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Research ArticleReceived: 19 August 2009 Revised: 13 May 2010 Accepted: 31 May 2010 Published online in Wiley Interscience: 13 June 2010

(www.interscience.com) DOI 10.1002/xrs.1264

Total bremsstrahlung spectra in targets of Al,Ti, Sn and Pb produced by complete absorptionof 90Sr β particlesTajinder Singh, K. S. Kahlon and A. S. Dhaliwal∗

Total bremsstrahlung (BS) spectra in thick targets of Al, Ti, Sn and Pb produced by complete absorption of 90Sr β particles(0–546 keV) are reported in the photon energy region of 10–30 keV. The experimental BS spectral photon distributions werecompared with the theoretical BS spectral photon distributions obtained from Elwert corrected (non-relativistic) Bethe–Heitlertheory, modified Elwert factor (relativistic) Bethe–Heitler theories for ordinary bremsstrahlung (OB) and the modified Elwertfactor (relativistic) Bethe–Heitler theory, which include the polarization bremsstrahlung (PB) into OB in stripped atomapproximation. It has been observed that the experimental results are showing better agreement with the modified Elwertfactor (relativistic) Bethe–Heitler theory having the contribution of PB at photon energy from 10 to 30 keV. This indicates theimportance of PB in BS spectra, while studying the spectral photon distributions produced by continuous β particles havingenergy range of 0–546 keV in thick metallic targets. Further, it is observed that the contribution of PB into OB increases withincrease in atomic number of the target and decreases with increase in photon energy. Copyright c© 2010 John Wiley & Sons,Ltd.

Introduction

The total bremsstrahlung (BS) amplitude is the sum of ordinarybremsstrahlung (OB) and polarization bremsstrahlung (PB) ampli-tudes. In OB, photon emission occurs due to the interaction ofelectron with static field of the target, while in PB, the photon isemitted by the target as a result of its polarization by incidentelectron. The OB in thin and thick targets has been describedby various theoretical models.[1 – 4] The BS spectrum is also de-scribed by several authors[5 – 8] by incorporating contribution ofPB into OB. Amusia et al.[9] has shown that PB can be addedto OB by applying stripped atom approximation (SAA). In SAA,the decrease in OB due to screening of outer shell electrons iscompletely compensated by additional PB produced by the sameouter shell electrons. Therefore, the BS is described simply by anion containing the outer shell electrons. As the emitted photonenergy exceeds the ionization potential of the inner most shell(1s), the bremsstrahlung occurs on the bare nucleus. The differ-ence between the OB from an ion and the bremsstrahlung on barenucleus gives the contribution of PB in the BS spectra. Avdon-ina and Pratt[10] modified the Elwert corrected (non-relativistic)Bethe and Heitler[1] theory for OB and described the BS spectra byapplying SAA.

In our earlier communication,[11] the results for BS spectrain thick targets of Al, Ti, Sn and Pb produced by completeabsorption of 204Tl β particles having end-point energy of 765 keVwere reported in the photon energy range of 10–30 keV. Theexperimental results were showing better agreement with themodified Elwert factor (relativistic) Bethe and Heitler theory[1]

having the contribution of PB at these energy regions. Thisindicated the importance of PB in the BS spectra produced bycontinuous β particles in thick target materials. Further studieson BS spectra in thick targets, in the photon energy region of10–30 keV produced by continuous β particles having differentenergy range, are required for checking the importance of PB in

the BS spectra and accuracy of various theories for BS. In thisstudy, efforts are made to study the BS spectra in thick targetsof Al, Ti, Sn and Pb produced by complete absorption of 90Srβ particles having end-point energy of 546 keV. 90Sr β sourceemits beam of continuous β particles whose energy spreads over0–546 keV.

For monoenergetic electron, few studies[12 – 14] are available forchecking the contribution of PB in the BS spectra. However, forcontinuous β particles of 90Sr, no measurement is reported sofar in the literature to check the theories that describe OB andBS spectra in the studied photon energy region of 10–30 keV.Various workers[15,16] have studied the OB spectra producedby complete absorption of continuous β particles of 90Sr fordifferent target elements at higher photon energies from 50 keVonwards and have compared their results with the theoreticalmodels that describe OB only. The present measurements weredesigned to compare BS spectra obtained from the completeabsorption of continuous β particles of 90Sr in thick targetsof Al, Ti, Sn and Pb with the theoretical BS spectra fromElwert corrected (non-relativistic) Bethe–Heitler theory (EBH),modified Elwert factor (relativistic) Bethe–Heitler theory (Fmod

BH) that describes OB and modified Elwert factor (relativistic)Bethe–Heitler theory (Fmod BH + PB) that describes the BS spectrain SAA.

The BS theories are applicable to the thin target BS spectraonly, in which the monoenergetic electron has only a singleradiative interaction. In the case of thick target, processes suchas electron scattering, excitation and ionization competing with

∗ Correspondence to: A. S. Dhaliwal, Department of Physics, Sant LongowalInstitute of Engineering and Technology, Longowal, Sangrur, Punjab 148106, India. E-mail: asdhal@yahoo.com

Department of Physics, Sant Longowal Institute of Engineering and Technology,Longowal, Sangrur, Punjab 148 106, India

X-Ray Spectrom. 2010, 39, 291–295 Copyright c© 2010 John Wiley & Sons, Ltd.

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T. Singh, K. S. Kahlon and A. S. Dhaliwal

bremsstrahlung are required to be taken into account. At mostcare is required to be taken while applying the self-absorptioncorrection to BS spectra. For continuous β particles, Bethe andHeitler[1] gave an expression for the bremsstrahlung spectraldistribution n(k, W ′

e, Z) in a sufficiently thick target to absorb anelectron of energy W ′

e with N atoms per unit volume. In case oflow-energy thick target bremsstrahlung, the correction for the self-absorption of BS photons in the target and electron backscatteringare also required for n(W ′

e, k, Z).[17] After absorption correction andelectron backscattering correction in thick target, the BS spectraldistribution [ncor(W ′

e, k, Z)] is given by

ncor(W ′e, k, Z) = RN

W′e∫

1+k

dσ (We, k, Z)/dk

(−dWe/dx)dWe × exp(−µx) (1)

where dσ (We, k, Z)/dk is the singly differential cross-section takenfrom different theoretical model.[1,2,10] Here −dWe/dx is the totalenergy loss per unit path length of an electron in a target materialtaken from the tabulations given by Berger and Seltzer,[18] Inabsorption factor exp(−µx), µ is the mass attenuation coefficientfor the given target element taken from the tabulations given byChantler et al.[19] and x is the optimum thickness of the target,which is equal to the range of the β particle in a target. R is theelectron backscattering factor.[17]

The BS spectral distribution in a thick target obtained oncomplete absorption of β particles of an end-point energyWmax is expressed as number of photons of energy k per unitm0c2 per β disintegration for continuous β particle is given byS(k, Z)

S(k, Z) =Wmax∫

1+k

ncor(W ′e, k, Z)P(W ′

e)dW ′e (2)

Here, P(W ′e)dW ′

e is the β spectrum of the β source under study. Inthe present measurement, the experimental β spectrum of a 90Srgiven by Laslett et al.[20] was used.

The BS photon yield T for the target, with kmin and kmax asthe lower and upper limits of photon energy of the BS spectrum,respectively, is given by

T =kmax∫

kmin

S(k, Z)dk (3)

Computer programs are developed to calculate the BS spectraldistribution S(K , Z) and BS photon yield ‘T ’ for the targetusing Eqn (1)–(3). The experimental and theoretical results werecompared in terms of the number of photons of energy k per m0c2

per unit total photon yield. Plots of S(k, Z)/T , i.e. the number ofphotons of energy k per unit m0c2 per unit of total photon yieldversus photon energy k, were obtained for Al, Ti, Sn and Pb targetsand were compared with the experimentally measured BS spectraldistributions.

Experimental Details

A β source of 90Sr β emitter having activity 5 µCi was usedfor the present measurements. The experimental arrangement isgiven in Fig. 1. The detail of experimental arrangement is givenelsewhere.[11,21] A high-resolution X-PIPS (Canberra make) Si (Li)

A

B1

2

3

4

8

6

5

7

7 mm

2.5 mm0.3 mm

3 mm

913.9 mm51.4 mm

40 mm18.5 mm

115 mm56 mm

Figure 1. Experimental setup: 1, source holder; 2, perspex stand; 3, perspexβ stopper 4, X-PIPS Si (Li) detector; 5, Be windows; 6, collimator; 7, Si (Li)chip; 8, shielding lead bricks; 9, standard working axis; A, position of thetarget on the Perspex β stopper; B, position of the target below the Perspexβ stopper.

detector was used to measure the BS spectral photon distributionsin Al, Ti, Sn and Pb targets produced by 90Sr β particles in thephoton energy region of 10–30 keV. The X-PIPS detector has apeltier cooler and temperature controller system. The resolutionof the detector is <190 eV (FWHM) at 5.9 keV photon energy. Inorder to limit the background to a low level, the lead bricks linedwith aluminium foil were used for shielding the detector. In orderto determine the geometrical full-energy peak detection efficiencyof the detector and for calibration of the detector, a γ ray sourceof 133Ba and the secondary X-ray peaks of Cu, Mo and Sn materialswere used.

To determine the BS produced in the target material, a Perspex β

stopper technique was employed for eliminating the contributionof internal bremsstrahlung (IB),[22] BS generated in the sourcematerial and room background. Targets of Al (198.6 mg cm−2),Ti (223 mg cm−2), Sn (194.3 mg cm−2) and Pb (203.6 mg cm−2)were used in the present measurements. After calibrating thespectrometer, two sets of measurements were taken for a timeinterval of 200 000 s each to improve the statistics of data. Inthe first measurement, the target was placed on the Perspex β

stopper at position A (Fig. 1). This measurement included thecontribution of BS (target), IB, BS generated in the source materialand room background and attenuated in the target and thePerspex β stopper. For the second measurement, at positionB, the target was placed below the Perspex β stopper, so thatthe β particle could not reach it. This measurement recorded

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BS spectra in targets of Al, Ti, Sn and Pb

10 15 20 25 30

105

106

107

108

109

1010

1011

1012

1013

1014

1015

1016

1017

1018N

um

ber

of

Ph

oto

ns

of

ener

gy

k p

er m

oc2

Photon Energy (keV)

AluminumTitaniumTinLead

90Sr

Figure 2. Plots of experimental BS spectral distributions in terms of numberof photons of energy k per m0c2 versus photon energy (k) for 90Sr β particles(end-point energy = 546 keV).

the contribution of IB, BS generated in the source material, BSgenerated in the Perspex stopper and room background. Thedifference of the above two measurements gives the informationabout the BS produced in target elements only. The BS producedin the Perspex (Z = 4.6) is small and is also incorporated in themeasurement. Statistical accuracy of the data was more than 1%for all the targets in the photon energy region of 10–30 keV.These measurements were taken with the targets of Al, Ti,Sn and Pb for obtaining the spectral photon BS distributionsproduced by complete absorption of continuous β particles of90Sr.

Corrections to BS Spectra

In order to convert the experimentally measured BS spectra forAl, Ti, Sn and Pb targets into a true spectrum, the corrections dueto absorption of BS into the target, electron backscattering anddetector efficiency were applied. The BS spectra are convertedinto a common channel width of 0.5 keV. The correction dueto absorption of BS in air, target thickness and the Perspex β

stopper was incorporated using the mass attenuation coefficientsrecently tabulated by Chantler et al.[19] The contribution of electronbackscattering factor R was also incorporated in the measured BSspectral distributions. The geometrical full-energy peak detectorefficiency for the detector is determined using the values ofthe intrinsic efficiency I(k) of the X-PIPS detector and photo-fraction f (k) values at different photon energies. The measuredexperimental BS spectra were than divided by the geometricalfull-energy peak detector efficiency for the detector and werereduced to the number of photons of energy k per unit m0c2.Finally, the corrected experimental BS spectra were convertedinto the number of photons of energy k per unit m0c2 per unit

of total photon yield by dividing them by the values of the totalphoton yields in the target materials. The experimental resultsfor Al, Ti, Sn and Pb targets for 90Sr β particles are shown inFig. 2.

Errors

The uncertainties in the present measurement of BS spectraldistributions are mainly due to the counting statistics, full-energydetection efficiency of the detector, electron backscattering andattenuation of BS photons in the target materials. Statisticalaccuracy of the data was more than 1% in the entire studiedphoton energy region of 10–30 keV. The values of photo-fractionwere uncertain by 1–2% which resulted in an overall uncertaintyof less than 3% in the geometrical full-energy peak detectorefficiency. The uncertainty in the mass attenuation coefficientsused in the correction of self-absorption of photon in air, targetthickness and Perspex β stopper was not more than 1%, exceptin the near-edge regions where uncertainties were higher asreported in the tabulations by Chantler et al.[19] The values ofthe electron backscattering factor R were uncertain by less than1%. The overall uncertainties in the present measurement wereestimated to be less than 10% in the entire studied photon energyregion of 10–30 keV.

Results and Discussions

The results of experimentally measured BS spectra for the targetsof Al, Ti, Sn and Pb produced by 90Sr β particles were comparedwith the theoretical BS spectral photon distributions obtainedfrom EBH, FmodBH that describes OB and FmodBH + PB withthe PB in the photon energy region of 10–30 keV. The plotsof number of photons of energy k per m0c2 per unit totalphoton yield for Al, Ti, Sn and Pb targets are shown in theFig. 3a–d.

It is observed from the plots that the experimental resultsare showing better agreement with the theoretical BS spectraobtained from FmodBH + PB theory that includes PB into OB inthe SAA within 10% at photon energy from 10 to 30 keV. Theexperimental results are showing deviation from EBH and FmodBHtheories describing OB only. These deviations are found to bevarying from 10 to 23% at 20 and 30 keV photon energy for Ti,Sn and Pb targets, respectively, from EBH and FmodBH theory.However, these deviations are found to be less than 15% in thecase of Al target throughout the studied photon energy region of10–30 keV.

It is concluded that for the target elements Al, Ti, Sn and Pb,FmodBH + PB theory that describes PB into OB is more accurate fordescribing the BS spectra in the studied photon energy region of10–30 keV. These results further strengthen our earlier results[11]

regarding the importance of PB in BS spectra distributions in thicktargets and clearly shows that the contribution of PB cannot beneglected in BS spectra, while studying the BS spectral photondistribution in thick metallic targets, in the studied photon energyregion of 10–30 keV, whenβ particles of energies from 0 to 546 keVcoming from 90Sr β emitter are used. Further, it is observed thatthe contribution of PB into OB increases with increase in atomicnumber of the target and decreases with increase in photonenergy.

X-Ray Spectrom. 2010, 39, 291–295 Copyright c© 2010 John Wiley & Sons, Ltd. www.interscience.com/journal/xrs

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T. Singh, K. S. Kahlon and A. S. Dhaliwal

10 20 30

10-3

10-2

10-1

100

(a) 90Sr

No

. of

ph

oto

ns

of

ener

gy

k p

er m

oc2

per

un

it t

ota

l ph

oto

n y

ield

Photon Energy (keV)

1

2

3

Experimental Points

Aluminum

1

23

10 20 3010-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

(b)

Titanium90Sr

32

1

No

. of

ph

oto

ns

of

ener

gy

k p

er m

oc2

per

un

it t

ota

l ph

oto

n y

ield

Photon Energy (keV)

FmodBH+PB

FmodBH

EBH

Experimental Points

10 20 3010-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

32

1

(c)Tin90Sr

No

. of

ph

oto

ns

of

ener

gy

k p

er m

oc2

per

un

it t

ota

l ph

oto

n y

ield

Photon Energy (keV)

FmodBH+PBFmodBHEBHExperimental Points

10 20 3010-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

32

1

(d)Lead90Sr

No

. of

ph

oto

ns

of

ener

gy

k p

er m

oc2

per

un

it t

ota

l ph

oto

n y

ield

Photon Energy (keV)

1

2

3

Experimental Points

FmodBH+PB

FmodBH

EBH

1

2

3

123

FmodBH+PB

FmodBH

EBH

Figure 3. (a–d) Plots of number of BS photons of energy k per m0c2 per unit total photon yield [S(k, Z)/T] versus photon energy k (keV) for Al, Ti, Sn andPb targets for 90Sr β particles (errors are lying within the experimental points).

References[1] H. Bethe, W. Hietler, Proc. R Soc. Lond. A 1934, 14, 83.[2] G. Elewert, Ann. Phys. 1939, 34, 178.[3] H. W. Kotch, J. H. Motz, Rev. Mod. Phys. 1959, 31, 920.[4] H. K. Tseng, R. H. Pratt, Phys Rev. A 1971, 3, 100.[5] V. Buimistrov, L. Trakhtenberg, Sov. Phys. JETP 1975, 42, 54.[6] M. Ya. Amusia, A. V. Korol, J. Phys. B: At. Mol. Opt. Phys. 1991, 24,

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and Atoms, Plennum Press: New York, 1992.[8] A. V. Korol, O. I. Obolensky, A. V. Solov’yov, J. Phys. B: At. Mol. Opt.

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[11] Tajinder Singh, K. S. Kahlon, A. S. Dhaliwal, J. Phys. B: At. Mol. Opt.Phys. 2008, 41, 235001.

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[13] Sal Portillo, C.A. Quarles, Phys. Rev. Lett. 2003, 91, 17.[14] S. Williums, K. Hayton, C.A. Quarles, Nucl. Instr. Meth. B 2007, 261,

184.[15] T. S. Mudhole, J. Phys. A: Math. Nucl. Gen 1973, 6, 533.[16] S. I. Shivaramu, Phys. Rev. A 1984, 30, 3066.[17] M. Semaan, C. A. Quarles, X-Ray Spectrom. 2001, 30, 37.[18] M. J. Berger, S. M. Seltzer, NASA SP 3012, 1964, Current

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[19] C. T. Chantler, K. Olsen, R. A. Dragoset, J. Chang, A. R. Kishore,S. A. Kotochigova, D. S. Zucker, X-Ray Form Factor, Attenuation and

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Scattering Tables (Version 2.1), 2005, National Institute of Standardsand Technology, Gaithersburg, MD, http://Physics.nist.gov./ffast[accessed June 2008].

[20] J. L. Laslett, E. N. Jensen, A. Paskin, Phys. Rev. 1950, 79, 412.

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[22] A. S. Dhaliwal, M. S. Powar, M. Singh, J. Phys. G: Nucl. Part. Phys. 1994,20, 135.

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