L Sub-Shell lonization Cross Sections for Low Energy
Protons on Elements with Z=39-42
Sam J. Cipolla
Physics Department, Creighton University, Omaha, NE 681 78, USA
Abstract L^M,), L^MO, La (LjM^), Lpl (l^k), Lp3,4,6 (I^My+LsN,), LptuO^Nw). VsOaNi+L^), and
LyaXLiN^) cross sections were used to find L sub-shell cross sections which are compared with the ECPSSR theory.
The x-ray production cross sections for protons of
incident energy E0, were determined from [4],
INTRODUCTION
L x-ray production has been studied extensively to
test the ECPSSR theory [1]. Compilations of
experimental L-shell cross sections [2] indicate that,
on average, ECPSSR agrees with experimental results
when the proton speed exceeds the L sub-shell
electron orbital speed, but ECPSSR increasingly
departs from experimental values as the ratio of proton
speed to electron speed decreases for all three L subshells. Testing of the theory for elements with Z < 43
has been limited because experiments have only
yielded total L x-ray cross sections. Presented in this
work are L sub-shell x-ray production cross section
measurements from low-energy protons (E < 300 keV)
impacting thick elemental targets of Y, Zr, Nb, and
Mo(39<Z<42).
(1)
where Y(E0) = NX/NP is the x-ray yield, with Nx being
the number of x-rays measured and Np being the
number of protons hitting the target, N is the target
atom density, 8 is the detector efficiency, S(E0) is the
proton stopping power in the target (from TRIM [5]),
jj/p is the mass absorption coefficient for x-ray self
absorption in the target (from XCOM [6]), and dY/dE0
is the slope of the measured Y(E0) vs E0 curve. Nx
was determined from stripping a linear background
from the L x-ray region and then fitting the cluster
with Gaussian curves until the residuals were random.
The number of protons, Np, were obtained from the
beam-current integrator count after correcting for
background current from the bias battery and for the
dead time of x-ray measurement.
EXPERIMENTAL PROCEDURE
The experimental system is the same as that used in
previous work [3]. A collimated, mass-analyzed
proton beam produced in a Cockcroft-Walton
accelerator impacts targets arranged on a vertical
ladder that allows the use of a different target spot for
each measurement. A secondary-electron suppression
cage suurounds the ladder which is connected to a
calibrated current integrator to measure the proton
charge delivered to a target. The targets are oriented at
45° to the beam direction and to the Si(Li) x-ray
detector that is equipped with an ultra-thin window.
An additional 6-^im aluminized-Mylar absorber was
used to reduce the high count rate from softer x-rays.
The yield slope dY/dE0 was obtained by fitting the
yield data to Y(E0) - A(E0-C)B and differentiating; A,
B and C are the fitted parameters. The detector
efficiencies e were determined from a combination of
radioactive standards and K x-ray yields from
bombarded thick foils using calculated ECPSSR
yields as a standard [7]. The data were separately
fitted below and above the Si-K edge using e(E) =
Qexp(aEp)(l-exp(yE8)), where E is the x-ray and
Q,a,P,y,8 are fitted parameters.
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
15
TABLE 1. Measured L subshell x-ray production cross sections(barns)8.
Y
E(keV) L\
75
100
125
150
175
200
225
250
275
300
1.53-2(2.7-3)
4.94-2(1.4-2)
1.12-1(2.6-2)
2.19-1(5.2-2)
3.61-1(6.7-2)
5.99-1(1.3-1)
8.92-1(6.0-1)
1.26(0.25)
1.72(0.32)
2.27(0.39)
Lp3,4,6,2,15
3.24-1(5.4-2)
1.14(0.27)
2.61(0.47)
4.94(0.93)
7.94(1.21)
12.5(2.2)
17.8(3.1)
24.3(4.1)
32.1(5.3)
41.4(6.8)
1.19-1(1.7-2) 1.08-2(8.1-3) 1.73-3(3.0-4)
3.53-1(6.6-2) 2.37-2(2.02-2) 4.40-3(1.38-3)
7.94-1(1.40-1) 3.82-2(2.49-2) 7.18-3(1.75-3)
5.41-1(2.62-2) 1.17-2(2.7-3)
1.52(0.27)
2.57(0.38)
7.45-2(3.86-2) 1.57-2(3.1-3)
4.18(0.69)
9.83-2(5.42-2) 2.30-2(4.5-3)
1.21-1(6.1-2) 2.88-2(5.0-3)
6.25(1.01)
8.93(1.40)
1.42-1(6.2-2) 3.78-2(6.4-3)
12.3(1.84)
1.63-1(2.0-2) 5.06-2(8.4-3)
16.2(2.4)
1.71-1(4.1-2) 6.45-2(1.04-2)
Zr
E(keV)
77
89
118
139
156
180
206
227
249
272
Lp3,4,6,2,15
8.29-3(1.57-3) 2.19-1(4.2-2) 7.37-2(1.49-2) 1.90-2(3.8-3) 5.11-3(9.7-4) 2.63-3(4.7-4)
2.37-2(8.3-3) 6.50-1(2.60-1) 2.12-1(9.8-2) 4.57-2(1.6-2) 1.32-2(4.7-3) 5.57-3(1.23-3)
7.97-2(1.70-2) 2.32(0.54)
7.77-1(1.98-1) 1.13-1(2.4-2) 3.86-2(8.1-3) 9.60-3(1.47-3)
1.68-1(3.4-2) 6.64-2(1.37-2) 1.25-2(1.9-3)
1.41-1(3.1-2) 4.17(0.96)
1.43(0.35)
2.03-1(4.7-2) 6.05(1.47)
2.12(0.58)
2.15-1(4.6-2) 9.61-2(2.07-2) 1.50-2(2.2-3)
3.28(0.85)
2.80-1(5.9-2) 1.42-1(2.9-2) 1.77-2(2.5-3)
3.00-1(6.4-2) 9.09(2,08)
4.13-1(7.8-2) 12.8(2.7)
4.71(1.09)
3.46-1(6.7-2) 1.92-1(3.4-2) 2.08-2(2.8-3)
4.08-1(8.4-2) 2.50-1(4.4-2) 2.32-2(3.0-3)
5.25-1(1.00-1) 16.3(3.6)
6.11(1.46)
4.68-1(9.6-2) 3.22-1(5.7-2) 2.75-2(3.6-3)
6.64-1(1.31-1) 20.4(4.5)
7.74(1.87)
5.52-1(1.22-1) 4.10-1(7.2-2) 3.50-2(4.7-3)
8.40-1(1.73-1) 25.5(5.8)
9.74(2.43)
Nb
E(keV) L\
Lp3,4,6
7.43-3(1.05-3) 1.44-1(2.3-2) 4.47-2(8.3-3) 1.08-2(1.8-3)
4.39-2(6.1-3) 8.31-1(1.32-1) 2.51-1(5.3-2) 3.84-2(7.0-3)
3.89-1(1.15-1) 4.99-2(9.9-3)
6.60-2(1.03-2) 1.26(0.25)
1.66-1(2.5-2) 3.22(0.60)
1.07(0.29)
8.94-2(1.8-2)
1.16-1(2.0-2)
2.60-1(3.7-2) 5.15(0.87)
1.80(0.43)
1.56-1(2.7-2)
3.11(0.65)
4.18-1(5.5-2) 8.42(1.30)
1.96-1(3.6-2)
6.01-1(8.2-2) 12.1(2.0)
4.63(0.98)
2.31-1(4.0-2)
6.46(1.19)
7.94-1(1.01-1) 16.2(2.4)
2.62-1(4.4-2)
9.92-1(1.27-1) 20.2(3.0)
8.24(1.51)
2.62-1(3.9-2)
271 1.17(0.15)
9.79(1.93)
23.9(3.7)
65
89
98
128
150
180
206
234
256
Mo
E(keV) L\
65
89
108
134
150
174
193
227
249
279
6.27-3(1.24-3) 1.54-3(2.0-4) 1.69- 3(2.9-4)
2.49-2(5.6-3) 9.61-3(1.19-3)5.17- 3(8.4-4)
3.61-2(1.17-2) 1.43-2(1.9-3) 6.82- 3(1.36-3)
8.67-2(2.63-2) 3.57-2(4.7-3) 1.12- •2(1.9-3)
1.38-1(3.9-2) 5.43-2(6.6-3) 1.44- •2(2.3-3)
2.22-1(5.0-2) 8.73-2(1.04-2) 1.80- •2(2.6-3)
3.16-1(7.1-2) 1.23-1(1.4-2) 2.21- •2(3.1-3)
4.27-1(8.4-2) 1.62-1(1.9-2) 2.52- •2(3.3-3)
5.33-1(1.05-1) 2.05-1(2.3-2) 2.69- •2(3.4-3)
6.30-1(1.40-1) 2.37-1(2.7-2) 3.19- •2(4.2-3)
LP1
3.13-3(4.8-4) 5.78-2(2.5-3) 1.78-2(2.9-3)
2.04-2(2.9-3) 3.97-1(5.7-2) 1.30-1(1.9-2)
4.58-2(7.1-3) 9.10-1(1.46-1) 3.05-1(5.1-2)
9.65-2(1.29-2) 1.96(0.27)
6.76-1(9.5-2)
1.48-1(2.4-2) 2.99(0.49)
1.04(0.18)
2.24-1(3.1-2) 4.61(0.66)
1.63(0.25)
3.09-1(4.5-2) 6.35(0.95)
2.27(0.36)
4.71-1(6.3-2) 9.79(1.34)
3.54(0.51)
6.12-1(8.3-2) 12.68(1.76) 4.61(0.68)
8.29-1(1.10-1) 17.19(2.34) 6.27(0.89)
6.30-3(1.1-3) 4.12-4(9.3-5) 5.48-4(7.1-5) 1.36-4(2.5-5)
2.62-2(3.8-3) 1.44-2(3.8-3) 1.55-3(3.6-4) 5.23-3(1.1-3)
4.70-2(8.3-3) 3.25-2(7.3-3) 3.81-3(3.8-3) 1.23-2(2.3-3)
7.80-2(1.19-2) 6.39-2(1.09-2) 9.13-3(9.94-3) 2.45-2(3.6-3)
1.08-1(1.7-2) 9.18-2(2.47-2) 1.14-2(5.8-3) 3.79-2(6.9-3)
1.43-1(2.1-2) 1.28-1(2.7-2) 2.25-2(1,74-2) 5.31-2(8.1-3)
1.67-1(2.4-2) 1.69-1(4.4-2) 2.54-2(8.3-3) 7.36-2(1.2-2)
2.50-1(3.6-2) 2,26-1(4.4-2) 5.96-2(3.91-2) 1.04-1(1.5-2)
2.81-1(4.3-2) 2.79-1(6.0-2) 8.19-2(4.96-2) 1.32-1(1.9-2)
4.21-1(6.6-2) 3.40-1(6.4-2) 1.34-1(8.1-2) 1.78-1(2.5-2)
a
Values of NxlO"n are given as N-n. Uncertainties are in parentheses.
16
7.46-4(1.1-4)
3.07-3(4.1-4)
5.18-3(7.5-4)
7.80-3(1.0-3)
1.05-2(1.5-3)
1.29-2(1.6-3)
1.50-2(1.8-3)
1.98-2(2.4-3)
2.24-2(2.7-3)
2.67-2(3.2-3)
The peak fitting procedure allowed separation of
the L^LsMO, L^(L2MO, La (L3M4,5), Lpl (L2M4),
Lp3A6 (L^s+LsNO, LP2^(L3N4,5), Lyl55(L2N1-fL2N4),
and LY253(LiN2,3) peaks, except that the Lfe^6
composite could not be separated from the L^is peak
for Zr.. Table 1 gives the results.
used to determine the LI cross section of Y instead of
Lps,4 because the LY2}3 peak was easily separated in the
spectrum. The Lpl peak was used to obtain the L2 xray cross sections, while the La peak yielded the L3
cross sections.
The cross sections were derived from the resolved
peaks using theoretical transition rates. The ECPSSR
LI, L2, and L3 x-ray production cross sections were
calculated from the ISICS program [8].
12 X-RAYS -
2-
-,. "H-<.«
RESULTS
AY
Figures 1-3 show the ratios, R = aexpt/^ECPSSR9 for
LI, L2, and L3 plotted against the reduced projectile
velocity, given by,
7Zr
0-
•Mo
-1
2vr
0.2
(2)
0.3
0.4
0.5
0.6
0.7
0.8
FIGURE 2. Ratios of L^ x-ray production cross sections
with ECPSSR predictions as a function of the reduced proton
velocity.
where Vi is the projectile speed, v2Ls is the orbital
speed of the Ls-shell electron, ms is the ECPSSR
relativity correction, and OLS is the reduced binding energy
for the Ls shell. The sub-shell cross sections were derived
from the peak cross sections using,
O"r
=
(3)
where ax is the x-ray transition cross section with
transition rate F^ and FLs is the total x-ray transition
rate for the Ls shell [9]. The weaker LY2j3 peak was
-1
0.2
0.3
0.7
0.8
FIGURE 3. Ratios of L3 x-ray production cross sections
with ECPSSR predictions as a function of the reduced proton
velocity.
Sub-shell cross section ratios and ECPSSR values
are shown in figures 4-6. Such ratios are sensitive to
nodal features of the electron wave functions and are
also less sensitive to absolute detector efficiency and
target atom density.
Only total x-ray production cross sections have been
measured by others [10-12] in this energy range.
Duggan, et al [10], using thin targets, measured the
total x-ray cross section for Y at 250 keV to be 33.4 b
-1
FIGURE 1, Ratios of LI x-ray production cross sections
with ECPSSR predictions as a function of the reduced
velocity
17
051000.4-
80 -
0.360 H
0.2-
40 -
0.1 -
20 -
0.0
100
200
E (k«V)
300
100
200
E (keV)
300
FIGURE 6. Ratios of LS and L2 x-ray production cross
sections compared with ECPSSR predictions.
FIGURE 4. Ratios of LI and L2 x-ray production cross
sections compared with ECPSSR predictions.
which agrees with our result of 34.9 ±4.5 keV. Kropf
[11] measured total x-ray cross sections for thick
targets of Zr and Nb over a proton energy range that
overlaps ours, with our results being slightly lower for
Zr and slightly higher for Nb. Petukhov, et al [12]
used a thick target of Mo for proton energies
overlapping our energy region, with our results being
overall slightly higher.
SUMMARY AND CONCLUSION
L x-ray production cross sections were measured
for the first time for elements with Z < 43. The
derived L sub-shell x-ray production cross sections
tend to agree better with ECPSSR theory as the
reduced projectile velocity, £, increases; results are
mixed for agreement as £ decreases. Good agreement
with ECPSSR is also obtained for cross section ratios,
with an indication that perhaps the atomic parameters
used in the calculations need refinement.
4-
-32-
ACKNOWLEDGMENTS
1-
100
200
E (keV)
The author is grateful to the University of NebraskaLincoln Physics Department for the use of their
accelerator for this experiment.
300
FIGURE 5. Ratios of L3 and LI x-ray production cross
sections compared with ECPSSR predictions.
REFERENCES
Figures 1-3 confirm the general trend that the
ECPSSR theory and experiments agree better as
^ increases. But it is not generally true from our
results that ECPSSR under-predicts for all targets as
£> decreases. The results of fig. 4-6 follow the
ECPSSR trends, especially for L3/L2. The absolute
differences may be due to inaccuracies of the atomic
parameters used in the calculations.
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Brandt, W. and Lapicki, G., Phys. Rev. A 23
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19