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VOLUME 16, NUMBER 3
K -shell x rays of selected elements from Nb through Gd for incident protons and alpha
particles from 0.6 to 2.4 MeV
S. R. Wilson, F. D. McDaniel, J. R. Rowe, and J. L. Duggan
Department of Physics, North Texas State University, * Denton, Texas 76203
(Received 28 February 1977)
K-shell x-ray production cross sections and K/3/Ka ratios are presented for 0.6- to 2.4-MeV protons and
alpha particles incident on thin targets of selected elements from Nb to Gd. The K/3/Ka ratios are
compared to the theoretical predictions of Scofield and agree within 10%. The experimental cross sections
are compared to the theoretical predictions of the plane-wave Born approximation (PWBA) and the PWBA
modified to include binding energy, Coulomb deflection, and relativistic effects. It is seen that the PWBA
modified for binding energy and Coulomb deflection effects agrees with the experimental data for Nb to
within uncertainties, but its predictions are lower than the data by larger amounts as the target Z increases.
Inclusion of an ad hoc semiclassical relativistic correction to the theoretical cross section, as suggested by
Hansen, improves the agreement with the data, but overestimates the data for the highest- Z elements.
I. INTRODUCTION
In the past few years there has been consider-
able interest in inner-shell ionization produced
in light-ion-atom collisions. Earlier experimen-
tal data have been summarized in review articles
by Rutledge and Watson' and by Garcia, Fortner,
and Kavanagh.2 These results have been com-
pared primarily to two theoretical models of Cou-
lomb ionization: (a) the binary-encounter approx-
imation3 (BEA) and (b) the plane-wave Born ap-
proximation (PWBA). The present data are out-
side the range of values tabulated by McGuire and
Richard4 for the BEA, and therefore the BEA
theory will not be compared to the data.
The PWBA developed by Merzbacher and Lewis5
has been found to be in good agreement with ex-
perimental cross sections for incident projectiles
of atomic mass -4 and for energies greater than
a few MeV.6'7 However, at lower incident pro-
jectile energies, the PWBA overpredicts the cross
sections.6'8 The PWBA has been modified by
Basbas, Brandt, and Laubert9'10 to include Cou-
lomb deflection of the incident ion by the target
nucleus and increased binding of the target elec-
tron due to penetration of the K shell by the pro-
jectile. Both of these modifications, which are
important at lower incident velocities, reduce
the theoretical cross sections and improve agree-
ment with experiment.8
Relativistic effects which are believed to be im-
portant particularly at low incident ion velocities
for heavier targets are expected to increase the
theoretical cross sections."'6-1 or targets with
high Z2, the crucial relativistic effect has its
origin in the singularity of the K-shell wave func-
tion at the origin. This increases the form factor
for the large values of momentum transfer which
are needed for ionization by projectiles with low
velocities. The enhancement of the form factor
increases the cross section at low velocities and
the effect subsides as velocity increases. Merz-
bacher and Lewis5 have noted that the apparent
agreement between K-shell cross sections of
uranium for proton bombardment and the nonrela-
tivistic PWBA is coincidental and is most likely
due to a cancellation of the effects of increased
binding energy and Coulomb deflection with rela-
tivistic effects. Merzbacher and Lewis5 discuss
a relativistic correction due to H6nl.12 Recently,
Caruso and Cesatil3 have also modified the PWBA
to include relativistic effects. Both of these cor-
rections12,13 modify the target screening param-
eter OK and do not depend on the incident particle's
velocity. Hansen'4 has suggested a semiclassical
relativistic correction for the BEA, and this cor-
rection has been applied in an ad hoc manner to
the PWBA in the present work. This correction
consists of a multiplicative factor applied to the
nonrelativistic theoretical cross section and de-
pends on the ratio of the incident particle velocity
squared to the average target K-shell electron
velocity squared.
The majority of K-shell x-ray production cross-
section data reported for 0.5-3.0-MeV proton7"26
and a-particle8'27-29 bombardment are for ele-
ments in the range of Z2 from 20 to 40. Gray and
co-workers21' 23 have reported proton-induced
cross sections for selected elements between 42Mo
and 57La. Liebert et al.26 reported proton data
for 42Mo, 47Ag, and 48Cd. McKnight, Thornton,
and Karlowicz27 present data for a particles on
42Mo, 47Ag, and 50Sn. Lin, Duggan, and Carlton28
have presented data for a particles on 47Ag.
Absolute cross sections for elements in the
range of Z2= 40-65 are needed to provide a test
16 903
PHYSICAL REVIEW A
SEPTEMBER 1977
