- Email: [email protected]
K and L shell X-ray cross sections for use in PIXE analysis systems
Nuclear Instruments North-Holland
and Methods
in Physics
Research
B49 (1990) l-9
Section I. X-ray production K AND L SHELL X-RAY CROSS SECTIONS
FOR USE IN PIXE ANALYSIS
SYSTEMS
David D. COHEN ANSTO,
PMBI,
Menai, N.S. W., 2234, Austrdia
In this review we look at the experimental K and L shell X-ray cross section data available up to the with the predictions of the ECPSSR theory for ionisation by MeV ions. Particular attention is paid energies between 1 and 3 MeV and most elements for the K shell and elements above Sn for individual Variations in the ratios of the bulk of existing experimental data to the predictions of the ECPSSR theory and proton and helium ion energy are presented and discussed.
1. Introduction
Particle induced X-ray emission (PIXE) has now become a well established technique for multielemental analysis of both thick and thin targets. An enormous variety of applications have been found as demonstrated in the Proceedings of the last few PIXE Conferences [l]. Thin target PIXE techniques are now well established. Good examples of this are the PIXE studies in aerosol science and in aerosol monitoring programs [2] where the properties of PIXE particularly lend themselves to large scale monitoring or urban pollution and many thousands of samples have now been run. Thick targets have also been analysed in large numbers using the PIXE technique. The group at Lucas Heights [3], for example. have analysed over 10000 thick obsidian glass samples over the past 10 years. They used the PIXE technique to characterise and source these archaeological artifacts to a variety of volcanoes through the Pacific region and hence unravelled some of the native trade patterns going back thousands of years. The key to these reliable PIXE results lie generally in a well characterised matrix and for the thin and thick samples quoted above elemental concentrations down to a few parts per million are typically quoted with errors of around 3 to 5%. Poorer results will be obtained from volatile matrices such as biological samples. Reliable predictions need good data bases. As early as 1981 Clayton et al. [4] wrote a computer program SOXS (synthesis of X-ray spectra) to generate both thin and thick X-ray spectra for a wide range of target matrices and for both the K and L characteristic peaks for most commonly occurring elements. This is now a fully developed commercial program PIXAN [5], which both analyses PIXE spectra and converts peak areas to elemental concentrations for a given matrix composition. The data bases used by the PIXAN package have been discussed at length by Cohen and Clayton [6] and 0168-583X/90/$03.50 (North-Holland)
6 Elsevier Science Publishers
B.V.
end of 1988 and compare it to protons and helium ion La. Lp and Ly transitions. with target atomic number
the peak area routines critically assessed by Campbell et al. [7] with most favourable results. There are many different parameters required for the prediction of X-ray yields [6]. These include fhtorescence yields and radiative widths [8-111, mass attenuation coefficients [12-151, ion stopping powers [16.17] and X-ray cross sections [l&29]. The errors associated with these data bases have gradually come down over the years to between 1 and 5% in absolute terms in some cases. In this paper we will discuss K and L subshell cross sections necessary to predict both thin and thick target PIXE X-ray yields for light ions. Typically. ion energies between a few hundred keV and 10 MeV are used and ion (Z,) to target (Z, ) atomic number ratios less than or of the order of 0.3. For (Z,/Z,) > 0.3 projectile electron capture contributions to the inner shell target vacancy production rates become significant and must be added to the direct ionisation contributions. The vast majority of experimental K and L data to date has been compared with the so-called ECPSSR theory of Brandt and Lapicki [30.31]. which is a derivative of the PWBA approximation with corrections for Coulomb repulsion (C), polarisation and binding energy changes via the perturbed stationary states (PSS). relativistic effects (R) and ion energy loss effects (E). Cohen [22,29] has published extensive ionisation cross section tables based on this model using hydrogenie electron wave functions while Chen and Crasemann [21,28] have published a more limited tabulation based on DHS wave functions. Inner shell vacancy production via direct Coulomb interaction between a projectile and a target electron has also been studied using the binary encounter approximation (BEA) [32,33] and the semiclassical approximation (SCA) [34]. However, since most comparisons for PIXE users have used the ECPSSR theory we will restrict ourselves to this approach here.
1. X-RAY PRODUCTION
D. D. Cohen / K and L shell X-ray cross secrions
2
2.Cross sections
and yields
cence
yields
fi3=0, The tions
ECPSSR
theory
predicts
ionisation
IJ,’ for a given shell or subshell
Experiments
generally
measure
given peak p which originates filling
the vacancy
sections
are related
cross
s = K. L,,
X-ray
yields
in the shell s. The
L,,
L,.
Yp in a
from an X-ray
in the following
sec-
yields
Coster-Kronig
as
manner
the
this reason
is the initial cross
stopping
section power
coefficient. that
for
a peak
for the ion,
that
including
p is the mass peak
p,
effects,
attenuation by weight
of
W is the atomic number,
D is
Q is the total
F is the detector
e is the ion charge,
and 0, and
0, are the angle of the incoming
beam and the outgoing surface
Eq. (1) is valid requires that
to the target for light
they have a unique
incident
energy.
the X-ray
along
charge
state
It does not account
yield
from
target
targets
and
paths
and
straight
as a function
for contributions
recoil
and
ion
of to
straggling
effects. The X-ray should
production
cross sections
not be confused
cross
section
these
for
u,’ and
with again
the K and
0,” for a peak p
the ionisation
(vacancy)
the relationships
L subshell
vacancies
=
out
experimental
with
that
between
cross
which
where
o K is the K shell fluorescence of the width
the total K shell width.
yield and (F,/r,
of the p transition Eq. (3) is relatively
the K shell has no subshells.
However
have three subshells,
and L,,
L,,
L,
relative
overlap
in the K shell case the
simple
)
since
for the L shell we and
emission
The
K and L subshell
exception fitted
of the L,
from
functions
the
L,
subshell.
CosterrKronig
The
transition
f,,
and
an initial the
vacancy
wL,
rates and the subshell
are
in the
fluores-
the
for L subshell rates of Chen
et
the recommended
[8] in the high target we have a preference
over the theoretical fluorescence
Z for
calcula-
of atomic
of Krause
yields.
are smoothly number
expressions
data and should Average
total
prove useful L shell
also been given by Cohen
with
the
varying
in-
and
are well
of the form
to the tabulated to better
Z
than
in PIXE
fluorescence
given
in
data of Krause, they reproduce f 3%. have been
given in table 2 of ref. [6] for K, L subshell from
for
enough.
with the range of Z for which
the numbers p originates
treatthat
favouring
computations
subshell,
by polynomial
together
the peak
is based
of the DHF
evidence
of Krause
rates
of imperfect
This preference
significantly
numbers
wave functions.
treatment
and Coster-Kronig
eq. (6) of ref. [6]. Fits
where
the
tions.
creasing
X (ILP
and
yields,
[39], but he suggests
and in these situations
the experimental
on DHS
superiority
wave function
values
Chen
et al. [38] and
is not yet convincing
yields
[6] suget al. [lo]
[35] points
of
later DHF
experimental
predictions
Cohen
fluorescence
of Chen
exchange.
ment
L shell
probabiland to be
Campbell the
a rigorous
the demonstrated
experimental
to
sets
[8]
subshell
[9] also form a self-consistent
upon
region
L
up to 1978
tabulations
Scofield’s
include
wave function
the
Krause
and
rates of Salem
with
transitions
he prefers
fluorescence
(3)
wK”:(rp/rK)*
section
data base founded
However,
K
data
emission
rates of Scofield
The DHS
are known
experimental
[21] together
theoretical [37]
data
less
and the available and has too much
of
the yield calculations. the
Crasemann emission
data bases.
is still a little
data bases
compilation
al. [38] do differ
is the ratio
acceptable
is still too sparse
gests the experimental
DHF
[6,36]: X uK~
consistent
emisrates of
yields and L shell Coster-Kronig
for most
Coster-Kronig
normal.
ions on heavy
that ions slow down
fluorescence ities
mea-
of eq. (3) the fluores-
one data base over another.
a complete
to complete
efficiency
X-ray
with respect
gives
For
section
et al. [lo] or the theoretical
data
to suggest
X-ray.
cross
[8] and the experimental
as to the preferred
scatter
the
ion loss
on thin targets.
conversions
of Krause
experimental
produc-
S(E) is the matrix
by the detector,
the target,
filter
p,
N, is Avogadro’s
the solid angle subtended hitting
is the X-ray
concentration
produced
of that element,
charge
e,“(E)
C is the relative
element
weight
ion energy,
since
no energy
production
[9,37] are considered
certain
are dis-
considerably
constant,
For the L shell eq. (4) the picture
/ E”COS(e,)s(E)
IL’x=IL
tion
Scofield
cos(0,)dE
widths
for the emerging
X-ray
are performed
yields
are
requires
absorption
the K shell
cence
dE
target
sion rates of Salem E
E,
For
and radiative
over
most
surements
and
uL3=fli=0.
eqs. (1) and (2) reduce
of a thin
and no X-ray
(1)
we put
below.
integrations
definition
[5.6.35]:
i = 1 we put uL2 = uL3 =
i=2
transition
further
For thin targets
and cross
well-known
For for
ionisation fix = I, and for i = 3 all three L subshell cross sections are used. The fluorescence yields, cussed
transition
respectively.
fi2=f13=1;
and M shell
computer yields
[40] for all targets
GL
codes. have
from Ni to
3
D.D. Cohen / K and L shell X-ray cross sections
Cm using the ECPSSR ionisation cross sections and the effective subshell fluorescence yields of ref. [S].
3. K shell
Experimental K shell ionisation cross section measurements were tabulated by Rutledge and Watson [23] as early as 1973. Gardner and Gray [24] tabulated all experimental Auger. X-ray production cross sections from 1973 to 1977. They chose to tabulate only directly experimentally determined quantities to facilitate the comparison of data and theory. Since 1977 Paul and co-workers at Linz have been the main group tabulating and collating K shell cross sections. The bulk of their work is summarised in an extensive report by Paul and Muhr [27] in 1986. In this work a data file containing 7800 total K X-ray or Auger production cross sections, with (Z,/Z,) < 0.3, are compared with the theoretical ECPSSR ionisation cross sections [30.31] using the K shell fluorescence yields of Krause [S]. The experimental cross sections ( ox ) were multiplied by the fluorescence yields ( wK ) and normalised to the theoretical ionisation cross section (u’) and the parameter S = ( o”wK)/u’ plotted as a function of the log,,, of the reduced ion velocity 5, where SK = 2m/B and. q = 40.32E,/[M,( Z, - 0.3)‘] and 19= 11(/( Zz - 0.3)’ Ry, describes the shielding by outer electrons. The experimental ionisation energies I, were taken from Lederer et al. [41]. Paul and Muhr [27] present extensive graphs of S versus log 5 for protons, alphas and other heavy ions (Li. B, C. N. 0, F and Cl) and we refer the reader to them for further detail. In fig. 1 we show the proton data for 4 I Z I 92 as the dashed curve together with N, 0 and F point data
001
I
-0 8
I
-04
I
I
00
I
1
04
1 08
Log cf 1 Fig. 1. Average normalised K shell cross sections S versus log,, reduced ion velocity for proton and heavy ions. The dashed curve is the proton fit of Paul for 4 I Z 5 92. The N, 0. F symbols are for nitrogen, oxygen and fluorine ions and the solid curves are the NECPSSR theory for oxygen bombardment of P. Ca and Cu targets.
as being representative of the heavy ion situation. The solid curves marked P, Ca and Cu are discussed further below. The proton dashed curve was obtained using the fits of eq. (4) and table 5 of ref. [27]. For protons the ratio S sits within f 5% of unity for -0.68 < log 5 < 0.36. This corresponds to a very broad range of targets and ion energies, for example, for an Al target this covers proton energies from 0.1 to 3 MeV and for a copper target energies from less than 0.2 to greater than 10 MeV. Below log [ < -0.7 the K shell ECPSSR theory overpredicts the experimental results by increasing amounts for increasing target Z and reducing ion energy. For 1 MeV protons on Au log .$ = -0.775 and S is only 0.56. however. the measured K shell ionisation cross section at this energy is only 0.1 mb and hence of little use to PIXE analysts when one considers that for 2 MeV protons on Cu the K shell cross section is nearly 100 b, some 6 orders of magnitude larger. The proton data also show a local minimum of about 4% at log 5 = - 0.24 and two local maxima, one at log .$ = -0.6 of around 1% and the other at log 5 = 0.36 of around 5%. These in themselves do not appear to be significant for proton data, however, the trend is clearly continued for the heavier ions as the oscillations in the N. 0 and F data of fig. 1 show. Paul [42] argued that the deviation of S around log 5 = - 0.6 is most probably due to a small deficiency of the binding correction in the ECPSSR theory and this may be backed up by the experiments of Lopes et al. [43]. Paul also attributes the steady rise in S for the heavy ion data above log [ = -0.1 to the projectile electron capture processes for (Z,/Z,) > 0.3. We feel that some of this rise may also be attributed to nonadiabatic effects described in the next section. The fits of Paul to the experimental data have enabled him to define reference cross sections for selected targets and energies. These reference cross sections have considerably smaller errors than any single experimental measurement. Recently extensive reference cross sections have been published by Paul [44] using the same techniques. The techniques of Paul compare experiment and theory. They do not provide the PIXE analysist with a complete data base of cross sections for computational purposes unless the ECPSSR cross sections have been calculated separately. Cohen has now produced K and L subshell ionisation cross sections for p, He [22] and D [29] ions calculated within the ECPSSR formalism, for most targets and ion energies between 100 keV and 10 MeV, using hydrogenic wave functions. Chen and Crasemann [21,28] have produced K. L and M shell ionisation cross sections for protons with a few selected energies from 100 keV to 5 MeV for a narrow range of selected targets, using DHS wave functions in a Brandt and Lapicki formalism [30]. Some results for K shell ionisation cross sections for protons from Paul, Cohen I. X-RAY PRODUCTION
and Harrigan, Brandt and Lapicki and Chen and Crasemann are given in table A of ref. [29]. There are small differences between the theoretical calculations of Cohen 122,293 and those of Brandt and Lapicki [30,31]. These differences have been discussed in detail [29,45] and tabulated for all ion and target combinations by Cohen [29]. Cohen [29] also tabulates the constant CXI = used 5 k/I E, (Mevtl”2 which converts the commonly ion energy E, for different target combinations into the reduced velocity parameter .$ used extensively by Paul and Muhr [27]. This should be of considerable help when using the K shell values of those tabulations which use this reduced velocity parameter [1X-20.27,44]. More recently Lapicki [46] has also tabulated 7418 K shell X-ray production cross sections from 161 different references for p and He ions on targets from beryllium to uranium. Comparisons of these with the ECPSSR theory arrive at similar conclusions to Paul’s compilations. He suggests the ECPSSR theory reproduces the experimental results to between 10 and 20% except for the lowest velocity regime. These deviations were associated with the influence of multiple outer-shell ionisations on the fluorescence yield of light elements, particularly in ionisation by helium ions.
4. Nonadiabatic effects The ECPSSR theory calculates the binding energy within the perturbed stationary state theory of Basbas et al. [47]. This assumes that all states of the atom respond adiabatically to the motion of the ion. However while the adiabatic aproximation will hold at sufficiently low velocities (5 -SC1). it will not be valid at higher velocities (5 2 1). Fortunately, for (5 > 1) the assumption of adiabaticity does not introduce a large error when the total ionisation cross section is calculated because the main contribution comes from distant collisions where binding energy changes are small. Land and Simons [48], using a dynamic model, show that the K shell electron behaves almost fully adiabatically for protons on copper at energies below 2 MeV (5 I 0.78). In general different shells will show different degrees of adiabaticity in response to the projectile. Two approaches to binding are commonly used: (1) United atom limit [49], where the outer electrons relax to their positions appropriate to a target atom having Z = (Z, + Za). (ii) Separated atom limit (ECPSSR theory) where outer electron atoms display no response to the ion and the effect of binding energy is a function of the distance between the two atoms. Sarkadi [50], following the separated atom approach of the ECPSSR theory. assumes only significantly large velocity components of the electron wave function can follow adiabatically the change of the Hamiltonian with time, and defines a parameter h,(v, ) which is conveni-
NON ADIABATIC FUNCTION FOR K AND L SHELLS I I I
121
001
01
1
IO
SCALED VELOCITYx-IV,h',s)
Fig. 2. A plot of the nonadiabatic function X, for the K and L subshells versus the scaled ion velocity.
ently included in the binding and polarisation ter of the ECPSSR theory, namely,
:K=l+gg 2K
K
[k?,
parame-
- hK1’
where the parameters of eq. (5) have their standard meanings defined in ref. 1301. Clearly X = 1 reproduces the ECPSSR theory. We have calculated the parameter X, for s = K. L,. and L,,, subshells as well a the K and L subshell ionisation cross sections and call these the NECPSSR theory. Fig. 2 shows the nonadiabatic function h, as a function of the scaled ion velocity. For the K and L2,1 shells the major effects occur around ( u,/u~~) = 1, whereas for the L, subshell h is actually greater than 1 for ( c!,/L)~~) I 0.5. In fig. 3 we plot the ratio of NECPSSR K shell cross sections to the ECPSSR for several different ions on copper against the relativistically corrected reduced velocity parameter tR defined in ref. [30]. This ratio rises around tR = 0.2. has a maximum near 5 R = 1 and falls again to unity around tR = 3. For protons on copper the maximum nonadiabatic effect is 1.6’% for 3-4 MeV protons, but increases for decreasing Z,, being 6.3% for protons on carbon with tR = 1. However for 0 ions on copper its effect is 13% for 50-60 MeV ions increasing again for lower Z,, being 26% for 0 on silicon. Maybe this nonadiabatic binding correction could fill in the local minimum in the plots of Paul and Muhr 1271 for -0.5 < log < < 0.4, that is for 0.3 < < < 2.5? To test this we have superimposed the ratio (NECPSSR/ECPSSR) on the S = ( o’/ECPSSR) plot of fig. 1 for 0 ions on P, Ca and Cu targets. Comparisons with the 0 symbols of this figure show that some of the deviations for the K shell ionisation by heavy ions for log 5 > - 0.5 can be explained by the nonadiabatic effects. The 1.6% nonadiabatic effect for K shell protons goes some of the way to filiing in the 4% or so local minimum in the experimental data for log 5 = -0.2 (5 = 0.6). However the peak in the nonadiabatic effect at 5 = 1 is clearly shifted to higher
5
D.D. Cohen / K and L shell X-ray cross sections HEAVY IONS ON COPPER
I /(“I
1
”
16 80
1.50-
2r
;ILI
“‘I’ 4060100 MeV 4“I 6 10 20
,' 2
4 6 10 20 40 MeV r I I11111 Proton 0 5 1 2 345710MeV
120 ~ --k 2 IIO4 9 b’
-
1.05-
1 01
0.5
1
2
6. L shell
REDUCED VELOCITY CR
Fig. 3. The ratio [NECPSSR/ECPSSR] ionisation cross sections for K shell ionisation of Cu by p. He. Li and 0 ions as a function of the reduced ion velocity with relativistic corrections.
ion velocities than experimental data.
5. Electron
needed
to fill in this dip in the
capture
For slow fully stripped ions electron capture (EC) from the target K shell into any empty ion shell may become as significant an ionisation process as that of direct ionisation (DI). The probability for EC is, like DI, ion velocity dependent and has a maximum when the ion velocity matches the velocity of the electron to be captured. We have calculated the EC cross sections
ELECTRON CAPTURE CONTRIBUTION I I I I I X@* X Be x0 qC 00 Ne
d:
l
0. 0’
@.
X
Max Contrlb for 0 55 E,slOO MeV
_ :
co .
X 0.
‘I
04
from the target K shell to any empty ion shell for fully stripped Be, C, 0 and Ne ions using the OBK formalism of Lapicki and McDaniel [51]. The results for the maximum contribution, for ion energies between 0.5 I E, 5 100 MeV. are shown in fig. 4 as a function (Z,/Z,). This figure shows a universal curve for ions lighter than Ne. For slow ions we expect (EC/DI) a ( Z,/n,Z,)3 and a fit to the data of the form [EC/(EC + DI)] = ax”/(b + x”) gives u = 1.871. h = 9.026 x lo-’ and n = 3.397, where x = ( Z,/Zz). If we set x = 0.3 in this expression we see that [ EC/(EC + DI)] < 29% for all energies between 0.5 I E I 100 MeV. For x 2 0.36 the maximum EC contribution is always greater than 50%. Fig. 4 also shows why EC contributions for x < 0.1 are considered negligible ( < 1%) and why for x > 0.3 EC contributions should be included in ionisation calculations.
05
[2,/Z,]
Fig. 4. The ratio of the maximum electron capture contributions to the total ionisation versus ion to target atomic number.
The L shell consists of three subshells: the L, subshell with transitions B,, B,, Bs.,,,, yz, yX. y4; the Lz subshell with transitions n, B,. y,. ys, ys and the L, subshell with transitions ~1,. (Y*. B2, Bs, 1. The transitions quoted are those observed by modern X-ray energy dispersive techniques for an initial vacancy in one of the three subshells. In eq. (4) we show how the X-ray production for a peak p, and hence the yields, eq. (1). are related to the three theoretical ionisation cross sections u’. Most L shell PIXE experiments will resolve about 10 of these peaks giving many possible ways to solve eq. (4) for the three unknowns u,’ (i = 1.2.3) for comparison with theory. Cohen [36] has discussed four commonly used methods for converting X-ray production cross sections to subshell ionisation cross sections and shows how both the selection of peaks Lp and the selection of data bases ( w,, f,, , r,,) can strongly affect the final answers obtained. For example, 25% differences in the L, cross sections can be obtained for He on Au using either the Salem et al. [lo] or Scofield (91 emission rates. It is therefore very important to compare experimental X-ray production cross sections for various peaks p, as this will considerably reduce the final experimental scatter. A lot of L subshell data to date has been published as already massaged ionisation cross sections or only in graphical form when comparing with the ECPSSR cross sections. The earlier L shell tabulations of Hardt and Watson [25] to 1976 including a selection of heavy ion data were followed by the tabulations of Sokhi and Crumpton [26] for proton data only between 1975 and 1982. For this review we include the above data and have searched the literature from 1982 to the end of 1988. It is not possible to treat the complex L subshell data in a similar fashion to the K shell data of Paul and I. X-RAY PRODUCTION
D.D.Cohen / K und L shell X-ruy
cross sections
Protons
protons
,”
0
90
60
30 Target
Rtomic
Number
5
0
2.0
MeV
Hsl i urn Ions
90
60
30 Torget
Z
Rtomic
Hel
i urn
Number
Z
Ions
~000~~
1. OMeV
101 0
60
30 Target
Rtomic
Number
90 2
Target
Rtomic
Number
Fig. 5. The normalised (to Lu) LB, Ly, LTotalX-ray production cross sections versus target atomic number. (a) MeV protons and (c) and (d) for 1 and 2 MeV He ions.
Muhr for comparison with the ECPSSR theory. So we only consider the larger X-ray peaks La, LB, Ly and the total L shell, the ion energies 0.6, 1, 2 and 3 MeV. proton and He ions for targets above Sn. With these restrictions the published data base is reduced to 45 separate measurements. These still cover fairly well the complete range of L shell measurements used by PIXE analysts. For comparison with the L subshell ECPSSR theory we use the (0,. _I,,, rLp) data bases of ref. [8,10] to reduce the theoretical ionisation cross sections to their corresponding X-ray cross sections. The results are shown in fig. Sa-d for the selected ion energies. The
and
Z
(b) for 1 and 2
data of fig. 5 have been normalised to the Lol X-ray production cross sections equai to 1000 to reduce systematic experimental errors. In figs. 6a, b we show these absolute La X-ray productions compared with the ECPSSR theory. Clearly this theory does well for a vast range of ion energies and targets. In table 1 we show the [Expt/Theory] ratio averaged over all target atomic numbers, the errors shown are the + 1 standard deviations for the numbers of the data points given in ( f. The first part of the tabte is for the raw published data and the lower half is for the same data normalised to its La cross section. Normalisation
D. D. Cohen / K and L shell X-ru,v cross sections Protons
z uY
:
---
:
0
7
Helium
3
Ions
ECPSSR EXPT
0.6
0.1"""'"'"""""""""" 40 60 Target
'g
\
' : ',O
80
Rtomic
100
Number
60
40
Target
Z
80 Atomic
Number
Fig. 6. The absolute La X-ray production cross sections for ion energies 0.6, 1, 2, 3 MeV versus target atomic (b) for He ions.
of this type considerably reduces the scatter (compare standard deviations) and also brings the [Expt/Theory] ratio closer to unity in many instances.
100 i!
number,
(a) for protons
The total X-ray production cross sections are within a few percent of theory with the theory underpredicting experiment for reducing ion energies down to (E/M) =
Table 1 Mean experiment to theory ratios for LaPy lines for published data up to December 1988. Errors are for + I standard the mean of the number of data points given in ( ) Line
[Expt/Theory]
on
ratio 1.O MeV
0.6 MeV
deviation
2.0 MeV
3 MeV
Protons ; Y Total Helium ions ru B Y
Total Line
1.2010.17 1.31 kO.22 1.34kO.28 1.26+0.19
(10) (10) (10) (10)
1.12kO.16 1.15 kO.25 1.26iO.30 1.14io.20
(37) (32) (31) (37)
1.01 kO.11 1.04kO.16 1.14*0.25 1.03+0.13
(43) (38) (37) (43)
0.99 + 0.14 1.05 +0.15 1.14+0.27 1.02iO.14
1.33*0.97 1.94+ 1.90 2.02 f 2.24 1.67f1.50
(5) (5) (5) (5)
1.30+0.28 1.53~0.25 1.54i0.26 1.42kO.26
(18) (18) (18) (18)
1.10+0.19 1.1s*o.22 1.24+0.26 1.14k0.21
(21) (21) (21) (21)
0.94*0.17 (18) 0.99+0.17 (18) 1.08+0.24(18) 0.95*0.1s (18)
[Expt/Theory]
ratio normalised to La
(33) (28) (27) (33)
0.6 MeV
1.O MeV
2.0 MeV
3 MeV
1.09 -I:0.07 (10) 1.11 kO.14 (10) 1.05io.05 (10)
1.01 kO.13 (32) 1.10*0.18 (31) 1.01 io.07 (37)
1.03kO.12 (38) 1.12*0.20 (37) 1.02 i 0.07 (43)
1.05 f 0.05 (28) 1.12+_0.1? (27) 1.03kO.03 (33)
1.31*0.31 (5) 1.2450.54 (5) 1.16kO.21 (5)
1.19kO.13 (18) 1.21 kO.20 (18) 1.10+0.09 (18)
1.07~0.08 (21) 1.12k0.14 (21) 1.03*0.05 (21)
1.05*0.06 (18) 1.14+0.10 (18) 1.01 kO.04 (18)
Protons P Y
Total Helium ions P Y
Total
1. X-RAY
PRODUCTION
150 keV/ amu. Recent work by Price et al. [52] for 0.5 to 2.5 MeV Be ions on targets from Z = 29 to 47 show this trend continues for decreasing ion energy down to only (E/M) = 5 keV/amu ions on Zr. They attribute part of this difference to multiple ionisation effects in the target atoms. The total L shell work of Marble et al. 1531, presented only in graphical form, appears to contradict this trend as their results for 100 to 225 keV protons on Cu to Y ((E/M) from 1-4 keV/amu) are well predicted by the ECPSSR theory. It should be pointed out that the work of refs. [52] and [53] originates from the same laborato~ in Denton, Texas. The Lp and Ly transitions of table 1 show a slight tendency to increase with reducing ion energy but these deviations are generally well within one standard deviation of the ECPSSR results. unfortunately, there is very little published data (not in graphical form) for targets below Sn (Z = 50) for Lfl and Ly peaks where large variations in theory, see fig. 5a-d, could be better tested. Cohen and Harrigan ]54] have also published ECPSSR L shell line intensities for proton and He ion impact for all targets from Ni upwards. These are for 16 different L lines using the atomic decay parametres of Krause f8] and Salem at al. [IO] and ion energies from 0.2 to IO MeV. Much of the L shell work has been published in graphical form as the ionisation cross section ratios (L,/L,) and (La/L,) as a function of ion energy or reduced velocity 4 f1,55-571. These data clearly show the ECPSSR L, subshell results are underpredicted for low ion velocities 5 < 0.5, whereas the L, and L, subshells are closely predicted by the ECPSSR theory. Two basic explanations have been put forward in recent times for this. Firstly. coupling of the I., subshells during the collision time of the ion transfers vacancies from L, to L, subshells [5?,58] and secondly a reassessment of the radiative and ra~ationIess yields may be needed ]36,55,5?3, since the values of Krause [8] are not entirely appropriate to ion atom collisions. The total answer to the L subshell data probably lies in a combination of both of these explanations 1571 and a detailed systematic study of both is required over a large range of ions, ion energies and target combinations. The L subshell coupling theories are better tested for ions heavier than protons and alphas 1581, but effects reaching 40% for the L, subshell have been observed for 0.15 keV protons on Au 1571. Sarkadi and Mukoyama in table II of ref. 157) show that the fluorescence yields and Costet-Kronig factors for Au can differ quite significantly for 4 different recent sets of measurements, For example. fig. 7, taken from their work. shows the effect of different decay parameters on the same data. A flattening, at ahout 0.4 MeV. appears in the re-evaluated data which uses the data bases from ref. f9,38]. The reason for the absence of this structure in the old data can be ascribed to the
041
SARKADIAND MUKOYAMA 1988 : I I I II/I, p-Au
,
03 .;
,b 02 t?
01 I
I 01
1
I
I,,,,,,
I
ENERG; (M&4
FROTGN
Fig. 7. Ratio of the Lz and L3 ionisation cross sections of Au versus proton energy. The dashed curve is the ECPSSR theory using DHS wave functions [21], the solid curve is the same theory including subsheil coupling effects 1561. The dots are data of .Iitschin et al. [55] with synchrotron atomic decay parameters of Jitschin 1591 and the open circles are the same data with the decay parameters of Chen and Crasemann [38] and Scofield (91.
larger fiz value of Krause [8] compared with the later value of Chen et al. [38]. The solid curve of fig. 7 which fits this re-evaluated proton data quite well is equivalent to the ECPSSR theory with DHS wave functions and the inclusion of subshell coupling effects. Finally, we feel that there is now clear evidence for the existence of L subsheli coupling effects, particularly for vacancies being transferred from the L, to L, subshell during the collision times of slow ions. The unravelling of these coupling effects from the published X-ray production cross sections critically depends on the atomic decay parameters used. A complete systematic study of these is required for a range of ion energies and ion target combinations.
7. Conclusion We have reviewed the K and L shell X-ray cross section data. The K she11 data is now well established with theoretical predictions matching experiment to within 3-5%, for all but the lowest ion energies, for proton and alphas. The L shell data is more complex, with 3 subshells and many more X-ray peaks and X-ray line production cross sections, compared with theory, are typically 515% accurate for a wide range of light ion energies and target combinations. In the ion energy range 0.5 -c: E I 3 MeV/amu, with (ZJZ,) < 0.1 the ECPSSR theory is most reliable in predicting X-ray ionisation cross sections. There are still large gaps in the L subshell X-ray production data for targets less than Sn. This is clearly due to the inadequate resolution of energy dispersive systems in this region. For the heavier ions systematic differences of several tens of percent and larger are apparent and these can be
D.D. Cohen / K und L shell X-rav crms sections
considerably reduced, if not fully explained, by the inclusion of electron capture, nonadiabatic effects or aubshell coupling effects for situations when (Z,/Z,) < 0.3. There is, however, a need to systematically assess the use of radiative and nonradiative decay parameters which for the main part have been produced for only single target vacancy situations, since clearly in ion atom collisions multiple vacancies are possible.
References [l] Nucl. Instr. and Meth. B3 (1984) 1-711; B22 (1987) l-484. [2] Nucl. Instr. and Meth. B3 (1984) 425-547. [3] J.R. Bird. P. Duerden and D.J. Wilson, Nucl. Sci. Appl. 1 (1983) 357-526. [4] E. Clayton, D.D. Cohen and P. Duerden, Nucl. Instr. and Meth. 191 (1981) 573. [5] E. Clayton, PIXAN, AAEC Report AAEC/M113 (November 1986) and Nucl. Instr. and Meth. B22 (1987) 64. [6] D.D. Cohen and E. Clayton. Nucl. Instr. and Meth. B22 (1987) 59. [7] J.L. Campbell et al., Nucl. Instr. and Meth. B14 (1986) 204. [8] M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307. [9] J.H. Scofield. Atom. Data and Nucl. Data Tables 14 (1974) 121. [lo] S.I. Salem. S.L. Panossian and R.A. Krause, Atom. Data and Nucl. Data Tables 14 (1974) 91. [ll] D.D. Cohen, Nucl. Instr. and Meth. B22 (1981) 55. [12] E. Storm and H.I. Israel, Nucl. Data Tables A7 (1970) 565. 1131 J. Veigele, Atom. Data and Nucl. Data Tables 5 (1973) 51. 1141 T.P. Thinh and J. Leroux, X-ray Spectrom. 8 (1979) 85. [15] J.W. Mayer and E. Rimini (eds.), Ion Beam Handbook of Materials Analysis (Academic Press. NY, 1977) p. 454. 1161 J.L. Ziegler. J.P. Biersack and U. Litmark (eds.). Stopping Powers and Ranges of Ions. vol. 1 (Pergamon, NY, 1985). 1171 J.F. Janni, Atom. Data and Nucl. Data Tables 27 (1982) 147. [18] R. Rice, G. Basbas and F.D. McDaniel, Atom. Data and Nucl. Data Tables 20 (1977) 503. 1191 0. Benka and A. Kroft, Atom. Data and Nucl. Data Tables 22 (1978) 219. 1201 D.E. Johnson, G. Basbas and F.D. McDaniel. Atom. Data and Nucl. Data Tables 24 (1979) 1. [21] M.H. Chen and B. Crasemann. Atom. Data and Nucl. Data Tables 33 (1985) 217. (221 D.D. Cohen and M. Harrigan, Atom. Data and Nucl. Data Tables 33 (1985) 255. [23] C.H. Rutledge and R.L. Watson, Atom. Data and Nucl. Data Tables 12 (1973) 195. 1241 R.K. Gardner and T.J. Gray, Atom. Data and Nucl. Data Tables 21 (1978) 515.
9
~251T.L. Hardt and R.L. Watson.
Atom. Data and Nucl. Data Tables 17 (1976) 107. WI R.S. Sokhi and D. Crumpton. Atom. Data and Nucl. Data Tables 30 (1984) 49. ~271H. Paul and J. Muhr, Phys. Rep. 135 (1986) 47. Atom. Data and Nucl. WI M.H. Chen and B. Crasemann, Data Tables 41 (1989) 257. ~291 D.D. Cohen. Atom. Data and Nucl. Data Tables 41 (1989) 287. [301 W. Brandt and G. Lapicki. Phys. Rev. A20 (1979) 465. [311 W. Brandt and G. Lapicki. Phys. Rev. A23 (1981) 1717. ~321 G.D. Garcia, Phys. Rev. Al (1970) 280. [331 G.D. Garcia, Phys. Rev. Al (1970) 1402. K. Dan Vidensk. Selsk. [341 J. Bang and J.M. Hansteen. Mat.-Fys. Medd. 31 (1959). 1351 J.L. Campbell. Nucl. Instr. and Meth. B31 (1988) 578. [361 D.D. Cohen. J. Phys. B17 (1984) 3913. [371 J.H. Scofield. Phys. Rev. A10 (1974) 1507. and H. Mark, Phys. Rev. A24 1381 M.H. Chen. B. Crasemann (1981) 177. I391 J.H. Scofield. Phys. Rev. A9 (1974) 1041. 141 D.D. Cohen. Nucl. Instr. and Meth. B22 (1987) 55. [411 C.M. Lederer and V.S. Shirley. Table of Isotopes. 7th ed. (Wiley, NY, 1987). 1421 H. Paul, Nucl. Instr. and Meth. B4 (1984) 211. [431 J.S. Lopes. A.P. Jesus and M.F. da Silva, J. Phys. B15 (1982) 1749. [441 H. Paul and Sacher. Atom. Data and Nucl. Data Tables 42 (1989) 105. [451 G. Lapicki, J. Phys. B20 (1987) L633. [461 G. Lapicki, J. Phys. Chem. Ref. Data 18 (1989) 111. [471 G. Basbas. W. Brandt and R.H. Ritchie. Phys. Rev. A7 (1973) 1971. [481 D.T. Lang and G. Simons, Nucl. Instr. and Meth. B4 (1984) 239. E. Leigsgaard and M. Lund, Nucl. Instr. [491 J.U. Andersen. and Meth. 192 (1982) 79. [501 L. Sarkardi. Nucl. Instr. and Meth. B9 (1985) 127. Phys. Rev. A22 (1980) [511 G. Lapicki and F.D. McDaniel. 1896. ~521 J.L. Price, J.L. Duggan, F.D. McDaniel, G. Lapicki and R. Mehta. Nucl. lnstr. and Meth. B24 (1987) 85. [531 D.K. Marble. J.D. Gressett, F.D. McDaniel, J.L. Duggan, J.F. Culwell and G. Lapicki, Nucl. Instr. and Meth. B40/41 (1989) 98. Atom. Data and Nucl. 1541 D.D. Cohen and M. Harrigan, Data Tables 34 (1986) 393. R. Hipler and H.O. Lutz, J. [551 W. Jitschin, A. Kaschuba, Phys. B15 (1982) 763. J. Phys. B13 (1980) 2255; [561 L. Sarkadi and T. Mukoyama, Nucl. Instr. and Meth. B4 (1984) 296. Phys. Rev. A37 (1988) [571 L. Sarkadi and T. Mukoyama, 4540. and D.H. Jakubassa-Amundsen. J. Phys. [581 P.A. Amundsen 821 (1988) L99. [591 W. Jitschin. G. Materlik, U. Werner and P. Funke, J. Phys. B18 (1985) 1139.
I. X-RAY
PRODUCTION
and Methods
in Physics
Research
B49 (1990) l-9
Section I. X-ray production K AND L SHELL X-RAY CROSS SECTIONS
FOR USE IN PIXE ANALYSIS
SYSTEMS
David D. COHEN ANSTO,
PMBI,
Menai, N.S. W., 2234, Austrdia
In this review we look at the experimental K and L shell X-ray cross section data available up to the with the predictions of the ECPSSR theory for ionisation by MeV ions. Particular attention is paid energies between 1 and 3 MeV and most elements for the K shell and elements above Sn for individual Variations in the ratios of the bulk of existing experimental data to the predictions of the ECPSSR theory and proton and helium ion energy are presented and discussed.
1. Introduction
Particle induced X-ray emission (PIXE) has now become a well established technique for multielemental analysis of both thick and thin targets. An enormous variety of applications have been found as demonstrated in the Proceedings of the last few PIXE Conferences [l]. Thin target PIXE techniques are now well established. Good examples of this are the PIXE studies in aerosol science and in aerosol monitoring programs [2] where the properties of PIXE particularly lend themselves to large scale monitoring or urban pollution and many thousands of samples have now been run. Thick targets have also been analysed in large numbers using the PIXE technique. The group at Lucas Heights [3], for example. have analysed over 10000 thick obsidian glass samples over the past 10 years. They used the PIXE technique to characterise and source these archaeological artifacts to a variety of volcanoes through the Pacific region and hence unravelled some of the native trade patterns going back thousands of years. The key to these reliable PIXE results lie generally in a well characterised matrix and for the thin and thick samples quoted above elemental concentrations down to a few parts per million are typically quoted with errors of around 3 to 5%. Poorer results will be obtained from volatile matrices such as biological samples. Reliable predictions need good data bases. As early as 1981 Clayton et al. [4] wrote a computer program SOXS (synthesis of X-ray spectra) to generate both thin and thick X-ray spectra for a wide range of target matrices and for both the K and L characteristic peaks for most commonly occurring elements. This is now a fully developed commercial program PIXAN [5], which both analyses PIXE spectra and converts peak areas to elemental concentrations for a given matrix composition. The data bases used by the PIXAN package have been discussed at length by Cohen and Clayton [6] and 0168-583X/90/$03.50 (North-Holland)
6 Elsevier Science Publishers
B.V.
end of 1988 and compare it to protons and helium ion La. Lp and Ly transitions. with target atomic number
the peak area routines critically assessed by Campbell et al. [7] with most favourable results. There are many different parameters required for the prediction of X-ray yields [6]. These include fhtorescence yields and radiative widths [8-111, mass attenuation coefficients [12-151, ion stopping powers [16.17] and X-ray cross sections [l&29]. The errors associated with these data bases have gradually come down over the years to between 1 and 5% in absolute terms in some cases. In this paper we will discuss K and L subshell cross sections necessary to predict both thin and thick target PIXE X-ray yields for light ions. Typically. ion energies between a few hundred keV and 10 MeV are used and ion (Z,) to target (Z, ) atomic number ratios less than or of the order of 0.3. For (Z,/Z,) > 0.3 projectile electron capture contributions to the inner shell target vacancy production rates become significant and must be added to the direct ionisation contributions. The vast majority of experimental K and L data to date has been compared with the so-called ECPSSR theory of Brandt and Lapicki [30.31]. which is a derivative of the PWBA approximation with corrections for Coulomb repulsion (C), polarisation and binding energy changes via the perturbed stationary states (PSS). relativistic effects (R) and ion energy loss effects (E). Cohen [22,29] has published extensive ionisation cross section tables based on this model using hydrogenie electron wave functions while Chen and Crasemann [21,28] have published a more limited tabulation based on DHS wave functions. Inner shell vacancy production via direct Coulomb interaction between a projectile and a target electron has also been studied using the binary encounter approximation (BEA) [32,33] and the semiclassical approximation (SCA) [34]. However, since most comparisons for PIXE users have used the ECPSSR theory we will restrict ourselves to this approach here.
1. X-RAY PRODUCTION
D. D. Cohen / K and L shell X-ray cross secrions
2
2.Cross sections
and yields
cence
yields
fi3=0, The tions
ECPSSR
theory
predicts
ionisation
IJ,’ for a given shell or subshell
Experiments
generally
measure
given peak p which originates filling
the vacancy
sections
are related
cross
s = K. L,,
X-ray
yields
in the shell s. The
L,,
L,.
Yp in a
from an X-ray
in the following
sec-
yields
Coster-Kronig
as
manner
the
this reason
is the initial cross
stopping
section power
coefficient. that
for
a peak
for the ion,
that
including
p is the mass peak
p,
effects,
attenuation by weight
of
W is the atomic number,
D is
Q is the total
F is the detector
e is the ion charge,
and 0, and
0, are the angle of the incoming
beam and the outgoing surface
Eq. (1) is valid requires that
to the target for light
they have a unique
incident
energy.
the X-ray
along
charge
state
It does not account
yield
from
target
targets
and
paths
and
straight
as a function
for contributions
recoil
and
ion
of to
straggling
effects. The X-ray should
production
cross sections
not be confused
cross
section
these
for
u,’ and
with again
the K and
0,” for a peak p
the ionisation
(vacancy)
the relationships
L subshell
vacancies
=
out
experimental
with
that
between
cross
which
where
o K is the K shell fluorescence of the width
the total K shell width.
yield and (F,/r,
of the p transition Eq. (3) is relatively
the K shell has no subshells.
However
have three subshells,
and L,,
L,,
L,
relative
overlap
in the K shell case the
simple
)
since
for the L shell we and
emission
The
K and L subshell
exception fitted
of the L,
from
functions
the
L,
subshell.
CosterrKronig
The
transition
f,,
and
an initial the
vacancy
wL,
rates and the subshell
are
in the
fluores-
the
for L subshell rates of Chen
et
the recommended
[8] in the high target we have a preference
over the theoretical fluorescence
Z for
calcula-
of atomic
of Krause
yields.
are smoothly number
expressions
data and should Average
total
prove useful L shell
also been given by Cohen
with
the
varying
in-
and
are well
of the form
to the tabulated to better
Z
than
in PIXE
fluorescence
given
in
data of Krause, they reproduce f 3%. have been
given in table 2 of ref. [6] for K, L subshell from
for
enough.
with the range of Z for which
the numbers p originates
treatthat
favouring
computations
subshell,
by polynomial
together
the peak
is based
of the DHF
evidence
of Krause
rates
of imperfect
This preference
significantly
numbers
wave functions.
treatment
and Coster-Kronig
eq. (6) of ref. [6]. Fits
where
the
tions.
creasing
X (ILP
and
yields,
[39], but he suggests
and in these situations
the experimental
on DHS
superiority
wave function
values
Chen
et al. [38] and
is not yet convincing
yields
[6] suget al. [lo]
[35] points
of
later DHF
experimental
predictions
Cohen
fluorescence
of Chen
exchange.
ment
L shell
probabiland to be
Campbell the
a rigorous
the demonstrated
experimental
to
sets
[8]
subshell
[9] also form a self-consistent
upon
region
L
up to 1978
tabulations
Scofield’s
include
wave function
the
Krause
and
rates of Salem
with
transitions
he prefers
fluorescence
(3)
wK”:(rp/rK)*
section
data base founded
However,
K
data
emission
rates of Scofield
The DHS
are known
experimental
[21] together
theoretical [37]
data
less
and the available and has too much
of
the yield calculations. the
Crasemann emission
data bases.
is still a little
data bases
compilation
al. [38] do differ
is the ratio
acceptable
is still too sparse
gests the experimental
DHF
[6,36]: X uK~
consistent
emisrates of
yields and L shell Coster-Kronig
for most
Coster-Kronig
normal.
ions on heavy
that ions slow down
fluorescence ities
mea-
of eq. (3) the fluores-
one data base over another.
a complete
to complete
efficiency
X-ray
with respect
gives
For
section
et al. [lo] or the theoretical
data
to suggest
X-ray.
cross
[8] and the experimental
as to the preferred
scatter
the
ion loss
on thin targets.
conversions
of Krause
experimental
produc-
S(E) is the matrix
by the detector,
the target,
filter
p,
N, is Avogadro’s
the solid angle subtended hitting
is the X-ray
concentration
produced
of that element,
charge
e,“(E)
C is the relative
element
weight
ion energy,
since
no energy
production
[9,37] are considered
certain
are dis-
considerably
constant,
For the L shell eq. (4) the picture
/ E”COS(e,)s(E)
IL’x=IL
tion
Scofield
cos(0,)dE
widths
for the emerging
X-ray
are performed
yields
are
requires
absorption
the K shell
cence
dE
target
sion rates of Salem E
E,
For
and radiative
over
most
surements
and
uL3=fli=0.
eqs. (1) and (2) reduce
of a thin
and no X-ray
(1)
we put
below.
integrations
definition
[5.6.35]:
i = 1 we put uL2 = uL3 =
i=2
transition
further
For thin targets
and cross
well-known
For for
ionisation fix = I, and for i = 3 all three L subshell cross sections are used. The fluorescence yields, cussed
transition
respectively.
fi2=f13=1;
and M shell
computer yields
[40] for all targets
GL
codes. have
from Ni to
3
D.D. Cohen / K and L shell X-ray cross sections
Cm using the ECPSSR ionisation cross sections and the effective subshell fluorescence yields of ref. [S].
3. K shell
Experimental K shell ionisation cross section measurements were tabulated by Rutledge and Watson [23] as early as 1973. Gardner and Gray [24] tabulated all experimental Auger. X-ray production cross sections from 1973 to 1977. They chose to tabulate only directly experimentally determined quantities to facilitate the comparison of data and theory. Since 1977 Paul and co-workers at Linz have been the main group tabulating and collating K shell cross sections. The bulk of their work is summarised in an extensive report by Paul and Muhr [27] in 1986. In this work a data file containing 7800 total K X-ray or Auger production cross sections, with (Z,/Z,) < 0.3, are compared with the theoretical ECPSSR ionisation cross sections [30.31] using the K shell fluorescence yields of Krause [S]. The experimental cross sections ( ox ) were multiplied by the fluorescence yields ( wK ) and normalised to the theoretical ionisation cross section (u’) and the parameter S = ( o”wK)/u’ plotted as a function of the log,,, of the reduced ion velocity 5, where SK = 2m/B and. q = 40.32E,/[M,( Z, - 0.3)‘] and 19= 11(/( Zz - 0.3)’ Ry, describes the shielding by outer electrons. The experimental ionisation energies I, were taken from Lederer et al. [41]. Paul and Muhr [27] present extensive graphs of S versus log 5 for protons, alphas and other heavy ions (Li. B, C. N. 0, F and Cl) and we refer the reader to them for further detail. In fig. 1 we show the proton data for 4 I Z I 92 as the dashed curve together with N, 0 and F point data
001
I
-0 8
I
-04
I
I
00
I
1
04
1 08
Log cf 1 Fig. 1. Average normalised K shell cross sections S versus log,, reduced ion velocity for proton and heavy ions. The dashed curve is the proton fit of Paul for 4 I Z 5 92. The N, 0. F symbols are for nitrogen, oxygen and fluorine ions and the solid curves are the NECPSSR theory for oxygen bombardment of P. Ca and Cu targets.
as being representative of the heavy ion situation. The solid curves marked P, Ca and Cu are discussed further below. The proton dashed curve was obtained using the fits of eq. (4) and table 5 of ref. [27]. For protons the ratio S sits within f 5% of unity for -0.68 < log 5 < 0.36. This corresponds to a very broad range of targets and ion energies, for example, for an Al target this covers proton energies from 0.1 to 3 MeV and for a copper target energies from less than 0.2 to greater than 10 MeV. Below log [ < -0.7 the K shell ECPSSR theory overpredicts the experimental results by increasing amounts for increasing target Z and reducing ion energy. For 1 MeV protons on Au log .$ = -0.775 and S is only 0.56. however. the measured K shell ionisation cross section at this energy is only 0.1 mb and hence of little use to PIXE analysts when one considers that for 2 MeV protons on Cu the K shell cross section is nearly 100 b, some 6 orders of magnitude larger. The proton data also show a local minimum of about 4% at log 5 = - 0.24 and two local maxima, one at log .$ = -0.6 of around 1% and the other at log 5 = 0.36 of around 5%. These in themselves do not appear to be significant for proton data, however, the trend is clearly continued for the heavier ions as the oscillations in the N. 0 and F data of fig. 1 show. Paul [42] argued that the deviation of S around log 5 = - 0.6 is most probably due to a small deficiency of the binding correction in the ECPSSR theory and this may be backed up by the experiments of Lopes et al. [43]. Paul also attributes the steady rise in S for the heavy ion data above log [ = -0.1 to the projectile electron capture processes for (Z,/Z,) > 0.3. We feel that some of this rise may also be attributed to nonadiabatic effects described in the next section. The fits of Paul to the experimental data have enabled him to define reference cross sections for selected targets and energies. These reference cross sections have considerably smaller errors than any single experimental measurement. Recently extensive reference cross sections have been published by Paul [44] using the same techniques. The techniques of Paul compare experiment and theory. They do not provide the PIXE analysist with a complete data base of cross sections for computational purposes unless the ECPSSR cross sections have been calculated separately. Cohen has now produced K and L subshell ionisation cross sections for p, He [22] and D [29] ions calculated within the ECPSSR formalism, for most targets and ion energies between 100 keV and 10 MeV, using hydrogenic wave functions. Chen and Crasemann [21,28] have produced K. L and M shell ionisation cross sections for protons with a few selected energies from 100 keV to 5 MeV for a narrow range of selected targets, using DHS wave functions in a Brandt and Lapicki formalism [30]. Some results for K shell ionisation cross sections for protons from Paul, Cohen I. X-RAY PRODUCTION
and Harrigan, Brandt and Lapicki and Chen and Crasemann are given in table A of ref. [29]. There are small differences between the theoretical calculations of Cohen 122,293 and those of Brandt and Lapicki [30,31]. These differences have been discussed in detail [29,45] and tabulated for all ion and target combinations by Cohen [29]. Cohen [29] also tabulates the constant CXI = used 5 k/I E, (Mevtl”2 which converts the commonly ion energy E, for different target combinations into the reduced velocity parameter .$ used extensively by Paul and Muhr [27]. This should be of considerable help when using the K shell values of those tabulations which use this reduced velocity parameter [1X-20.27,44]. More recently Lapicki [46] has also tabulated 7418 K shell X-ray production cross sections from 161 different references for p and He ions on targets from beryllium to uranium. Comparisons of these with the ECPSSR theory arrive at similar conclusions to Paul’s compilations. He suggests the ECPSSR theory reproduces the experimental results to between 10 and 20% except for the lowest velocity regime. These deviations were associated with the influence of multiple outer-shell ionisations on the fluorescence yield of light elements, particularly in ionisation by helium ions.
4. Nonadiabatic effects The ECPSSR theory calculates the binding energy within the perturbed stationary state theory of Basbas et al. [47]. This assumes that all states of the atom respond adiabatically to the motion of the ion. However while the adiabatic aproximation will hold at sufficiently low velocities (5 -SC1). it will not be valid at higher velocities (5 2 1). Fortunately, for (5 > 1) the assumption of adiabaticity does not introduce a large error when the total ionisation cross section is calculated because the main contribution comes from distant collisions where binding energy changes are small. Land and Simons [48], using a dynamic model, show that the K shell electron behaves almost fully adiabatically for protons on copper at energies below 2 MeV (5 I 0.78). In general different shells will show different degrees of adiabaticity in response to the projectile. Two approaches to binding are commonly used: (1) United atom limit [49], where the outer electrons relax to their positions appropriate to a target atom having Z = (Z, + Za). (ii) Separated atom limit (ECPSSR theory) where outer electron atoms display no response to the ion and the effect of binding energy is a function of the distance between the two atoms. Sarkadi [50], following the separated atom approach of the ECPSSR theory. assumes only significantly large velocity components of the electron wave function can follow adiabatically the change of the Hamiltonian with time, and defines a parameter h,(v, ) which is conveni-
NON ADIABATIC FUNCTION FOR K AND L SHELLS I I I
121
001
01
1
IO
SCALED VELOCITYx-IV,h',s)
Fig. 2. A plot of the nonadiabatic function X, for the K and L subshells versus the scaled ion velocity.
ently included in the binding and polarisation ter of the ECPSSR theory, namely,
:K=l+gg 2K
K
[k?,
parame-
- hK1’
where the parameters of eq. (5) have their standard meanings defined in ref. 1301. Clearly X = 1 reproduces the ECPSSR theory. We have calculated the parameter X, for s = K. L,. and L,,, subshells as well a the K and L subshell ionisation cross sections and call these the NECPSSR theory. Fig. 2 shows the nonadiabatic function h, as a function of the scaled ion velocity. For the K and L2,1 shells the major effects occur around ( u,/u~~) = 1, whereas for the L, subshell h is actually greater than 1 for ( c!,/L)~~) I 0.5. In fig. 3 we plot the ratio of NECPSSR K shell cross sections to the ECPSSR for several different ions on copper against the relativistically corrected reduced velocity parameter tR defined in ref. [30]. This ratio rises around tR = 0.2. has a maximum near 5 R = 1 and falls again to unity around tR = 3. For protons on copper the maximum nonadiabatic effect is 1.6’% for 3-4 MeV protons, but increases for decreasing Z,, being 6.3% for protons on carbon with tR = 1. However for 0 ions on copper its effect is 13% for 50-60 MeV ions increasing again for lower Z,, being 26% for 0 on silicon. Maybe this nonadiabatic binding correction could fill in the local minimum in the plots of Paul and Muhr 1271 for -0.5 < log < < 0.4, that is for 0.3 < < < 2.5? To test this we have superimposed the ratio (NECPSSR/ECPSSR) on the S = ( o’/ECPSSR) plot of fig. 1 for 0 ions on P, Ca and Cu targets. Comparisons with the 0 symbols of this figure show that some of the deviations for the K shell ionisation by heavy ions for log 5 > - 0.5 can be explained by the nonadiabatic effects. The 1.6% nonadiabatic effect for K shell protons goes some of the way to filiing in the 4% or so local minimum in the experimental data for log 5 = -0.2 (5 = 0.6). However the peak in the nonadiabatic effect at 5 = 1 is clearly shifted to higher
5
D.D. Cohen / K and L shell X-ray cross sections HEAVY IONS ON COPPER
I /(“I
1
”
16 80
1.50-
2r
;ILI
“‘I’ 4060100 MeV 4“I 6 10 20
,' 2
4 6 10 20 40 MeV r I I11111 Proton 0 5 1 2 345710MeV
120 ~ --k 2 IIO4 9 b’
-
1.05-
1 01
0.5
1
2
6. L shell
REDUCED VELOCITY CR
Fig. 3. The ratio [NECPSSR/ECPSSR] ionisation cross sections for K shell ionisation of Cu by p. He. Li and 0 ions as a function of the reduced ion velocity with relativistic corrections.
ion velocities than experimental data.
5. Electron
needed
to fill in this dip in the
capture
For slow fully stripped ions electron capture (EC) from the target K shell into any empty ion shell may become as significant an ionisation process as that of direct ionisation (DI). The probability for EC is, like DI, ion velocity dependent and has a maximum when the ion velocity matches the velocity of the electron to be captured. We have calculated the EC cross sections
ELECTRON CAPTURE CONTRIBUTION I I I I I X@* X Be x0 qC 00 Ne
d:
l
0. 0’
@.
X
Max Contrlb for 0 55 E,slOO MeV
_ :
co .
X 0.
‘I
04
from the target K shell to any empty ion shell for fully stripped Be, C, 0 and Ne ions using the OBK formalism of Lapicki and McDaniel [51]. The results for the maximum contribution, for ion energies between 0.5 I E, 5 100 MeV. are shown in fig. 4 as a function (Z,/Z,). This figure shows a universal curve for ions lighter than Ne. For slow ions we expect (EC/DI) a ( Z,/n,Z,)3 and a fit to the data of the form [EC/(EC + DI)] = ax”/(b + x”) gives u = 1.871. h = 9.026 x lo-’ and n = 3.397, where x = ( Z,/Zz). If we set x = 0.3 in this expression we see that [ EC/(EC + DI)] < 29% for all energies between 0.5 I E I 100 MeV. For x 2 0.36 the maximum EC contribution is always greater than 50%. Fig. 4 also shows why EC contributions for x < 0.1 are considered negligible ( < 1%) and why for x > 0.3 EC contributions should be included in ionisation calculations.
05
[2,/Z,]
Fig. 4. The ratio of the maximum electron capture contributions to the total ionisation versus ion to target atomic number.
The L shell consists of three subshells: the L, subshell with transitions B,, B,, Bs.,,,, yz, yX. y4; the Lz subshell with transitions n, B,. y,. ys, ys and the L, subshell with transitions ~1,. (Y*. B2, Bs, 1. The transitions quoted are those observed by modern X-ray energy dispersive techniques for an initial vacancy in one of the three subshells. In eq. (4) we show how the X-ray production for a peak p, and hence the yields, eq. (1). are related to the three theoretical ionisation cross sections u’. Most L shell PIXE experiments will resolve about 10 of these peaks giving many possible ways to solve eq. (4) for the three unknowns u,’ (i = 1.2.3) for comparison with theory. Cohen [36] has discussed four commonly used methods for converting X-ray production cross sections to subshell ionisation cross sections and shows how both the selection of peaks Lp and the selection of data bases ( w,, f,, , r,,) can strongly affect the final answers obtained. For example, 25% differences in the L, cross sections can be obtained for He on Au using either the Salem et al. [lo] or Scofield (91 emission rates. It is therefore very important to compare experimental X-ray production cross sections for various peaks p, as this will considerably reduce the final experimental scatter. A lot of L subshell data to date has been published as already massaged ionisation cross sections or only in graphical form when comparing with the ECPSSR cross sections. The earlier L shell tabulations of Hardt and Watson [25] to 1976 including a selection of heavy ion data were followed by the tabulations of Sokhi and Crumpton [26] for proton data only between 1975 and 1982. For this review we include the above data and have searched the literature from 1982 to the end of 1988. It is not possible to treat the complex L subshell data in a similar fashion to the K shell data of Paul and I. X-RAY PRODUCTION
D.D.Cohen / K und L shell X-ruy
cross sections
Protons
protons
,”
0
90
60
30 Target
Rtomic
Number
5
0
2.0
MeV
Hsl i urn Ions
90
60
30 Torget
Z
Rtomic
Hel
i urn
Number
Z
Ions
~000~~
1. OMeV
101 0
60
30 Target
Rtomic
Number
90 2
Target
Rtomic
Number
Fig. 5. The normalised (to Lu) LB, Ly, LTotalX-ray production cross sections versus target atomic number. (a) MeV protons and (c) and (d) for 1 and 2 MeV He ions.
Muhr for comparison with the ECPSSR theory. So we only consider the larger X-ray peaks La, LB, Ly and the total L shell, the ion energies 0.6, 1, 2 and 3 MeV. proton and He ions for targets above Sn. With these restrictions the published data base is reduced to 45 separate measurements. These still cover fairly well the complete range of L shell measurements used by PIXE analysts. For comparison with the L subshell ECPSSR theory we use the (0,. _I,,, rLp) data bases of ref. [8,10] to reduce the theoretical ionisation cross sections to their corresponding X-ray cross sections. The results are shown in fig. Sa-d for the selected ion energies. The
and
Z
(b) for 1 and 2
data of fig. 5 have been normalised to the Lol X-ray production cross sections equai to 1000 to reduce systematic experimental errors. In figs. 6a, b we show these absolute La X-ray productions compared with the ECPSSR theory. Clearly this theory does well for a vast range of ion energies and targets. In table 1 we show the [Expt/Theory] ratio averaged over all target atomic numbers, the errors shown are the + 1 standard deviations for the numbers of the data points given in ( f. The first part of the tabte is for the raw published data and the lower half is for the same data normalised to its La cross section. Normalisation
D. D. Cohen / K and L shell X-ru,v cross sections Protons
z uY
:
---
:
0
7
Helium
3
Ions
ECPSSR EXPT
0.6
0.1"""'"'"""""""""" 40 60 Target
'g
\
' : ',O
80
Rtomic
100
Number
60
40
Target
Z
80 Atomic
Number
Fig. 6. The absolute La X-ray production cross sections for ion energies 0.6, 1, 2, 3 MeV versus target atomic (b) for He ions.
of this type considerably reduces the scatter (compare standard deviations) and also brings the [Expt/Theory] ratio closer to unity in many instances.
100 i!
number,
(a) for protons
The total X-ray production cross sections are within a few percent of theory with the theory underpredicting experiment for reducing ion energies down to (E/M) =
Table 1 Mean experiment to theory ratios for LaPy lines for published data up to December 1988. Errors are for + I standard the mean of the number of data points given in ( ) Line
[Expt/Theory]
on
ratio 1.O MeV
0.6 MeV
deviation
2.0 MeV
3 MeV
Protons ; Y Total Helium ions ru B Y
Total Line
1.2010.17 1.31 kO.22 1.34kO.28 1.26+0.19
(10) (10) (10) (10)
1.12kO.16 1.15 kO.25 1.26iO.30 1.14io.20
(37) (32) (31) (37)
1.01 kO.11 1.04kO.16 1.14*0.25 1.03+0.13
(43) (38) (37) (43)
0.99 + 0.14 1.05 +0.15 1.14+0.27 1.02iO.14
1.33*0.97 1.94+ 1.90 2.02 f 2.24 1.67f1.50
(5) (5) (5) (5)
1.30+0.28 1.53~0.25 1.54i0.26 1.42kO.26
(18) (18) (18) (18)
1.10+0.19 1.1s*o.22 1.24+0.26 1.14k0.21
(21) (21) (21) (21)
0.94*0.17 (18) 0.99+0.17 (18) 1.08+0.24(18) 0.95*0.1s (18)
[Expt/Theory]
ratio normalised to La
(33) (28) (27) (33)
0.6 MeV
1.O MeV
2.0 MeV
3 MeV
1.09 -I:0.07 (10) 1.11 kO.14 (10) 1.05io.05 (10)
1.01 kO.13 (32) 1.10*0.18 (31) 1.01 io.07 (37)
1.03kO.12 (38) 1.12*0.20 (37) 1.02 i 0.07 (43)
1.05 f 0.05 (28) 1.12+_0.1? (27) 1.03kO.03 (33)
1.31*0.31 (5) 1.2450.54 (5) 1.16kO.21 (5)
1.19kO.13 (18) 1.21 kO.20 (18) 1.10+0.09 (18)
1.07~0.08 (21) 1.12k0.14 (21) 1.03*0.05 (21)
1.05*0.06 (18) 1.14+0.10 (18) 1.01 kO.04 (18)
Protons P Y
Total Helium ions P Y
Total
1. X-RAY
PRODUCTION
150 keV/ amu. Recent work by Price et al. [52] for 0.5 to 2.5 MeV Be ions on targets from Z = 29 to 47 show this trend continues for decreasing ion energy down to only (E/M) = 5 keV/amu ions on Zr. They attribute part of this difference to multiple ionisation effects in the target atoms. The total L shell work of Marble et al. 1531, presented only in graphical form, appears to contradict this trend as their results for 100 to 225 keV protons on Cu to Y ((E/M) from 1-4 keV/amu) are well predicted by the ECPSSR theory. It should be pointed out that the work of refs. [52] and [53] originates from the same laborato~ in Denton, Texas. The Lp and Ly transitions of table 1 show a slight tendency to increase with reducing ion energy but these deviations are generally well within one standard deviation of the ECPSSR results. unfortunately, there is very little published data (not in graphical form) for targets below Sn (Z = 50) for Lfl and Ly peaks where large variations in theory, see fig. 5a-d, could be better tested. Cohen and Harrigan ]54] have also published ECPSSR L shell line intensities for proton and He ion impact for all targets from Ni upwards. These are for 16 different L lines using the atomic decay parametres of Krause f8] and Salem at al. [IO] and ion energies from 0.2 to IO MeV. Much of the L shell work has been published in graphical form as the ionisation cross section ratios (L,/L,) and (La/L,) as a function of ion energy or reduced velocity 4 f1,55-571. These data clearly show the ECPSSR L, subshell results are underpredicted for low ion velocities 5 < 0.5, whereas the L, and L, subshells are closely predicted by the ECPSSR theory. Two basic explanations have been put forward in recent times for this. Firstly. coupling of the I., subshells during the collision time of the ion transfers vacancies from L, to L, subshells [5?,58] and secondly a reassessment of the radiative and ra~ationIess yields may be needed ]36,55,5?3, since the values of Krause [8] are not entirely appropriate to ion atom collisions. The total answer to the L subshell data probably lies in a combination of both of these explanations 1571 and a detailed systematic study of both is required over a large range of ions, ion energies and target combinations. The L subshell coupling theories are better tested for ions heavier than protons and alphas 1581, but effects reaching 40% for the L, subshell have been observed for 0.15 keV protons on Au 1571. Sarkadi and Mukoyama in table II of ref. 157) show that the fluorescence yields and Costet-Kronig factors for Au can differ quite significantly for 4 different recent sets of measurements, For example. fig. 7, taken from their work. shows the effect of different decay parameters on the same data. A flattening, at ahout 0.4 MeV. appears in the re-evaluated data which uses the data bases from ref. f9,38]. The reason for the absence of this structure in the old data can be ascribed to the
041
SARKADIAND MUKOYAMA 1988 : I I I II/I, p-Au
,
03 .;
,b 02 t?
01 I
I 01
1
I
I,,,,,,
I
ENERG; (M&4
FROTGN
Fig. 7. Ratio of the Lz and L3 ionisation cross sections of Au versus proton energy. The dashed curve is the ECPSSR theory using DHS wave functions [21], the solid curve is the same theory including subsheil coupling effects 1561. The dots are data of .Iitschin et al. [55] with synchrotron atomic decay parameters of Jitschin 1591 and the open circles are the same data with the decay parameters of Chen and Crasemann [38] and Scofield (91.
larger fiz value of Krause [8] compared with the later value of Chen et al. [38]. The solid curve of fig. 7 which fits this re-evaluated proton data quite well is equivalent to the ECPSSR theory with DHS wave functions and the inclusion of subshell coupling effects. Finally, we feel that there is now clear evidence for the existence of L subsheli coupling effects, particularly for vacancies being transferred from the L, to L, subshell during the collision times of slow ions. The unravelling of these coupling effects from the published X-ray production cross sections critically depends on the atomic decay parameters used. A complete systematic study of these is required for a range of ion energies and ion target combinations.
7. Conclusion We have reviewed the K and L shell X-ray cross section data. The K she11 data is now well established with theoretical predictions matching experiment to within 3-5%, for all but the lowest ion energies, for proton and alphas. The L shell data is more complex, with 3 subshells and many more X-ray peaks and X-ray line production cross sections, compared with theory, are typically 515% accurate for a wide range of light ion energies and target combinations. In the ion energy range 0.5 -c: E I 3 MeV/amu, with (ZJZ,) < 0.1 the ECPSSR theory is most reliable in predicting X-ray ionisation cross sections. There are still large gaps in the L subshell X-ray production data for targets less than Sn. This is clearly due to the inadequate resolution of energy dispersive systems in this region. For the heavier ions systematic differences of several tens of percent and larger are apparent and these can be
D.D. Cohen / K und L shell X-rav crms sections
considerably reduced, if not fully explained, by the inclusion of electron capture, nonadiabatic effects or aubshell coupling effects for situations when (Z,/Z,) < 0.3. There is, however, a need to systematically assess the use of radiative and nonradiative decay parameters which for the main part have been produced for only single target vacancy situations, since clearly in ion atom collisions multiple vacancies are possible.
References [l] Nucl. Instr. and Meth. B3 (1984) 1-711; B22 (1987) l-484. [2] Nucl. Instr. and Meth. B3 (1984) 425-547. [3] J.R. Bird. P. Duerden and D.J. Wilson, Nucl. Sci. Appl. 1 (1983) 357-526. [4] E. Clayton, D.D. Cohen and P. Duerden, Nucl. Instr. and Meth. 191 (1981) 573. [5] E. Clayton, PIXAN, AAEC Report AAEC/M113 (November 1986) and Nucl. Instr. and Meth. B22 (1987) 64. [6] D.D. Cohen and E. Clayton. Nucl. Instr. and Meth. B22 (1987) 59. [7] J.L. Campbell et al., Nucl. Instr. and Meth. B14 (1986) 204. [8] M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307. [9] J.H. Scofield. Atom. Data and Nucl. Data Tables 14 (1974) 121. [lo] S.I. Salem. S.L. Panossian and R.A. Krause, Atom. Data and Nucl. Data Tables 14 (1974) 91. [ll] D.D. Cohen, Nucl. Instr. and Meth. B22 (1981) 55. [12] E. Storm and H.I. Israel, Nucl. Data Tables A7 (1970) 565. 1131 J. Veigele, Atom. Data and Nucl. Data Tables 5 (1973) 51. 1141 T.P. Thinh and J. Leroux, X-ray Spectrom. 8 (1979) 85. [15] J.W. Mayer and E. Rimini (eds.), Ion Beam Handbook of Materials Analysis (Academic Press. NY, 1977) p. 454. 1161 J.L. Ziegler. J.P. Biersack and U. Litmark (eds.). Stopping Powers and Ranges of Ions. vol. 1 (Pergamon, NY, 1985). 1171 J.F. Janni, Atom. Data and Nucl. Data Tables 27 (1982) 147. [18] R. Rice, G. Basbas and F.D. McDaniel, Atom. Data and Nucl. Data Tables 20 (1977) 503. 1191 0. Benka and A. Kroft, Atom. Data and Nucl. Data Tables 22 (1978) 219. 1201 D.E. Johnson, G. Basbas and F.D. McDaniel. Atom. Data and Nucl. Data Tables 24 (1979) 1. [21] M.H. Chen and B. Crasemann. Atom. Data and Nucl. Data Tables 33 (1985) 217. (221 D.D. Cohen and M. Harrigan, Atom. Data and Nucl. Data Tables 33 (1985) 255. [23] C.H. Rutledge and R.L. Watson, Atom. Data and Nucl. Data Tables 12 (1973) 195. 1241 R.K. Gardner and T.J. Gray, Atom. Data and Nucl. Data Tables 21 (1978) 515.
9
~251T.L. Hardt and R.L. Watson.
Atom. Data and Nucl. Data Tables 17 (1976) 107. WI R.S. Sokhi and D. Crumpton. Atom. Data and Nucl. Data Tables 30 (1984) 49. ~271H. Paul and J. Muhr, Phys. Rep. 135 (1986) 47. Atom. Data and Nucl. WI M.H. Chen and B. Crasemann, Data Tables 41 (1989) 257. ~291 D.D. Cohen. Atom. Data and Nucl. Data Tables 41 (1989) 287. [301 W. Brandt and G. Lapicki. Phys. Rev. A20 (1979) 465. [311 W. Brandt and G. Lapicki. Phys. Rev. A23 (1981) 1717. ~321 G.D. Garcia, Phys. Rev. Al (1970) 280. [331 G.D. Garcia, Phys. Rev. Al (1970) 1402. K. Dan Vidensk. Selsk. [341 J. Bang and J.M. Hansteen. Mat.-Fys. Medd. 31 (1959). 1351 J.L. Campbell. Nucl. Instr. and Meth. B31 (1988) 578. [361 D.D. Cohen. J. Phys. B17 (1984) 3913. [371 J.H. Scofield. Phys. Rev. A10 (1974) 1507. and H. Mark, Phys. Rev. A24 1381 M.H. Chen. B. Crasemann (1981) 177. I391 J.H. Scofield. Phys. Rev. A9 (1974) 1041. 141 D.D. Cohen. Nucl. Instr. and Meth. B22 (1987) 55. [411 C.M. Lederer and V.S. Shirley. Table of Isotopes. 7th ed. (Wiley, NY, 1987). 1421 H. Paul, Nucl. Instr. and Meth. B4 (1984) 211. [431 J.S. Lopes. A.P. Jesus and M.F. da Silva, J. Phys. B15 (1982) 1749. [441 H. Paul and Sacher. Atom. Data and Nucl. Data Tables 42 (1989) 105. [451 G. Lapicki, J. Phys. B20 (1987) L633. [461 G. Lapicki, J. Phys. Chem. Ref. Data 18 (1989) 111. [471 G. Basbas. W. Brandt and R.H. Ritchie. Phys. Rev. A7 (1973) 1971. [481 D.T. Lang and G. Simons, Nucl. Instr. and Meth. B4 (1984) 239. E. Leigsgaard and M. Lund, Nucl. Instr. [491 J.U. Andersen. and Meth. 192 (1982) 79. [501 L. Sarkardi. Nucl. Instr. and Meth. B9 (1985) 127. Phys. Rev. A22 (1980) [511 G. Lapicki and F.D. McDaniel. 1896. ~521 J.L. Price, J.L. Duggan, F.D. McDaniel, G. Lapicki and R. Mehta. Nucl. lnstr. and Meth. B24 (1987) 85. [531 D.K. Marble. J.D. Gressett, F.D. McDaniel, J.L. Duggan, J.F. Culwell and G. Lapicki, Nucl. Instr. and Meth. B40/41 (1989) 98. Atom. Data and Nucl. 1541 D.D. Cohen and M. Harrigan, Data Tables 34 (1986) 393. R. Hipler and H.O. Lutz, J. [551 W. Jitschin, A. Kaschuba, Phys. B15 (1982) 763. J. Phys. B13 (1980) 2255; [561 L. Sarkadi and T. Mukoyama, Nucl. Instr. and Meth. B4 (1984) 296. Phys. Rev. A37 (1988) [571 L. Sarkadi and T. Mukoyama, 4540. and D.H. Jakubassa-Amundsen. J. Phys. [581 P.A. Amundsen 821 (1988) L99. [591 W. Jitschin. G. Materlik, U. Werner and P. Funke, J. Phys. B18 (1985) 1139.
I. X-RAY
PRODUCTION