Nuclear Instruments and Methods in Physics Research B 129 (1997) 137-138

ELSEVIER

A method for

Nikolay Uzunov ‘,*, Ilia Penev b a Konsranrin Prmlavski University, Department of Applied Physics, Shumen 9700, Bulgaria

’ INRNE, Bulgarian Academy of Sciences, Sojia 1784, Bulgaria

Received I8 February 1997

Beam Interactions Letter to the Editor with Materials & Atoms

quantitative analysis of adjacent elements using particle-induced gamma emission

Abstract An experimental method for quantitative analysis of sample containing adjacent elements of the periodic table using (p,y)

and ( p,p’y) reaction is proposed. The method is based on the analysis of gamma emission originated from the transitions

through certain levels of a common nucleus.

Methods. based on the analysis of particle-induced emis-

sion such as PIXE (Proton-Induced X-ray Emission) and PIGE (Proton-Induced Gamma-ray Emission), often do not give precise results when the sample contains two adjacent

elements of the periodic system. A big part of the uncertain- ties for PIXE comes from the incomplete separation of the spectral lines from the spectral overlap, which is inevitably occurring for the elements of the first half of the periodic system when semiconductor detectors with finite energy res- olution are used. The other part of the experimental error is due to the absorption of the X-rays in the specimen and the uncertainties from the secondary excitations [ I ,2]. In PIGE there is a possibility to induce an error in the measured quan-

tity of the elements, because of possible interfering reactions with both elements, leading to a common excited state.

For the case when the target consists of two adjacent elements N and M of the type ;T:M and $N, where 2 is the charge of the nucleus and A is the mass number, we suggest

an alternative method based on the analysis of an appropriate gamma line which is common for both elements. To excite the gamma emission of the sample, a proton beam with a

possibility to vary the energy of the incoming protons is used. Unlike the standard PIGE, in this method we analyse the intensity of a gamma line which is a result of two possible reactions: a reaction of the type (p,y) and a reaction of the

type (p,p’y). The intensity of the gamma line depends on one hand on the quantities of the elements in the sample and

on the other hand depends on the energy of the incoming protons thus giving the possibility to write a system of linear algebraic equations for the quantities of the elements.

*Corresponding author. Fax +359 54 631 71, e-mail uzunov@uni-

shoumen.bg

For the elements of the type $I:M and $N there is a probability to excite gamma transitions as a result of the following reactions with protons:

;I;M + p -;N+y, (1)

;N+P -;N+p’+y (2)

The energy spectrum of the gamma rays is compounded by gamma particles emitted from the first excited states of the nuclei provided that the quantum characteristics allow

their excitation. Both reactions ( 1) and f 2) lead to different excited states of a common nucleus. In such a case one can

expect possible de-excitation through a common state. This would produce gamma rays in the energy spectrum with the

same energy value from both reactions. As a matter of fact such excited states have low spin and energy values. Varying the energy of the proton beam one can obtain different values of the gamma yield for the same value of the beam current. This is due to the fact that the cross section for the reactions ( 1) and (2) strongly depends on the energy of the incoming particles [ 3-81.

The number of gamma rays emitted from a thick target is given by the expression:

I =N,TfeAw - J

(+(h') dE SC&l) p'

Ep=E

(3)

where Np is the number of incoming protons having initial energy Ep; T is the number concentration of atoms of the

element in the target; f is the probability to emit a gamma particle with a certain energy; a( Ep) is the cross section for the reaction at energy Ep of the protons; e is the detector

0168-583X/97/$17.00 @ 1997 Published by Elsevier Science B.V. All rights reserved

P/ISOl68-583X(97)00292-9

138 N. Uzunov, I. Penev/Nucl. Instr. and Meth. in Phys. Res. B 129 (1997) 137-138

Table 1 Most appropriate pairs of elements for element analysis

Element A-IM Z-l

Relative

abundance ( S)

Element

9 Relative

abundance (%)

9Be

“B

‘9F

22Ne

24MMg

“AI

28Si 30Si

3lP

39K

46Ti

100

80.26

100

8.82

78.70

100

92.21

3.09

100

93.10

7.93

‘OB

‘ZC

‘ONe

23Na

23Na

26Mvlg

“Al 3lP

?S

‘l°Ca

++z

19.8

98.89

90.92

100

100

Il.17

100

100

9.5

96.97

100

efficiency for the energy of the gamma rays; Aw is the solid angle; S( Er) is the stopping power.

Using the notation

0

a(E,) = feAo s atEPf dE ~

StEpI ” (4)

E,,=E

Eq. ( 1) can be simplified:

I = N,Tu( Ep). (5)

When a sample contains elements of the type g:!M and

;N, and the energy of the proton beam is high enough to ensure both reactions (1) and (2), then for the resulting intensity of the gamma line one can obtain:

I = (uN(EP)TN + ~M(E~)TM)N~, (6)

where indexes N and M denote terms in the intensity corre- sponding to the elements N and M, respectively.

Applying (6) for two different values of the energy Epl and Eps of the incoming protons one can obtain two equa- tions for the intensity of the same gamma line:

II =(uNI(E~I)TN+uMI(E~~)TM)N~I

at energy El of the proton beam and

Iz = (&rz(Epz)~~ +a~z(E~z)G4)Np2 (8)

at energy E2 of the proton beam. Eqs. (7) and (8) could be independent since the cross

section for the reactions ( 1) and (2) are non-linearly depen-

dent on the energy of the protons [ 3-81. Thus it is possible to find a solution of (7) for the unknown quantities of the elements TN and TM provided that the coefficients tzMMi ( Epi) and aNi ( E,) (i = 1,2) are measured prior to the experiment. For a given geometry the values of the coefficients ONi and &ri can be measured experimentally from a sample with known quantity of the elements M and N. The numbers of N,I and Np2 can be obtained from the measured beam current for the corresponding energy of the proton beam. A simpler way to obtain the coefficients in Eqs. (7) and (8) is when aM1 = 0 or aM2 = 0. This is possible for energies of the proton beam below the threshold for the reaction ( 1) . Varying the energy of the proton beam one can obtain a larger system of linear equations for the quantities of the two elements TN and TM and to try to optimise the solution of such a system with respect to the experimental error.

If the procedure described above is applied for a different energy of the emitted gamma rays, then one can obtain a new set of algebraic equations:

1~ = (UNi)(Ept)TN + aMi&(Epk)TM)Npi;

i= 1,2,...,m; k= I,2 ,..., n. (9)

Here Irk is the intensity of the gamma rays for the kth gamma peak, measured at the ith initial energy of the proton beam Epi. Thus one can extend the optimisation procedure for the whole set of equations (9). The method could be applied to pairs of elements with Z < 20 when PIXE is not suit- able because of the low energy of the induced gamma rays and PIGE could lead to an experimental error because of the interfering reactions ( 1) and (2). The combinations for the pairs of stable isotopes for the most suitable elements to which the method could be applied is given in Table 1. The method for quantitative analysis of samples using a com- mon gamma peak, in particular for calcium and potassium is described earlier [ 91.

References

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and Techniques (Dekker, New York. 1993)

[ 21 S.A.E. Johansson, J.L. Campbell, PIXE: A Novel Technique for

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[ 41 P.M. Endt, C. Van der Lean, Nucl. Phys. A 105 (1967) I. [ 51 F. Ajzenberg-Selove, T. Lamitsen, Nucl. Phys. A I14 (1968) 1.

[ 61 F. Ajzenberg-Selove, T. Lauritsen, Nucl. Phys. A 152 (1970) 1. [7] P.M. Endt, C. Van der Leon, Nucl. Phys. A 235 (1974) 27.

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