
bilities, the level and line widths for different elements 
is very important in the study of some basic phenome-
na such as in atomic, molecular and radiation physics 
and in non-destructive trace element analysis of vari-
ous sample using the energy dispersive X-ray fluores-
cence method. Both some nuclear process like orbital 
electron capture or internal conversion and interaction 
of photons or charged particles such as heavy ions and 
protons are create primer vacancies in the inner shells 
/sub-shells of the atoms. In this study, vacancies in 
atomic shells/sub-shells were created by using a pho-
toionization method. In the K shell, one of the higher 
shell electrons will fall into the vacated orbital followed 
by the emission of either a K X-ray photon or an Auger 
electron from one of the higher shells. In the radiative 
transfer process, a vacancy in the shell is filled by the 
jump of an electron from the higher shell and the dif-
ference in energy of two shells/sub-shells is emitted in 
the form of characteristic X-ray. These radiation transi-
tions, which obey a definite set of selection rules, are 
called allowed lines.  
Ertuğral et al. [1] determined K to L shell vacancy 
transfer probabilities for 25 elements in the atomic 
range 58 ≤ Z≤ 92 by measuring the K X-ray yields from 
targets excited by 123.6 keV photons and using IK  /IK  
intensity ratios. Santra et al. [2] measured K to L shell 
vacancy transfer probabilities ( KL) of Mo, Pd, and Cd 
by successively exciting them with the K X-rays of Ni 
and Sn induced by the bremsstrahlung emanating from 
an X-ray tube. The radiative vacancy transfer probabil-
ities from L3 to M shell, 
3
( )L M R  and L3 to N shell, 
3
( )L N R , have been determined for W, Re and Pb using 
synchrotron radiation by Bonzi [3]. The vacancy trans-
fer probabilities of K to L1, L2 and L3 shells measured 
for Ho and Er using L X-ray yields at 59.54 keV inci-
dent photons by Ertuğrul [4].  
In this study, we determined K to L2, L3, M2, M3 
sub-shells radiative vacancy transfer probabilities for 
some elements (V, Co, Zn, Se) by using the experi-
mental K level widths and theoretical partial radiative 
transitions. The determined probabilities are compared 
with theoretical predictions, theoretical values and the 
other available experimental values.  
 
2. EXPERIMENTAL AND CALCULATION PRO-
CEDURES  
 
2.1 Experimental Procedure For K X-Ray Fluo-
rescence Cross Sections 
 
The values of experimental K X-ray fluorescence 
cross-sections were calculated using the following equa-
tion: 
 
0
i
i
i i
K
K
K K
N
I G t
  (I = α, β) (2.1) 
where 
iK
N is the number of counts per second under 
the corresponding Ki X-ray photopeak, I0 is the intensi-
ty of the exciting radiation, G is the geometrical factor 
dependent on the source-sample-detector geometry, 
iK
 
is the detector efficiency for Ki X-rays, t is the thickness 
of target in g/cm2 unit and 
iK
 is the self-absorption 
correction factor for the target material and is given by: 
 
 
1 exp cos cos
cos cosi
i i e e
K
i i e e
t
t
 (2.2)  
 
where i and e are the total mass absorption coeffi-
cients of the target material at the incident photon 
(nano-wavelenght 0.0208 nm) and emitted Ki X-ray 
energies, respectively. The values of i and e were 
taken from WinXCom program [6]. The angles of i and 
e which correspond to incident and emission angles 
with sample surface were set to 45 , respectively. 
 
 R. DURAK, M.F. TURHAN, M. SAĞLAM, A. ATEŞ PROC. NAP 1, 04RES10 (2012) 
 
 
04RES10-2 
2.2 Experimental procedure for K shell fluores-
cence yields and K shell level widths and 
radiative vacancy transition probabilities 
 
The experimental K shell fluorescence yields were 
calculated from using the following expression: 
 
( )
iK
K
K E
(i = α,β)  (2.3) 
where 
iK
 is the total K X-ray fluorescence cross-
section obtained experimentally, K(E) is the theoreti-
cal K-shell photoionization cross-section of a given 
element for the excitation energy taken from Scofield 
[7]. 
The experimental values of K shell level widths 
were evaluated from the following equation: 
 
 
( )K
K
K
R
, (2.4) 
 
where ( )K R  is radiative transition rate [8], K is the 
K shell fluorescence yield obtained experimentally.  
Some experimental radiative vacancy transition 
probabilities ( ( )
i tX Y
R  X = (K), Y = (L2, L3 M2, M3) and  
t = (1, 2, 3, …) from K shell to L, M sub-shells were 
evaluated from following equation: 
 
 
( )
( ) i t
i t
i
X Y
X Y
X
R
R ,  (2.5) 
 
( )
i tX Y
R  is the partial radiative transition rate and 
taken from Scofield [8], 
iX
 is the level width obtained 
experimentally.  
 
3. RESULT AND DISCUSSIONS 
 
The experimental Kα, Kβ and Kt X-ray fluorescence 
cross sections, K shell fluorescence yields, K shell level 
widths and K to L2, L3, M2, M3, sub-shells vacancy 
transfer probabilities were measured for some ele-
ments. The measured values of X-ray fluorescence cross 
sections, X-ray fluorescence yields and ГK level widths 
values were listed in Table 1. For the measured and 
calculated radiative vacancy transfer probabilities, eqs. 
(5) were used to include partial radiative transition 
rates [8] and level widths from Table 1.   The measured 
values of K to L2,3, M2,3 radiative vacancy transfer 
probabilities were listed in Table 2 with the calculated 
values. The present results are generally in the good 
agreement with theoretical prediction and other exper-
imental results can be obtained from literature. 
 
Table 1 –  Experimental and theoretical Ki (i = α, β, t) X-ray fluorescence cross sections (barn/atom), X-ray fluorescence yields and 
ГK level widths (eV) values  
 
Ele-
ment 
σKα σKβ σKtotal ωK ГK 
 Experi-
mental 
Theoreti-
cal 
Experi-
mental 
Theoreti-
cal 
Experi-
mental 
Theoreti-
cal 
Experi-
mental 
Theoreti-
cal 
Experi-
mental 
Theoreti-
cal 
23V 11.54±0.70 10.87 1.48±0.09 1.26 13.01±1.1 12.13 0.260±0.023 0.243[9] 0.88±0.08 1.01[10] 
27Co 35.12±1.99 32.46 4.73±0.28 3.95 39.85±3.21 36.41 0.408±0.033 0.373[9] 1.15±0.09 1.33[10] 
30Zn 62.18±3.53 63.39 8.70±0.52 7.87 70.88±5.77 71.26 0.471±0.038 0.474[9] 1.59±0.13 1.67[10] 
34Se 126.90±7.23 128.08 19.49±1.17 18.25 146.38±11.91 146.33 0.589±0.048 0.589[9] 2.22±0.18 2.33[10] 
 
Table 2 –  Experimental and theoretical K shell to L2, L3, M2, M3 sub-shells radiative vacancy transfer probability  
 
Element ηKL2 (R) ηKL3 (R) ηKM2 (R) ηKM3 (R) 
 Experi- 
mental 
Theore- 
tical 
Experi- 
mental 
Theore- 
tical 
Experi-
mental 
Theore- 
tical 
Experi-
mental 
Theore- 
tical 
23V 0.079±0.007 0.068a 
0.076[11] 
0.154±0.014 0.134a 
0.151[11] 
0.0091±0.0008 0.0079a 
 
0.0179±0.0016 0.0156a 
27Co 0.123±0.010 0.106a 
0.116[11] 
0.241±0.019 0.0208a 
0.228[11] 
0.0149±0.0012 0.0129a 
 
0.0293±0.0024 0.0253a 
 
30Zn 0.142±0.012 0.135a 
0.142[11] 
0.277±0.022 0.263a 
0.278[11] 
0.0176±0.0014 0.0167a 
 
0.0344±0.0028 0.0326a 
34Se 0.176±0.014 0.167a 
0.173[11] 
0.340±0.028 0.323a 
0.336[11] 
0.0237±0.0019 0.0226a 
 
0.0464±0.0038 0.0441a 
 
a Theoretical calculation of radiative vacancy transfer probability from eq. (5) obtained theoretical level widths from Krause [10]. 
 
REFERENCES 
 
1. B. Ertuğral, G. Apaydın, H. Baltaş, U. Çevik, A.I. Kobya, 
M. Ertuğrul, Spectrochim. Acta B 60, 519 (2005).  
2. S. Santra, A.C. Mandal, D. Mitra, M. Sarkar, 
D.B. Bhattacharya, Radiat. Phys. Chem. 74, 282 (2005). 
3. E.V. Bonzi, Nucl. Instrum. Meth. B 245, 363 (2006). 
4. M. Ertuğrul, Spectrochim. Acta B 57, 63 (2002). 
5. L. Gerward, N. Guilbert, K.B. Jensen, H. Levring, Radiat. 
Phys. Chem. 60, 23 (2001). 
6. J.H. Scofield. Theoretical photoionization cross-section 
from 1 to 1500 keV. Theoretical Report No. UCRL 51326 
1973; Lawrance Livermore Laboratory, Livermore, CA. 
7. J.H. Scofield, Relativistic Hartree-Slater values for K and L X-
ray emission rates. At Data Nucl Data Tables 1974;14:121. 
8. M.O. Krause, J. Phys. Chem. 8, 307 (1979).  
9. M.O. Krause, J.H. Oliver, J. Phys. Chem.8, 329 (1979). 
10. P.V. Rao, M.H. Chen, B. Crasemann, Phys. Rev. A 5, 997 
(1972). 


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Measurements of Radiative Vacancy Transfer Probabilities for Some Elements Irradiated with Photons of 0.0208 Nanometer Wavelengths

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