Theoretical X-ray relative intensities at incident photon energies across the L_i(i=1-3) absorption edges for Yb

Theoretical X-ray relative intensities at incident photon energies across the L_i(i=1-3) absorption edges for Yb

Sanjiv Puri

Department of Basic & Applied Sciences, Punjabi University, Patiala-147002, Punjab, India.

E-mail address: sanjivpurichd@yahoo.com

Abstract

The intensity ratios,

ILk

/ IL 1

based PCS [3] in order to highlight the importance of electron exchange and overlap effects at photon energies in vicinity of the absorption edge energies.

(k l, ,

2 , 1 ,

2,15 , 3 ,

4 , 9,10 ,

1,5 ,

6,8 ,

2,3 , 4 )

and

ILj

/ IL

(j = ) have been evaluated at incident

2. Evaluation Procedure

The production cross sections ( X ) for the

photon energies across the Li(i=1-3) absorption edge energies of 70Yb using theoretical data sets of

Lk (k

l, , 1 ,

2 , 1 ,

2,15 ,

3, 4 ,

9,10 ,

1,5 ,

Lk

6,8 ,

2,3 , 4 )

different physical parameters, namely, the Dirac-

Hartree-Slater (DHS) and the Dirac-Fock (DF)

X-rays at incident photon energy, Einc, have been

evaluated using the equations

model based Li(i=1-3) sub-shell photoionization

X

Lk Li

i Fik (1)

cross sections, the DF model based X-ray emission rates, and the DHS model based fluorescence and Coster-Kronig yields in order to highlight the importance of electron exchange effects at photon energies in vicinity of the absorption edge energies.

Where, Fik (i=1-3) represents the fractional emission rate, i (i=1-3) represents the Li sub-shell fluorescence yields and Li denotes the total number of vacancies in the Li(i=1-3) sub-shells including those transferred through the CK transitions and can be calculated using the equation

1. Introduction

P

Li Li

k i Lk

f ki (2)

Accurate data on the relative intensities of

Where, P i

(i=1-3) represent the Li sub-shell

L

different X-ray lines are of considerable importance

for investigation of atomic inner-shell ionization

photoionization cross sections and the fki are the Li sub- shell CK transitions probabilities. The intensity ratios,

processes as well as for a variety of applications

including the quantitative elemental analysis of

ILk

/ IL 1 (k

l, ,

2 , 1 ,

2,15 ,

3, 4 ,

1,5 ,

6,8 ,

2,3 ,

4 ) and

different types of samples using X-ray emission techniques (EDXRF and PIXE). The relative

ILj / IL (j = ) have been deduced from the Lk XRP cross sections using the equations,

intensities of different X-ray lines can be deduced

ILk

/ IL 1

X X

/

Lk La1

(3)

from the X-ray production (XRP) cross sections which, in turn, can be evaluated using theoretical data on physical parameters, namely, photoionization cross sections (PCS), fluorescence and Coster-Kronig (CK) yields and X-ray emission rates. Different sets of these physical parameters evaluated using the Dirac-Hartree-Slater (DHS) and Dirac-Fock (DF) models are available in literature [1]. In the DHS model, the potential is assumed to be equal for the initial and final states of the atom undergoing transitions. In the DF model, the potential is assumed to be different for initial and final states and hence electron exchange and overlap effects were included. In the present work, the Li(i=1-3) sub-shell intensity ratios have been evaluated at incident photon energies just above (within 100 eV) the Li edge energies of the

In these evaluations, the DF model based X-ray emission rates [4], the DHS model based Li(i=1-3) sub-shell fluorescence and Coster-Kronig yields [5] and two sets of the photoionization cross sections (PCS) based on the DHS [3] and the DF [2] models were used. The DHS model based photoionization cross sections [3] are available at selected incident photon energies across the Li(i=1-3) absorption edge energies. These cross sections at required incident photon energies have been interpolated from the available limited data assuming a dependence of the form (aEb).

3. Results and Discussion

The two sets of calculated intensity ratios,

Ytterbium (Z=70) using the DF model based PCS [2] for

ILk / IL 1 (k

l, ,

2 , 1 ,

2,15 , 3 ,

4 , 1,5 ,

6,8 ,

2,3 , 4 )

comparison with those calculated using the DHS model

and ILj / IL (j = ) for 70Yb are given in Tables 1 &

2. It may be mentioned that the DF model [2] based PCS in the considered photon energy range are lower than the DHS model [3] based values by ~14-27% for the L1 sub-shell and by ~6-15% for the L2 and the L3 sub-

overlap effects are found to be significant, predominantly, in vicinity of the Li sub-shell absorption edge energies.

shells. The X-ray intensity ratios,

ILk / IL 1

References

(k ,

1 , 1,5 ,

6,8 )

evaluated using the DF model

1. Sanjiv Puri, X-ray Spectrom. 40, (2011) 348.

   based PCS are found to be lower than those calculated using the DHS model based PCS values by

2. Private Communication (2013).

3. J.H. Scofield, Lawrence Livermore Laboratory Report No. UCRL 51326 (1973).

   40-45%. Similarly, the ratios,

   ILk / IL 1

4. J.L. Campbell and J.X. Wang, Atom. Data Nucl. Data

   (k 3, 4 ,

   9,10 ,

   2,3 ,

   4 ) evaluated using the DF model

   Tables 43 (1989) 281.

5. Sanjiv Puri, D. Mehta, B.Chand, N.Singh and P.N.

based PCS are lower than those evaluated using the DHS values by 40-48%. Therefore, the exchange and

Trehan, X-ray Spectrom. 22 (1993) 358.

Table 1: The intensity ratios, ILk / IL 1 (DHS) (k

l, ,

2 , 1 ,

2,15 , 3 ,

4 , 9,10 ,

1,5 ,

6,8 ,

2,3 ,

4 ) and ILj / IL (j

= ), at incident photon energies across the Li(i=1-3) sub-shell absorption edges of Yb.

Table 2: The intensity ratios, ILk / IL 1 (DF) (k l,

, 2 ,

1 , 2,15 ,

3 , 4 ,

9,10 ,

1,5 ,

6,8 ,

2,3 , 4 )

and ILj / IL

(j =

), at incident photon energies across the Li(i=1-3) sub-shell absorption edges of Yb.