PHYSICAL REVIEW A 81, 062709 (2010)
L
3
-subshell alignment of Au and Bi in collisions with 12–55-MeV carbon ions
Ajay Kumar,
1,*
A. N. Agnihotri,
2
S. Chatterjee,
2
S. Kasthurirangan,
2,3
D. Misra,
2
R. K. Choudhury,
1
L. Sarkadi,
4
and L. C. Tribedi
2
1
Nuclear Physics Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India
2
Tata Institute of Fundamental Research, Colaba, Mumbai 400 005, India
3
Institute of Chemical Technology, Mumbai 400 019, India
4
Institute of Nuclear Research of the Hungarian Academy of Sciences (ATOMKI), Post Office Box 51, H-4001 Debrecen, Hungary
(Received 30 October 2009; revised manuscript received 26 April 2010; published 24 June 2010)
Angular distribution of the L x-ray intensities in Au and Bi induced by 12–55-MeV carbon ions has been
measured. The L
α
, L
β
, and L
γ
x-ray intensities were found to be isotropic within experimental uncertainty. The
alignment parameter A
20
of the L
3
(2p
3/2
) subshell was deduced from the measured anisotropy parameter β
value of the well-resolved L
l
line, obtained from the angular distribution of the I
Ll
/I
Lα
, I
Ll
/I
Lβ
, and I
Ll
/I
Lγ
x-ray intensity ratios. The measured A
20
values have been compared with those obtained using theoretical
models that involve the plane-wave Born approximation; projectile’s energy loss and its Coulomb deflection
from the straight-line trajectory, perturbed-stationary-state, and relativistic effects (ECPSSR); and ECPSSR with
the intrashell effect.
DOI: 10.1103/PhysRevA.81.062709 PACS number(s): 34.50.Fa
I. INTRODUCTION
The removal of an inner-shell electron with total angular
momentum j 3/2 from an atom by a charged particle leads
the ionized atom to be aligned with respect to the incident
beam direction, quantization axis [1]. This alignment is
owing to different numbers of vacancies in different magnetic
substates |m
j
| and is reflected through the anisotropic angular
distribution (and polarization) of the characteristic x rays (and
Auger electrons) emitted from the aligned ions [1–7]. For
dipole-type x rays resulting from the decay of an aligned
vacancy created by a collimated unpolarized charged particle,
the differential intensity I (θ ) of the x rays relative to the
incident beam direction is described by [3–5]
I (θ )/d = I
0
/4π [1 + βP
2
(cos θ )], (1)
where d is the solid angle subtended by the detector at the
target, I
0
is the total intensity of the x rays, P
2
(cos θ ) is the
second-order Legendre polynomial, and β (=ακA
20
) is called
the “anisotropy parameter” of a particular x-ray line. Here
α is a constant depending on the total angular momentum
of the initial and final state of the vacancy [3], κ is the
Coster-Kronig correction factor, and A
20
is the “degree of
alignment” or “alignment parameter” for a given subshell [3,4].
The theoretical value of α for different transitions in a singly
ionized atom has been given by Berezhko and Kabachnik [3].
For an initial vacancy created in the L
3
(2p
3/2
) subshell, A
20
is defined by [3–5]
A
20
=
σ
(
3
2
,|
3
2
|)
− σ
(
3
2
,|
1
2
|)
σ
(
3
2
,|
3
2
|)
+ σ
(
3
2
,|
1
2
)|
, (2)
where σ
(J,|m
J
|)
corresponds to the (partial) ionization cross
section of the magnetic substates. As reflected from Eq. (2),
the A
20
provides information on vacancies (ionization) and
their relative distribution in different |m
j
|’s. It is not feasible
to obtain this knowledge from only the L
3
-subshell ionization
cross-section measurements [σ
L
3
= σ
(
3
2
,|
3
2
|)
+ σ
(
3
2
,|
1
2
|)
]. In order
*
atomar@barc.gov.in/ajayktomar@gmail.com
to generalize the alignment parameter for different collision
systems and compare experimental results with theoretical cal-
culations, the relative projectile velocity V ≡ v
p
/v
t
has cus-
tomarily been used. Here v
p
corresponds to the projectile ve-
locity and v
t
= (2E/m
e
)
1/2
, with E the binding energy of the
involved electron, m
e
the electron mass, and v
t
the velocity of
the involved electron (in the present case L
3
-subshell electron).
The sensitivity of ionization cross section to the collision
dynamics makes the alignment parameter a crucial quantity.
Understanding of the behavior of the A
20
parameter as a
function of the collision velocity and projectile and target
atomic number is required for good testing of the various the-
oretical models, namely, semiclassical approximation (SCA)
[8–13]; plane-wave Born approximation (PWBA) [14–21]; the
improved approach based on the PWBA by introducing correc-
tions for the projectile’s energy loss and its Coulomb deflection
from the straight-line trajectory, perturbed-stationary-state,
and relativistic effects (ECPSSR) [22]; and ECPSSR with
intrashell effect (ECPSSR-IS) [23–29]. The IS (intrashell)
correction takes care of the collision-induced IS transition
of a vacancy between the L subshells [23–29]. In this
two-step IS process, a vacancy created by direct Coulomb
ionization decays through a collision-induced IS transition of
an electron from the remaining two subshells. Inclusion of the
IS correction in ECPSSR substantially improves agreement for
L-subshell cross sections, their impact parameter dependent
ionization probabilities, and the L
3
-subshell alignment.
The x-ray detection at a single observation angle θ may
require anisotropic emission correction for correct information
of the x-ray yield, unless the value of α or A
20
or P
2
(cos θ )
[Eq. (1)] becomes zero. For experimental study of the L
3
-
subshell alignment, it is customary to use the L
l
(3s
1/2
→
2p
3/2
) x ray since it is a single line and well resolved in
high-Z atoms with the Si(Li) or Ge detectors. Furthermore, L
l
has maximum predicted anisotropy (α = 0.5[3]) among all
the x rays from the L
3
subshell. The A
20
value can be deduced
from the anisotropy parameter β of an L
l
x ray, obtained either
from the measurement of absolute yield of the L
l
line or from
L
l
line intensity relative to the intensity of any other x ray in
1050-2947/2010/81(6)/062709(10) 062709-1 ©2010 The American Physical Society