Probabilities for radiative vacancy transfer from Li (iZ1, 2, 3) sub-shells

to the M, N and higher shells for elements with 77%Z%92

Manju Sharma a, Sanjeev Kumar a, Prem Singh a, Sanjiv Puri b, Nirmal Singh a,*

a Department of Physics, Panjab University, Chandigarh 160014, Indiab Department of Physics, SLIET, Longowal 148106, India

Abstract

The probabilities for transfer of the Li (iZ1, 2, 3) subshell vacancy to the M, N and higher shells through radiative decay, hLiJðRÞ, have been

deduced for the elements with 77%Z%92 using the measured L X-ray production cross-sections at (i) the 59.54 keV g-rays such that BL1!

Einc !BK and (ii) the K X-rays of a suitable secondary target chosen such that BL3!EKa !BL2

and BL1=L2!EKb !BK; where BK=Li

is the K

shell/Li subshell ionisation threshold of the target element. The deduced probabilities are compared with those calculated using the radiative and

nonradiative transition rates based on the Dirac–Fock (DF) and the relativistic Dirac–Hartree–Slater (RDHS) calculations, respectively.

q 2005 Elsevier Ltd. All rights reserved.

1. Introduction

An atomic inner-shell vacancy produced following ionis-

ation by photons/charged particles decays either by the

radiative (X-ray) or nonradiative [Auger (A) and Coster-

Kronig (CK)] transitions. In the radiative and Auger transitions

the primary vacancy shifts to an outer shell where as in the CK

transitions it is displaced to an outer subshell of the native shell.

Additional vacancies are also created in the outer shell through

the Auger and CK transitions. The probabilities, hLiJðRÞ (iZ1,

2, 3 and JZM, N and higher shells), can be deduced by using

the measured intensity of the Li–J X-ray transition and

information of the primary Li (iZ1, 2, 3) subshell vacancy

distribution. The measurements for these parameters are

scarce. The probability of vacancy transfer from the L to M

shell via the radiative and nonradiative transitions, �hLM, have

been deduced by Puri et al.[1] for elements with 70%Z%92

by measuring the M X-ray yields from the targets excited by

photons of energy below and above the L shell binding energy

of the elements. Recently, Onder Simsek[2] have reported the

probabilities, hL3JðRÞ (JZM, N and higher shells), for Pb, Th

and U, deduced using the measured L3 subshell X-ray

intensities from the targets excited by K X-ray of Rb, Nb and

Mo secondary exciters used in conjunction with the 241Am

source. The method used for estimation of additional

0022-3697/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jpcs.2005.09.070

* Corresponding author.

contribution to the L3 subshell X-rays due to excitation by

the scattered 59.54 keV photons is not dependable[3].

In the present work, the probabilities, hLiJðRÞ (iZ1, 2, 3

and JZM, N and higher shells), have been deduced for the

77Ir, 78Pt, 79Au, 80Hg, 81Tl, 82Pb, 83Bi, 90Th and 92U elements

using the theoretical photoionisation cross sections[4] and the

X-ray production (XRP) cross-sections measured by us[5–8]

following the Li subshell ionisation by (i) the 59.54 keV g-rays

such that BL1!Einc !BK and (ii) the K X-rays of a suitable

secondary target chosen such that BL3!EKa!BL2

and

BL1=L2!EKb!BK; where BK=Li

is the K shell/Li subshell

ionisation threshold of the target element. The deduced

probabilities are compared with the theoretical ones calculated

using the radiative and nonradiative transition rates based on

the Dirac–Fock (DF)[9,10] and the RDHS calculations[11],

respectively.

2. Measurements of vacancy transfer probabilities

The experimental set up involved a Si(Li) detector and

an annular source geometry in the direct and secondary excita-

tion modes[5]. In the direct excitation mode, the 59.54 keV

g-rays from an annular source of 241Am were used for target

excitation. The production cross-sections for the Ll, La, Lh

X-rays and the resolved components of the Lg (Lg1,5, Lg2,3,

Lg4) and Lb (Lb1,5,7, Lb3,4,6, Lb2,15, Lb9,10) X-rays following

ionisation in the Li (iZ1, 2, 3) subshells by the 59.54 keV

g-rays have been measured for 77Ir, 78Pt, 79Au, 80Hg, 81Tl,

82Pb, 83Bi, 90Th and 92U. In the secondary excitation mode,

the KBr/RbCl/RbNO3/SrCO3/Y/Mo secondary exciters in

the pellet/foil form were excited by the 59.54 keV g-rays to

Journal of Physics and Chemistry of Solids 66 (2005) 2220–2222

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Table 1

The deduced radiative vacancy transfer probabilities, hLiJðRÞ (iZ1, 2, 3 and JZM, N and higher shells), for different elements

Elements Vacancy transfer probability

hL1MðRÞ hL2MðRÞ hL3MðRÞ hL1NðRÞ hL2NðRÞ hL3NðRÞ

77Ir 0.086 0.288 0.248 0.025 0.057 0.048

78Pt 0.086 0.290 0.242 0.024 0.062 0.048

79Au 0.076 0.288 0.250 0.021 0.057 0.049

80Hg 0.078 0.293 0.262 0.020 0.066 0.051

81Tl 0.086 0.291 0.256 0.022 0.066 0.055

82Pb 0.088 0.312 0.270 0.023 0.069 0.055

83Bi 0.088 0.324 0.284 0.024 0.071 0.060

90Th 0.119 0.365 0.346 0.027 0.093 0.072

92U 0.143 0.367 0.363 0.032 0.098 0.075

M. Sharma et al. / Journal of Physics and Chemistry of Solids 66 (2005) 2220–2222 2221

obtain the K X-rays of Br/Rb/Sr/Y/Mo, which were further

used for target excitation. The measurements were done for

resolved components of the L3 subshell X-rays following

ionisation mainly in the L3 subshell by the K X-rays of

secondary exciter. The secondary exciter-target combina-

tions were chosen such that BL3!EKa !BL2

and

BL1=L2!EKb !BK; where BK=Li

is the K shell/Li subshell

ionisation threshold of the target element. The details of the

experimental set up and evaluation procedure are given

elsewhere[12].

76 80 84 88 92

0.04

0.08

0.12

0.16

0.24

0.28

0.32

0.36

0.24

0.28

0.32

0.36

0.40

Atomic number (Z)

Vac

ancy

tran

sfer

pro

baba

ility

(b) ηL2M

(c) ηL3M

(a) ηL1M

Measured

Calculated

Fig. 1. The measured and calculated vacancy transfer probabilities, hLiJðRÞ (iZ

The measured XRP cross-sections have been used to deduce

the probabilities, hLiJðRÞ (iZ1, 2, 3 and JZM, N and higher

shells), using the equation hLiJðRÞZ

Pp sLXp=s

tLi

; the sum-

mation over p in the numerator is for the Li subshell X-ray

components, viz., pZb3,4,9,10 for hL1MðRÞ; pZg2,3,11 for

hL1NðRÞ; pZh, b1,17 for hL2MðRÞ; pZg1,5 for hL2NðRÞ; pZl,

a,t ands for hL3MðRÞ; and pZb2,6,15 for hL3NðRÞ. The stLi

represents the total number of Li subshell vacancies including

those transferred through the CK transitions and is given by

stLi

ZP

k%iðsLiCsLk

fkiÞ; sLibeing the Li subshell

76 80 84 88 92

0.01

0.02

0.03

0.04

0.06

0.08

0.04

0.08

0.12

Atomic number (Z)

(e) ηL2N

(f) ηL3N

(d) ηL1N

Measured

Calculated

1, 2, 3 and JZM, N and higher shells) as a function of atomic number.

M. Sharma et al. / Journal of Physics and Chemistry of Solids 66 (2005) 2220–22222222

photoionisation cross-section. sLibased on the RDHS model

were taken from the tables of Scofield[4] and the f12 CK yields

were taken from the tables of Puri et al.[13].

The measured L XRP cross-sections at 59.54 keV have

been used for evaluation of the hL1JðRÞ and hL2JðRÞ. The L3

XRP cross-sections measured using K X-rays of the

secondary targets have been used for evaluation of the

hL3JðRÞ. These were evaluated using sLi[4], ui and fij[12,14]

and fractional X-ray emission rates (Fik)[10] in Eqs. (4)–(6)

of Refs.[7]. The cross-section ratio, sLb2;15=sLa, measured

following selective L3 subshell ionisation was used to

deduce (i) sLb3(L1–M3) in 77Ir, 78Pt[7] and 79Au[8] from

sLb3;2;15, (ii) sLb1

(L2–M4) in 82Pb and 83Bi from sLb1;2;15[7]

and (iii) sLb1;3(L1–M3, L2–M4) in 80Hg and 81Tl, from

sLb1;3;2;15[8] measured at 59.54 keV. In 80Hg and 81Tl, sLb3

(L1–M3) was deduced by normalizing the measured cross-

sections for rest of the L2 subshell X-rays in accordance

with the DF emission rates[10], our earlier measured u1 and

f13 yields[8,15], and the RDHS model based f12 and f23

yields[13]. These sLb3were used for evaluating hL1MðRÞ and

to deduce sLb1required for evaluating hL2MðRÞ.

3. Results and discussion

The present measured probabilities, hLiJðRÞ (iZ1, 2, 3

and JZM, N and higher shells), for the 77Ir, 78Pt, 79Au, 80Hg,

81Tl, 82Pb, 83Bi, 90Th and 92U elements are listed in Table 1.

The error in the measured vacancy transfer probabilities is

mainly due to uncertainties in the measured XRP cross-

sections and is estimated to be w7% except for hL1MðRÞ

which bear the error of w10%. The measured values of hLiM

ðRÞ and hLiNðRÞ are compared with the theoretical ones.

Theoretical probabilities, hLiJðRÞ (iZ1, 2, 3 and JZM, N

and higher shells), are evaluated using the equation,

hLiJðRÞZ

Pk GRðLi/JkÞ=GðLiÞ; where GR is the partial

width (transition rate) corresponding to the radiative transition

between the subshells given in parentheses and G(Li) is the

total Li subshell width, i.e. sum of the radiative and non-

radiative transition rates. In the present calculations, more

reliable[16,17] radiative transition rates based on the DF

model [10] and the nonradiative transition rates based on the

RDHS model [11] have been used. The nonradiative transition

rates are available for limited number of elements with

25%Z%92. While interpolating for the intermediate elements,

the cutoffs and onsets of different CK transitions were taken

into account in accordance with the CK transition energy

calculations of Chen et al. [18]. The measured and calculated

values of hLiMðRÞ and hLiN

ðRÞ are plotted in Fig. 1. The

measured hL2JðRÞ and hL3JðRÞ values exhibit a good agreement

with the calculated ones for all the elements under

investigation. The measured hL1JðRÞ values are on the average

higher by w27% and the deviations are exceptionally higher

(w60%) in case of 78Pt. Nearly same values of the measured

hL1MðRÞ and hL1NðRÞ for 77Ir and 78Pt indicate that the

jump, predicted in the calculated values due to the onset of

the L1–L3M4 CK transition at ZZ78, does not exist. Rather, it

is likely that the observed decrease of w15% in the measured

hL1MðRÞ and hL1NðRÞ values at ZZ79 corresponds to the onset

of the L1–L3M4 CK transition, which is of smaller magnitude

compared to the predicted value w25% at ZZ78. The total L1

subshell level width, G(L1), is mainly contributed by the CK

transitions and hence, the observed higher values of hL1JðRÞ

can be due to lower values of G(L1). For the elements in the

atomic region 77%Z%92, the L1 subshell vacancies decay

mainly via the CK transitions (w70%) with the L1–L3 CK

transition being the dominating channel[13]. The observed

L1–L3 CK yield (f13) are found to be lower by w15% than the

RDHS values in this atomic region[12] except for 77Ir and 78Pt

where the values are w35% lower. In summary, the theoretical

transition rates for the CK transitions based on independent

particle approximation (IPA) are overestimated.

Acknowledgements

Financial support from the University Grants Commission,

New Delhi, under the centre of advance study programme,

and the Department of Science and Technology, New Delhi,

is gratefully acknowledged. MS and SK acknowledge the

financial support from Council of Scientific and Industrial

Research, New Delhi.

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