ARTICLE IN PRESS

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Applied Radiation and Isotopes 65 (2007) 669–675

www.elsevier.com/locate/apradiso

Measurement of K X-ray fluorescence cross-sections, fluorescence yieldsand intensity ratios for some elements in the atomic range 22pZp68

I. Hana,�, M. S-ahinb, L. Demira, Y. S-ahina

aFaculty of Arts and Sciences, Department of Physics, Ataturk University, 25240 Erzurum, TurkeybIspir Hamza Polat Proession High Scholl, Ataturk University, Ispir, Erzurum,Turkey

Received 30 June 2006; received in revised form 10 January 2007; accepted 16 January 2007

Abstract

The Ka, Kb, and total K X-rays fluorescence cross-sections, as well as the average fluorescence yields for 24 elements with 22pZp68

have been measured at an excitation energy 59.54 keV g-rays from an Am-241 filtered point source. Furthermore, the IKa/IKb intensity

ratios for these elements have been investigated. The K X-rays emitted by samples have been counted by a Si(Li) detector. Experimental

values of the K X-ray fluorescence cross-sections, fluorescence yields, and the IKa/IKb intensity ratios have been compared with

theoretical values. In most cases, there is an agreement between the experimental and theoretical values within the standard uncertainties

r 2007 Elsevier Ltd. All rights reserved.

Keywords: X-ray fluorescence; Cross-section; Fluorescence yield; Intensity ratio

1. Introduction

Accurate experimental values of X-ray fluorescencecross-sections, fluorescence yields and IKa/IKb intensityratios for various elements at various photoionizationenergies are important because of their extensive use inatomic, molecular, radiation and medical physics. They arealso used in practical applications, such as elementalanalysis by the X-ray emission technique, and basic studiesof the nuclear and atomic processes leading to the emissionof X-rays and irradiation processes.

In the recent years, Rao et al. (1993) have determined KX-ray fluorescence cross-sections for some light elements inthe energy range 20–60 keV. The Ka and Kb X-rayfluorescence cross-sections for some elements with73pZp82 have been studied by Saleh and Al-Saleh(1987). K-shell fluorescence cross-sections and yields of14 elements in the atomic number range 25pZp47 havebeen measured by Durak and Ozdemir (2001). The Ka andKb X-ray fluorescence cross-sections for ten elements ateight excitation energies ranging from 8 to 47 keV have

e front matter r 2007 Elsevier Ltd. All rights reserved.

radiso.2007.01.009

ing author.

ess: ihan@atauni.edu.tr (I. Han).

been measured by Singh et al. (1990). Karabulut et al.(1999) have measured Ka and Kb X-ray fluorescence cross-sections in the atomic region 26pZp42 excited by59.5 keV photons and Ka and Kb fluorescence cross-sections for elements in the range 44pZp68 at 59.5 keVhave been studied by Budak et al. (1999). Kumar et al.(1986) measured K-shell photoelectric cross-sections forintermediate elements at 26 keV energies. Horakeri et al.(1997, 1998) determined K-shell fluorescence yields using asimple method for some elements in 62 pZp83 at 123.6and 320 keV energies. Seven (2002) measured photon-induced K X-ray cross-sections for some heavy elements.Durak and Sahin (1998) measured K-shell fluorescenceyields for Cs, Sm, Eu, Ho, Ta, W, Hg and Pb. The Ka, Kb,and total K X-rays fluorescence cross-sections, as well asthe average fluorescence yields for six elements with16pZp23 at 5.96 keV have been measured by Sahin etal. (2005). Krause (1979) compiled oK adopted values forelements 54pZp110. Hubbell et al. (1994) have collectedmore recent experimental values of oK. Theoretical valuesof oK were obtained in the region 44pZp54 by McGuire(1970a, b). Chen et al. (1980) used a Dirac–Hartree–Slaterapproach to calculate the oK values of elements in the18pZp96 range. Bambynek et al. (1972) in a review article

ARTICLE IN PRESSI. Han et al. / Applied Radiation and Isotopes 65 (2007) 669–675670

have fitted their collection of selected most reliableexperimental values of oK in the 13pZp92 range.Rebohle et al. (1996) have measured Kb/Ka intensity ratiofor pure 3d elements and some of their chemicalcompounds. Baydas et al. (2003) have studied dependencesof the Kb/Ka intensity ratios of Ti and V in halogencompounds on the excitation energy in the interval5.5–12.1 keV.

In the present work, the Ka, Kb and total K X-raysfluorescence cross-sections, average fluorescence yields andIKb/IKa intensity ratios were experimentally determined forTi, V, Cr, Mn, Fe, Ni, Cu, Zn, Ge, As, Br, Rb, Y, Zr, Nb,Cd, In, Sn, Ba, Sm, Gd, Dy, Ho and Er at an excitationenergy 59.54 keV g-rays from an Am-241 filtered pointsource. The experimental values have been compared withthe theoretical ones.

2. Experimental arrangement

The geometry and the shielding arrangement of theexperimental set-up employed in the present work are asshown in Fig. 1. The samples were excited with an Am-241

Pb shield

(R=0.6mm)

Be window

28mm

point source

Am-241

point source

Target

Pb

Fe

Al

Si(

Li)

Be window

45ο

target

34mm

41mm

Fig. 1. The experimental setup.

(overall diameter ¼ 4mm, active diameter ¼ 3mm andcapsule dimension 10mm) radioisotope source at 59.54 keVabout 100mCi. The Am-241 (100mCi) radioisotope sourceemits monoenergetic (59.5 keV) g-rays. The g-rays of 26.4,33.2, 43.4 keV and the characteristic L series of Np comingfrom Am-241 are completely (approximately 99.99%)filtered out with their help of graded filter of Pb, Fe andAl of thickness 0.1, 0.1 and 1mm, respectively, becauseeven a small fraction of these radiations would producesizable interference due to their large interaction cross-sections with K-shell electrons. The spectrum of filteredexcitation radiation is shown in Fig. 7. Spectroscopicallypure rectangular samples of thickness ranging from 0.011to 0.378 g/cm2 have been used for the measurement. Thedirect beam from the source was directly incoming on thesample. The samples were placed at a y1 ¼ 451 angle withrespect to the beam from the source and fluorescent X-raysemitted in a direction perpendicular to (y2 ¼ 901)the source were detected by a Si(Li) detector. The KX-ray spectrum from various targets were recordedwith a Si(Li) detector (full-width at half-maximum(FWHM) ¼ 160 eV at 5.9 keV, active diameter ¼ 3.91mm,active area ¼ 12mm2, sensitivity depth ¼ 3mm, Be win-dow thickness ¼ 0.025mm) coupled to a 16384 computer-ized multi-channel analyzer. The spectrums wereaccumulated in time intervals ranging from 7200 to28800 s in order to obtain sufficient statistical accuracy.A typical K-shell X-ray spectrum of Rb is shown in Fig. 2.Also typical K-shell X-ray spectrum of Fe and Ho weregiven in Figs. 8 and 9 respectively. The spectrums wereanalyzed by using Microcal Origin 7.5 Demo Versionsoftware program with least-squares fit method. Todetermine the net peak areas, the areas under thepeak Gaussian function were subtracted to correct for

3200 3400 3600 3800 4000 4200 4400

0

500

1000

1500

2000

2500

3000

3500

4000 Kα

Kβ

Co

un

ts

Channel number

Peak Analysis

Corr Coef=0,99984

COD=0,99967 # of Data Points=1250

Degree of Freedom=1244SS=211304,0465

Chi2=169,8585583

Source File: Rb

Fitting Results

MaxHeight

3851.88661

745.13903

AreaFitTP

82.36344

17.63656

FWHM

62.76834

69.47943

CenterGrvty

3622.65529

4052.47636

AreaFitT

257362.89782

55109.36182

312472.25965

Peak Type

Gaussian

Gaussian

Peak #

1 Kα2 Kβ

Fig. 2. Typical K X-ray spectra of Rb recorded with a Si(Li) detector.

ARTICLE IN PRESSI. Han et al. / Applied Radiation and Isotopes 65 (2007) 669–675 671

background in the peak region. The peak areas of allelements were given in Table (5).

3. Experimental and calculation procedures

The theoretical K X-ray fluorescence cross-sections sKi

listed in Table (1) were calculated using the fundamentalparameter equation

sKi ¼ sK ðEÞoK FKi, (1)

where sK ðEÞ is the K-shell photoionization cross-sectionfor the given elements at the excitation energy E and oK isthe fluorescence yield of the K-shell line. The values ofsK(E) used in these calculations were taken from the reportby Scofield (1973). The values of oK were taken from theannotated bibliography by Hubbell et al. (1994). The valueFKi is the fractional ratio of the Ki X-rays, and FKa and FKb

are defined as

FKa ¼ ð1þ IKb=IKaÞ�1 and F Kb ¼ ð1þ IKa=IKbÞ

�1,

(2)

where IKb/IKais the Kb-to-Ka X-ray intensity ratio. Theseratios were obtained from the table published by Scofield(1974).

The experimental Ki X-ray fluorescence cross-sectionswere evaluated using the relation

sKi ¼NKi

I0G�Kibt, (3)

Table 1

Experimental and theoretical values of Ki X-rays fluorescence cross-section fo

sKa sKb

Element Experimental Theoretical Experimen

22Ti 8.6970.70 8.37 0.9770.

23V 11.7970.94 11.45 1.1270.

24Cr 15.7971.26 15.48 1.8770.

25Mn 21.0071.68 20.39 2.6370.

26Fe 26.6572.13 26.41 3.2870.

28Ni 43.9773.52 42.55 5.5270.

29Cu 52.7474.22 52.98 6.5170.

30Zn 63.8375.11 64.96 8.1370.

32Ge 95.0777.61 94.09 12.7471.

33As 112.8779.03 111.56 15.2671.

35Br 172.92713.83 170.75 23.5571.

37Rb 204.17716.33 201.30 31.3172.

39Y 235.67718.85 234.88 38.6673.

40Zr 297.38723.79 292.81 47.0973.

41Nb 326.62726.13 328.29 59.6074.

48Cd 648.14751.85 649.78 133.82710

49In 703.42756.27 705.94 143.77711

50Sn 763.37761.07 764.64 158.90712

56Ba 1171.51793.72 1172.21 267.91721

62Sm 1680.587134.45 1681.91 398.40731

64Gd 1866,09149,29 1879.66 452.80736

66Dy 2054.877164.39 2062.29 500.86740

67Ho 2166.657173.33 2175.69 541.00743

68Er 2293.677183.49 2292.22 570.68745

where NKi is the net number of counts under thecorresponding photopeak, the product I0G is the intensityof the exciting radiation falling on the area of the targetsamples visible to the detector, eKi, is the detector efficiencyfor Ki X-rays, t is the areal mass of the sample in g/cm2 andb is the self-absorption correction factor for the incidentphotons and emitted K X-ray photons. b was calculatedusing the relation:

b ¼1� exp ½�ðmi= cos y1 þ me= cos y2Þt�

ðmi= cos y1 þ me= cos y2Þt, (4)

where mi and me are the attenuation coefficients (cm2/g) ofincident photons and emitted characteristic X-rays, re-spectively.The values of mi and me are taken from the tablesof Hubbell and Seltzer (1997). The angles of incidentphotons and emitted X-rays with respect to the normal atthe surface of the sample are y1 and y2 in the present setup.In this study, the effective incident photon flux I0GeKi,

which contain terms related to the incident photon flux,geometrical factor and the efficiency of the X-ray detector,was determined by measuring t; b and the K X-rayintensities from thin samples of Ca, Co, Se, Mo, Ag, Sb, Euand Tm and using theoretical sKi values in Eq. (3). Themeasured I0GeKi values for the present geometry wereplotted as a function of the mean K X-ray energy in Fig. 3.The fluorescence yield of an atomic shell or subshell is

defined as the probability that a vacancy in that shell orsubshell is filled through a radiative transition. Thus, for asample containing many atoms, the fluorescence yield of a

r some elements in the atomic range 22pZp68 (barns/atom)

sK

tal Theoretical Experimental Theoretical

08 0.95 9.6670.77 9.32

09 1.33 12.9271.03 12.78

15 1.79 17.6671.41 17.26

21 2.36 23.6371.89 22.75

26 3.19 29.9372.39 29.60

44 5.22 49.4973.96 47.77

52 6.44 59.2574.74 59.42

65 8.06 71.9675.76 73.02

02 12.43 107.8278.63 106.51

22 15.30 128.13710.25 126.86

88 24.72 196.47715.72 195.47

50 32.21 235.48718.84 233.50

09 39.84 274.33721.95 274.72

77 50.86 344.48727.56 343.68

77 58.17 386.22730.90 386.47

.17 129.63 781.96762.56 779.42

.50 143.09 847.18767.77 849.03

.71 157.59 922.28773.78 922.24

.43 266.44 1439.427115.15 1438.65

.87 401.81 2078.987166.32 2083.72

.22 456.01 2318.897185.51 2335.67

.07 505.06 2555.737204.46 2567.34

.28 535.87 2707.667216.61 2711.56

.65 567.56 2864.347229.15 2859.78

ARTICLE IN PRESSI. Han et al. / Applied Radiation and Isotopes 65 (2007) 669–675672

shell is equal to the number of photons emitted whenvacancies in the shell are filled divided by the number ofprimary vacancies in the shell. The average K-shell

0 10 20 30 40 50

2000

2500

3000

3500

4000

4500

5000

I 0G

ε

Energy (keV)

Fig. 3. I0Ge versus K X-ray energy.

20 30 40 50 60 70

0

500

1000

1500

2000

2500Exp.Theo.

σ Kα

Atomic number

20 30 40 50 60 70

0

500

1000

1500

2000

2500

3000

3500Exp.

Theo.

σ K

Atomic number

Fig. 4. The Ka, Kb and total K X ray fluorescence c

fluorescence yields for the 24 elements with 22pZp68were derived from the measured Ki X-ray fluorescencecross-sections using the relationship:

oK ¼sKi

sK ðEÞ, (5)

where sKi is the Ki X-ray fluorescence cross-section andsK(E) is the total K-shell photoionization cross-sectiontaken from the tables published by Scofield (1973).The experimental K-shell X-ray intensity ratios IKb/IKa

were evaluated using the equation

IKb

IKa¼

NKb

NKa

bKa

bKb

�Ka

�Kb, (6)

where NKb and NKa represent the counts under the Kb andKa peaks, respectively, bKa/bKb is the ratio of the self-absorption correction factors of the target, and eKa/eKb isthe ratio of the detector-efficiency values for the Ka andKb X-rays, respectively.

20 30 40 50 60 70

0

100

200

300

400

500

600

700Exp.Theo.

σ K

Atomic number

20 30 40 50 60 70

0

500

1000

1500

2000

2500

3000

σKα

σKβ

σK

σ Ki

Atomic number

ross-section (barns/atom) versus atomic number.

ARTICLE IN PRESS

20 30 40 50 60 70

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Exp.Theo.

ωK

Atomic number

Fig. 5. K X-ray fluorescence yields versus atomic number.

Table 2

The experimental and theoretical values of K-shell fluorescence yields (oK)

oK

Element Experimental Theoretical

22Ti 0.23470.019 0.226

23V 0.26470.021 0.256

24Cr 0.29570.024 0.289

25Mn 0.35170.028 0.321

26Fe 0.35870.029 0.355

28Ni 0.43570.035 0.421

29Cu 0.45270.036 0.454

30Zn 0.47770.038 0.486

32Ge 0.55270.044 0.546

33As 0.58270.047 0.575

35Br 0.63670.051 0.628

37Rb 0.68470.055 0.674

39Y 0.71870.057 0.716

40Zr 0.74570.060 0.734

41Nb 0.74770.060 0.751

48Cd 0.83970.067 0.842

49In 0.84870.068 0.851

50Sn 0.85870.069 0.859

56Ba 0.89970.072 0.900

62Sm 0.92570.074 0.926

64Gd 0.93270.075 0.939

66Dy 0.93470.075 0.938

67Ho 0.93670.075 0.940

68Er 0.94370.075 0.943

Table 3

Experimental and theoretical values of IKb/IKa intensity ratios of some

elements in the atomic range 22pZp68

IKb/IKa

Element Experimental Theoretical

22Ti 0.11070.009 0.114

23V 0.11370.009 0.116

24Cr 0.11370.009 0.115

25Mn 0.10670.008 0.116

26Fe 0.12070.010 0.121

28Ni 0.11970.009 0.123

29Cu 0.12270.010 0.122

30Zn 0.12670.010 0.124

32Ge 0.13170.010 0.132

33As 0.13670.011 0.137

35Br 0.14370.011 0.145

37Rb 0.15870.013 0.160

39Y 0.16970.014 0.170

40Zr 0.17170.014 0.174

41Nb 0.17870.014 0.177

48Cd 0.20070.016 0.200

49In 0.20370.016 0.203

50Sn 0.20670.017 0.206

56Ba 0.22770.018 0.227

62Sm 0.23970.019 0.239

64Gd 0.24470.020 0.243

66Dy 0.24670.020 0.245

67Ho 0.24770.020 0.246

68Er 0.24770.020 0.248

20 30 40 50 60 70

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

Exp.Theo.

I Kβ/

I Kα

Atomic number

Fig. 6. The IKb/IKa intensity ratios versus atomic number.

I. Han et al. / Applied Radiation and Isotopes 65 (2007) 669–675 673

4. Result and discussion

The experimental and theoretical values of Ka, Kb andtotal K X-rays fluorescence cross-sections for 24 elementsin the atomic range 22pZp68 for the energy 59.54 keV arelisted in Table (1). They are plotted as functions of theatomic number in Fig. 4. The average K-shell fluorescenceyields (oK) for these elements were calculated from presentKa X-ray fluorescence cross-sections using Eq. (5) andthese values are listed in Table (2) together with our

theoretical values. The average K-shell fluorescence yieldsare plotted as function of the atomic number in Fig. 5. Theexperimental values of IKb/IKa X-ray intensity ratios forthese elements were calculated from present Ki X-rayfluorescence cross-sections using Eq. (6) and these valuesare given Table (3) together with theoretical values. Theintensity ratios are plotted as functions of the atomicnumber in Fig. 6.

ARTICLE IN PRESS

Table 4

Uncertainties in the quantities used to determine K X-ray fluorescence cross-sections in Eq. (3)

Quantity Nature of uncertainty Uncertainity(%)

NKaNKb Statistical and other possible errors in area evaluation 5

I0Ge Errors in different parameters used to evaluate I0Ge 5

b Error in the absorption coefficients at incident and emitted photon energies p1

t Thickness of target p1

Table 5

Peak areas of elements

Element Ka peak area Kb peak area Total K peak area

22Ti 828271.35 102176.5 949671.57

23V 1184571.43 194175.02 1271071.87

24Cr 2401670.88 397773.52 2774071.17

25Mn 2643070.77 462172.65 3168770.92

26Fe 5315470.48 945771.52 6261170.54

28Ni 4194270.53 608071.61 4867870.53

29Cu 4608870.49 667571.58 5354570.50

30Zn 3725570.55 547671.65 4271070.61

32Ge 10425570.32 1944770.81 12414470.33

33As 13051270.29 2453170.73 15564070.30

35Br 11388370.31 2304570.76 13558070.35

37Rb 25736270.21 5510970.51 31247270.23

39Y 35814170.18 8079570.41 43592970.20

40Zr 17939470.25 3518770.68 21279070.33

41Nb 50847270.15 12114670.35 61856770.20

48Cd 82127870.13 17689270.31 99817070.34

49In 75980270.13 15246470.35 91226670.37

50Sn 197486770.08 40758270.22 238244970.23

56Ba 56427470.16 10437870.44 66865270.47

62Sm 48688470.19 8550070.62 57238470.65

64Gd 14824470.36 2493571.40 17317971.45

66Dy 16114170.36 2696171.22 18810271.27

67Ho 37414570.24 6795470.78 44210070.82

68Er 19324670.35 3307171.11 22631771.16

25 30 35 40 45 50 55 60

0.0

1.0x103

2.0x103

3.0x103

4.0x103

5.0x103

6.0x103

7.0x103

8.0x103

9.0x103

1.0x104

1.1x104 59.54 keV

Am-241

Co

un

ts

Energy

Fig. 7. Spectrum of Am-241 filtered point source.

1500 1600 1700 1800 1900 2000 2100 2200

0

200

400

600

800

1000

1200

Kβ

Kα

Co

un

ts

Channel number

Peak Analysis

Corr Coef=0,99989

COD=0,99977

Degree of Freedom=604SS=7683,973469

Chi2=12,72181038

Source File: Fe

Fitting Results

MaxHeight

1035.13346

175.68845

AreaFitTP

84.89519

15.10481

48.24022

50.57019

CenterGrvty

1737.44062

1913.64523

AreaFitT

53154.18244

9457.35271

62611.53516

Peak Type

Gaussian

Gaussian

Peak #

1 Kα 2 Kβ

FWHM

# of Data Points=610

Fig. 8. Typical K X-ray spectra of Fe recorded with a Si (Li) detector.

12000 12500 13000 13500 14000 14500 15000 15500

0

500

1000

1500

2000

Kβ

Kα

Counts

Channel number

Peak Analysis

Corr Coef=0,99863

COD=0,99727 # of Data Points=3281

Degree of Freedom=3269SS=1120810,772

Source File: Ho

Fitting Results

MaxHeight

1224.46813

2063.9188

397.90308

98.16273

AreaFitTP

32.39317

52.2359

12.34811

3.02282

FWHM

109.87402

105.1152

128.8879

127.89542

CenterGrvty

12632.87008

12861.86012

14558.45302

14962.31156

AreaFitT

143210.31401

230935.08608

54591.02427

13363.90624

442100.33061

Peak Type

Gaussian

Gaussian

Gaussian

Gaussian

Peak #

1 Kα 2

3 Kβ4

Chi2=342,8604382

Fig. 9. Typical K X-ray spectra of Ho recorded with a Si (Li) detector.

I. Han et al. / Applied Radiation and Isotopes 65 (2007) 669–675674

The overall error in the measured Ka, Kb and total KX-rays fluorescence cross sections is estimated to be 8–9%,which arises due to the uncertainties in various parameters

ARTICLE IN PRESSI. Han et al. / Applied Radiation and Isotopes 65 (2007) 669–675 675

required to evaluate the experimental values of crosssections using Eq. (3). The uncertainty in each parameteris described in Table (4). Although the relative intensitiescan be evaluated from cross section data, the error wouldget added up on a quadrature basis and be 9–11%.Therefore, the evaluations of the intensity ratios and theirerrors have been done by using Eq. (6). The errors in themeasured relative intensity values, evaluated using Eq. (6),are 5–7% Table (5) (Fig. 7).

It can be seen from Table (1), Fig. 4, Table (2), Fig. 5 andTable (3), Fig. 6, the measured fluorescence cross-sectionsfor production of Ki X-ray, oK fluorescence yields and IKb/IKa X-ray intensity ratios determined in this sutdy for someelements in the atomic range 22pZp68 are in agreementwith theoretical values calculated by using Eq. (1)(Figs. 8 and 9).

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