Measurement and parameterization of proton elastic scattering crosssections for nitrogen
I. Bogdanović Radović*, Z. Siketić and M. Jakšić
Ruđer Bošković Institute, P.O. Box 180, 10000 Zagreb, Croatia
A.F. Gurbich
Institute of Physics and Power Engineering, Bondarenko sq. 1, 249033 Obninsk, Russian
Federation
The cross-sections for the elastic scattering of protons from natural nitrogen at
non-Rutherford scattering energies were measured at three laboratory scattering angles:
118°, 150° and 165°. The experimental data were parameterized in the framework of
nuclear physics models. A benchmark experiment was performed in order to prove that
the excitation functions obtained in the present work can be used to adequately simulate
the yield from a thick target containing nitrogen.
*
Author to whom correspondence should be addressed. Electronic mail: iva@irb.hr
1
I. INTRODUCTION
For materials analysis, Rutherford Backscattering Spectroscopy is an established
analytical technique. It can provide information about thickness, elemental composition
or stochiometry of the analyzed material. For light element detection, analytical use of
protons instead of alpha particles is more and more common due to a larger probing
depth and enhanced scattering cross-sections coming from the nuclear component of the
interaction above the Coulomb barrier. The presence of this non-Rutherford component
in the scattering cross-section implies the need of detailed measurements of excitation
functions at different scattering angles. A significant amount of work has been done in
the last few decades in order to achieve a reliable database for the scattering of both
protons and alpha particles from light elements. This work is summarized in the IBANDL
database.1 The database contains most of the available experimental nuclear crosssections relevant to Ion Beam Analysis. For some projectile-nucleus scattering systems
evaluated cross sections are also available.2 The evaluation consists in the elaboration of
the most accurate available cross-sections through the incorporation of the all relevant
experimental data in the framework of nuclear physics theory.3 The advantage of
evaluated cross-sections is that excitation functions for analytical purposes can be
calculated for any scattering angle or energy, with a reliability exceeding that of any
individual measurement.
Nitrogen is often present as a main constituent in bulk targets or as an important
constituent in thin films. Analysis with protons of samples containing nitrogen is
typically done at energies above the Coulomb barrier where the cross-section is no longer
2
Rutherford. Therefore, for a quantitative analysis and depth profiling of nitrogen it is
important to know the exact cross-sections. The motivation for the present work was to
supply new data for the 14N(p,p)14N cross-sections, especially at energies above 3 MeV.
Up to now, scattering of protons from nitrogen has been reported in numerous
publications for angles important for backscattering analysis (>120°) mainly at energies
not exceeding 3 MeV.4-14 In works published almost half a century ago, authors have
used gaseous N target and CsI(Tl) crystal detectors to study states in compound nucleus
15
O. 4-9 In more recent works measurements have been done with nitrogen-containing thin
films deposited on the carbon substrate, similar to that used in the present work. 10-14 For
detection, silicon surface barrier detectors were applied at scattering angles important for
the backscattering analysis. Previously acquired data were used to produce the evaluated
cross-sections in the energy range up to 3.4 MeV.15 The motivation for the present work
was lack of the reliable cross-section data for the elastic scattering of protons from
nitrogen up to 5 MeV.
II. EXPERIMENTAL METHODS
A. The apparatus
Measurements were performed using proton beams from the 6.0 MV Tandem Van de
Graaff accelerator at the Ruđer Bošković Institute in Zagreb. The beam was extracted
from a sputtering ion source using a TiH2 cathode. The energy calibration of the
accelerator was done using narrow resonance in 27Al(p,γ)28Si at 991.88 keV and neutron
3
threshold reaction 7Li(p,n)7Be at 1880.6 keV. Final energy spread of the beam was
calculated to be 0.1% of the incident beam energy.
The proton beam, delimited by horizontal and vertical slits to a spot of 2×2 mm2
impinged on the sample at normal incidence. To detect backscattered protons from the
target, three surface barrier detectors with a 2.5 msr solid angle each were positioned at
118°, 150° and 165°. The energy resolution of the detectors used was 12 keV for protons
in the measured energy range. The excitation function of the
14
N(p,p)14N was measured
between 2.4 and 5.0 MeV with minimum step of 10 keV where the cross-section varied
rapidly and 25 keV elsewhere.
B. Samples
It is quite difficult to select solid target appropriate for the N cross section
measurements. As we wanted to have a N signal well separated from signals coming
from other elements, a thin AlN film deposited by reactive sputtering on a vitreous
graphite substrate was used. On the top, a 6 nm Au layer was evaporated for
normalization purposes, assuming that cross-sections for backscattering of protons from
Au are Rutherford in the entire energy range studied in this work. In addition, the
normalization to gold eliminates further corrections due to the dead time, knowledge of
absolute solid angle value and errors due to imperfect charge collection. Target stability
was examined regularly by measuring N and Au intensity ratios at 3 MeV. It was found
that this ratio was within 2.7% during the measurements.
4
III. DATA ANALYSIS
The average differential cross-section for backscattering of protons from N at
scattering angle  is given by:
d N
d
E AlN 
AN

,  
,
 E  EAu 
2

 Q   N N
(1)
where E is incident proton energy, EAu is energy loss in Au layerEAlN is energy loss in
AlN film, AN is area under the N peak, Q the number of incident H ions, () the
detector solid angle and NN the number of nitrogen atoms per unit area (at/cm2), and
where the detected counts are actually given by an integral of the differential crosssection over the energy thickness of the film. Very sharp resonances cannot be resolved
by this method.
The differential cross section for backscattering of protons from Au for an angle θ is
given by the following equation:
d Au
d
EAu 
AAu

,  
,
E
2

 Q   N Au
(2)
where AAu is area under the Au peak, and NAu the number of Au atoms per unit area.
Normalization against Au signal leads to:
d N
d
EAlN  AN N Au d Au 
EAu 

,  
, 
 E  EAu 
E
2
2

 AAu N N d  

5
(3)
To calculate the cross sections using Eq. (3) it is necessary to know the NAu/NN
ratio. Therefore, the thin film was carefully investigated by 2 MeV 4He backscattering
since for this beam all the cross-sections are pure Rutherford to determine the
stochiometry, layer thickness, homogeneity and presence of impurities that could affect
the results. It was found that NN=(639±30)x1015 at/cm2 and NAu=(38.6±0.6)x1015 at/cm2
which gives NAu/NN ratio equal to 0.0604±0.0030.
The energy loss of protons in the Au and AlN layers was calculated using
stopping power data incorporated in the program SRIM 2003.16 The energy loss of
protons in the Au layer varied between 0.5 and 0.3 keV and in the AlN layer between 5.5
and 3.2 keV for the minimum and maximum projectile energy, respectively. Because of
its small value, the correction E Au in Eq. (3) can be neglected.
IV. PARAMETERIZATION
The experimental data obtained were parameterized in the framework of the Rmatrix theory with optical model phases being used instead of hard spheres ones. The
initial values for the resonance parameters were taken from the paper by M.L.West et al.9
Because the substitution of optical model phases for hard sphere ones influenced the
interference between potential and resonance scattering, the shape of the resonances
changed and so some of the resonances were assigned spins and parities different from
those assumed by West et al. The final list of the resonance parameters is presented in
Table 1. The natural boundary conditions were set at the resonance energies listed in
6
Table 2. The parameters of spin and orbital momentum mixing are presented in Table 1
following Nelson et al. definitions.19 The channel spin mixing ratio is defined as


s ,l
/,
(4)
l
where s> is the higher channel spin and  is the total width of the decay channel. The lmixing ratio is defined as
 s  s ,l  2 / s ,l 1 / 2
(5)
with corresponding mixing angles s = atan (s) introduced for convenience. The range
of  is from 0 to 1, and the range of  is from -90 to +90.
With two s values and two l values contributing there are a maximum of four
elastic scattering partial widths s,l . These widths may be expressed in terms of three
mixing ratios , <, > and the total elastic scattering width  by the following relations:
s , l 
s , l 
1 
1   2s

1   2s
,
,
s , l  2 
s , l  2 
(1  ) 2s
1   2s
 2s
1   2s
,
(6)
.
The potential parameters were found by fitting the non-resonance background in
the excitation functions. In order to accurately reproduce shape resonances the real
potential well was split on the l-number. The final set of the optical parameters is
presented in Table 3 (in usual optical model notation). The real potential has energy
dependence V=V0-bE, where V0 values are listed in the Table 3 and b=2.865. The
imaginary potential at energies less than 4 MeV was assumed to be zero. Fig.1
demonstrates behavior of the theoretical cross-section on scattering angle and energy.
7
V. RESULTS AND DISCUSSION
Experimentally determined proton backscattering cross-sections from N together
with theoretical calculations and all other available experimental data are plotted for
laboratory angles of 118°, 150° and 165° in Fig. 2. In the entire investigated energy
region the cross-sections are significantly higher then Rutherford. The energies to which
the reported cross sections are assigned correspond to incident proton energies minus half
the energy loss in the AlN layer. The uncertainty in the measured cross-sections is
calculated to be less then 6% for energies below 4.6 MeV and between 6% and 8% for
energies from 4.6 and 5 MeV for 165° and 150°. For 118° the relative uncertainty was
below 5% for all energies. The following factors were taken into consideration for
estimating the uncertainty: the counting statistics of the peak areas and the systematic
error in determining the NAu/NN ratio. Uncertainties due to dead time, solid angle and
improper charge measurement are eliminated with the normalization to backscattering
protons from gold. Errors of the detector angular settings were estimated to be negligible.
Numerical values of the cross sections together with the corresponding uncertainties are
available on request from the authors. They will be also uploaded to the IBANDL
database.1 The agreement between calculated and measured cross sections is very good
for larger scattering angles (165° and 150°) in the entire energy region where calculations
were performed. Calculations predict only one strong and narrow resonance at 3196 keV
with FWHM of 12 keV. The experimental points are shifted about 5 keV compared to
theoretical predictions toward the lower energies. For 118° and below 3.3 MeV
theoretical calculations predict for about 15% higher cross sections. Except narrow
8
resonance at 3196 keV another strong but significantly broader resonance is measured at
3870 keV with cross sections value 85 times larger then Rutherford. From Fig. 2 is
visible that excitation functions are characterized with broad regions where cross section
is almost constant and considerably larger than Rutherford. Those plateaus with enhanced
cross sections can be used for analysis of smaller amounts of nitrogen in heavier matrices
for backscattering analysis.
For comparison with our results, other available experimental data are shown at
the same figure. For the investigated energy region, our measurements can be compared
with data from several references4-8,14. Cross sections at 118° are compared with data
from Ref. 4 for 121.1°. In the region from 2.4 up to 3.25 MeV present data are for about
10% lower than data from Ref. 4. Above 3.25 MeV agreement is better. Data from West
et al.9 are given for 124° and are for around 10% higher than present data. Around 150°
there are three data sets that can be compared with our results. Those from Ref. 7 for
153,4° are slightly higher, but data from Ref. 8 for 155.2° are in fair agreement with the
present ones. Recently measured data from Jiang et al.14 are for about 30% lower then
other measurements in the region between 2.5 and 3.2 MeV. Results for 165° can be
compared with data for 159.5° from Bashkin et al.5, 167.2° from Olness et al.6 and 165°
from Lambert and Durand8. Again, in the energy range from 2.6 to 3.5 MeV, our data are
up to 10% lower than those data but above 3.5 MeV agreement is satisfactory.
In order to examine if N excitation function measured in the present work and
incorporated into simulation program SIMNRA (Ref. 17) can interpret properly the
experimentally obtained N thick target yield we have performed benchmark experiment.
For that, thick BN target was selected. Target was covered with 8 nm Au layer for the
9
normalization purposes. In order to separate
coming from
10
B(p,) 10B,
11
14
N(p,p)14N spectrum from the background
B(p,) 11B as well as possible pile-up contribution, E-E
telescope was used. 15.9 m thick E Si detector was placed 15 mm in front of thick
energy Si particle detector (300 m). Telescope solid angle was 1.4 msr. E detector was
thick enough to stop completely low energy alphas coming from 10B(p,)10B (Q = 1447
keV) and
11
10
B(p,)10B (Q=717 keV) reactions. For more energetic alphas coming from
B(p,)11B reaction (Q = 8591 keV), energy loss in E detector was significantly larger
than energy loss for protons and signals can be well separated. Fig. 3(a) shows two
dimensional maps of E-E coincident events. Small contribution coming from pile-up
can be also seen. Projection of all events to the x (energy) axis is done on Fig. 3(b),
events belonging only to (p,p) scattering are shown on Fig. 3(c) and those coming from
(p,) on Fig. 3(d). Simulations of backscattering spectra of BN target at 150° and two
energies 3.24 and 4.50 MeV are shown on Figs. 4(a) and 4(b). In the simulation program
(Ref. 17), the step width of incident ions was chosen that for each point in the cross
section file there was at least one sub-layer in the simulation program. Stopping power
data incorporated in SRIM 2003 were used.16 For simulation at 3.24 MeV, cross sections
from Chiari et al. for
10
B(p,p)10B and
11
B(p,p)11B were applied.18 For energies higher
than 3.8 MeV there are no experimental data for proton elastic scattering from boron and
therefore simulation at 4.5 MeV is shown without part belonging to boron. Result of our
benchmark experiment shows that difference between fit with our measured cross
sections and the best fit to experimental data is in all cases less than 5%.
10
VI. CONCLUSIONS
We have measured the elastic
14
N(p,p)14N scattering non-Rutherford cross
sections in the energy region from 2.4 to 5 MeV for three different scattering angles,
118°, 150° and 165°. Experimentally obtained excitation functions are in good agreement
with theoretical predictions especially for 150° and 165° in the entire energy region
where calculations were preformed. The parameterization of the experimental data within
physical approach provides a possibility to interpolate/extrapolate the
14
N(p,p)14N cross
section for any scattering angle. Calculations can be made using the on-line SigmaCalc
calculator at http://www-nds.iaea.org/sigmacalc/.
ACKNOWLEDGMENTS
The authors are grateful to Dr. C. Jeynes for useful comments and for his help in
preparing the manuscript. This work was supported by IAEA contracts #13274 and #
CRO 13269/R0. A.G. acknowledges the support of Sandia National Laboratories (USA)
through the ISTC project #3748p.
11
TABLE CAPTIONS:
Table 1. Resonance parameters for 14N(p,p0)14N
Table 2. Energies for definition of boundary conditions (MeV).
Table 3. Optimal parameters of the optical potential obtained for 14N(p,p0)14N
Table 1. Resonance parameters for 14N(p,p0)14N
Ep, MeV
lab, keV
J

1/2, deg
3/2, deg
3.405
3.387
3.872
3.903
4.205
4.565
4.581
4.631
4.740
4.780
4.880
5.046
5.220
27
97
60
100
25
10
25
25
10
80
80
39
160
3/2ˉ
3/2+
7/2+
1/2+
3/2+
3/2+
3/2ˉ
1/2ˉ
3/2ˉ
3/2+
5/2ˉ
5/2ˉ
5/2+
0.0
1.0
1.0
1.0
1.0
0.8
1
0.0
1.0
1.0
1.0
0.26
1.0
0
0
0.0
90
-
0
5
90
90
70
90
90
90
0
0
0
Table 2. Energies for definition of boundary conditions (MeV).
J/L,S
1/2+
1/23/2+
3/25/2+
5/27/2+
7/29/2+
9/2-
0,1/2
1.000
-
0,3/2
3.900
-
1,1/2
3.996
3.410
-
1,3/2> 2,1/2 2,3/2> 3,1/2
3.903
3.996
3.900 3.440
4.580
3.880 3.880
4.580
4.580
3.880
4.780
-
12
3,3/2
4.580
4.580
4.780
4.780
4,1/2 4,3/2 > 5,1/2
4.575
3.880 3.880
3.880 3.880
4.780
5,3/2
4.780
4.780
Table 3. Optimal parameters of the optical potential obtained for 14N(p,p0)14N
VR0
VR1
VR2
VR3
VR>3
rR
aR
WD
rD
aD
VSO
rSO
aSO
rC
MeV
MeV
MeV
MeV
MeV
fm
fm
MeV
fm
fm
MeV
fm
fm
fm
77.64 69.87 70.89 92.16 72.60 1.21 0.66 E-4
13
1.22 0.40 6.00
1.22 0.40
1.22
FIGURE CAPTIONS:
Fig 1. Evaluated elastic scattering cross sections for N(p,p)N as a function of scattering
angle and proton energy.
Fig 2. Differential cross sections for elastic backscattering of protons from nitrogen for:
(a) 118°, (b) 150° and (c) 165°.
Fig 3. a) Backscattering of 3.24 MeV protons from thick BN target at 150°; (a) two
dimensional E-E coincidence map showing well separated (p,p) from (p,) and pile-up
events; (b) all events projected to x (energy) axis; (c) events belonging to (p,p) scattering;
(d) contribution coming from (p,).
Fig 4.
Comparison between experimental and simulated spectra of BN target at 150°
and two proton energies: (a) 3.24 and (b) 4.50 MeV. Solid line is SIMNRA simulation,
and circles represent experimental data.
14
REFERENCES
1
http://www-nds.iaea.org/ibandl/
2
http://www-nds.iaea.org/sigmacalc/
3
A.F. Gurbich, Nucl. Instrum. Methods Phys. Res. B 261, 401 (2007)
4
C.R. Bolmgren, G.D. Freier, J.G. Likely, K.F. Famularo, Phys. Rev. 105, 210 (1957)
5
S. Bashkin, R. R. Carlson and R. A. Douglas, Phys. Rev. 114, 1552 (1959)
6
J. W. Olness, J. Vorona, H. W. Lewis, Phys. Rev. 112, 475 (1958)
7
A. J. Ferguson, R. L. Clarke. H. E. Gove, Phys. Rev. 115, 1655 (1959)
8
M. Lambert and M. Durand, Phys. Let. 24B, 287 (1967)
9
M.L.West, C.M. Jones, J.K. Bair, H.B. Willard, Phys. Rev. 179, 1047 (1969).
10
E.Rauhala, Nucl. Instrum. Methods Phys. Res. B 12, 447 (1985)
11
Y. Guohua, Z. Dezhang, Xu Hongjie and P. Haochang, Nucl. Instrum. Methods Phys.
Res. B 61, 175 (1991).
12
13
V.Havranek, V.Hnatowic, J.Kvitek, Czech.J.Phys. 41, 921 (1991)
A.R. Ramos, A. Paul, L. Rijniers, M.F. da Silva and J.C. Soares, Nucl. Instrum.
Methods Phys. Res. B 190, 95 (2002).
14
W.Jiang, V. Shutthanandan, S. Thevuthasan, C. M. Wang and W.J. Weber, Surf.
Interface Anal. 37, 374 (2005).
15
A.F.Gurbich, Nucl. Instr. and Meth. B 266, 1193 (2008).
16
J.F. Ziegler, Nucl. Instrum. Methods Phys. Res. B 219, 1027 (2004).
17
M. Mayer, Technical Report IPP 9/113, Max-Planck Institut fur Plasmaphysik,
Garching, Germany, 1997
15
18
M. Chiari, L. Giuntini, P.A. Mando and N. Taccetti, Nucl. Instrum. Methods Phys. Res.
B 184, 309 (2001).
19
R.O. Nelson, E.G. Bilpuch, G.E. Mitchel, Nucl. Instrum. Methods A 236, 128 (1985).
16