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European	Journal	of	Chemistry	5	(2)	(2014)	363‐369	

	

European	Journal	of	Chemistry	
ISSN	2153‐2249	(Print)	/	ISSN	2153‐2257	(Online)		2014	Eurjchem	Publishing	‐	Printed	in	the	USA	

http://dx.doi.org/10.5155/eurjchem.5.2.363‐369.1016	

	
	

	

	

European	Journal	of	Chemistry	
Journal	homepage:	www.eurjchem.com	

	 	 	

M	sub‐shell	X‐ray	fluorescence	cross‐section	measurements	in	high	Z	elements	
with	X‐ray	tube	photon	source	

Sheenu	Gupta,	Gurpreet	Kaur,	Himani	Bansal,	Vijay	Kumar	Mittal,	and	Raj	Mittal	*	

Nuclear	Science	Laboratories,	Physics	Department,	Punjabi	University,	Patiala‐147002,	India	

*Corresponding	author	at:	Nuclear	Science	Laboratories,	Physics	Department,	Punjabi	University,	Patiala‐147002,	India.		
Tel.:	+91.941.7284302.	Fax:	+91.175.3046163.	E‐mail	address:	rmsingla@yahoo.com	(R.	Mittal).	

	
	

	 	

	 	 	
ARTICLE	INFORMATION	 	 ABSTRACT	

	
DOI:	10.5155/eurjchem.5.2.363‐369.1016	

Received:	16	January	2014	
Received	in	revised	form:	27	February	2014	
Accepted:	28	February	2014	
Online:	30	June	2014	

KEYWORDS	

	 X‐ray	tube	has	been	used	for	selective	M	sub‐shell	excitations	in	a	single	reflection	set‐up	for
Pt,	 Au,	 Pb,	 Th	 and	 U	 required	 for	 M	 sub‐shell	 fluorescence	 cross‐sections	 measurements.
Weighted	photon	energy	and	 total	 intensity	 of	 the	 incident	 flux	 between	EM5	 edge	and	 tube
anode	voltage	were	evaluated	following	a	specific	procedure.	Comparison	of	measured	cross‐
sections	 with	 the	 calculated	 ones	 from	 existing	 DHS/DF	 model	 based	 theoretical	 data	 on
atomic	parameters	lend	support	to	the	present	findings.	

M	sub‐shell	X‐rays	
Selective	excitation	
Bremsstrahlung	X‐rays	
Variable	energy	photons	
X‐ray	tube	photon	source	
X‐ray	fluorescence	cross‐section	

	
1.	Introduction	
	

In	 X‐ray	 fluorescence	 (XRF)	 studies,	 the	 probabilities	 of	
photon	 induced	 X‐ray	 emission/production	 known	 as	 X‐ray	
fluorescence	 cross‐section	 (σ*)	 is	 an	 important	 most	 sought	
parameter.	 It	 is	 a	 composite	 parameter	 as	 product	 of	 photo	
ionization	 cross‐section	 (I),	 fluorescence	 yield	 ()	 and	
fractional	 radiative	 decay	 rates	 (F).	 The	 applications	 of	 low	
energy	 fluorescent	 X‐rays	 in	 various	 fields	 such	 as	 material	
science,	 forensic	 science,	 dosimetric	 computation,	 elemental	
analysis	 and	 nuclear,	 atomic	 and	molecular	 physics	 etc.	 have	
raised	 the	 importance	 of	 data	 on	 L	 and	 M	 shell	 X‐ray	
fluorescence	 cross	 sections.	The	experimental	data	 for	K‐shell	
cross‐sections	as	compared	to	 that	of	L	and	M	shells	 is	almost	
well	 established	while	 it	 is	 scanty	 for	M	and	higher	 shells	but	
moderate	 for	 L	 X‐ray	 fluorescence	 cross‐sections	 [1].	 The	
scantiness	 of	 data	 on	 M	 X‐ray	 cross‐section	 is	 because	 of	 M	
shell	 structural	 complexities	 as	 it	 consists	 of	 five	 sub‐shells.	
There	are	a	number	of	intra‐shell	Coster‐Kronig	/	Super	Coster‐
Kronig	transitions	leading	to	modification	of	initial	M	sub‐shell	
vacancy	 distribution	 from	 excitations.	 The	 interaction	 of	
photons	 of	 energies	 <10	 keV	with	 elements,	 Z	 ≥	 70,	 involves	
only	 M	 and	 higher	 shell	 electrons	 and	 it	 has	 raised	 the	
importance	 of	 M	 X‐ray	 productions	 in	 low	 energy	 range.	
Moreover,	to	check	the	fine	details	of	the	atomic	structure,	data	

on	XRF	cross‐sections	for	individual	M	X‐ray	line/group	of	lines	
would	play	a	dominant	role.	

In	 the	 context	 of	 fluorescent	 X‐ray	 measurements,	 the	
dependence	 of	 X‐ray	 emission	 probability	 on	 incident	 photon	
energy	 requires	 the	 pre‐hand	 knowledge	 of	 incident	 photon	
energies	 hence	 the	 photon	 sources.	 The	 widely	 used	 photon	
sources	are	radioactive	sources	in	single/double	reflection	set‐
up,	 X‐ray	 tubes	 in	 double	 reflection	 set‐up	 and	 synchrotron	
sources.	The	use	of	 radioactive	sources	 in	single	reflection	[2‐
11]	and	double	reflection	set	up	[12‐13]	imposes	limitations	on	
energies	 and	 intensities	 of	 incident	 photons.	 The	 synchrotron	
photon	sources	 take	 care	of	 these	 limitations	but	only	 limited	
numbers	of	these	facilities	are	available	in	the	world.	Therefore,	
X‐ray	tube	as	photon	source	with	photon	intensities	better	than	
that	 from	 radioactive	 sources	 became	 the	 appropriate	 choice	
for	the	laboratory	experiment.	

Available	 M	 XRF	 measurements	 with	 X‐ray	 tube	 photon	
sources	 are	 at	 some	specific	discrete	photon	energies	derived	
from	primary	excitations	of	suitable	targets	in	double	reflection	
set	ups	[14‐15].	Again	this	results	in	limitations	on	energies	of	
exciting	photons.	Moreover,	 due	 to	 the	 complexity	 of	M	X‐ray	
spectra,	 it	 is	 more	 difficult	 to	 measure	 individual	 line/group	
production	 cross‐section	 for	 the	 shell.	 Only	measurements	 of	
[16]	on	individual	M	sub‐shell	X‐ray	fluorescence	cross‐section	
are	available	for	elements	71	≤	Z	≤	92	at	5.96	keV.		

	



364	 Gupta	et	al.	/	European	Journal	of	Chemistry	5	(2)	(2014)	363‐369	
	

	
Table	1.	Weighted	M	X‐ray	group	energies	for	elements	Pt,	Au,	Pb,	Th	and	U.	
M	X‐ray	group	 EMg	(keV)

Pt	 Au Pb Th U	
M	 1.60	 1.66	 1.84	 2.35	 2.49	
Mβ	 2.09	 2.16 2.39 3.07	 3.26
M	 2.33	 2.40 2.65 3.39	 3.58
Mm	 2.71	 2.80 3.12 4.07	 4.34
	
	
	

Still,	 more	 data	 is	 required	 on	 M	 sub‐shell	 X‐ray	
fluorescence	 cross‐sections	 at	 different	 energies	 to	 have	 a	
better	insight	into	atomic	structure	and	to	check	theory	against	
experiment.	

In	 the	present	 study,	X‐ray	 tube	Bremsstrahlung	has	been	
used	as	photon	source	of	desired	energies	simply	by	adjusting	
its	 anode	 voltages	 and	 individual	 M‐line/group	 of	 lines	 Mξ,	
Mαβ,	 M	 and	Mm	 XRF	 cross‐sections	 have	 been	measured	 at	
five	different	energies	for	each	of	Pt,	Au,	Pb,	Th	and	U	elements.	
The	selective	creation	of	only	M	shell	vacancies	at	five	energies	
in	 experimental	 targets	has	been	done	with	photons	 from	 the	
tube.	 Since,	 continuous	 Bremsstrahlung	 X‐rays	 from	 the	 tube	
lying	between	M5	edge	energy	of	 target	element	and	 the	 tube	
anode	 voltage	 were	 able	 to	 create	 M	 sub‐shell	 vacancies,	
therefore,	 weighted	 average	 energy	 Eavg	 of	 incident	 tube	
photons	 was	 determined	 following	 a	 specific	 calculation	
procedure	 to	 evaluate	 single	 energy	value	at	which	 the	 cross‐
sections *

Mg for	groups	of	M	X‐rays	were	measured.	The	details	

of	 the	 measurements,	 adopted	 procedure,	 results	 and	
discussions	are	being	given	here.	
	
2.	Experimental	
	

The	experimental	set	up	consisted	of	100	Watt	 low	power	
Neptune	 Rh	 anode	 X‐ray	 tube	 from	 Oxford,	 USA	 as	 a	 photon	
source	 along	 with	 a	 Peltier	 cooled	 Amptek	 XR‐100CR	 Si‐PIN	
detector	 of	 resolution	 ~220	 eV	 at	 5.959	 keV	 in	 a	 90°	 single	
reflection	set	up	(Figure	1).	The	compact	geometry	employed	in	
the	setup	was	made	from	a	single	iron	block	of	dimensions	4	×	
4	 ×	 2.5	 cm	with	 1	 mm	 thick	 Al	 lining	 of	 internal	 surfaces	 of	
collimations	and	outer	exposed	area	of	the	block	for	absorption	
of	 iron	 K‐X	 rays.	 A	 beam	 size	 ~0.9	 ×	 1.4	 cm	 is	 allowed	 to	
impinge	on	 the	 target	 surface.	The	Spec‐pure	metallic	 targets;	
Pt,	Au,	Pb,	Th	and	U,	each	of	diameter:	4	cm	were	used.	

	

	
	
Figure	 1.	 90	 Single	 reflection	 geometry	 made	 from	 single	 iron	 block.	
(Diameter	of	 collimation	between;	 X‐ray	 tube	window	and	 target	=	 0.8	 cm,	
target	 and	 detector	 =	 1.0	 cm.	 Length	 of	 collimation	 between;	 X‐ray	 tube	
window	and	target	=	3.5	cm,	target	and	detector	=	0.5	cm).	

	
Selective	 excitation	 of	M	 shell	 of	 each	 target	was	done	by	

adjusting	 the	 tube	 anode	 voltages	 at	 five	 different	 values	
between	 the	 L3	 and	M1‐edge	 energies	 of	 the	 target.	 The	 total	
range	 of	 excitation	 energy	 of	 all	 the	 targets,	 comprising	 five	
energies	 for	 each	 target,	 was	 obtained	 by	 adjusting	 the	 tube	
power	in	the	range	6‐14	kV	in	steps.	The	filament	current	of	the	
tube	 was	 0.2‐0.9	 mA	 to	 maintain	 the	 dead	 time	 loses	 of	 the	
detector	<1%.	In	order	to	assure	the	reproducibility	of	results,	

minimum	 three	 sets	 of	 spectra	 for	 each	 element	 and	 energy	
combination	 were	 recorded.	 In	 each	 measurement,	 the	 tube	
radiation	scattered	from	the	target	was	accounted	by	recording	
the	spectrum	with	equivalent	Al	target	[17]	of	the	experimental	
one	and	subtracted	from	the	target	M	X‐ray	spectrum.	

Since	M‐shell	consists	of	five	sub‐shells	the	X‐rays	from	the	
target	consist	of	a	number	of	transition	lines.	But	due	to	limited	
resolution	 of	 the	 set‐up,	 the	 X‐ray	 lines	 fall	 within	 different	
groups.	 The	 grouping	 of	M	X‐rays	has	been	 done	 by	 selecting	
the	M	X‐ray	line	energies	falling	in	the	regions	of	intense	M	line	
±	detector	resolution.	The	emerged	four	main	groups	(Mg)	are	
Mξ,	Mαβ,	M	and	Mm.	The	transitions	grouped	under	different	
groups	 are	Mξ	 (M4‐N2,3;	 M5‐N3	 ),	 Mαβ	 (M5‐N6,7,O3;	 M4‐N7),	 M	
(M2‐N1;	M3‐N4,5)	and	Mm	(M3‐O1,4,5;	M3‐N6,7;	M2‐N4;	M1‐N2,3).	

The	 weighted	 X‐ray	 energy	 of	 different	 groups	 EMg	 were	
calculated	using	 radiative	 transition	probabilities	 of	 Chen	 and	
Crasemann	 [18]	 and	 level	 energies	 from	 tables	 of	 Storm	 and	
Israel	 [19].	 The	 group	 energies	 were	 marked	 in	 the	 net	
subtracted	 spectra	 after	 their	 precise	 energy	 calibrations	 and	
are	listed	in	Table	1.		

The	 experiment	 was	 run	 for	 sufficient	 time	 to	 obtain	 the	
statistics	of	counts	<1%	under	various	peaks	of	the	background	
subtracted	 net	 spectrum.	 A	 typical	 set	 of	 spectra	 for	 Au	 and	
equivalent	Al	 (weight	of	Al	 target	with	electron	number	equal	
to	 that	 of	 Au	 target	weight	 i.e.	 Al(wt.)=(Z(Au)/Z(Al))*(M(Al)/	
M(Au))*(Au(wt),	where	Z	and	M	represent	atomic	number	and	
atomic	mass,	respectively)	at	anode	voltage/filament	current	9	
kV/0.2	mA	is	shown	in	Figure	2a.	The	scattered	tube	flux	from	
the	 target	 comprising	 scattered	 Rh	 L	 X‐rays	 of	 tube	 anode	 at	
2.94	 keV	 that	 merged	 with	 atmospheric	 Ar	 K	 X‐rays	 are	
eliminated	 in	the	net	background	subtracted	spectrum,	shown	
in	Figure	2b.	

Since,	 the	 M	 shell	 excitations	 were	 with	 continuous	
Bremsstrahlung	 photons	 lying	 in	 the	 region,	 M5	 level	 edge	
energy	 to	 energy	 corresponding	 to	 the	 tube	 anode	 voltage,	
therefore,	a	separate	experiment	and	calculation	procedure	has	
been	 followed	 to	 find	 a	 single	 average	 energy	 for	 the	 exciting	
continuous	Bremsstrahlung	for	M	shell	excitations.	
	
2.1.	Evaluation	of	weighted	average	energy	and	intensity	of	
continuous	Bremsstrahlung	
	

High	flux	output	of	X‐ray	tube	is	difficult	to	record	directly	
with	 Si‐PIN	 detector	 because	 of	 its	 dead	 time	 problem.	
Therefore,	 for	 each	 excitation,	 the	 spectrum	 of	 tube	 photons	
scattered	 from	 the	 aluminum	 (Al)	 target	 in	 the	 same	 set‐up	
with	the	same	anode	voltage/filament	current	of	the	tube	as	in	
case	 of	 experimental	 target	 was	 processed.	 The	 continuous	
Bremsstrahlung	 regions	 in	 Al	 spectrum	 free	 from	 observed	
peaks	 were	 then	 fitted	 with	 a	 polynomial	 fit	 in	 origin	 6.0	 to	
have	 a	 best	 smooth	 Bremsstrahlung	 spectrum	 close	 to	 actual	
count	values.	To	evaluate	weighted	average	energy	of	 incident	
flux,	 the	 fitted	 region	 above	 M5	 edge	 energy	 of	 experimental	
target	 and	 energy	 corresponding	 to	 applied	 voltage	 was	
divided	into	n	number	of	strips.	Each	strip	was	of	width	200	eV	
(<detector	 resolution).	A	 typical	Al	 spectrum	at	 tube	power	7	
kV/	0.2	mA	is	shown	in	Figure	3.		

A	procedure	has	been	adopted	to	determine	the	intensity	of	
incident	flux	In	in	nth	strip	that	is	falling	on	target	area	seen	by	
the	detector	from	the	collected	number	of	scattered	count	rate	
Nn

	
in	the	strip	using	extrinsic	detector	efficiency	(En)	at	the	strip		



Gupta	et	al.	/	European	Journal	of	Chemistry	5	(2)	(2014)	363‐369	 365	
	

(a)	
	

	(b)	
	
Figure	2.	(a)	Typical	spectrum	Au	and	equivalent	Al	taken	at	9 kV/ 0.2 mA,
(b)	Background	subtracted	net	spectrum	of	Au.	
	

	
	
Figure	3.	Polynomial	fitting	of	scattered	Bremsstrahlung	in	Al	scatter	taken	
at	7	kV/0.2	mA.	(Peak	at	2.92	keV	is	merged	peak	of	atmospheric	Ar	K	X‐rays	
and	scattered	Rh	L	X‐rays	of	tube	anode,	peak	at	3.78	keV	is	the	sum	peak	of	
Si	K	X‐rays	of	the	Si	(PIN)	detector,	peak	at	4.35	keV	is	sum	peak	of	first	peak	
energy	 and	 Al	 K	 X‐rays	 and	 peak	 at	 6.16	 keV	 is	 sum	 of	 Ar	 K	 X‐rays	 and	
scattered	Rh	L	X‐rays).	
	
mean	energy	En	and	self‐absorption	correction	 factor	 for	Al	at	
incident	 and	 scattered	 photon	 energies	 [βEn(i,e)]Al	 from	 the	
relation	

    
N .M
E A ln

n
. . . .

to ta l n E A l E vn nA l 90 ° A l

I
σ E β i,e t ε A 

  
	 (1)	

where	Av	 is	Avogadro’s	number,	MAl	 is	molecular	weight	of	Al	
target,	 tAl	 is	 the	 Al	 target	 thickness	 in	 g/cm2.’s	 (En)	 are	 the	
coherent	 and	 incoherent	 scattering	 cross‐sections	 of	 Al	 in	
barns/atom.	

For	all	strips,	 the	factor
A v t A lM A l

,	number	of	atoms	per	

unit	area	of	 target	are	same,	but	 incoherent	Klien‐Nishina	and	
coherent	 Rayleigh	 scattering	 cross‐sections	 of	 Al	 [20]	 at	 90°,	
effective	 thickness	 βt	 of	 Al	 target	 and	 extrinsic	 detector	
efficiency	 ε(En)	 change	 due	 to	 changed	 strip	 energy	 and	need	
evaluations	at	each	strip	mean	energy.	

Coherent	and	incoherent	scattering	cross‐sections	at	90	at	
the	strip	mean	energies	were	calculated	using	formulation	and	
tabulations	of	Hubbell	et	al.	[20]	and	the	total	scattering	cross‐
section	for	Al	at	90	is	evaluated	as	

           σ 	 σ 	 σinctotal coh Al	 90°Al	 90° Al	 90°
	 	 (2)	

	
Al	self‐absorption	correction	factor,	

	

 

   

   n

μ i μ e
1‐exp ‐ 	 t Alcos	θ cos	θei

β i,eE
μ i μ eAl

	 t Alcos	θ cos	θei

  
  
      

    
 
 
 

	 	

(3)	

	
where	 µ’s	 are	 Al	 absorption	 coefficients	 at	 incident	 i	 and	
emitted	e	photon	energies	and	i		and	e	are	the	angles	between	
incident	 radiation	 &	 target	 normal	 and	 target	 normal	 &	
detector	 and	were	 evaluated	 for	 i	=	 e	=	 45	 with	 µ’s	 values	
known	from	XCOM	program	[21].	

At	energies	<10	keV,	the	incoherent	scattered	energy	is	just	
<200	eV	(strip	width)	away	from	incident	energy,	therefore,	in	
a	 strip	 both	 incident	 and	 scattered	 energies	 were	 taken	 as	
mean	energy	En	of	the	strip	i.e.	En(i)	=	En(e)	=	En.	

The	ε(En),	efficiency	of	detector	was	calculated	at	the	strip	
mean	energy	with	formulation,		
	

	 a ir n a ir B e n B en

S i n S i

ε E 	e xp 	 ‐μ E t e xp ‐μ E t

1 ‐e xp ‐μ E t

 
   
      

  
    

	(4)	

	
where,	μair,	μBe	and	μSi	are	the	absorption	coefficients	of	air,	Be	
and	Si	at	En	energy	and	tair,	 tBe	and	tSi	are	air	column	between	
target	 and	 detector	 window,	 Beryllium	window	 and	 detector	
thickness,	respectively.	

From	Equation	 (1),	 intensity	of	 each	 strip	 In	 falling	 on	 the	
target	area	was	evaluated	and	the	weighted	average	energy	of	
the	exciting	Bremsstrahlung	was	calculated	as	
	

n n

avg n

E I
nE

I
n




	 	 	 	 	 (5)	

	
Total	intensity	falling	on	the	target,		
	

n
n

I 	 	 I 	 	 	 	 	 (6)	

	
For	experimental	targets	Au,	Pt	and	Pb,	 the	scattered	Rh	L	

X‐rays	at	2.88	keV	also	produce	M	vacancies.	But	in	Al	scattered	
spectrum	 it	 is	 cumbersome	 to	 extract	 scattered	 Rh	 L	 X‐ray	
intensity	 from	 the	 combined	 atmospheric	 Ar	 K	 X‐rays	 and	
scattered	Rh	L	X‐rays	peak.		

	



366	 Gupta	et	al.	/	European	Journal	of	Chemistry	5	(2)	(2014)	363‐369	
	
	
Table	2.	List	of	M5‐edge	energies	of	experimental	elements	and	K‐edge	energies	of	low	Z	elements	in	combination.	
Experimental	target	 Low	Z	element	 M5‐edge(keV)	 K‐edge	(keV)	
U	 K	 3.552 3.607	
Th	 K	 3.332	 3.607	
Pb	 S	 2.484	 2.472	
Au	 P	 2.206	 2.144	
Pt	 P	 2.122		 2.144	
	
	
Table	3.	Weighted	average	energies	and	total	evaluated	intensity	(counts/sec	in	the	region)at	different	voltages	for	each	combination.	
Voltage(kV)	 Eavg	(keV)/I	

Pt	/	P	 Au	/	P	 Pb	/	S	 Th	/	K	 U	/	K	
6	 3.011/8301	 3.011/8301 3.174/6964 4.145/2	 ‐	
6.5	 ‐	 ‐ ‐ ‐ 4.47/1
8	 3.15/32	 3.15/32 3.46/23 5.19/6	 5.19/6
9	 3.27/39	 3.27/39 ‐ ‐ ‐	
10	 3.37/41	 3.37/41 3.50/44 5.27/11	 5.27/11
11	 3.56/53	 3.56/53	 ‐	 ‐	 ‐	
12	 ‐	 ‐	 3.95/66	 6.29/20	 6.29/20	
13	 ‐	 ‐	 4.46/58	 ‐	 ‐	
14	 ‐	 ‐ ‐ 7.38/31	 7.38/31
*	“‐“:	Not	measured	at	these	energies.	

	
Therefore,	 to	 determine	 the	 total	 intensity	 (Rh	 L	 X‐ray	 +	

Bremsstrahlung)	in	each	strip	of	the	combined	peak	region,	the	
ratio	 of	 total	 intensity/	 Bremsstrahlung	 intensity	 was	
determined	from	the	direct	tube	output,	recorded	with	filament	
current	0.01‐0.05	mA	and	highly	collimated	detector	placed	at	
the	 position	 of	 Al	 target	 and,	 in	 turn,	 In	 in	 the	 strip	 was	
multiplied	 with	 the	 ratio	 to	 include	 the	 contribution	 of	
scattered	Rh	L	X‐rays	in	production	of	M	vacancies.	

Hence	 the	 weighted	 average	 energy	 and	 intensity	 values	
were	 calculated	and	have	been	used	 as	 characters	 of	 incident	
exciting	flux	from	X‐ray	tube.	
	
2.2.	Calculations	of	Mg	X‐ray	fluorescence	cross‐sections	
	

With	 counts	 NMg	 under	 the	 Mg	 group	 of	 X‐rays	 *Mg	 the	
fluorescence	 cross‐section	 for	 Mg	 group	 of	 X‐rays	 was	
calculated	from	the	relation,		

 
M g M*

M g

v M g 0M g

N M
σ 	

A t .β .ε .S .G
	 	 	 (7)	

Where	SoG	accounts	for	incident	photons	falling	upon	the	target	
area	 seen	 by	 the	 detector	 with	 absorption	 of	 incident	 and	
emitted	photons	in	the	air.	

The	 factor	 1 2

O O air air
	 	 i e

4π 4π
Ω ΩS G S a .a ,	 with	 S0	 as	 incident	

photon	 flux	 from	 the	 source;	1	 &	2	 target‐source	&	 target‐
detector	 solid	 angles;	 aair(i),	 aair(e)	 the	 absorption	 of	 the	
incident	photon	in	air	column	between	source	and	target	and	of	
emitted	photons	in	the	air	column	between	target	and	detector,	
was	 determined	 for	 each	 experimental	 target	 in	 the	 present	
set‐up	at	each	excitation	energy	by	irradiating	the	selected	low	
Z	target	to	excite	its	K	shell	in	the	same	set‐up	with	same	flux.	
The	selection	of	 low	Z	for	each	experimental	 target	was	made	
such	 that	K	edge	energy	of	 low	Z	 target	was	equal	 to	M5	edge	
energy	 of	 experimental	 target	 nearly	 within	 the	 detector	
resolution.	Table	2	shows	the	combination	of	 low	Z	target	and	
experimental	targets.	

Wherever	 the	 difference	 in	 the	 K‐edge	 and	 M5‐edge	
energies	 were	 greater	 than	 200	 eV,	 the	 width	 of	 the	 strip	 at	
lowest	 energy	 was	 increased	 exactly	 equal	 to	 the	 difference	
energy	(e.g.	in	case	of	(Th,	K)	it	was	made	275	eV).		

In	 this	 way,	 the	 weighted	 average	 energy	 and	 intensity	
remained	the	same	for	each	combination	and	are	being	given	in	
Table	3.	

For	K	excitations	of	low	Z	targets,	
	

 
K K

o *
v K KK

N .M
S G

A t .β ε σ
	 	 	 	 (8)	

where	the	terms	on	R.H.S.	are	for	K	X‐ray	targets.	
From	relations	(7)	and	(8)	

 
 

K

*
Mg M K* K

Mg

K K MgMg

N .M . t.β .ε .σ
σ

N .M . t.β .ε 	 	 	

(9)	

For	 each	 *Mg	 calculation,	 ’s	 	 and	 ε’s	 were	 evaluated	 as	
mentioned	 in	 relations	 (3)	 &	 (4)	 for	 desired	 incident	 and	
emitted	energies.	K	X‐ray	production	cross‐section	 *

Kσ 	
has	been	

known	at	the	weighted	average	incident	energy	from	computer	
code	KCSPIF	developed	earlier	in	our	laboratory	[22].	

Peak	area	extraction	for	gth	(g	=	,	,	)	group	of	M	X‐rays	
has	 been	 done	 by	 marking	 the	 centroid	 of	 groups	 on	 a	
calibrated	energy	scale.	In	case	of	hump,	the	gross	area	of	half	
peak	 on	 the	 side	 of	 centroid	 that	 is	 comparatively	 free	 from	
adjacent	 peak	 interference	 was	 selected	 by	 highlighting	 the	
channels	under	half	peak.	Doubling	this	area	gives	us	the	total	
gross	area	for	the	gth	group.	For	background	subtraction,	lowest	
background	 counts	 on	 that	 side	 was	 multiplied	 by	 the	 total	
number	of	channels	covered	by	the	group	and	subtracted	from	
the	gross	area.	A	typical	illustration	of	extracted	different	M	X‐
ray	peaks	 for	Au	 in	background	subtracted	spectrum	at	9	kV/	
0.2	 mA	 tube	 power	 is	 given	 in	 Figure	 4	 that	 shows	 the	
replication	 of	 different	 peaks	 with	 Gaussian	 fit	 with	 same	
counts	under	each	peak.	The	spectrum	consists	of	many	peaks	
say	Mg	(g	=	,	,	,	,	,	,	m1	and	m2)	but	in	the	present	method	
only	 four	 group	were	 extracted	 as	 the	 individual	 peaks	 could	
not	be	resolved	further	due	to	poor	detector	resolution.	

After	 determining	 the	 peak	 area	 under	 various	 peaks,	
target	 self‐absorption	 corrections	 factors	 and	 detector	
efficiency	at	element	energies	and	production	cross‐section	for	
low	 Z	 element	 used	 in	 combination,	 M	 sub‐shell	 X‐ray	
fluorescence	 cross‐section	have	been	 evaluated	 and	 are	 listed	
in	Table	4.	
	
3.	Results	and	discussion	
	

The	measured	 experimental	M	X‐ray	 group	 cross‐sections	
are	listed	in	Table	4.	The	error	in	the	values	is	the	squared	root	
sum	of	uncertainties	in	different	individual	parameters	used	to	
measure	 X‐ray	 production	 cross‐section	 as	 target	 self‐
absorption	correction	factor	(~7%),	detector	efficiency	(5‐7%),	
peak	 area	 extraction	 (0.1	 to	 10%	 for	 M	 and	 Mm,<	 0.5%	 for	
M,	<1%	for	M)	etc.		

The	 authenticity	 and	 reliability	 of	 present	 method	 of	
measurements	and	calculations	has	been	judged	 in	 terms	L	X‐
ray	 fluorescence	 cross‐section	 measurements	 as	 data	 on	 L	
cross‐section	is	moderate	as	compared	to	that	for	M	X‐rays.		

	



Gupta	et	al.	/	European	Journal	of	Chemistry	5	(2)	(2014)	363‐369	 367	
	

	
Table	4.	List	of	measured	and	theoretical	M	X‐ray	production	cross‐sections.	
Elements	 Voltage	(kV)	 Incident		

Energy	
Cross‐section	(b/atom)
σMξ	 σMαβ σMγ σMm	
Exp.		
(Error)	

Theory		
DF/	DHS.

Exp.		
(Error)

Theory		
DF/	DHS.

Exp.		
(Error)

Theory		
DF/	DHS.	

Exp.		
(Error)	

Theory		
DF/	DHS.

Pt	 6	 3.01 494(49)	 554/ 11259(788) 12059/ 275(19) 339/	 38(4)	 36/
516	 11230	 302	 32	

8	 3.15 422(42)	 538/ 11139(780) 11603/ 336(23) 347/	 135(14)	 134/
501 10804 309	 118

9	 3.27	 354(35)	 491/	 10168(712)	 10584/	 324(23)	 326/	 104(10)	 128/	
457 9855 290	 112

10	 3.37	 469(47)	 478/	 9346(654)	 10314/	 319(22)	 358/	 157(16)	 182/	
445 9604 319	 160

11	 3.56 312(31)	 418/ 7050(494) 9015/ 231(16) 327/	 128(13)	 169/
389 8394 291	 148

Au	 6	 3.01	 511(51)	 606/ 11886(832)	 13466/ 300(21)	 377/	 64(6)	 61/
531	 11822	 341	 55	

8	 3.15	 480(48)	 533/	 9476(663)	 11856/	 384(27)	 368/	 63(6)	 60/	
500	 11142	 329	 53	

9	 3.27 385(38)	 582/ 10474(733) 12723/ 435(30) 422/	 196(20)	 292/
547 11950 377	 256

10	 3.37 460(46)	 586/ 9678(677) 12936/ 404(28) 405/	 164(16)	 161/
550 12154 362	 142

11	 3.56 501(50)	 448/ 11306(791) 9905/ 319(22) 379/	 246(25)	 203/
421 9306 339	 	 180

Pb	
6	 3.17 565(57)	 659/ 14646(1025) 15394/ 202(14) 447/	 111(11)	 88/

632 14748 377	 74
8	 3.46 350(35)	 528/ 9018(631) 12352/ 289(20) 398/	 95(9)	 78/

506 11834 335	 66
10	 3.5	 486(49)	 513/ 8170(572) 11996/ 87(6) 391/	 98(10)	 65/

491 11493 330	 77
12	 3.95 337(34)	 428/ 7356(515) 9938/ 62(4) 386/	 143(14)	 179/

411	 9523	 326	 206	
13	 4.46	 217(22)	 319/	 5298(371)	 7405/	 63(4)	 329/	 95(9)	 131/	

306 7095 278	 	 174
Th	 6	 4.15 691(55)	 610/ 21273(1489) 15641/ 668(53) 593/	 ‐	 ‐

596 15468 551	
8	 5.19	 373(30)	 387/	 11210(785)	 9844/	 484(39)	 520/	 ‐	 ‐	

378	 9747	 480	
10	 5.27	 365(29)	 314/	 11103(777)	 9471/	 505(40)	 506/	 ‐	 ‐	

364 9377 467	 ‐	 ‐
12	 6.29	 275(22)	 238/	 7635(534)	 6043/	 386(31)	 368/	 ‐	 ‐	

232 5984 340	 ‐	 ‐
14	 7.38 171(14)	 158/ 4700(329) 4009/ 263(21) 274/	 ‐	 ‐

154 3970 253	 ‐	 ‐
U	 6.5	 4.47	 556(44)	 567/	 15276(1069)	 15025/	 686(55)	 588/	 ‐	 ‐	

571 15125 559	 ‐	 ‐
8	 5.19	 385(31)	 381/	 9239(647)	 10126/	 452(36)	 463/	 ‐	 ‐	

384	 10190	 440	 ‐	 ‐	
10	 5.27 385(31)	 400/ 9168(642) 10493/ 528(42) 490/	 ‐	 ‐

404	 10580	 466	 ‐	 ‐	
12	 6.29 308(25)	 266/ 6243(437) 6994/ 415(33) 408/	 ‐	 ‐

269	 7050	 388	 ‐	 ‐	
14	 7.38 208(17)	 177/ 3936(276) 4641/ 271(22) 304/	 ‐	 ‐

178 4678 290	 ‐	 ‐
*	“‐“:	Not	measured	at	these	energies.	
	
	

	
	

Figure	4.	Various	M	X‐ray	groups	(M,	M,	M,	Mm) resolved	for	Au	at	9 kV/ 0.2 mA.
	



368	 Gupta	et	al.	/	European	Journal	of	Chemistry	5	(2)	(2014)	363‐369	
	
Table	5.	List	of	measured	L,	L,	L	and	L	fluorescence	cross‐sections	along	with	semi‐empirical/theoretical	values	generated	from	software	LCSGEN	[23]	for	
Ag	at	4.466	keV	photon	energy.	
L	X‐ray	group,	Lg	 *

Lg (b/atom)		

Experimental	 Semi‐empirical Theoretical
L	 218(15)	 169	 193	

L	 4664(326)	 4647	 5328	
L	 2494(175)	 2793 2910	
L	 237(17)	 259	 260	

	
	

   

   

4ξ

* M M M M M M M M M M M M M M M M M M
M ξ 4 34 3 24 23 34 2 14 13 34 12 24 12 23 34 1 4

M M M M M M M M M M M M M M M M
5 45 4 35 34 45 3 25 24 45 23 35 23 34 45 2

M M M M M M M M M M
15 14 45 13 35 12 25 13 34 45 12

σ σ f σ f f f σ f f f f f f f f σ ω F

σ f σ f f f σ f f f f f f f f σ

f f f f f f f f f f f

 
 

 
5ξ

M M M M M M M M M M M M M
24 45 12 23 35 12 23 34 45 1 5
f f f f f f f f f σ ω F

 
 
 
 
  

	 	 	

(10)	

	
	

   

   

4αβ

* M M M M M M M M M M M M M M M M M
M αβ 4 34 3 24 23 34 2 14 13 34 12 24 12 23 34 1 4

M M M M M M M M M M M M M M M M
5 45 4 35 34 45 3 25 24 45 23 35 23 34 45 2

M M M M M M M M M M
15 14 45 13 35 12 25 13 34 45 1

σ σ f σ f f f σ f f f f f f f f σ ω F

σ f σ f f f σ f f f f f f f f σ

f f f f f f f f f f f

 
 

 
5αβ

M M M M M M M M M M M M M
2 24 45 12 23 35 12 23 34 45 1 5
f f f f f f f f f σ ω F

 
 
 
 
  

	 	

(11)	

	

 
3γ 2γ

* M M M M M M M M M M M M M M
Mγ 3 23 2 13 12 23 1 3 2 12 1 2σ σ f σ f f f σ ω F σ f σ ω F      		 	 	 	 (12)	

	
	

 * M M M M M M M M M M M M M M M M
Mm 3 23 2 13 12 23 1 3 3m 2 12 1 2 2m 1 1 1mσ σ f σ f f f σ ω F σ f σ ω F σ ω F      	 	 	 	

(13)	

	
	
	

Therefore,	 the	 measurements	 on	 Ag	 L	 X‐rays	 at	 6.5	 kV	
anode	 voltage	 i.e.	 Eavg	 =	 4.466	 keV	 were	 performed	 with	
potassium	as	K	X‐ray	 target	 for	 incident	 flux	normalization	as	
the	 edge	 energies	 3.351	 and	 3.607	 keV	 for	 L3	 of	 Ag	 and	 K	 of	
potassium	are	 just	256	eV	apart.	The	measured	cross‐sections	
with	7%	uncertainties	 for	L,	L,	L	 and	L	 group	of	Ag	along	
with	 semi‐empirical/theoretical	 values	 generated	 from	
software	LCSGEN	[23]	are	listed	in	Table	5.	

The	fair	agreement	of	measured	values	within	uncertainties	
with	 semi‐empirical/theoretical	 values	 supports	 the	 present	
method	of	measurement	and	result	evaluation	procedure.	

At	 this	 stage	 no	 experimental	 or	 theoretical	 values	 of	 the	
cross‐sections	 at	 such	 low	 energies	 are	 available	 for	
comparison	 and	 to	 check	 the	 present	 measurements.	
Therefore,	 theoretical	 cross‐section	 values	 at	 these	 energies	
were	 evaluated	 from	 the	 available	 tabulated	 data	 on	 fine	
parameters.	 Two	 sets	 of	 fluorescence	 yields	 and	 fractional	
radiative	decay	rates	based	on	DHS	and	DF	models	were	used	
in	the	formulations	(10)‐(13).	

Two	 sets	 of	 theoretical	 values	 of	 M	 XRF	 cross‐sections	
based	on	DF	and	DHS	models	have	been	calculated.	In	first	set	
DF	model	 based	 fluorescence	 [24]	 and	 fractional	 decay	 rates	
were	 used	 [25].	 In	 the	 second	 set,	 DHS	 model	 based	
fluorescence	 yields	 [24]	 and	 fractional	 radiative	 decay	 rates	
were	used	[26].	In	both	the	sets	Coster‐Kronig	transition	yields	
of	 Chauhan	 and	 Puri	 [24]	 and	 photo	 ionization	 cross‐
sections M

i of	 Scofield	 [27]	 were	 used.	 The	 calculated	
theoretical	values	are	also	listed	in	Table	4.	

The	comparison	of	measured	values	of	M	X‐ray	production	
cross‐section	for	the	groups	Mξ,	Mαβ,	Mγ	and	Mm	for	Pt,	Au,	Pb,	
Th	 and	 U	with	 the	 calculated	 theoretical	 values	 based	 on	 DF	
and	DHS	models	 shows	 the	 experimental	 values	 of	 the	 cross‐
sections,	 generally,	 agree	 with	 the	 theoretical	 values	 within	
experimental	 uncertainties.	 An	 overview	 points	 closeness	 of	
present	 results	with	DHS	model	 based	 values	 as	 compared	 to	
those	based	upon	DF	model.	

For	Th	and	U,	measurements	could	not	be	possible	for	Mm	
group	 as	 it	 falls	 in	 the	 region	 of	 Bramsstrahlung	where	 some	
spurious	peaks	are	there	from	the	experimental	set‐up.	So,	the	
chances	 of	 accurate	 peak	 area	 extraction	 become	 rare.	
Otherwise,	 the	 results	 are	 almost	 overlapping	 with	 theory	
except	for	Mαβ	of	Th.	In	case	of	Pb	deviations	are	on	higher	side,	
even	 in	 case	 of	 Mm	 and	M	 these	 are	 more	 than	 50%	 and	 in	
some	rare	cases	agreement	is	very	good.	For	Au	and	Pt,	overall	
agreement	 is	 very	 good	 except	 at	 energy	 3.56	 keV	
corresponding	to	11	kV	anode	voltage	in	Pt.	

From	 all	 the	 above	 comparisons,	 it	 is	 justified	 that	 the	
present	 method	 of	 analysis	 for	 XRF	 cross‐section	 measure‐
ments	 is	compatible	with	the	existing	methods	in	 literature	as	
mentioned	 in	 the	 introduction	 section.	 So	 far	 in	 literature,	 to	
the	 best	 of	 authors’	 knowledge	 such	 approach	 to	 quantify	
continuous	 Bremsstrahlung	 in	 terms	 of	 weighted	 average	
energy	and	intensity	has	not	been	followed	for	similar	work	but	
present	measurements	 lead	 to	 the	 confidence	 to	make	 use	 of	
such	an	approach.	The	approach	resulted	 in	measurements	at	
such	low	energies	3.01‐7.38	keV	those	are	not	possible/difficult	



Gupta	et	al.	/	European	Journal	of	Chemistry	5	(2)	(2014)	363‐369	 369	
	

with	conventionally	available	radioactive	sources/synchrotron	
sources.	

	
4.	Conclusion	
	

The	quantification	of	continuous	Bremssrahlung	in	terms	of	
weighted	 average	 energy	 and	 intensity	 that	 produced	 L/M	X‐
ray	 fluorescence	cross‐sections	fairly	supported	by	theoretical	
or	semi‐empirical	values	can	be	used	confidently	 in	 future	 for	
XRF	studies.	The	approach	is	capable	of	measurements	at	such	
low	energies	3.01‐7.38	keV	those	are	not	possible/difficult	with	
conventionally	 available	 radioactive	 sources/	 synchrotron	
sources.	
	
Acknowledgments	
	

The	financial	assistance	from	BRNS,	Government	of	India	in	
the	 form	 of	 project	 grant	 (Ref	 no:	 2007/37/6/BRNS)	 for	 this	
work	 is	 highly	 acknowledged.	 Ms.	 Sheenu	 Gupta	 and	 Ms.	
Gurpreet	 Kaur	 acknowledge	 the	 meritorious	 fellowship	 from	
University	Grand	Commission,	New	Delhi,	India.	
	
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