Probabilities of X-Ray satellites spectra by Coster Kronig and Shake off
Process.
Surendra Poonia
Division of Natural Resources and Environment,
Central Arid Zone Research Institute, Jodhpur - 342 003, Rajasthan, India
E-mail: [email protected]
Abstract: The X-ray satellite spectra arising due to 2p-13x-1-3x-13d-1 (x º s, p, d) transition array, have been
calculated, using available Hartree-Fock-Slater (HFS) data on 1s-1-2p-13x-1 and 2p-1-3x-1,3x'-1 Auger transition
energies. The relative intensities of all the possible transitions have been estimated by considering cross - sections
for the Auger transitions simultaneous to a hole creation and then distributing statistically the total cross sections
for initial two hole states 2p-13x-1 amongst various allowed transitions from these initial states to 3x-13d-1 final
states by Coster-Kronig (CK) and shake off processes. In both these processes initial single hole creation is the
prime phenomenon and electron bombardment has been the primary source of energy.
Keywords: X-ray satellites, Coster Kronig transition, Shake off processes.
1. Introduction
A survey of the literature reveals that six decades
For several past years, the identification of
ago Parratt [11] reported the high-resolution
the transitions in doubly and triply inner shell
measurement for the complete L X-ray spectrum of
ionized atoms, which can be assigned to various X-
Silver. This work has been extended by McGuire
ray satellites [1-7], has been in progress in this
[12], who used radiative, Coster-Kronig and Auger
laboratory. The method adopted is more reliable than
transition rates and Wentzel’s hypothesis to compute
Wentzel's Z+1 approximation [8,9]. The transition
the Ag L X-ray satellite spectrum. The same
energies have been calculated using Hartree-Fock-
spectrum has been interpreted on the basis of one
Slater (HFS) model [10] in the intermediate coupling
addition of M and N shell vacancy by Chen et. al.
scheme and their relative intensities have been
[13]. In the spectrum of silver, four lines reported on
estimated
In
high energy side of and comparatively far away from
continuation of the same work, we present here the
La line have been identified by Soni [14] as
Probabilities of X-Ray satellites spectra by Coster
hypersatellites. Krause et. al. [15] have interpreted
Kronig and Shake off Process.
the L X-ray emission spectrum of 40Zr in terms of an
in
the
L-S
coupling
scheme.
extra M3 or M5 vacancy. In this paper, we report the
Probabilities of X-Ray satellites spectra by Coster
Kronig and Shake off Process. The complete data
have been compiled by Cauchois and Sénémaud
[16].
2. Results and Discussion
For the emission of L satellites, in hand, those
transitions are being considered in which the initial
states are doubly ionized, one vacancy lying in 2p3/2
sub-shell and second one in any of M-sub-shells.
Such states are formed by two processes.
Figure 2. Shake off Process
(i) 2s-1-2p3/2-13x-1 Coster-Kronig transitions, namely
conversion of one-hole state 2s-1 to a two hole
In both these processes the initial single hole
state 2p3/2-13x-1 (x º s, p, d) through the Auger
creation is the prime phenomenon. Various efforts
transition 2s-1-2p3/2-13x-1.
have been made for calculating, theoretically, the
cross sections for such single ionization. Moores et
al.[17] have presented formulas for these crosssections in which electron bombardment has been
the primary source of energy. Their formula for
probability of formation of a hole in a ‘nl’ state, is
snl = (p n4 a02 Znl / Z4) snl (R)
---(2)
or, say
snl = (1.628 * 10-14) Znl snl (R)/ Enl2
Figure 1. Coster Kronig transitions L1®L2M
In these formulas n and l denote the sub-
(ii) By shake-off process, namely an electron from
M-shell
of
the
atom
may
escape
---(3)
out
simultaneous to the formation of a 2p3/2 vacancy.
This additional vacancy is created due to
shaking of the atomic orbits caused by a sudden
change in the potential field in the atom, taking
shell of the atom in which a hole is created, Znl
denotes the total number of electrons in this subshell and Enl denotes the binding energy of the
electron in this sub-shell. snl(R) is known as reduced
cross-section, and is calculated by the formula given
in equs. (4)
place when a 2p3/2 electron leaves the atom with
a fast speed.
snl (R) = (1/u) [A ln u +B (1-1/u)2 +
(C/u+D/u2) (1-1/u)] ---(4)
The A, B, C and D are constants, whose
s', taken from table of McGuire [19]. It should be
values for ionization in 2s1/2 sub-shell are A = 0.823,
noted that the Coster-Kronig transitions help in
B = 3.69, C = 0.62, D = 1.79 and in 2p3/2 sub-shell
forming only 2p3/2-1-3d-1 states, and that too only in
are A = 0.530, B = 5.07,
C = 1.20 and D = 2.50
the elements [19] up to Z = 47. The other 2p3/2-13x-1
[Ref. 17]. The dimensionless parameter u denotes
transitions are not allowed energetically in these
the ratio:
elements. Further, no such Coster Kronig transitions
u = E0/Enl = Incident energy of incoming
electron/Binding Energy of the nl electron.
take place in elements [19] with Z = 48 to 73.
Coming to shake-off process, we have first
We have calculated the values of snl for
calculated the cross - section s(2p3/2-1) using
initial single hole states, namely 2s1/2-1 and 2p3/2-1,
formulas given in Equs. (2) to (4) and have, then,
involved in the present study by using these
multiplied it with the shake-off probability of a M-
formulas.
sub-shell electron. This probability has been
calculated by interpolation from the percentage
Since different
researchers,
who have
measured satellite spectra of various elements
experimentally, have used different
probabilities of shake-off processes occurring with a
single photo-ionization in inert gases [20].
excitation
energies, we have taken arbitrarily the value of u as
Subsequently
the
total
probability
of
2.5, a practical value found [18] to give a
creation of an initial state 2p3/2-13x-1 has been
measurable intensity of satellites.
determined by adding these two cross – sections as,
calculated above.
We understand that after creation of a single
hole state, it is the probability of a particular
The cross - section for a set of 2p3/2-13x-1
subsequent process that will lead to the formation of
levels with x denoting any one sub-shell of M -
two-hole state. If the single hole so created gets
shell, so calculated, has been assumed as the total
converted through a Coster Kronig transition, to a
probability of all the transitions from this set. This
double hole state, the probability of formation of
has been distributed statistically among all the
double hole state via this process is written as s.s',
allowed transitions
where s is the 2s1/2 sub-shell ionization cross section
considering first all the multiplets of super-
of the atom and s' is the probability of its decay
multiplets from various
through the CK transition 2s-1-2p3/2-13x-1.
from this
(2S+1)
set
of
levels,
(L) levels of the set and
then using tables of White and Eliason for relative
probabilities of the transitions of each multiplet, as
The value of s' have been taken for the
31
given by Condon and Shortley [Ref. 10] for relative
work of McGuire , who has presented the
probabilities of the transitions of each multiplet. The
calculated values of s' for almost all possible Coster
detailed method of this distribution have been used
Kronig transitions in various elements.
by Poonia and Soni in our earlier reports [1-7].
The value of s(2s-1), so calculated, has been
multiplied with Coster-Kronig transition probability
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