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Proton-induced X-ray production in titanium, nickel, copper, molybdenum and silver
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1976 J. Phys. B: At. Mol. Phys. 9 455
(http://iopscience.iop.org/0022-3700/9/3/014)
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J. Phys. B: Atom. Molec. Phys., Vol. 9, No. 3, 1976. Printed in Great Britain. @ 1976
Proton-induced x-ray production in titanium, nickel,
copper, molybdenum and silver
Md Rashiduzzaman Khan?., D Crumpton and P E Francois
Department of Physics, University of Aston in Birmingham, Gosta Green, Birmingham
B4 7ET, England
Received 25 June 1975, in final form I October 1975
Abstract. Measurements have been made of the K x-ray production from elements bombarded with protons. Thick targets of Ti, Cu, Ni, M O and Ag have been used and the
yield of x-rays measured as a function of proton energy in the range 1-3 MeV. From
these measurements values of the K-shell ionization cross sections in this energy range
have been calculated and these have been compared with the results of other workers
and with the predictions of the plane wave Born approximation (PWBA) and the binary
encounter approximation (BEA).
1. Introduction
In recent years there has been considerable interest in the production of characteristic
x-rays by the proton bombardment of materials (Wheeler and Chaturbedi 1974:
Rutledge and Watson 1973, Garcia et a1 1973, Duggan et al 1972). An important
experimental observation is the measurement of the yield from thick targets from which
cross section information can be deduced. A number of workers have reported thick
target yields for low-energy incident protons but data for protons with energies greater
than 1 MeV are relatively sparse. This energy region is of particular interest because
the rapid increase in yield with energy makes it valuable for analytical purposes.
In this paper we report measurements made on titanium, nickel, copper,
molybdenum and silver in the proton energy region 1 to 3 MeV.
2. Experimental
A beam of protons from a 3 MV Dynamitron accelerator at the Joint Birmingham
Radiation Centre was collimated to a diameter of 1 mm and allowed to impinge
on selected targets. The beam currents employed were typically 10nA to 1 pA depending on the target under investigation and were chosen so as to obtain x-ray yields
compatible with the input characteristics of the detecting electronics. These low currents also had the advantage of keeping the target heating small. Spectroscopically
pure elemental targets were mounted at 45" to the incident proton beam inside a
stainless steel T-piece. The beam collimator consisted of three tantalum apertures,
A I , A2 and A3, of 1, 2 and 5 m m diameter respectively. The aperture AI, furthest
i. O n leave from University of Dacca, Bangladesh.
455
456
M d Raslziduzzainan Khan, D Crunzpton arzd P E Francois
from the target, defined the beam while AZ, which was electrically connected to
A l , prevented scattered protons or secondary electrons released at Al from reaching
the T-piece. The final aperture A 3 was connected electrically to the target and T-piece
and this assembly was insulated from the main system. Thus the T-piece, together
with the aperture A3, acted as a Faraday cage collecting the majority of secondary
electrons from the target. This arrangement permitted accurate measurement of the
beam current. The T-piece was fitted with a thin Melinex or aluminium window
through which the x-rays were transmitted.
The detector employed was a 3 mm thick lithium-drifted silicon x-ray detector
with an area of 30.3 mm'. The entrance window to the detector was made of 125 pm
thick beryllium. The associated electronic circuits consisted of a pulsed optical feedback preamplifier, main amplifier and pulse pile-up rejector. A 'live timer' was also
incorporated and enabled corrections to be made for dead-time effects. The output
pulses were taken to the input of a 200MHz ADC of an on-line Hewlett-Packard
computer system employed for data acquisition and analysis. The resolution of the
detector system was measured to be 161 eV at 5.9 keV at a counting rate of 1 kHz.
The detector was positioned outside the vacuum chamber at a distance of 56.7cm
from the position of the beam spot on the target. The angular position of the detector
was determined by specular reflection of a laser beam incident on the target along
the direction of the beam path. An aperture of 13.2"'
was positioned in front
of the detector to define the geometry and to eliminate detector edge effects.
3. Results
The photon yields per proton I,, obtained for K x-radiation for thick targets of
titanium, copper, nickel, molybdenum and silver are given in table 1. These results
have been corrected for geometry, detector efficiency and x-ray absorption after leaving the target. These results, together with those of other workers, are shown in
graphical form in figure 1.
Table 1. Thick target K x-ray yields and derived ionization cross sections.
Titanium
= 0,219
IO
1.1
1.2
1.3
1.4
15
1.6
I 7
1.8
1.02
1.50
2.10
1.9
I0 3
20
2.1
2.2
2.3
2.4
12.2
14.0
16.1
18.0
20.2
22.2
24 6
26.5
29.0
31.1
33.3
2.5
2.6
2.7
2.8
2.9
3n
2 82
3.71
469
5.94
7.32
8.88
10-3
Nickel
Copper
oiK = 0.435
"2* = 0.414
249
3 12
3.82
4 65
5 37
621
7.06
7.93
879
9.5 I
105
11.4
I22
13.0
I3 7
14.5
15 I
15.8
I64
17.11
17.6
102
I 55 x
2 31
3 51
3.87
6.66
8 83
11.7
14.0
18.2
22.4
27 4
32.4
38.4
44.7
51.8
58.8
66.7
74.9
83.6
90.9
100
in-' 2.42
3 09
3.87
4 77
576
x 101 1.13 x I O - "
Mol!bdenum
Silier
<ok = 0 7 6 4
LI)K
I 6 1 x 101 2 6 4 x
!OPx l o - ' 0 7 0 9
2.56
271
6.82
5 51
494
6 67
422
8.09
9 42
108
I3 3
8.?2
6 04
148
206
27.7
9.10
II 4
I4 I
14.3
8.14
48 8
20.7
138
15.3
16.9
21 3
in4
80.3
28 8
6.87
184
I99
213
22.6
23 7
24,8
25 6
263
5 10
31.3
12.6
I25
38.2
41 2
183
216
258
48 2
540
146
156
16.4
65 0
179
347
66 3
79.8
189
141
72.2
46.3
=
53 2
57.9
I22
1.99
2 86
4.36
6.15
8.53
117
155
20 4
26.2
33 4
41 1
47 9
61.8
74 3
87.3
I 04
I20
118
154
0.830
x IO-"
850 x IO-'
119
16.2
21 5
27.9
35 7
44 6
55.1
66 7
79.9
94 2
II O
I26
I44
I61
I79
196
213
228
242
752
._.
X-ray production in Ti, N i , Cu, M O and Ag
457
Energy (MeV)
Figure 1. Proton-induced thick target yield of K x-rays
K-shell ionization cross sections were obtained from the thick target yields in
the following manner. Assuming isotropic emission of x-rays (Lewis et a1 1972) and
that the angle of incidence of the proton beam to the normal to the target is equal
to the angle of emergence of the detected x-rays, then the photon yield per proton,
I!(. of K x-rays for incident protons of range Ro is given by
I,, = IC'
loRo
exp[ - p(Ro - R)]o(R)dR
where R is the residual range, N is the number of reaction centres per unit volume
in the target, p is the appropriate linear absorption coefficient and G ( R )is the K
x-ray production cross section.
Application of Leibniz rule gives dI,/dRo = N o(Ro)- pI,(Ro) from which o(R0)
can be obtained. Introducing the specific energy loss dE/dRo enables the cross section
to be expressed in terms of known parameters, i.e.
1 d l dE
p
o(R0) = - 2 __ + -Ip(Ro).
N dE dR,
N
A smooth curve was fitted to the experimental points of the thick target yield for
each element using a sixth-order polynomial fit. Values of dI,,/dE were then obtained
from this data. The specific energy-loss data were taken from Janni (1966) and the
linear absorption coefficients from Storm and Israel (1974) and Miller and Greening
(1974). Finally the ionization cross sections were obtained from the production cross
Md Rashiduzzaman Khan, D Criimpton and P E Francois
458
10-z3i
i
t
i
10-231
,
,
,
, ,
,
t
,
,
J
io-z4
I
2
3
i
._1
10-25 I
2
3
Energy (MeV1
Figure 2. Proton-induced K-shell ionization cross sections for ( a ) Ti. (h) Ni. ( e ) Cu. ( d )
M O and (e) Ag. +, present work: 0,Rutledge and Watson (1973): 0.Akselsson .and
Johansson (1974); 0 , Liebert et ai (1973); A, Bearse et al (1973); 0 , Criswell and Gray(1974):8, Khelil and Gray (1975). Full curve, PWBA (Basbas et ai 1973): broken curve.
BEA (Garcia et ai 1973).
X-ray production in Ti, N i , Cu, M O and Ag
10-22
!
I
10-23(
459
I
/
I
lo-'
IB2
I
FIG
Figure 3. Scaled K-shell ionization cross sections. ( U ) full curve, BEA (Garcia et id 1973):
(b) full curve, PWBA (Basbas et ai 1973): (c) full curve. PWBABC (Basbas et a / 1973). t,
Ti; A,Ni; 0 , Cu; El, MO; (3, Ag.
sections using the appropriate values of the K-shell fluorescence yield wK taken from
Bambynek et al (1972). The K-shell ionization cross sections, oK, are also given in
table 1. These results are also shown in graphical form in figure 2 together with
the results of other workers who have reported measurements in the same energy
range. Where authors have quoted production cross sections we have converted their
results to ionization cross sections using the appropriate fluorescence yield.
Also shown on the same graphs are the ionization cross sections predicted by
the plane wave Born approximation (PWBA) (Basbas et al 1973) and the binary
encounter (BEA) theory (Garcia et al 1973). Both theories predict a universal function
for the ionization cross section and our results, reduced to the standard form by
the appropriate scaling factors, are shown with the respective universal functions
in figure 3.
In all cases the uncertainty associated with the experimental measurements is
2 1.4% due to the counting statistics and uncertainty in beam current measurements.
We estimate that this gives rise to an uncertainty of about 2 4 % in the derived
values of dI,/dE. In the calculation of absolute yield systematic uncertainties arise
due to the detection efficiency and absorption corrections. These amount to 1% in
the case of nickel, copper and molybdenum, 2.5% for silver and 9% for titanium.
The accuracy of the calculated values of the cross section depends on the assumed
values of dE/dRo and p , as well as the experimental measurements. The uncertainty
associated with the values of dE/dRo has been estimated by considering the departure
of Janni's values from other published figures (Williamson et al 1967. Northcliffe
and Schilling 1970). These range from about &4% at 1 MeV to f 1% at 3 MeV.
The uncertainty quoted for p by Miller and Greening is i1%. Combining these figures
gives an uncertainty of not more than +5% for nickel, copper and molybdenum,
k 6% for silver and f 10% for titanium.
4. Discussion
The lack of experimental data for thick target yields in the 1 to 3 MeV region is
clearly demonstrated in figure 1. Where measurements have been reported by other
460
M d Rashidiizzanzan Khar?, D Crumpton and P E Francois
authors there is reasonable agreement with the present work, except for silver and
molybdenum. For both of these elements our results are systematically lower than
those reported by Messelt (1958) and those of Lewis et a1 (1953).
Our results for the ionization cross sections (figure 2) compare favourably with
results obtained from thin target yields by other authors, except for the measurements
of Bearse et nl (1973) on nickel. These results are systematically below ours and
others by some 2&30"/,.
In the cases of silver and molybdenum the ionization cross sections derived by
Messelt and Lewis et a1 from their thick target yields are considerably higher than
ours and other measurements.
In general our results lie between the ionization cross section curves predicted
by the PWBA and BEA theories, and they d o not allow us to distinguish between
them. This is also shown in figures 3(a) and (h) where our results are compared
with the universal functions predicted by the BEA and PWBA theories. The PWBA
universal function. corrected for binding energy and Coulomb correction (PWBABC),
is compared with our results in figure 3(c). The agreement is similar to that obtained
with the other universal functions.
Acknowledgments
We wish to thank Mr M Still" for his assistance with the experimental programme.
We acknowledge the help received from the staff of the Joint Birmingham Radiation
Centre and the support given by Professor S E Hunt.
We thank the Science Research Council for a research grant. One of us (MRK)
is also indebted to the Commonwealth Scholarship Commission, UK, for a grant.
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