Target and Projectile K-vacancy Production by Fast Heavy Ions
in the Molecular Orbital Regime
V. Horvat*, @. [mit†, R. L. Watson *, A. N. Perumal*, and Y. Peng*
*
Cyclotron Institute, and Department of Chemistry,
Texas A&M University, College Station, TX 77843, USA
†
Department of Physics, University of Ljubljana, Jadranska 19,
and J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
Abstract. Cross sections for target atom and projectile ion K vacancy production have been measured using solid targets
of Mo, Ag,and Sn bombarded by 10 MeV/amu beams of H, Ne, Ar, Cr, Kr, Mo, Ag, Sn, Xe, Nd, Ho, Ta, Au, and Bi. It
was found that the target K vacancy production cross sections reach a local maximum as the projectile atomic number Z1
approaches the atomic number Z 2 of the target. In this work, the measured cross sections are compared to the results of
calculations based on existing theories of K-vacancy production. It was found that the predictions of current theories of
the molecular orbital mechanism describe the shape of the Z 1-dependence of the cross sections in the near-symmetric
collision regime reasonably well. The contributions from direct electron capture and ionization were represented by a
second-order polynomial in Z 1 because the validity of available theoretical descriptions of these processes does not extend
into the near-symmetric region.
INTRODUCTION
EXPERIMENT
oooAn increase in the K x-ray production cross section
as the atomic number of the projectile (Z1 ) approaches
the atomic number of the target atom (Z 2) is a
characteristic of the molecular-orbital (MO)
mechanism. In this process, K vacancy production in
the target atom and in the projectile ion is due to
interactive level crossings that occur as the two
collision partners dynamically combine to form a
quasi-molecule. This mechanism is expected to be
predominant when the projectile speed v 1 is
significantly smaller than the orbital speed vK of the K
electrons.
oooThe objective of the work described here was to
investigate MO effects in the intermediate velocity
regime by measuring the cross sections for target and
projectile K vacancy production using a wide range of
collision partner combinations. At 10 MeV/amu, the
projectile speed (20 a.u.) is roughly equal to the speed
of the K electron in atomic vanadium (Z = 23).
oooCross sections for target atom and projectile ion K
vacancy production have been measured using selfsupporting solid targets of Mo, Ag, and Sn, all in the
form of metallic foils, having thickness of 2.55, 2.67,
and 2.44 mg/cm2, respectively. The targets were
positioned at 45 o relative to the beam.
oooBeams of H, Ne, Ar, Cr, Kr, Mo, Ag, Sn, Xe, Nd,
Ho, Ta, Au, and Bi were extracted from the Texas
A&M K500 superconducting cyclotron, collimated,
and focused on the targets. A plastic scintillator
mounted on a photomultiplier tube was positioned
directly behind the target and used to count the
outgoing beam particles.
oooEmitted x rays were measured with a Si(Li)
detector, positioned at 90o relative to the beam, viewing
the beam-impact surface of the target at 45 o. The
signals from the detector were fed into two pulseheight analyzers. One analyzer was set up to measure
in the singles mode, while the other was gated in order
to accept only x rays detected in coincidence with beam
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
7
particles. Finer details of the experiment are essentially
identical to those described in a previous publication
[1].
copper target, both in the near-symmetric collision
region and also for heavier projectiles. The same was
found for contributions from REC [6] involving Sm
and Ta targets [7].
oooTherefore, the measured cross sections were
compared with those calculated using the MO
approach, assuming that all other contributing
processes could be represented by a second-order
polynomial in Z 1. The coefficients of this polynomial
were determined in a least-squares fit to the difference
between the measured and calculated cross sections.
CALCULATIONS
oooContributions from the MO mechanism were
calculated using the diffusion model of Mittleman and
Wilets [2], and the hidden crossing model of Janev [3].
The former model describes the ionization process as
a gradual vacancy diffusion from the continuum into
the ground state while the molecule is being formed,
followed by the migration of the vacancy into the K
shell of one collision partner while the molecule
dissociates. The latter model considers inner-shell
vacancy creation and transfer associated with hidden
crossings of adiabatic energy surfaces in the complex
plane of internuclear distance.
oooOther processes may also contribute to target Kvacancy production. These include direct ionization of
the target electron in a binary collision with the
projectile (DI) and non-radiative capture of the target
electron to a projectile bound state (NREC). For targets
with large atomic numbers, significant contributions
from the radiative electron capture mechanism (REC)
can be expected. DI also contributes to projectile Kvacancy production.
oooThe contributions from DI and NREC are typically
calculated using the ECPSSR theory [4]. However, this
theory is expected to be valid only when 0.03 # Z 1 / Z 2
# 0.3, which means that it does not apply in the nearsymmetric region. Indeed, the K-vacancy production
cross sections for a Cu target bombarded by 10
MeV/amu projectiles with Z 1 $ Z 2 (measured
previously [5]), were found to be significantly smaller
than the ECPSSR cross sections for DI alone. A theory
of DI that would be valid for near-symmetric collisions
involving heavy projectiles is not presently available.
oooThe tentative contributions to target K-vacancy
production from NREC were also calculated using the
ECPSSR theory, taking into account the availability of
projectile states for capture while the projectile is
inside the target. It also found that these contributions
alone overestimate the measured cross sections for the
RESULTS
oooFig. 1 shows the dependence on projectile atomic
number of the target vacancy sharing fraction (TVSF),
i.e., the probability that the molecular orbital vacancy
created in the collision ends up in the target K shell
when the two collision partners separate. The
experimental data points represent the measured ratio
of target to total (projectile plus target) K vacancy
production cross sections. It was found that the
measured values were not properly described by the
FIGURE 1. Target K vacancy sharing fraction as a function
of the projectile atomic number. Solid diamonds, hollow
circles, and solid squares represent the measured data for Mo,
Ag, and Sn targets, respectively. Thick solid curves represent
a semiempirical fit to the measured data. For comparison,
results of the calculations based on the methods of Refs. 8, 9,
and 3 for Ag targets are shown by the dash-dotted, dashed,
and dotted curves, respectively.
8
formulas given by Meyerhof [8], Stolterfoht [9], or
Janev [3]. However, a good fit to the data for all three
targets was obtained from Solterfoht's formula by
changing the value of its empirical parameter β from
2.73 to 3.54 [or 2π1/2]. Consequently, it was decided to
use Stolterfoht's formula with β = 2π 1/2 to determine the
TVSF in the MO calculations, instead of the methods
proposed in the original papers.
projectile atomic number. Good overall representations
of the data are achieved. The shapes of the regions of
enhanced cross sections are well reproduced by the MO
contributions calculated using the hidden crossing
oooCross sections for projectile K-vacancy production
in the silver target are shown in Fig. 2. Those for the
Mo and Sn targets are not shown, since they are
comparable in magnitude. From Fig. 2 it can be
concluded that the contributions from other K-vacancy
production processes are comparable in magnitude to
those from the MO mechanism as calculated using the
method of Janev [3] in conjunction with measured
vacancy sharing fraction. The method of Mittleman and
Wilets [2] yields smaller values of the MO cross
sections and, consequently, requires even larger
contributions from other processes.
oooK-vacancy production cross sections for Mo, Ag,
and Sn targets are shown in Fig. 3 as a function of
FIGURE 2. Cross section for projectile K-vacancy
production as a function of projectile atomic number, in
collisions with the silver target. Solid circles represent the
measured data. Calculations based on the theory of Janev [3],
using measured vacancy sharing fractions, are represented by
the dotted line. A polynomial fit to the residuals is
represented by the dashed line, while the total is represented
by the thick solid line.
FIGURE 3. Cross section for K-vacancy production in Mo,
Ag, and Sn targets as a function of projectile atomic number.
Solid circles represent the measured data. Calculations based
on the theory of Janev [3], using measured vacancy sharing
fractions, are represented by the dash-dotted line. A
polynomial fit to the residuals is represented by the dashed
line, while the total is represented by the thick solid line. The
dotted lines denote the center of the symmetric region.
9
model [3] in conjunction with measured vacancy
sharing fractions. This mechanism contributes about
75% of the measured cross section at the peak of the
enhancement. The agreement with the experimental
data is almost as good when the diffusion model [2] is
used to calculate the contributions from the MO effects
under the same conditions. Those cross sections are
lower and have a slightly different Z 1-dependence,
which then has to be compensated for by increasing the
contribution and modifying the shape of the secondorder polynomial in Z 1.
available theories because they do not apply in this
region and therefore they were represented by a
second-order polynomial in Z 1, A comprehensive
theory of K-vacancy production in near-symmetric
regions is needed to describe the individual
contributing mechanisms on a quantitative basis.
ACKNOWLEDGMENTS
oooThis work is supported by the Robert A. Welch
Foundation.
oooSome notable systematic deviations of the data
points from the best-fit curves may suggest that there
could be some fine structure in the Z 1 dependence of
these cross sections. The high value of the target Kvacancy production cross section for a Cr beam and a
molybdenum target corresponds to the peak in the
contribution from NREC calculated using the ECPSSR
theory. Although this theory does not apply in this
regime and it overestimates the measured cross
sections, this could indicate that NREC contributes
significantly to target K-vacancy production.
REFERENCES
1. Watson, R., L., Horvat, V., Blackadar, J. M., and
Zaharakis, K. E., Phys. Rev. A 62, 052709 1-7 (2000).
2. Mittleman, M. H., and Wilets, L., Phys. Rev. 154, 12-16
(1967).
3. Janev, R. K., Nucl. Instrum. Methods in Physics Research
B 124, 290-297 (1997); Janev, R. K., J. Phys. B 30, 30193030 (1997).
4. Brandt, W., and Lapicki, G., Phys. Rev. A 23, 1717-1729
(1981); Lapicki, G., and McDaniel, F. D., Phys. Rev. A 22,
1896-1905 (1980).
5. Watson, R. L., Horvat, V., Blackadar, J., M., and
Zaharakis, K. E., Phys. Rev. A 60, 2959-2969 (1999).
6. Raisebeck, G., and Yiou, F., Phys. Rev. A 4, 1858-1868
(1971).
7. Watson, R. L., Horvat, V., and Zaharakis, K. E.,
“Projectile and Target Z-scaling of Target K-vacancy
Production Cross Sections at 10 MeV/amu,” in Application
of Accelerators in Research and Industry, edited by J. L.
Duggan and I. L. Morgan, AIP Conference Proceedings,
576, New York, 2001, pp. 93-95.
8. Meyerhof, W. E., Phys. Rev. Lett. 31, 1341-1344 (1973).
9. Stolterfoht, N., Ziem, P., and Ridder, D., J. Phys B 7,
L409-413 (1974).
CONCLUSIONS
oooK-vacancy production cross sections for target
atom and projectile ion K vacancy production have
been measured using solid targets of Mo, Ag, and Sn
bombarded by 10 MeV/amu (20 a.u.) beams of H, Ne,
Ar, Cr, Kr, Mo, Ag, Sn, Xe, Nd, Ho, Ta, Au, and Bi. It
was found that the predictions of current theories of the
molecular orbital mechanism describe the shape of the
Z1-dependence of the cross sections in the nearsymmetric collision regime reasonably well if
experimental values of the vacancy sharing fractions
are used. The contributions from direct ionization and
electron capture could not be calculated using the
10