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Absolute differential cross sections for single-electron capture of H0 in Ar at keV energies
Nuclear
44
Instruments
ABSOLUTE DIFFERENTIAL CROSS SECTIONS OF Ho IN Ar AT keV ENERGIES H.
MARTiNEZ,
A. MORALES,
Instrtutode Fisitu,
UNAM,
P.O.
Box
J. DE URQUIJO.
139-B.
Cuernauaca,
Mu.,
and Methods
in Physics Research B40/41 North-Holland.
FOR SINGLE-ELECTRON
I. ALVAREZ 62191.
(1989) 44-46 Amsterdam
CAF’TURE
and C. CISNEROS
Mexico
Absolute differential and total cross sections for H- formation in Ho +Ar collisions have been measured over the energy range 1.0-4.0 keV. Differential cross sections are strongly peaked in the forward direction and exhibit well-resolved oscillations over the range of angles and energies studied. Total cross sections also show an oscillatory behavior. In order to explain such oscillatory behavior for both differential and total cross sections, a multichannel model was used and very good agreement was found when a crossing radius for the potential curves, RI = 0.5 A. was assumed.
In
recent
theoretical sions
years
effort
between
negative
a great
has been
hydrogen
hydrogen
deal
of
done
ions
and
ion formation.
sons for choosing
and
angular
distributions
the colli-
and 3’
with a parallel-plate
experimental
in studying atoms,
resulting
In particular.
the argon-hydride
in
the rea-
collisional
channel
electron
of H - were measured electrostatic
multiplier.
cross section
was calculated
where
is the number
The
between
analyzer
absolute
0 o
and a
differential
from the relation
system
for study were the following. (1)
Many important
and
cross-sectional
exist
applications
information
for H-
beams
on the production
of
HP.
N(0)
angle
(2) Excellent sections.
work has been published
exhibiting
a well defined
it was felt that measurements tions
might
collision
serve
dynamics
(3)
In order
fectiveness
sensitive
probe
compare
the
for
the
sections
all the
net
ef-
for differ-
important
atmo-
and theoretical
charge-changing
cross
of the hydrogen-argon
arrangement
were
accelerated
velocity-selected
sys-
has been described
to energies by a Wien
gas target
cally.
The beam emerging
a transverse
of thickness
electric
components
of
uncertainty
and
target
by numerical
in the
cross
to describe
the differential has been
on
the
processes.
scattering
amplitude
section
is esti-
absolute
as a function
ion production
based
total
integration.
by the uncertainty
the measured
du,&dQ
scattering
Absolute
thickness.
In fig. 1 we present A model
AD the solid
system.
differen-
of the energy.
cross
section
developed
multichannel
treatment
It is shown
in ref.
can be expressed
for
by Russek
[ll]
of
the
that
the
in atomic
units in
in
and
1 and
5 x 1013 atoms/cm’,
from this cell passed
field which
deflected
4
deflected on typithrough
the charged
out of the beam and also served to quench
metastable
HO (2s)
was then incident
thickness
between filter
field. The ions were then incident
a N,
the
were calculated
total
of
I,, the intensity
on the target
by the detector
in the effective
[ll],
sections
[lo] and only a brief description will be ion here. H + ions formed in a Colutron
10 o by an electric
beam
thickness,
at laboratory
e the efficiency
the form:
The experimental
source
incident
tial cross section
detail elsewhere
keV.
The
aurora1
tem [4-91.
presented
beam
the target
subtended
negative
states
II
cross sections
curves
[6].
in determining
and potential-energy
for
various
(4) There has been much experimental activity
the H” angle
sec-
counts
mated to be + 10% and is dominated
of the cross
is needed
gas species
structure;
[4.5].
to quantitatively
the detector,
cross
the potential-energy
phenomena
knowledge
processes
spheric
as a more
of H+ and Ho in sponsoring
phenomena. ent
oscillatory
of differential
regarding
and interference
on total cross
of H-
0, T the time of observation.
3 X lOI
The
atoms/cm*.
0168-583X/89/$03.50 (North-Holland
state.
Physics
neutral
on a cell containing
‘i! Elsevier Publishing
typically. Science
where tude
[ll]
lowed during variables
B.V.
that
development, differential experiment
ion
function
radius.
5, is computed the trajectory. cross results
section different
the amplithe
impact
development
and
It was shown
kh = I+ with
(2)
A(b)
phase
with
dh,
when
of order zero.
0 = d&/dI.
for three
kb0)
formation
is b. < the channel
J,, is the Bessel
hydrogen
Publishers
negative
parameter ref.
b) exp(it).J,(
b_Y is the level-crossing for
Ar gas of Laboratory
Division)
f( 0) = -ikJh’M( 0
&. The
in
phase
the potentials
fol-
Fig. 2 shows the calculated plotted
in
energies
for 1.0 keV.
terms together
In order
of
scaled
with
the
to make
the
H. Mortine:
I
I
et al. / Cross sectmns for single-electron
I
45
capture of H” rn Ar
r
I 05
H'.Ar ,+H
-
10“'
-
1
keV
_A
1.0 keV
----
50
-
Expement
3
keV
=
10 keV (normalized)
li _1
10-l
kc’4
10-l
kc’4
10-l L
OUT+i
2.0 keV
9 E"'
(keV1'2deg)
(x0.1)
2
10-l
Fig. 2. Calculated differential cross sections for energies 0.5. 1.0 and 5.0 keV. and experimental curve for 1.0 krV.
s
2.5 keV
where o, corresponds to the single-channel cross section which is only a function of the crossing radius. R,. and $I describes the interference between different channels and is a function of the incident velocity. In order to
10“
3.0 keV
lo-
(x01)
lo-
I
0.5
,h,
1.0
e Fig.
1.
15
4.0 keV 2.0
(dcg)
Measured absolute differential cross sections
oscillations agree with the experiment, a crossing radius of approximately 0.54 A had to be used. Fig. 3 shows the total cross section, o,_. along with the work of different authors. Taking into account the corrections proposed in different works [4], the agreement is excellent over the energy range studied here. A simple model to explain the oscillations in the total cross section qualitatively has been discussed in ref.
Lo,, , , , ,I
WI. The relationship between the crossing total cross section can be written as
0
radius and the
sin’(+),
(3)
3
2
Energy
Fig.
o,~=u,(R,)
1
3. Total
cross
sections for collisions.
4
5
6
(keV)
H-
formation
in
Ho +Ar
I. ATOMIC PHYSICS
H. Martinez
46
make
the experimental
absolute
values
value, a crossing
To our knowledge ion
pair
indication tween
are
still
agree both
radius
the detailed
curves for a separation not
shape of the potential
available.
Our
is an adiabatic
the ionic
curve
H- + Ar+
explains
and
of less than 2 A for the H- + Ar+
there 0.54
in shape
of 0.54 A was used.
that
H + Ar at about
et al. / Cross sections for single-electron
A which
both the differential
data
provide
an
intersection
be-
and the ground
state
in turn
satisfactorily
and total cross sections.
References [l] Proc. 2nd Int. Symp. on the Production and Neutralization of Negative Ions and Beams, Brookhaven National Laboratory (1980) ed. T. Sluyters. [2] Proc. USA-Mexico Joint Seminar on the Atomic Physics of Negative Ions, Mexico (1981) eds. I. Alvarez and C. Cisneros.
capture of Ho in Ar
[31 Proc. 3rd Int. Symp. on the Production and Neutralization of Negative Ions and Beams, ed. K. Prelec, AIP Conf. Proc. no. 111 (1983). [41 B. Van Zyl, T.Q. Lee. H. Newman and R.C. Amme. Phys. Rev. Al5 (1977) 1871. [51 B. Van Zyl, H. Newman, H.L. Rothwell. Jr. and R.C. Amme, Phys. Rev. A21 (1980) 716. WI R.J. McNeal and J.H. Birely, Rev. Geophys. Space Phys. 11 (1973) 633. [71 F. Roussel, P. Pradel and G. Spiess. Phys. Rev. Al6 (1977) 1854. PI J.F. Williams, Phys. Rev. 153 (1967) 116. [91 P.M. Stier and C.F. Barnett, Phys. Rev. 103 (1956) 896. DOI H. Martinez, I. Alvarez, J. de Urquijo, C. Cisneros and A. Amaya-Tapia, Phys. Rev. A36 (1987) 5425. ~ 1111A. Russek, Phys. Rev. A20 (1979) 113. WI E.H. Pedersen, J.V. Mikkelsen, J. Vaaben and K. Taulbjerg, Phys. Rev. Lett. 41 (1978) 1541.
44
Instruments
ABSOLUTE DIFFERENTIAL CROSS SECTIONS OF Ho IN Ar AT keV ENERGIES H.
MARTiNEZ,
A. MORALES,
Instrtutode Fisitu,
UNAM,
P.O.
Box
J. DE URQUIJO.
139-B.
Cuernauaca,
Mu.,
and Methods
in Physics Research B40/41 North-Holland.
FOR SINGLE-ELECTRON
I. ALVAREZ 62191.
(1989) 44-46 Amsterdam
CAF’TURE
and C. CISNEROS
Mexico
Absolute differential and total cross sections for H- formation in Ho +Ar collisions have been measured over the energy range 1.0-4.0 keV. Differential cross sections are strongly peaked in the forward direction and exhibit well-resolved oscillations over the range of angles and energies studied. Total cross sections also show an oscillatory behavior. In order to explain such oscillatory behavior for both differential and total cross sections, a multichannel model was used and very good agreement was found when a crossing radius for the potential curves, RI = 0.5 A. was assumed.
In
recent
theoretical sions
years
effort
between
negative
a great
has been
hydrogen
hydrogen
deal
of
done
ions
and
ion formation.
sons for choosing
and
angular
distributions
the colli-
and 3’
with a parallel-plate
experimental
in studying atoms,
resulting
In particular.
the argon-hydride
in
the rea-
collisional
channel
electron
of H - were measured electrostatic
multiplier.
cross section
was calculated
where
is the number
The
between
analyzer
absolute
0 o
and a
differential
from the relation
system
for study were the following. (1)
Many important
and
cross-sectional
exist
applications
information
for H-
beams
on the production
of
HP.
N(0)
angle
(2) Excellent sections.
work has been published
exhibiting
a well defined
it was felt that measurements tions
might
collision
serve
dynamics
(3)
In order
fectiveness
sensitive
probe
compare
the
for
the
sections
all the
net
ef-
for differ-
important
atmo-
and theoretical
charge-changing
cross
of the hydrogen-argon
arrangement
were
accelerated
velocity-selected
sys-
has been described
to energies by a Wien
gas target
cally.
The beam emerging
a transverse
of thickness
electric
components
of
uncertainty
and
target
by numerical
in the
cross
to describe
the differential has been
on
the
processes.
scattering
amplitude
section
is esti-
absolute
as a function
ion production
based
total
integration.
by the uncertainty
the measured
du,&dQ
scattering
Absolute
thickness.
In fig. 1 we present A model
AD the solid
system.
differen-
of the energy.
cross
section
developed
multichannel
treatment
It is shown
in ref.
can be expressed
for
by Russek
[ll]
of
the
that
the
in atomic
units in
in
and
1 and
5 x 1013 atoms/cm’,
from this cell passed
field which
deflected
4
deflected on typithrough
the charged
out of the beam and also served to quench
metastable
HO (2s)
was then incident
thickness
between filter
field. The ions were then incident
a N,
the
were calculated
total
of
I,, the intensity
on the target
by the detector
in the effective
[ll],
sections
[lo] and only a brief description will be ion here. H + ions formed in a Colutron
10 o by an electric
beam
thickness,
at laboratory
e the efficiency
the form:
The experimental
source
incident
tial cross section
detail elsewhere
keV.
The
aurora1
tem [4-91.
presented
beam
the target
subtended
negative
states
II
cross sections
curves
[6].
in determining
and potential-energy
for
various
(4) There has been much experimental activity
the H” angle
sec-
counts
mated to be + 10% and is dominated
of the cross
is needed
gas species
structure;
[4.5].
to quantitatively
the detector,
cross
the potential-energy
phenomena
knowledge
processes
spheric
as a more
of H+ and Ho in sponsoring
phenomena. ent
oscillatory
of differential
regarding
and interference
on total cross
of H-
0, T the time of observation.
3 X lOI
The
atoms/cm*.
0168-583X/89/$03.50 (North-Holland
state.
Physics
neutral
on a cell containing
‘i! Elsevier Publishing
typically. Science
where tude
[ll]
lowed during variables
B.V.
that
development, differential experiment
ion
function
radius.
5, is computed the trajectory. cross results
section different
the amplithe
impact
development
and
It was shown
kh = I+ with
(2)
A(b)
phase
with
dh,
when
of order zero.
0 = d&/dI.
for three
kb0)
formation
is b. < the channel
J,, is the Bessel
hydrogen
Publishers
negative
parameter ref.
b) exp(it).J,(
b_Y is the level-crossing for
Ar gas of Laboratory
Division)
f( 0) = -ikJh’M( 0
&. The
in
phase
the potentials
fol-
Fig. 2 shows the calculated plotted
in
energies
for 1.0 keV.
terms together
In order
of
scaled
with
the
to make
the
H. Mortine:
I
I
et al. / Cross sectmns for single-electron
I
45
capture of H” rn Ar
r
I 05
H'.Ar ,+H
-
10“'
-
1
keV
_A
1.0 keV
----
50
-
Expement
3
keV
=
10 keV (normalized)
li _1
10-l
kc’4
10-l
kc’4
10-l L
OUT+i
2.0 keV
9 E"'
(keV1'2deg)
(x0.1)
2
10-l
Fig. 2. Calculated differential cross sections for energies 0.5. 1.0 and 5.0 keV. and experimental curve for 1.0 krV.
s
2.5 keV
where o, corresponds to the single-channel cross section which is only a function of the crossing radius. R,. and $I describes the interference between different channels and is a function of the incident velocity. In order to
10“
3.0 keV
lo-
(x01)
lo-
I
0.5
,h,
1.0
e Fig.
1.
15
4.0 keV 2.0
(dcg)
Measured absolute differential cross sections
oscillations agree with the experiment, a crossing radius of approximately 0.54 A had to be used. Fig. 3 shows the total cross section, o,_. along with the work of different authors. Taking into account the corrections proposed in different works [4], the agreement is excellent over the energy range studied here. A simple model to explain the oscillations in the total cross section qualitatively has been discussed in ref.
Lo,, , , , ,I
WI. The relationship between the crossing total cross section can be written as
0
radius and the
sin’(+),
(3)
3
2
Energy
Fig.
o,~=u,(R,)
1
3. Total
cross
sections for collisions.
4
5
6
(keV)
H-
formation
in
Ho +Ar
I. ATOMIC PHYSICS
H. Martinez
46
make
the experimental
absolute
values
value, a crossing
To our knowledge ion
pair
indication tween
are
still
agree both
radius
the detailed
curves for a separation not
shape of the potential
available.
Our
is an adiabatic
the ionic
curve
H- + Ar+
explains
and
of less than 2 A for the H- + Ar+
there 0.54
in shape
of 0.54 A was used.
that
H + Ar at about
et al. / Cross sections for single-electron
A which
both the differential
data
provide
an
intersection
be-
and the ground
state
in turn
satisfactorily
and total cross sections.
References [l] Proc. 2nd Int. Symp. on the Production and Neutralization of Negative Ions and Beams, Brookhaven National Laboratory (1980) ed. T. Sluyters. [2] Proc. USA-Mexico Joint Seminar on the Atomic Physics of Negative Ions, Mexico (1981) eds. I. Alvarez and C. Cisneros.
capture of Ho in Ar
[31 Proc. 3rd Int. Symp. on the Production and Neutralization of Negative Ions and Beams, ed. K. Prelec, AIP Conf. Proc. no. 111 (1983). [41 B. Van Zyl, T.Q. Lee. H. Newman and R.C. Amme. Phys. Rev. Al5 (1977) 1871. [51 B. Van Zyl, H. Newman, H.L. Rothwell. Jr. and R.C. Amme, Phys. Rev. A21 (1980) 716. WI R.J. McNeal and J.H. Birely, Rev. Geophys. Space Phys. 11 (1973) 633. [71 F. Roussel, P. Pradel and G. Spiess. Phys. Rev. Al6 (1977) 1854. PI J.F. Williams, Phys. Rev. 153 (1967) 116. [91 P.M. Stier and C.F. Barnett, Phys. Rev. 103 (1956) 896. DOI H. Martinez, I. Alvarez, J. de Urquijo, C. Cisneros and A. Amaya-Tapia, Phys. Rev. A36 (1987) 5425. ~ 1111A. Russek, Phys. Rev. A20 (1979) 113. WI E.H. Pedersen, J.V. Mikkelsen, J. Vaaben and K. Taulbjerg, Phys. Rev. Lett. 41 (1978) 1541.