Nuclear Instruments and Methods in Physics Research B 267 (2009) 737–741

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Nuclear Instruments and Methods in Physics Research B

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Total bremsstrahlung spectral photon distributions in metallic targetsin the photon energy range of 5–10 keV by 204Tl beta particles

Tajinder Singh, K.S. Kahlon, A.S. Dhaliwal *

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

a r t i c l e i n f o a b s t r a c t

Article history:Received 11 November 2008Received in revised form 25 December 2008Available online 21 January 2009

PACS:34.50.Bw

Keywords:BremsstrahlungContinuous beta particles

0168-583X/$ - see front matter � 2009 Elsevier B.V.doi:10.1016/j.nimb.2009.01.009

* Corresponding author. Tel.: +91 1672 280123; faxE-mail address: asdhal@yahoo.com (A.S. Dhaliwal)

Total bremsstrahlung spectral photon distributions produced by beta particles of the 204Tl beta emitter inthick targets of Al, Ti, Sn and Pb targets were evaluated at photon energies from 5 keV to 10 keV. Exper-imental measurements were compared with the theoretical total bremsstrahlung spectral photon distri-butions obtained from Elwert corrected (non-relativistic) Bethe–Heitler theory and modified Elwertfactor (relativistic) Bethe–Heitler theories for ordinary bremsstrahlung, and the modified Elwert factor(relativistic) Bethe–Heitler theory which includes polarization bremsstrahlung in the stripped atomapproximation. The experimental results show better agreement with the modified Elwert factor (relativ-istic) Bethe–Heitler theory which includes the contribution of polarization bremsstrahlung. The contribu-tions of polarization bremsstrahlung decrease with increased photon energy, particularly for medium andhigh Z elements. Hence its contribution cannot be neglected while studying the total bremsstrahlungspectral photon distributions in thick targets, produced by continuous beta particles in the studiedenergy region.

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1. Introduction

The fundamental character of the ordinary bremsstrahlung (OB)process, in which a photon is emitted by an electron deceleratingin the static field of the target material, has been intensively stud-ied theoretically and experimentally over a wide range of the inci-dent electron and emitted photon energies [1–5]. In the OBprocess, the dynamic response of the target atom under the actionof the field created by the incident electron is neglected. Buimist-rov and Traktenberg [6] considered the target atom as a structuredobject that could be polarized by the incident electron and sug-gested a new kind of phenomenon, called polarization bremsstrah-lung (PB), in which the photon is emitted by the target atom as aresult of its polarization by incident electron. The total bremsstrah-lung (BS) amplitude is the sum of the OB and PB amplitudes.

Calculations of PB amplitude have been presented by severalauthors [7–9] in terms of an atomic dynamic polarizability. TheBorn approximation and the distorted partial wave approximation(DPWA) are used to calculate the PB. For non-relativistic electronenergies, in the Born approximation, Amusia et al. [10] has de-scribed that PB can be added with OB in a stripped approximation(SA). Korol et al. [11] and Avdonina and Pratt [12] have given theequivalent method for the total bremsstrahlung spectra in thestripped approximation, which is efficient for obtaining the BS

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spectra for photon energies greater than the ionization potentialof the outer shell electrons of the target atom. In SA, the decreaseof OB due to screening of outer shell electrons is completely com-pensated by additional PB produced by the same outer shell elec-trons. Therefore, the total bremsstrahlung is described simply byan ion containing the outer shell electrons. As the emitted photonenergy exceeds the ionization potential of the innermost shell (Kshell), bremsstrahlung occurs on the bare nucleus. The differencebetween the OB from an ion and the bremsstrahlung on a bare nu-cleus gives the contribution of PB in the BS spectra. The SA ap-proach neglects the specific structure of the bremsstrahlungcross section near each sub-shell threshold, where PB often be-comes large compared with OB. Avdonina and Pratt [12] modifiedthe Elwert corrected (non-relativistic) Bethe and Heitler [1] theoryfor OB and described the BS spectra i.e. (OB + PB) over a wide rangeof photon energies by applying the SA. They further described thatin the non-relativistic case PB decreases with increasing photonenergy in the same way as the screening contribution to OB, lead-ing to the Coulombic behavior of the spectrum. They also describedthat for relativistic electron energies, the contribution of PB to thesoft photon region of the bremsstrahlung spectra is larger than inthe non-relativistic case.

The theories discussed above are applicable to thin target OB orBS spectra only, in which the mono-energetic electron has only asingle radiative interaction. In the case of a thick target, processessuch as electron scattering, excitation and ionization that competewith bremsstrahlung must be taken into account. In this case an

738 T. Singh et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 737–741

electron loses a significant part of its energy while coming to restin the target. For continuous beta particles Bethe and Heitler [1]gave an expression for the bremsstrahlung spectral distributionnðk;W 0

e; ZÞ in a target sufficiently thick to absorb an electron of en-ergy W 0

e with N atoms per unit volume. At lower photon energiesin thick targets, the correction due to absorption of BS photons inthe target and electron backscattering from the target cannot beneglected. Semaan and Quarles [13] have reported that the correc-tion for self-absorption of BS photons in the target and electronbackscattering are required for nðW 0

e; k; ZÞ in the case of low energythick target bremsstrahlung. The BS spectral distribution½ncorðW 0

e; k; Z� after absorption correction and electron backscatter-ing correction in thick target is given by

ncorðW 0e; k; ZÞ ¼ RN

Z W 0e

1þk

drðWe; k; ZÞ=dkð�dWe=dxÞ dWe � expð�lxÞ: ð1Þ

Here �dWe/dx is the total energy loss per unit path length of anelectron in a target material taken from the tabulations given byBerger and Seltzer [14]. The term exp(�lx) is the absorption factor,l is the mass attenuation coefficient for the given target element ta-ken from the tabulations given by Chantler et al. [15], x is the opti-mum thickness of the target which is equal to the range of the betaparticle in a target and R is the electron backscattering factor

R ¼ 1� gðWe; ZÞ1� gðWe; ZÞ k2

W2e

: ð2Þ

Here We = 0.4Wmax, Wmax is the end point energy of beta particlesand g(We,Z) is the total backscattering factor. The BS spectral distri-bution in a thick target obtained on complete absorption of betaparticles of an end point energy Wmax is expressed as the numberof photons of energy k per unit moc2 per beta disintegration for con-tinuous beta particle distribution given by S(k,Z)

Sðk; ZÞ ¼Z Wmax

1þkncorðW 0

e; k; ZÞPðW0eÞdW 0

e: ð3Þ

Here PðW 0eÞdW 0

e is the beta spectrum of the source under study. Inthe present measurements, the experimental beta spectrum of Parkand Christman [16] was used.

The BS photon yield T for the target, with kmin and kmax as thelower and upper limit of photon energy of the BS spectrum, respec-tively, is given by

T ¼Z kmax

kmin

Sðk; ZÞdk: ð4Þ

While there are a variety of calculations of PB are available in theliterature and experimental results for mono-energetic electrons,there are very few measurements [17–19] to check the existenceof PB in the BS spectra. For continuous beta particles, no measure-ment is reported so far to check these theories which describesthe OB and BS spectra i.e. (OB + PB) in the soft photon energy region.So there is need to study the BS spectra produced by continuousbeta particles in thick targets using a high resolution Si(Li) detectorto check the contributions of PB, particularly at photon energies of5–10 keV with better understanding of the background and thedetector response. The aim of the present measurements is to dem-onstrate the polarization mechanism in the formation of the BSspectra produced by 204Tl beta particles in a metallic target in thisphoton energy region.

204Tl (DJ = 2, yes) is a unique first order forbidden beta emitterwith a half life of 3.77 yrs and a beta end point energy of 765 keV. A204Tl beta source emits a beam of continuous beta particles withenergies from 0 to 765 keV. Absorption of these particles in the tar-get material produces BS photons having energies ranging from 0to 765 keV. The OB spectra generated by complete absorption of

beta particles produced by 204Tl, in thick targets have been re-ported by various workers for different target element at higherphoton energies from 100 keV onwards [20,21]. They comparetheir results with Elwert [2] corrected (non-relativistic) Bethe–Hei-tler theory (EBH) and Tseng and Pratt [4] theories which describesOB only. The present measurements were designed to compare theBS spectral distribution from thick target of Al, Ti, Sn and Pb, pro-duced by beta particles of 204Tl in the photon energy region 5–10 keV, with the theoretical bremsstrahlung distribution obtainedfrom EBH theory, modified Elwert factor (relativistic) Bethe–Hei-tler theory (Fmod BH) which only describes OB and modified Elwertfactor (relativistic) Bethe–Heitler theory (Fmod BH + PB) which de-scribes the total bremsstrahlung i.e. (OB + PB) in SA.

The present measurements were taken with a high resolutionX-PIPS Si (Li) detector (Canberra) which is sensitive to ionizingradiation, particularly X-rays and low energy gamma rays. Thedetector is more suitable for the study of BS spectra owing to itshigh efficiency and high resolution.

For various theories, the BS spectral photon distributions in theforms of number of photons of energy k per moc2 per beta disinte-gration i.e. S(k,Z) were obtained by developing computer codesusing Eqs. (1) and (3). A graphical integration method was usedfor calculating the values of the total photon yield T for all targetsfrom the plots of S(k,Z) versus photon energy k between photonenergies of 5–10 keV. To remove uncertainties in the sourcestrength measurement and the inadequacy of the normalizationprocedure, the experimental and theoretical results were con-verted into the form of number of photons of energy k per moc2

per unit total photon yield. Fig. 4 shows the comparison of theexperimental and the theoretical BS spectral photon distributionsfor Al, Ti, Sn and Pb targets in the forms of the number of photonsof energy k per unit moc2 per unit of total photon yield i.e. S(k,Z)/Tversus photon energy. These results are reported for first time witha high resolution X-PIPS Si (Li) detector for the continuous betaparticles in the photon energy region of 5–10 keV and are expectedto be useful for studies of BS spectral photon distributions inmetallic targets.

2. Experimental details

A beta source of 204Tl having activity 500 lCi was used for thepresent measurements. The experimental arrangement is givenin Fig. 1. A high resolution X-PIPS Si(Li) detector shielded with leadbricks was used to measure the BS spectral photon distributions inAl, Ti, Sn and Pb targets. This detector has a silicon wafer of thick-ness 500 lm, a Be window of thickness 25 lm, Preamplifier, HVbias supply, Peltier cooler and Temperature controller system. Acollimator of width 1.1 mm is embedded in the detector. Its intrin-sic efficiency varies from 100% to 97% at 5 keV and 10 keV photonenergies, respectively. Its resolution is <190 eV FWHM at a 5.9 keVphoton energy. In order to protect the detector from scattered pho-tons and limit the background to a low level, lead bricks lined withaluminum foil were used for shielding. Photo-fractions i.e. the ratioof the count rate under full-energy peak to the total count rate un-der the pulse height spectrum, were calculated at different ener-gies by using a gamma ray source of 133Ba and the X-rays peaksof Ti, Cu and Mo elements for determining the geometrical full-en-ergy peak detection efficiency of the detector and for calibrating it.

To obtain the correct information for the BS produced in the tar-get material, a Perspex beta stopper method was employed foreliminating the contribution of internal bremsstrahlung (IB), BSgenerated in the source material and room background. Targetsof Al (293 mg cm�2), Ti (288 mg cm�2), Sn (281 mg cm�2) and Pb(286 mg cm�2) having diameters 4 cm each were used. It was ver-ified that the detector was fully exposed to the surface of the target

A

B 1

2

3

4

8

6

5

7

7mm

2.5mm 0.3mm

3mm

9 13.9mm

51.4mm 40 mm

18.5mm

115 mm 56 mm

Fig. 1. Experimental setup: (1) source holder; (2) perspex stand; (3) perspex betastopper; (4) X-PIPS Si(Li) detector; (5) Be window; (6) collimator; (7) Si(Li) chip; (8)shielding lead bricks; (9) standard working axis; (A) position of the target on thePerspex beta stopper; (B) position of the target below the Perspex beta stopper.

5 6 7 8 9 104x103

5x103

6x103

7x103

8x103

9x103

1x104

1x104

Num

ber o

f cou

nts

Photon energy (keV)

B

A

204Tl

Lead

Fig. 2. Typical plots of number of counts versus photon energy (k) for a lead targetat position A and B for beta particles in the photon energy range of 5–10 keV.

5 6 7 8 9 10105

1015

1x1025

1035

1x1045

1x1055

1x1065

1x1075

1x1085

1x1095

Experimental Data204Tl

No. o

f pho

tons

of e

nerg

y k

per u

nit m

oc2

Photon energy (keV)

ALUMINUM TITANIUM TIN LEAD

Fig. 3. Plots of experimental BS spectral photon distributions in terms of number ofphotons of energy k per moc2 versus photon energy (k) for 204Tl beta particles.

T. Singh et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 737–741 739

in order to gather maximum BS photons emitted from the targetmaterial. The collimated beta source was placed on a Perspex standat a distance of 1.6 cm from the face of the detector (Fig. 1). Aftercalibrating the spectrometer, two sets of measurements were ta-ken over a time interval of 200,000 s each to improve the data sta-tistics. In the first measurement the target was placed on thePerspex beta stopper at position A (Fig. 1). This measurement in-cluded the contribution of BS (target), IB, BS generated in thesource material and room background, attenuated in the targetand the Perspex beta stopper (thickness of 325 mg cm�2). For thesecond measurement, the target was placed below the Perspexbeta stopper at position B, so that the beta particles did not reachit. This measurement recorded the contribution of IB, BS generatedin the source material, BS generated in the Perspex stopper androom background. The difference of the above two measurementsgives the information only about the BS produced in target ele-ments. Typical measurements for a Pb target taken at positions Aand B are shown in Fig. 2. The BS produced in the Perspex(Z = 4.6) is small and is also incorporated in the measurement.The statistical accuracy of the data was better than 1% for all thetargets in the photon energy region of 5–10 keV. Reproducibilityof the data and any peak shift due to electronic shift were checkedby taking the intermediate measurements. The BS spectral distri-butions for Al, Ti, Sn and Pb target materials were obtained forcomparison with various theoretical results.

3. Corrections to BS spectral photon distributions

The experimentally measured BS spectra for Al, Ti, Sn and Pbtargets were converted into true spectra by applying the correc-

tions due to absorption of BS in the target, electron backscatteringand detector efficiency. The BS spectra were converted into a com-mon channel width of 0.5 keV. Absorption of BS in air, target thick-ness and the Perspex beta stopper was incorporated by using the

5 6 99 10

1x10-70

1x10-60

1x10-50

10-40

10-30

1x10-20

1x10-10

1x100

204Tl Tin

No. o

f pho

tons

of e

nerg

y k

per m

oc2 p

er u

nit t

otal

pho

ton

yiel

d

Photon Energy k (keV)

32

5 6 7 8 9 1010-20

10-18

1x10-16

1x10-14

1x10-12

1x10-10

1x10-8

1x10-6

1x10-4

1x10-2

1x100204Tl

32

1

AluminumNo

. of p

hoto

ns o

f ene

rgy

k pe

r moc2 p

er u

nit t

otal

pho

ton

yiel

d

Photon Energy k (keV)

1 F modBH+PB 2 EBH 3 F modBH

EXPERIMENTAL POINTS

87

a

c

5 6 7 8 9 10

1x10-70

1x10-60

1x10-50

10-40

10-30

1x10-20

1x10-10

1x100

3

2

1

Lead204Tl

No. o

f pho

tons

of e

nerg

y k

per m

oc2 p

er u

nit t

otal

pho

ton

yiel

d

Photon Energy k (keV)

1 FmodBH+PB 2 FmodBH 3 EBH

EXPERIMENTAL POINTS

5 6 7 8 9 10

1x10-60

1x10-50

10-40

10-30

1x10-20

1x10-10

1x100

3

21

204TlTitanium

No. o

f pho

tons

of e

nerg

y k

per m

oc2 per

uni

t tot

al p

hoto

n yi

eld

Photon Energy k (keV)

1 FmodBH+PB 2 FmodBH 3 EBH

EXPERIMENTAL POINTS

d

b

1

1 F modBH+PB

3 EBH 2 F modBH

EXPERIMENTAL POINTS

Fig. 4. (a–d) Plots of number of photons of energy k per moc2 per unit total photon yield [S(k,Z)/T] versus photon energy k (keV) for Al, Ti, Sn and Pb targets for 204Tl betaparticles.

740 T. Singh et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 737–741

mass attenuation coefficients recently tabulated by Chantler et al.[15]. The contribution of the electron backscattering factor R wasincorporated in the measured BS spectral distributions using thevalues of g(We,Z), given by August and Wernich [22]. The intrinsicefficiency I(k) of the X-PIPS detector and photo-fraction f(k) valuesat different photon energies were used to determine the geometri-cal full-energy peak detector efficiency for the detector. The mea-sured experimental BS spectra were then divided by thegeometrical full-energy peak detector efficiency for the detectorfor obtaining the true spectra and then reduced to the number ofphotons of energy k per unit moc2. In order to remove the uncer-tainties associated in the measurement of the source strength

and removing the inadequacy of the normalization procedure forcomparison of theoretical and experimental results, the correctedexperimental BS spectra were converted into the number of pho-tons per unit moc2 per unit of total photon yield by dividing themby the values of the total photon yields in the target materials. Theexperimental results are shown in Fig. 3.

4. Errors

The present measurement of BS spectra contain errors due tothe counting statistics, full-energy detection efficiency of thedetector, electron backscattering and attenuation of BS photons

T. Singh et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 737–741 741

in the target materials. The statistical accuracy of the data was bet-ter than 1% recording the measurements over a time interval of200,000 s. The uncertainty in the values of the photo-fraction were1–2%, so the uncertainty in the geometrical full-energy peak detec-tor efficiency was found to be less than 3%. The mass attenuationcoefficients used in the correction of self-absorption of photonsin air, target thickness and Perspex beta stopper were uncertainby 1%, except in the near-edge regions where uncertainties werehigher, as reported in the tabulations by Chantler et al. [15]. Theuncertainties in the values of the electron backscattering factor Rwere less than 1%. The overall uncertainties in the present mea-surement were estimated to be less than 10% in the entire photonenergy range of interest. In case of a Ti target, the uncertainties areup to 15% near the edge region at photon energy 5 keV.

5. Results and discussions

The results of experimentally measured BS spectra were com-pared with the theoretical BS spectral distributions obtained fromEBH theory, Fmod BH theory without the contribution of polariza-tion bremsstrahlung and Fmod BH with the polarization brems-strahlung (Fmod BH + PB). The plots of number of photons ofenergy k per moc2 per unit total photon yield for Al, Ti, Sn and Pbtargets are shown in Fig. 4.

It is clear that the experimental BS spectral distributions are inagreement with the theoretical BS spectral distributions obtainedfrom Fmod BH + PB theory, which include PB into OB within 10%.The experimental results show deviations from the theoreticalOB spectral distributions obtained from EBH theory and Fmod BHtheory for all the target elements. These deviations vary from15% to 20% for Al and Ti targets and in case of Sn and Pb targetsthese deviations vary from 40% to 20% at photon energies of 5–10 keV, respectively. From the theories, it is clear that the contribu-tions of PB into OB vary from 10% to 20% for Al and Ti targets in thephoton energy region of 5–10 keV. In the case of Sn and Pb targets,the variations in the contributions are higher i.e. 20–13%, decreas-ing with photon energy.

It is concluded that for the target elements Al, Ti, Sn and Pb, Fmod

BH + PB theory, which includes PB into OB in the stripped atom

approximation is more accurate than the others theories fordescribing the BS spectra in the studied photon energy range. Thisindicates that the contribution of PB in the BS spectra cannot be ne-glected as the experimental results are in agreement with the BStheory having the contribution of PB into OB. Furthermore, thecontribution of PB decreases with photon energy, particularly formedium and high Z elements. Extensive studies are required tocheck the contribution of PB into OB in the BS spectra at differentphoton energy regions to test these theories.

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