Angular dependence of vibrational excitation in Li+ + N2, CO collisions at medium energies

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Angular dependence of vibrational excitation in Li+ + N2, CO collisions at medium energies

C. Benoit, D. Dhuicq

To cite this version:

C. Benoit, D. Dhuicq. Angular dependence of vibrational excitation in Li+ + N2, CO col- lisions at medium energies. Journal de Physique II, EDP Sciences, 1993, 3 (4), pp.465-476.

�10.1051/jp2:1993144�. �jpa-00247847�

Classification

Physics

Abstracts

34.50E

Angular dependence of vibrational excitation in Li+ ₊ N~, ^CO

collisions at medium energies

C. Benoit and D.

Dhuicq

Laboratoire des Collisions

Atomiques

et Moldculaires (*), Universitd Paris-Sud, Bit. 351, 91405

Orsay

Cedex, France

(Received 9 October J992,

accepted

in

final farm

23 December J992)

Abstract. We have measured the vibrational

populations

of

N~(X)

and

CO(X), produced by

Li+

projectiles,

_at collision

energies

100 WE w500eV _{as a} function of the

scattering angle.

Though vibrational excitation is _a weak process in the angular range studied, it is found to

strongly

vwy with the

angle.

Other inelastic processes ^such as

charge exchange

_or electronic excitation _are

negligible.

A theoretical model

developed previously

to describe vibrational excitation in this energy range is

applied

to the considered collisional systems. The reasonable agreement ^with

experiment

thus obtained shows that the observed vibrational excitation results

only

from

ground

state interactions.

1. Introduction.

The

study

of vibrational excitation of

simple

^molecules

produced by light

ions is of fundamental interest in collision

physics.

A lot of works have thus been devoted _to this

subject

in the

past

two decades. Collisions such _as H+ ₊

H~,

Li+ ₊

N~

and CO have been studied-first

especially

at low energy

(E

_~ 30 eV for

example).

^In this _case vibrational excitation

depends only

_on the interactions

arising

from the

ground

state

potential

energy surface _: it is _a

« pure »

vibrational excitation. In the intermediate energy

regime (30

eV

~ E

~ l 000 eV

)

interactions due to other

potential

surfaces may also _come into

play

and lead _{to «} anomalous _» vibrational excitation. Because of such

complication

few studies _were

performed

in this energy range. In

previous

studies _on He+ ₊

N~,

CO

Ill

^{and H+} +

H~ [2]

collisions at intermediate energy, ^we found _cases of anomalous vibrational excitation

arising

from

charge exchange

_or electronic

excitation processes. One of the purposes of the

present study

is to see to what extent, in the Li+ ₊

N~

^and CO _cases, such anomalous excitation _can be observed.

At low energy vibrational _or rotational excitations of

N~

and CO

by

Li+

projectiles

have been studied _as functions of the

scattering angle

lf

by

the Toennies' group

[3-5].

At moderate

energies (E>70eV),

Tanuma etal.

[6]

and Kita etal.

[7]

measured and

explained theoretically charge exchange

and electronic excitation processes

occurring

in these collisions

(*) Unitd de Recherche Associ£e _au CNRS _n D0281.

at

large angles

O

(or

_« reduced

angles

_{» r}

=

Ed).

Such studies had been

preceded

_at

high energies (E

> 500 eV

by

the work of Kita _et al.

[8]

who tried to determine the

repulsive

_part

of the

ground

state interaction

potential by integral scattering

measurements. In the _same energy range Sato _et al.

[9]

measured _«

pseudo-elastic

_»

(elastic plus

rovibrational

excitation)

and inelastic processes

(electronic

excitation and

ionisation)

ⁱⁿ Li+ ₊

N~(CO)

collisions and

interpreted

them in _terms of _a classical

impulse approximation.

Pseudo-elastic _or elastic

scattering

had also been

investigated

at low and moderate energy in the

pioneering

work of Aberth and Lorents

([10],

see also

[I II)

and _at

high energies by

^Kalinin et al.

[12].

Inversion

procedures

for the determination of the

isotropic

_part of the interaction

potential

have also been used

by

Budenholzer and Lee

[13]

and

by

^Gislason et al.

[14]

^from

integral

cross-sections

measurements.

The

ground

state interaction

potentials

V for Li+ ₊

N2

and Li+ ₊ CO collisions _were first

computed by

Staemmler

[15, 16]. They

_were used _to

study

ro-vibrational excitation at low energy

by

Eckelt _et al.

[17], then, by

_means of

analytic

fits of these

potentials, by

Thomas et al.

[18, 19]

and

by Billing [20].

Other determinations of V have also been obtained _more

recently (see

for instance

[21-23]

and Ref. in

[14]).

Between the low and

high

_energy

experiments

few studies _were devoted _to vibrational excitation.

Kobayashi

et al.

[24, 25]

measured the

integral

cross-sections for the excitation _to the v ₌ I and 2 levels of the electronic

ground

state of

N2

and CO for E

=

70 to 500 eV.

They interpreted

their results in terms of

multipolar

interactions within the Bom

approximation.

Then Iwamatsu _et al.

[26]

found _a

scaling

law for this

type

^of

experiment involving

_a

dipolar

interaction and

applied

it _to the _case of Li+ ₊ CO

(and NO). However,

to _our

knowledge,

_no

study

of the variation of vibrational excitation with the

scattering angle

O

(or r)

has been made in this energy range : this is the second purpose of the

present

^work.

Another

interesting

aspect ^{of the Li+} +

N2

_or Li+ ₊ CO

systems

^{is that}

they

_are

good

model systems ^{for the}

study

of vibrational excitation in their electronic

ground

state, because this state is well isolated from other states. The energy

separation

at intermolecular distance R

= cc between the

ground

state and the first electronic _state

leading

to

charge exchange

_: Li+ ₊

N~ (CO )

- Li ₊

N( (CO+ )

is indeed Mm10.2 eV

(respectively

8.6

eV).

In such conditions it may be

expected

that

vibrational excitation remains pure in _a

large

scale of

energies

and

scattering angles.

In

comparison

with the He+ ₊

N~,

CO and H+ ₊

H~

_cases, this circumstance will facilitate the

analysis

of the

experimental

results

by

_means of _a theoretical model described in

[Il.

After _a

presentation

^of

typical experimental

^results

(Sect. 2),

_we

apply

_our model _to the

cases of Li+ ₊

N~

and CO collisions and

finally

_compare the

experimental

and theoretical

results

(Sect. 3).

2.

Experimental.

Vibrational

populations

^of

N2(X)

and

CO(X) resulting

from collisions with Li+

projectiles

have been measured _as functions of

scattering angle

Oat three

energies

_: E

=

100,

200 and

500 eV.

Except

for _{a new} source the

apparatus

^{is the} same as described in

previous

_papers

[27, 28].

Here Li+ ions _are extracted from the surface of _an

electrically

^heated _porous

tungsten plug containing

lithium aluminosilicate

(Spectra-Mat, Inc., Califomia).

Two types ^{of Li+} sources

have been used _: the first _one,

producing

^7Li+

ions,

_was used in the measurements with

N2,

the other _one,

isotopically

enriched in

6Li, supplied

ions for the

experiment

with CO. After

mass

analysis

and energy

selection,

the incident beam is accelerated to the desired collision energy and _{crosses at}

right angles

the

target

^beam

emerging

from _a

multicapillary

_array. In the

crossing region

the section of the ion beam is 0.6 _{mm x} 3 _mm and the diameter of the

molecular beam is 2 _mm. The

intensity

of the incident Li+ beam in the

target region

is 1 5 _x lo ^~~

A,

that is a factor 4 _to 20 less than the

intensity

obtained with H+ _or He+. This

low

intensity justifies partly

the _use of _a

multicapillary

_array to form the target ^{beam in}

place

of

a

supersonic

nozzle beam, with the

counterpart

^of a loss of energy resolution. The scattered ions _are then

angle selected, electrostatically analysed

and

finally

detected _{on a} microchannel-

plate

based

position

sensitive device. It is thus

possible

to detect

simultaneously

ions that have lost energy over a range AE 2 eV. Neutrals

resulting

from

charge exchange

can be detected but _not energy

analysed.

The ion spectra ^{obtained from} a

microprocessor

_are deconvoluted in _a

microcomputer.

At each

scattering angle,

the

apparatus

^{function used for the} deconvolution of

the recorded energy

spectrum

^{is deduced from the}

corresponding

_v

=

0

peak.

The

angular spread

is ad 0.4° FWHM and the energy resolution &E 0. I eV FWHM _at O

~

0°.

Owing

to thermal effects, the energy

spread

becomes &E 0.2 eV _{at a} few

degrees

in _our energy range. This energy

spread

and the low

signals

detected _{are sources} of

larger

_errors than in _our

previous experiments.

Examples

of

spectra

^{obtained for}

N~

and CO at the _same energy and

angle

_are shown in

figure

I. The v _> I vibrational

peaks

_are

generally

too weak in the E and O range

studied,

_so that we measured

only

the

population

ratios

Pj/Po (1f

or

r)

at each energy. The data

points

obtained from various series of measurements and after deconvolution _are fitted

by

a least- square method. In _a

log-log plot

the

resulting

best fit _{curves can} be

practically represented by straight

lines

(Figs. 2, 3).

This result may be

approximately justified by

the

predictions

of _a

simple

model

explained

in

[28],

which leads _to the relation:

Pj/Po~kr~ (I «n«2,

k

= constant at a

given energy).

As _a test of the

validity

of the fits

obtained,

in

spite

of the

relatively large

scatter of the data

points,

_we have verified that the removal of _one of the sets of measurements does _not

change

the fit

significantly.

Note that in

figures 2,

3 and in the

following figures,

the

angular dependences

will be

conveniently presented

_as functions of the reduced

angle

_r

=

Elf

(see

the

corresponding

discussion in

[2]).

It may be _seen from

figures 2,

3 that vibrational excitation

generally

decreases _as energy increases _at fixed _r. One can observe

an overall

larger

excitation for CO than for

N~.

The latter observation is in agreement ^{with the}

integral

cross-section measurements of

Kobayashi

et al.

[24, 25], although

the

angular

_ranges

taken into _{account are not} the _same. In both _cases vibrational excitation increases

strongly

^with

r, but _our studied

angular

_range is not

large enough

to find _a strong ^{excitation such} as

Pi

_m P

o.

v=21 O v=2 O

~~1

0

AE

(eV)

~a) (b)

Fig.

I.

Examples

of Li+ _energy loss spectra obtained at E

=

200 eV, d

= 2° in the collision with _: a) N21 b) ^CO.

~°~

ln(P~/Pi)

P~/P~ ⁺

#+

(c)

lo ⁺ ++ +F

+

'++~+

+

+

$

+

% + +

+

+

4

~ +

"

(b)

Jo +

~ ⁺

+ +

++

i

+

+

(a)

+ ~

+++

lo 2

~ ~ ~

ln[~(evdeg)j

o-I

~(kev dog)

Fig.

2. Vibrational

population

ratios

Po/Pj

measured for the Li+ ₊ N~ collision _as functions of the

reduced

scattering

angle r=EO at the three studied collision

energies:

a) E=looev,

b) E

=

200 eV, c) E

=

soo eV. The _{curves are} linear fits of the

experimental

data

points.

We have also measured the reduced differential _cross sections _p

(r)

₌

«(lf)

O sin O in

each case and at each energy for the elastic process po

(v =0)

and for the sum

£

J of all scattered ions _at fixed O. The

resulting

_po curves are

presented

in section 3

along

with the theoretical _curves and the pi

(v

=

I _curves deduced from

figures 2,

3. The summed

cross sections

if

_are

displayed

ⁱⁿ

figure

4 _as well _as the

corresponding

_curves deduced

from Kita _et al.

[7]

at E

= 200 eV.

According

to the _«

scaling principle

_» used in atomic collisions for

large energies

and small

scattering angles [29, 1II

the _curves obtained _at various

energies

_are matched _at small _r. The present measurements at 200 eV agree well with the

curves of Kita _et al.

[7],

inclusive of the small

perturbation

observed at _r 2.8 kev

deg

in the

case of CO. At each studied energy the

z

I _curve looks like the po curve

(see

Sect.

3)

ⁱⁿ a

'_n

eo/Pi)

Po/Pi

+ +

(c)

+ +

i

+ ++ +

b)

lo $ +

++ ₊ +

+ ++ ⁺ +~

++j

^{~ +}

~y+ +

# +

i

(a)

5 6 7 1n

[~ (eV

_deg

)j

o.I

~(kev deg)

Fig.

3. SanJe _as

figure

2 in the _case of the Li+ ₊ CO collision.

electronic excitation _{are not} very efficient. In fact direct measurements of electronic excitation in the spectra ^{have shown that this excitation is} very weak in _our range of

energies

and

angles

and _can be

neglected.

In the _{same manner we} have tried to measure neutrals

resulting

from

charge exchange,

but

they

_are

practically

undetectable. The last two

types

^{of inelastic} processes

actually

arise at

larger

E and _r values

[7].

3. Theoretical and discussion.

The model used here _assumes that

only

the

ground

state

potential

_energy surface is involved in the collision

[Il.

As

pointed

out in section

I,

Li+

-N~,

-CO systems are

good

candidates to

apply

this model _: this surface is well

separated

from the other

potential

surfaces _so that inelastic processes ^{other than} ro-vibrational excitation _are

probably negligible. Consequently perturbations

of the molecular target

by

the

projectile

_are weak. This

justifies

the second

assumption

of _our model

namely:

^the

expansion

of the

potential V(R,r, y) (where

y ₌

(r, R))

in powers of the bond distance _r is limited to the linear term. In this _case the

'

la>

o

x

~0 ~~~~~~~~~'~~

~

,~

,~ X ~ o

I "I ^A

~

rm

~ l

~

lb)

xx

"

$~§

o ~Ox~o~ % 4 ~, fi x x x

~

f/4*~44

4 % "~X*" ^{x 4}

°

,-

, , ,

~

l 2 3 4

~

(kev deg)

Fig.

4. Reduced differential cross-sections _p (r)

= ~ (d) d sin d measured for the sum

jjJ

of Li+ scattered ions _at E

= loo eV (O), 200 eV (x) and soo eV (A) for a) N~, b) CO. The continuous

curves are the

corresponding

cross-sections at 200 eV deduced from the measurements of Kita _et al. [7].

The absolute _p scale is obtained from their calculations.

reduced vibrational energy transfer _e

= ~ ~

[I

_[~ with I

= F

(t)

^e'"~ dt is

given by

m~ w

i~j

the

linearly

forced harmonic oscillator

approximation

_(m~ and _{w are}

respectively

the reduced

mass and the

frequency

of the oscillator and

F(t)

is the force

acting

_on

it).

In this

approximation

the vibrational

probability

distribution p~ is

given by

_a ^Poisson distribution _: p~ =

(e~/vl )

e~ ^~ The first term of the

expansion Vo(R,

_y

)

determines the deflection function

r(b, &, 4~)

which is calculated

by assuming straight-line trajectories R(t) (the

considered

scattering angles

dare indeed

small).

In the second _term

(r r~) Vi (R,

_y

), Vi

=

3V/3r

=

F

(t )

allows _one to calculate the energy transfer

e(b, &,

_4~,

E) (r~

is the

equilibrium distance,

b is the

impact

_parameter and

&,

4~ _are the orientation

angles

of the molecule which _are

assumed _to be

kept

fixed in space

during

the

collision).

For convenience _we used for the

Li+N~

and CO

potentials

the

analytic

fits

(with

⁴

terms)

derived

by

Thomas

[18]

from the ab initio

potentials

^{of Staemmler}

[15, 16].

In order to _use the

analytical

formulae derived in

[I]

for _r and _e, V has been fitted

by

_{a sum} of

multipolar

terms,

functions of

R,

_r and _y, and of

exponential

terms, functions of

R~, R~(R,r, y)

(R~, R~

_are the intemudear distances between Li+ and the _{two atoms} of the target

molecule).

The

equilibrium

distance r~ and the vibration

frequency

_{w are}

kept equal

to their values at R

= cc. The

multipolar

moments and their derivatives _are the _{same as} in

[I].

The fit of V obtained with an

exponential

component ^of the form

V~

₌

~j a,(e~~'~~

₊

e~~'~~) _(I

= 1, 2,

3),

with the values of the parameters

given

in the table

I,

accounts for the wells and _most of the

variations of

Vo

^and

Vi

with R and _y.

Examples

of results obtained for

r and _{e are} shown in

figures

5 and 6. These _{curves are}

Table I.

Coefficients of

the

exponential

terms used in the

fit of

the interaction

potential Vo (in

^atomic

units).

Li+ ₊

N~

^Li+ + CO

at 0.2726 0.1044

a~ 7.782 4.663

a~ 31.15 53.48

A~ = o.8 I (I

= 1, 2, 3) in both _cases.

~ c

~'~~

A

B

A C

b(ao)

~ '

,

In

~

(eV dog)) ^~

'

B

2

~ ~

Fig.

5. -Deflection function r(b) (---) and vibrational energy transfer E(r) (-) computed for Li+ ₊ N2 at E

= 2ooeV and for the orientations (&, 4l) (A) ₌ (o,

4l),

(B) (90°, 90° ),

(C)

=

(90°, o). (& is the

polar angle

of the molecular orientation relative _to the direction

x of the incident

particle

^and 4l is the azimuthal

angle

relative _to the (bx)

plane.)

similar to those obtained in

[I]

^{for He+} +

N~,

CO collisions. Rainbow and

glory

effects may be

recognized,

Here too the rainbow

positions

24

~ r~ ~ r~~~~ m 38 eV

deg (in

_case of

N2

for

instance)

_agree with the

empirical

relation r~ =

97.4 V~~~

(eV deg, eV)

recalled in

[I],

with 0.2 _~

V~i~

_~ 0.56 eV

[15].

After

averaging

_over all orientations

(&,

4~

)

the functions

r(b, ff,

4~

)

and

e(b, &,

4~

)

allow the determination of the _cross sections «~ or p~ and of the

population

ratio

PjPo

=

p~/po.

Examples

of theoretical reduced _cross sections p~ are

compared

^{with the}

corresponding

experimental

_cross sections in

figures

?-lo

(see

also

[30]).

An averall

agreement

^{between the}

D

-lnE

~ D

4

B A D

b(aa) ',

2 4 _,

#

'

In

(eV dog)j ^A

4

2

B A

Fig.

6.-SanJe _as

figure

5 for Li+ ₊ CO at E=2ooeV, with the additional orientation D

=

(90°,

180°).

log[p(a/)j

I I

I

)

v

=

o ^~

(kev deg)

o

o.6 o.8

v=i

-I

Fig. ^7. Reduced cross-sections pv(r ) (v

=

o, I) for Li+ ₊ N2 at E

= loo eV

experiment

(fit) (---),

theory

(-). Vertical bars are

representative

of the scatter of the

experimental

data

points.

The horizontal bar represents ^the angular resolution. The

experimental

_curves have been

positioned

in the y- axis direction _so that po = p~j = p~ > p

jjJ

at small angles (see text and

Fig.

4).

~

~(kevdeg)

O

v=o

v =i -1

Fig.

8. SanJe _as

figure

7 at E

= 500 eV (note the

change

in the _r scale at this

energy).

log[p(a()j

~ ~

~(kev deg)

o.6 o.8

V=I

-1

Fig. ^{9. Sante} as

figure

7 for Li+ ₊ CO at E

= loo eV.

calculated and measured po and pi curves is found in fact at the three

energies

and in both

cases

N2

and CO. The

agreement

is

satisfactory

not

only

for the ratios _p

j/po

of the _curves

[31]

but also for their

shapes.

The variations _seen in section 2 of vibrational excitation with

E,

_r and the

target

may be

recognized.

The stronger ^{excitation for CO rather than for}

N2

is in fact

'og[p(a/)]

i

V

=

0

~

(kev deg)

0A o.6 0.8

V=I

-I

v

= 2

Fig.

lo. Same _as

figure

9 at E

= 200 eV, with the additional _curve

computed

for _v

=

2.

visible in the small _r

region

around the rainbow. One finds here r~ > 28 eV

deg

for

N2

^and

CO,

in

agreement

^with determinations

given by

other authors

(see

_e.g.

[3, 14]).

It is obvious

that the stronger ^{excitation in the} case of CO for small

angles

is

essentially

due to the derivative of the

dipole

moment

(m'

=

d~/dr).

^Note that the

large

difference between the

integral

_cross

sections for vibrational excitation of

N2

and CO obtained

by Kobayashi

et al.

[24, 25]

results

essentially

^{from the} differences found here _at small

scattering angles.

The calculations show that _a strong vibrational excitation, such _{as pi p}

o, does _occur in fact _at

larger angles, beyond

the

experimental angular

limits. One finds for instance _at E

= 200eV,

O(pj

=

po)w

II ° for

N~

and

m 15° for CO.

Finally,

for

comparison

with the results of Kita _et al.

[7],

the theoretical classical cross-section p~j, calculated here _at 200 eV

(Fig. lo),

_agrees well with their cross-section pK

(Fig. 4)

_{: one} obtains

pK/p~j

=

I _to 1.4 at small

angles

for

N2

^and CO.

If _we compare now the

presently

observed vibrational excitation to the _cases He+ ₊

N~,

^{CO and H+} +

H~

studied

previously [1, 2]

_we ^{find that} the excitation of

N~

and CO

by

Li+ in about the _same range of

energies

and

scattering angles

is often weaker than in the other

cases,

especially

the H+

H~

case. The main difference is here the absence of

charge exchange

or

electronically

inelastic processes that

participate

in the

production

of _an anomalous vibrational excitation in the

previous

systems. ^Thus we

observe,

for the Li+

N~,

^CO systems,

examples

of pure vibrational excitation,

resulting only jfom ground

_state interactions.

Apart

from the well known

r-dependent multipolar

interactions

prevailing

at

large

distances and

contributing

to the vibrational excitation observed at small

r

values,

the

present

work puts ⁱⁿ evidence the influence of the bond

length dependence of

the

repulsive

_part

(V~) of

the

potential.

The latter

dependence

is

responsible

^{for the} strong ^{variation of the} vibrational excitation _at

large

r

angles (I.e.

small

impact parameters).

4. Conclusion.

Our measurements of vibrational excitation in Li+ ₊

N~

and CO collisions in the energy range loo _« E _« 500 eV show that it is

relatively

weak for

scattering angles

1f _{~ a} few

degrees.

This excitation

strongly

increases with 1f and

generally

decreases with E _at fixed _r. It is stronger ^for CO than for

N~

ⁱⁿ most

part

^{of the}

angular

_range

investigated

but

especially

at small

angles.

We have _not detected other inelastic processes ^such as

charge exchange

_or electronic

excitation. The latter property

explains why

we found _a reasonable agreement ^{between the} measurements and the results of the theoretical model

developed

in

[I]

and

applied

to the present

study.

The Li+

N~

^{and CO} systems are thus

good examples

where the

target

^{molecule is}

not very much

perturbed by

the

projectile approach

and where _{one can} observe pure vibrational excitation _even at collision

energies

_as

high

as 500 eV and at

relatively large

_r

scattering angles.

Acknowledgments.

We wish to thank Dr V. Sidis for his critical

reading

of the

manuscript.

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