- Email: [email protected]
Differential and absolute-total cross section measurements on elastic Ne* (3P0,2)-He collisions at 64 meV
Chemical Physics I21 (1988) North Holland, Amsterdam
155-160
DIFFERENTIAL AND ABSOLUTE-TOTAL ON ELASTIC Ne* ( 3P,,2) -He COLLISIONS P. FERON, Ph. GIRARD
CROSS SECTION MEASUREMENTS AT 64 meV
‘, J. ROBERT, J. REINHARDT
and J. BAUDON
Laboratoire de Physique des Lasers, Universitt! ParwNord, Avenue J.B. CIPment, 93430 Villetaneuse, France Received
29 June 1987; in final form 2 1 December
1987
Two crossed beam experiments on Ne*( 2ps3s, ‘P,,,)-He collisions are described. In the first one a cw tunable dye laser is used to perform a state and velocity selection of the metastable atoms. The elastic differential cross section in the c.m. frame is given for a collision energy of 64 meV. In the second experiment, the elastic total cross section is measured in absolute value, using a torsion pendulum for the determination of the target molecule density. Some discrepancy is found with the differential cross section calculated with existing potentials,
if two monokinetic crossed beams are used and only elastic collision occurs it is necessary to analyse the final velocity to obtain physically significant c.m. differential cross section. The present paper is devoted to the study of thermal energy collision (64 meV) between a metastable neon atom Ne*( 2p53s, 3P,,z) and a ground state helium atom. This system is interesting for several reasons: (i) excitation transfers are impossible; the only accessible inelastic process would be the fine structure transition 3Po+3P2, for which the cross section has been found to be beyond our detection efficiency, therefore the collision process is purely elastic; (ii) because of the heteronuclear character, a relatively small number of potential curves is involved (one Q state dissociating into Ne( 3Po) +He, and three into Ne( 3P2) + He); (iii) the determination of the Ne*-He potentials is useful for further investigation of the excitation transfer mechanisms occurring in He*-Ne collisions: (iv) it has been shown, in a recent experiment [ 21, that if Ne* atoms are prepared in a coheris the coherence ent state: a0 ( 3Po) + a, 13P,), preserved to a high degree by thermal collisions with He. Differential Ne*-He cross sections in the laboratory frame have already been measured in a crossed monokinetic beams experiment [ 11, without selection of the final velocity. Potential calculations have
1. Introduction From an experimental point of view, the system formed by a metastable rare gas atom and a ground state one is easily produced in a discharge cell or in crossed beams; metastable atoms are readily detectable; in addition, they can be excited to upper radiative levels by means of a tunable cw dye laser operating in the visible range, which allows preparation and analysis of specific atomic states. From the theoretical point of view, these systems are relatively simple examples of excited diatomics, for which potential calculations and collision treatment are practicable. Most of the crossed beam studies have been devoted to homonuclear systems, or to heteronuclear systems in which the metastable atom is the lightest one. If the metastable projectile is the heaviest atom, experimental difficulties appear, due to the collision kinematics: in the laboratory frame, the heavy particle elastic or inelastic scattering is limited to a given angle range. At the edges of this domain, the solid angle ratio dSZ,.,,/dQ,,,, becomes infinite, giving rise to a rainbow-type artefact [ 11. Moreover the observed scattered intensity in the lab frame arises from two c.m. contributions, corresponding to two different values of the c.m. scattering angle, and two values of the lab final metastable velocity. Therefore, even I Present address: CEN, Valrho, France.
0301-0104/88/$ (North-Holland
03.50 0 Elsevier Science Publishers Physics Publishing Division)
B.V.
P. F&-on et al. / Cross sections of elastic Ne*(‘PO,J-He
156
been carried out by Siska [ 31 and by Hennecart Masnou [ 41.
and
2. Experiment 2.1. Differential
collisions
to the statistical weights 1: 5), has been selected by means of a double chopping technique, using a pulsed electron bombardment and a slotted disk operating at a width and a frequency comparable to the pulsed electron gun. The resulting 1/r distribution (see fig. 2a) has a spread 6 v,/ I/, of about 10% ( fwhm).
cross section measurements
A schematic view of the crossed beam apparatus is shown in fig. 1. The experimental setup has been described in details elsewhere [ 51 and only its main features are recalled here. The Ne* atom beam is produced by a 55 eV electron bombardment of a thermal Ne beam emitted by a capillary array. For time of flight (TOF) experiments, the 55 V bias is pulsed with a pulse width variable from 10 to 30 us and a repetition rate of 600-900 Hz. The electron beam crosses the atomic beam at right angle. Electrostatic deflectors remove ions from the beam. The excited beam is then collimated to lo (fwhm). The velocity distribution of the resulting Ne* beam is a modified Maxwellian distribution:
hv
:: .: *. :: :: :: : .:
b
’ 0.4
t
a where U= 500 m/s. In a first experiment, the initial velocity VI of Ne*, for both 3P0 and ‘P2 levels (produced proportionally
;I :: ij . .
:: ::: :: i:
Ne h”
; i :
: :
: :
: :
:
! :
:
:
!
1: . : : : : ! ,:
He-k= \ 8
>a
Fig. 1. Experimental setup. G: electron gun; SD: slotted disk; L: laser beam; synchronizing pulses delayed by TG, trigger the electron gun voltage Va; DE is the detector.
;
:
, i,.
0
Fig. 2. (a) Time of flight distribution at &=O” using a mechanical double chopping technique; curve a: pulsed electron gun, without disk; curve b: continuous gun with disk, curve c: double chopping. (b) TOF using double chopping by laser at eL.=O”; curve a: pulsed gun without laser; curve b: pulsed gun and continuous laser (A = 6 14.3 nm) ; curve c: pulsed gun and pulsed “off” laser.
P. F&-on et al. / Cross sections of elastic Ne*(‘P,,,)-He
In a second experiment, a velocity and metastable level selection has been performed by using a periodically interrupted laser beam, acting as a slotted disk for a specific level. For instance with a laser tuned to the l~,(~P~)-2p, transition (A=614.3 nm), the 3P, level of “Ne is specifically depopulated. Good optical pumping conditions are required: (i) a suficiently high power ( 220 mW), to get a stationary pumping regime (for this we used a multipath device); (ii) owing to the long acquisition times (hours) required in differential measurements, the laser frequency needs to be carefully stabilized. This is performed by locking the laser to the (Doppler free) saturated absorption line, observed in an auxiliary low-pressure Ne discharge [ 6,7]. In the resulting TOF spectrum shown in fig. 2b, a pure 20Ne( 3P2) peak is seen on the background spectrum due to “Ne( 3Po,2) and 20Ne(3Po). The velocity spread is again about 10% ( fwhm). The supersonic helium beam is generated by a high-enthalpy Campargue-type generator [ 81 working at room temperature: the velocity distribution pz( V2) is centered at V2= 1716 m/s with a width 6 V2/V25 1%. The angular aperture is 0.8% (fwhm). The two beams cross at 90”. Scattered metastable atoms are detected by a rotatable channel-plate electron multiplier. The finite dimensions of the collision volume combined with the collimation apertures give an overall angular spread of 1.5 ’ ( fwhm). TOF spectra at fixed lab angles are obtained by means of a time-to-amplitude converter, of which the output pulses are stored in a pulse-height analyzer. Another background spectrum stored with the beam flag closed, is used for background gas correction. Owing to this chopping technique, the two final elastic velocities can be separated (see fig. 3). This allows the determination of the c.m. differential cross section (in relative units, see fig. 4b). In the present case, the relative velocity is close to that of He ( I’,= 1922 m/s), the corresponding collision energy is 64 meV.
b
-
collisions
157
d5
t v-w
Fig. 3. TOF at 0,,=7” after collision on He; curve a: without laser; curve b: with contiuous laser; (dotted line) with laser chopping.
outcoming
flux of Ne* atoms as
where f, ,z( r, ,2) are the radial profiles of Ne* and He beams; nJ2(r2) is the total He density. With cylindrical coordinates defined with respect to axis z, of the Ne* beam (see fig. 5a) one has r2= (z: +r: Xsin28) “’ . In the case where both profiles are Gaussian, an analytic expression of I can be derived, by expanding the exponential factor in a serie of the variable 1 -IL= X= (27t)l12a2 I2 VI V,
’
where a,,, are the standard deviations of distributionsf,,* and Z2= n2V22,2n:a: is the total He-beam intensity. When a, =a, the resulting attenuation coefficient a = (IO- Z)lZo can be expressed as follows:
2.2. Absolute total cross section measurement o!= 1
(-
l)k+‘(/?+
l)“Z[(k+
l)!]-‘Xk
.
k=l
The absolute value of the total cross section has been measured by using a crossed beam attenuation method. Considering mean velocities Vi, V,, V, and an effective total cross section C, averaged over the velocity spreads of the two beams, one can write the
For low attenuations (X<< 1) only single collisions contribute to the attenuation and (Yis linear in Xand for X-+co, lim (Y= 1. From the experimental point of view, values of (Y are readily obtained, for various
158
P. F&on et al. / Cross sections ofelastic Ne*(‘P,,,)-He
collisions
I
10-4Ul
&I5 -d
15
b Fig. 5. (a) Geometry of crossed beams. (b) Experimental TW: torsion wire (0~0.05 mm; L= 110 mm).
Fig. 4. (a) Potential curves used in the calculation of differential cross sections. Dotted line: Siska’s potentials [ 31; full line: experimental single potential of ref. [ 1 ] ; broken line: modified version of this potential. (b) Differential cross sections. at 64 meV in the c.m. frame. Theoretical cross sections are calculated for the mixture I : 5 of Ne*(‘Pa) and Ne*(jP*), by using Siska’s potentials [ 31 (dotted curve), the experimental single potential [ 1 ] (full line), and its modified version (broken line). Experimental points are obtained: (0) by mechanical double chopping; (0) by laser double chopping.
setup.
flight times, i.e. for various relative velocities, provided that the contribution of small-angle scattering is negligible. An estimate of this contribution can be obtained from the calculated differential cross sections, which are almost identical at small angles (8,.,. 5 5’ ) for all potentials considered further, owing to the similarity of their behaviours at large distances. With an improved beam collimation (68,_xO.5” ) and an averaged differential cross section of 2.8 X lo4 ailsr one gets a small-angle scattering contribution of 6.3%. For Vr = 866 m/s, V, = 17 16 m/s ( V,= 1922 m/s, EC=64 meV), the measured attenuation is c~=O.335 kO.017, which leads to X=0.249&0.012. The beam profiles, analyzed by means of movable slits, have been observed to be approximately Gaussian, with standard deviations a, = a2 = 0.94 + 0.055 mm. In order to achieve the determination of Z in absolute value, one has only to measure 1,, the total He-beam intensity. This measurement is performed by means of a torsion pendulum. A horizontal rod, holding a light vertical plate (1 x 1 cm2) at one end, is sustended by a 50 pm diameter tungsten wire (fig.
P. F&on et al. / Cross sections of elastic Ne+(‘P&-He
5b). The torque resulting from the supersonic Hebeam impact on the plate causes a typical rotation of 10’ to 15 O, compensated by a rotation 0 of the upper end of the wire. In the present case the atomic beam is entirely intercepted by the plate, and its profile is symmetric with respect to a vertical plane. Under such conditions the resulting torque can be written as T=m,d(
v*+ (v;))z,
where m, is the He mass, d=25.4 mm is the distance between the wire and the beam center; ( V;) is the mean recoil velocity of the He atoms (for a Maxwellian distribution at room temperature, ( I’$ ) = 3 15.4 m/s). The equilibrium of the rod writes I’ = ‘%?B where %‘=7.081 x lo-‘N m. In the present case 8= 10.3”, which leads to Z2=(3.71+0.18)x10” atom s-‘. Knowing Iz and X= 0.249, one deduces z= 437 + 100
0(3P,)
collisions
159
%z(T”< .
If no selection of the metastable level is performed, the observed differential cross section is
Up to now, three sets of potentials for the Ne*( 3P0,2)-He( ‘So) system are available: (i) the model potentials of Siska [ 31 already mentioned, (ii) a model-potential calculation of the outer 3~0 orbital energy, by Hennecart and Masnou-Seeuws [ 41, (iii) a single “experimental” potential curve, determined by Fukuyama and Siska [ 1 ] to reproduce their measured lab-differential cross sections (see fig. 4a). Potentials (i) have been fitted, in the distance range of interest (R 2 4.5 ao), by the following analytic forms:
Vn,,=ARPexp(-aR)-&,
a;.
V,=ARP exp( -aR)+C,
exp( -a,R)
3. Discussion -C, As already has been seen in section 1, the Ne*-He collision at 64 meV can be considered as purely elastic. Three molecular states Q= 0, 1, 2 dissociate into Ne* ( 3P,) + He, whereas a unique one (Q= 0) dissociates into Ne*( 3P0) +He. In the former case, as no analysis is made of Zeeman sublevels, any coupling between 52 states can be ignored, which leads to the averaged differential cross section rr(3P*)=f(2an,,
+2a,,z+a&o).
+30x)
A.
The coefficients are given in table 1. The Vz potential has a hump of 117 meV at 4.54 a,. It results from the addition of the repulsive 3~0 energy to the well of the ‘I: ionic core potential. The 3~0 energy calculated in (ii) is more repulsive than in (i), leading to a uniformly repulsive Vz curve. All these potentials are very close to each other for R k 6.5 ao, which explains why the 3Pz-3Po coherence is almost unaffected by Ne*-He collisions [ 21. Calculated total cross sections, for the mixture (1: 5) ‘PO, 3Pz, at E,= 64 meV are 429.7 a$ for potentials (i), 45 3.3 a; for potentials (iii). They are in good agreement with the experimental one (437 k 100 a; at 64 meV). This was expected in as much as the longrange potentials are well predicted. On the other hand, at the present collision energy, the differential cross sections, especially at large angle, involve shorter dis-
In fact, according to the model-potential calculation of Siska [ 31, both 52~0 and L2=2 potentials are very close to each other ( Vn,,,x Vn,zz V,) whereas I’, = Vn , , the largest II potential. Therefore the above expression simplifies to a(3P2) z+ (2an,
exp(-a,R)-
)
whereas
Table 1 State
n< n> z
A
P
a
3.46930( -4) 5.766706( -4) 9.541236( -6)
9.67306 9.13946 13.2415
2.59554 2.51995 3.06517
c,
4.0237.66
aI
5.43
1491
3.956
24.45 24.45 24.45
160
P. Fh-on et al. / Cross sections ofelastic Ne*(‘P,,J-He
Table 2
A=3.9572 B= 1058.46 6= 1275.25 cx= 1.1695 C,=24.70 6’=4554
a,=0.217643 a,= -6.88663( -2) a>=8.961216( -3) a,= -5.61585( -4) a,=1.346379(-5) cr=o.4500 p=2 RO= 12.5 C,=24.70 a=4554
tances, and are a more severe test of the potential in the short range (approximately 5-8 a,,). Calculated differential cross sections for potentials (i) and (iii) are shown in fig. 4b together with the experimental one. If one normalizes the experimental data at f3,= 40” (i.e. at a rather small angle, with not too large an uncertainty) one observes that the calculated cross section (i) is too slowly decreasing at large angle. The use of potential (iii) reduces this discrepancy but a similar behaviour is seen. In order to get some idea about the short-range potential defect responsible for this situation we have tried to modify, as slightly as possible, the repulsive branch of the single “experimental” potential (iii). This latter potential, called VE, has the following form [ 1] : VE =
v, -
c, R6 +d’
Acknowledgement The authors are grateful to J.P. Raulin for his participation to the experimental work, and to Ch. Lerminiaux for his assistance in the laser experiments.
References
[ 21
with .=,(l+
[ 31
&)exp(-aR).
The proposed wd “=
The coefficients in VE and V; are given in table 2. The VL potential is repulsive at moderately short distance (R 5 10 a,), it exhibits a well around 10.8 a, and it is attractive in R -6 for large R. For small R, V; is lower than V,, leading to a distance of closest approach of about 5.08 a0 for the backward scattering instead of 5.59 ao. The differential cross section a; calculated with V; is larger than rrE at small angles (o&45” ) and smaller than (TEby a factor of about 1.35 at 8, = 180”. The overall agreement with the experiment has been improved (see fig. 4b). The total cross section calculated at 64 meV with V; is 503.5 ai, i.e. rather close to that calculated with V,. Actually V; represents an effective potential equivalent to the several (coupled) potentials 8 which describe the real collision, at least in an experiment in which neither prepration nor analysis of Zeeman sublevels are made.
[ 1] T. Fukuyama
’
”
modified
[4]
potential
-P(R-&)I
1 +exp[ -P(R-R,)]
_-
[ 51
I’; is of the form:
[6[
c6
R6+6
’ [ 71
with V2=(a,,+a,R+a2R2+a3R3+a,R4)
exp(-aR)
.
collisions
[8]
and P.E. Siska, Chem Phys Letters 39 (1976) 418. S. Saoudi, C. Lerminiaux and M. Dumont, Phys Rev. Letters 56 (1986) 2164. P.E. Siska, J. Chem. Phys. 73 (1980) 2372. D. Hennecart and F. Masnou-Seeuws, J. Phys B 18 (1985) 657. V. Bocvarski, J. Robert, 1. Colomb, J. Reinhardt and J. Baudon, J. Phys. (Paris) 46 (1985) L13. V. Bocvarski, J. Robert, I. Colomb, M. Dumont, J. Reinhardt and J. Baudon, 2nd ECAMP, Amsterdam 1985, Book of Abstracts, p. 275. N. Courtier and M. Dumont, Rev. Phys. Appl. I6 (198 I ) 601. R. Campargue, J. Chem. Phys. 73 (1970) 1773.
155-160
DIFFERENTIAL AND ABSOLUTE-TOTAL ON ELASTIC Ne* ( 3P,,2) -He COLLISIONS P. FERON, Ph. GIRARD
CROSS SECTION MEASUREMENTS AT 64 meV
‘, J. ROBERT, J. REINHARDT
and J. BAUDON
Laboratoire de Physique des Lasers, Universitt! ParwNord, Avenue J.B. CIPment, 93430 Villetaneuse, France Received
29 June 1987; in final form 2 1 December
1987
Two crossed beam experiments on Ne*( 2ps3s, ‘P,,,)-He collisions are described. In the first one a cw tunable dye laser is used to perform a state and velocity selection of the metastable atoms. The elastic differential cross section in the c.m. frame is given for a collision energy of 64 meV. In the second experiment, the elastic total cross section is measured in absolute value, using a torsion pendulum for the determination of the target molecule density. Some discrepancy is found with the differential cross section calculated with existing potentials,
if two monokinetic crossed beams are used and only elastic collision occurs it is necessary to analyse the final velocity to obtain physically significant c.m. differential cross section. The present paper is devoted to the study of thermal energy collision (64 meV) between a metastable neon atom Ne*( 2p53s, 3P,,z) and a ground state helium atom. This system is interesting for several reasons: (i) excitation transfers are impossible; the only accessible inelastic process would be the fine structure transition 3Po+3P2, for which the cross section has been found to be beyond our detection efficiency, therefore the collision process is purely elastic; (ii) because of the heteronuclear character, a relatively small number of potential curves is involved (one Q state dissociating into Ne( 3Po) +He, and three into Ne( 3P2) + He); (iii) the determination of the Ne*-He potentials is useful for further investigation of the excitation transfer mechanisms occurring in He*-Ne collisions: (iv) it has been shown, in a recent experiment [ 21, that if Ne* atoms are prepared in a coheris the coherence ent state: a0 ( 3Po) + a, 13P,), preserved to a high degree by thermal collisions with He. Differential Ne*-He cross sections in the laboratory frame have already been measured in a crossed monokinetic beams experiment [ 11, without selection of the final velocity. Potential calculations have
1. Introduction From an experimental point of view, the system formed by a metastable rare gas atom and a ground state one is easily produced in a discharge cell or in crossed beams; metastable atoms are readily detectable; in addition, they can be excited to upper radiative levels by means of a tunable cw dye laser operating in the visible range, which allows preparation and analysis of specific atomic states. From the theoretical point of view, these systems are relatively simple examples of excited diatomics, for which potential calculations and collision treatment are practicable. Most of the crossed beam studies have been devoted to homonuclear systems, or to heteronuclear systems in which the metastable atom is the lightest one. If the metastable projectile is the heaviest atom, experimental difficulties appear, due to the collision kinematics: in the laboratory frame, the heavy particle elastic or inelastic scattering is limited to a given angle range. At the edges of this domain, the solid angle ratio dSZ,.,,/dQ,,,, becomes infinite, giving rise to a rainbow-type artefact [ 11. Moreover the observed scattered intensity in the lab frame arises from two c.m. contributions, corresponding to two different values of the c.m. scattering angle, and two values of the lab final metastable velocity. Therefore, even I Present address: CEN, Valrho, France.
0301-0104/88/$ (North-Holland
03.50 0 Elsevier Science Publishers Physics Publishing Division)
B.V.
P. F&-on et al. / Cross sections of elastic Ne*(‘PO,J-He
156
been carried out by Siska [ 31 and by Hennecart Masnou [ 41.
and
2. Experiment 2.1. Differential
collisions
to the statistical weights 1: 5), has been selected by means of a double chopping technique, using a pulsed electron bombardment and a slotted disk operating at a width and a frequency comparable to the pulsed electron gun. The resulting 1/r distribution (see fig. 2a) has a spread 6 v,/ I/, of about 10% ( fwhm).
cross section measurements
A schematic view of the crossed beam apparatus is shown in fig. 1. The experimental setup has been described in details elsewhere [ 51 and only its main features are recalled here. The Ne* atom beam is produced by a 55 eV electron bombardment of a thermal Ne beam emitted by a capillary array. For time of flight (TOF) experiments, the 55 V bias is pulsed with a pulse width variable from 10 to 30 us and a repetition rate of 600-900 Hz. The electron beam crosses the atomic beam at right angle. Electrostatic deflectors remove ions from the beam. The excited beam is then collimated to lo (fwhm). The velocity distribution of the resulting Ne* beam is a modified Maxwellian distribution:
hv
:: .: *. :: :: :: : .:
b
’ 0.4
t
a where U= 500 m/s. In a first experiment, the initial velocity VI of Ne*, for both 3P0 and ‘P2 levels (produced proportionally
;I :: ij . .
:: ::: :: i:
Ne h”
; i :
: :
: :
: :
:
! :
:
:
!
1: . : : : : ! ,:
He-k= \ 8
>a
Fig. 1. Experimental setup. G: electron gun; SD: slotted disk; L: laser beam; synchronizing pulses delayed by TG, trigger the electron gun voltage Va; DE is the detector.
;
:
, i,.
0
Fig. 2. (a) Time of flight distribution at &=O” using a mechanical double chopping technique; curve a: pulsed electron gun, without disk; curve b: continuous gun with disk, curve c: double chopping. (b) TOF using double chopping by laser at eL.=O”; curve a: pulsed gun without laser; curve b: pulsed gun and continuous laser (A = 6 14.3 nm) ; curve c: pulsed gun and pulsed “off” laser.
P. F&-on et al. / Cross sections of elastic Ne*(‘P,,,)-He
In a second experiment, a velocity and metastable level selection has been performed by using a periodically interrupted laser beam, acting as a slotted disk for a specific level. For instance with a laser tuned to the l~,(~P~)-2p, transition (A=614.3 nm), the 3P, level of “Ne is specifically depopulated. Good optical pumping conditions are required: (i) a suficiently high power ( 220 mW), to get a stationary pumping regime (for this we used a multipath device); (ii) owing to the long acquisition times (hours) required in differential measurements, the laser frequency needs to be carefully stabilized. This is performed by locking the laser to the (Doppler free) saturated absorption line, observed in an auxiliary low-pressure Ne discharge [ 6,7]. In the resulting TOF spectrum shown in fig. 2b, a pure 20Ne( 3P2) peak is seen on the background spectrum due to “Ne( 3Po,2) and 20Ne(3Po). The velocity spread is again about 10% ( fwhm). The supersonic helium beam is generated by a high-enthalpy Campargue-type generator [ 81 working at room temperature: the velocity distribution pz( V2) is centered at V2= 1716 m/s with a width 6 V2/V25 1%. The angular aperture is 0.8% (fwhm). The two beams cross at 90”. Scattered metastable atoms are detected by a rotatable channel-plate electron multiplier. The finite dimensions of the collision volume combined with the collimation apertures give an overall angular spread of 1.5 ’ ( fwhm). TOF spectra at fixed lab angles are obtained by means of a time-to-amplitude converter, of which the output pulses are stored in a pulse-height analyzer. Another background spectrum stored with the beam flag closed, is used for background gas correction. Owing to this chopping technique, the two final elastic velocities can be separated (see fig. 3). This allows the determination of the c.m. differential cross section (in relative units, see fig. 4b). In the present case, the relative velocity is close to that of He ( I’,= 1922 m/s), the corresponding collision energy is 64 meV.
b
-
collisions
157
d5
t v-w
Fig. 3. TOF at 0,,=7” after collision on He; curve a: without laser; curve b: with contiuous laser; (dotted line) with laser chopping.
outcoming
flux of Ne* atoms as
where f, ,z( r, ,2) are the radial profiles of Ne* and He beams; nJ2(r2) is the total He density. With cylindrical coordinates defined with respect to axis z, of the Ne* beam (see fig. 5a) one has r2= (z: +r: Xsin28) “’ . In the case where both profiles are Gaussian, an analytic expression of I can be derived, by expanding the exponential factor in a serie of the variable 1 -IL= X= (27t)l12a2 I2 VI V,
’
where a,,, are the standard deviations of distributionsf,,* and Z2= n2V22,2n:a: is the total He-beam intensity. When a, =a, the resulting attenuation coefficient a = (IO- Z)lZo can be expressed as follows:
2.2. Absolute total cross section measurement o!= 1
(-
l)k+‘(/?+
l)“Z[(k+
l)!]-‘Xk
.
k=l
The absolute value of the total cross section has been measured by using a crossed beam attenuation method. Considering mean velocities Vi, V,, V, and an effective total cross section C, averaged over the velocity spreads of the two beams, one can write the
For low attenuations (X<< 1) only single collisions contribute to the attenuation and (Yis linear in Xand for X-+co, lim (Y= 1. From the experimental point of view, values of (Y are readily obtained, for various
158
P. F&on et al. / Cross sections ofelastic Ne*(‘P,,,)-He
collisions
I
10-4Ul
&I5 -d
15
b Fig. 5. (a) Geometry of crossed beams. (b) Experimental TW: torsion wire (0~0.05 mm; L= 110 mm).
Fig. 4. (a) Potential curves used in the calculation of differential cross sections. Dotted line: Siska’s potentials [ 31; full line: experimental single potential of ref. [ 1 ] ; broken line: modified version of this potential. (b) Differential cross sections. at 64 meV in the c.m. frame. Theoretical cross sections are calculated for the mixture I : 5 of Ne*(‘Pa) and Ne*(jP*), by using Siska’s potentials [ 31 (dotted curve), the experimental single potential [ 1 ] (full line), and its modified version (broken line). Experimental points are obtained: (0) by mechanical double chopping; (0) by laser double chopping.
setup.
flight times, i.e. for various relative velocities, provided that the contribution of small-angle scattering is negligible. An estimate of this contribution can be obtained from the calculated differential cross sections, which are almost identical at small angles (8,.,. 5 5’ ) for all potentials considered further, owing to the similarity of their behaviours at large distances. With an improved beam collimation (68,_xO.5” ) and an averaged differential cross section of 2.8 X lo4 ailsr one gets a small-angle scattering contribution of 6.3%. For Vr = 866 m/s, V, = 17 16 m/s ( V,= 1922 m/s, EC=64 meV), the measured attenuation is c~=O.335 kO.017, which leads to X=0.249&0.012. The beam profiles, analyzed by means of movable slits, have been observed to be approximately Gaussian, with standard deviations a, = a2 = 0.94 + 0.055 mm. In order to achieve the determination of Z in absolute value, one has only to measure 1,, the total He-beam intensity. This measurement is performed by means of a torsion pendulum. A horizontal rod, holding a light vertical plate (1 x 1 cm2) at one end, is sustended by a 50 pm diameter tungsten wire (fig.
P. F&on et al. / Cross sections of elastic Ne+(‘P&-He
5b). The torque resulting from the supersonic Hebeam impact on the plate causes a typical rotation of 10’ to 15 O, compensated by a rotation 0 of the upper end of the wire. In the present case the atomic beam is entirely intercepted by the plate, and its profile is symmetric with respect to a vertical plane. Under such conditions the resulting torque can be written as T=m,d(
v*+ (v;))z,
where m, is the He mass, d=25.4 mm is the distance between the wire and the beam center; ( V;) is the mean recoil velocity of the He atoms (for a Maxwellian distribution at room temperature, ( I’$ ) = 3 15.4 m/s). The equilibrium of the rod writes I’ = ‘%?B where %‘=7.081 x lo-‘N m. In the present case 8= 10.3”, which leads to Z2=(3.71+0.18)x10” atom s-‘. Knowing Iz and X= 0.249, one deduces z= 437 + 100
0(3P,)
collisions
159
%z(T”< .
If no selection of the metastable level is performed, the observed differential cross section is
Up to now, three sets of potentials for the Ne*( 3P0,2)-He( ‘So) system are available: (i) the model potentials of Siska [ 31 already mentioned, (ii) a model-potential calculation of the outer 3~0 orbital energy, by Hennecart and Masnou-Seeuws [ 41, (iii) a single “experimental” potential curve, determined by Fukuyama and Siska [ 1 ] to reproduce their measured lab-differential cross sections (see fig. 4a). Potentials (i) have been fitted, in the distance range of interest (R 2 4.5 ao), by the following analytic forms:
Vn,,=ARPexp(-aR)-&,
a;.
V,=ARP exp( -aR)+C,
exp( -a,R)
3. Discussion -C, As already has been seen in section 1, the Ne*-He collision at 64 meV can be considered as purely elastic. Three molecular states Q= 0, 1, 2 dissociate into Ne* ( 3P,) + He, whereas a unique one (Q= 0) dissociates into Ne*( 3P0) +He. In the former case, as no analysis is made of Zeeman sublevels, any coupling between 52 states can be ignored, which leads to the averaged differential cross section rr(3P*)=f(2an,,
+2a,,z+a&o).
+30x)
A.
The coefficients are given in table 1. The Vz potential has a hump of 117 meV at 4.54 a,. It results from the addition of the repulsive 3~0 energy to the well of the ‘I: ionic core potential. The 3~0 energy calculated in (ii) is more repulsive than in (i), leading to a uniformly repulsive Vz curve. All these potentials are very close to each other for R k 6.5 ao, which explains why the 3Pz-3Po coherence is almost unaffected by Ne*-He collisions [ 21. Calculated total cross sections, for the mixture (1: 5) ‘PO, 3Pz, at E,= 64 meV are 429.7 a$ for potentials (i), 45 3.3 a; for potentials (iii). They are in good agreement with the experimental one (437 k 100 a; at 64 meV). This was expected in as much as the longrange potentials are well predicted. On the other hand, at the present collision energy, the differential cross sections, especially at large angle, involve shorter dis-
In fact, according to the model-potential calculation of Siska [ 31, both 52~0 and L2=2 potentials are very close to each other ( Vn,,,x Vn,zz V,) whereas I’, = Vn , , the largest II potential. Therefore the above expression simplifies to a(3P2) z+ (2an,
exp(-a,R)-
)
whereas
Table 1 State
n< n> z
A
P
a
3.46930( -4) 5.766706( -4) 9.541236( -6)
9.67306 9.13946 13.2415
2.59554 2.51995 3.06517
c,
4.0237.66
aI
5.43
1491
3.956
24.45 24.45 24.45
160
P. Fh-on et al. / Cross sections ofelastic Ne*(‘P,,J-He
Table 2
A=3.9572 B= 1058.46 6= 1275.25 cx= 1.1695 C,=24.70 6’=4554
a,=0.217643 a,= -6.88663( -2) a>=8.961216( -3) a,= -5.61585( -4) a,=1.346379(-5) cr=o.4500 p=2 RO= 12.5 C,=24.70 a=4554
tances, and are a more severe test of the potential in the short range (approximately 5-8 a,,). Calculated differential cross sections for potentials (i) and (iii) are shown in fig. 4b together with the experimental one. If one normalizes the experimental data at f3,= 40” (i.e. at a rather small angle, with not too large an uncertainty) one observes that the calculated cross section (i) is too slowly decreasing at large angle. The use of potential (iii) reduces this discrepancy but a similar behaviour is seen. In order to get some idea about the short-range potential defect responsible for this situation we have tried to modify, as slightly as possible, the repulsive branch of the single “experimental” potential (iii). This latter potential, called VE, has the following form [ 1] : VE =
v, -
c, R6 +d’
Acknowledgement The authors are grateful to J.P. Raulin for his participation to the experimental work, and to Ch. Lerminiaux for his assistance in the laser experiments.
References
[ 21
with .=,(l+
[ 31
&)exp(-aR).
The proposed wd “=
The coefficients in VE and V; are given in table 2. The VL potential is repulsive at moderately short distance (R 5 10 a,), it exhibits a well around 10.8 a, and it is attractive in R -6 for large R. For small R, V; is lower than V,, leading to a distance of closest approach of about 5.08 a0 for the backward scattering instead of 5.59 ao. The differential cross section a; calculated with V; is larger than rrE at small angles (o&45” ) and smaller than (TEby a factor of about 1.35 at 8, = 180”. The overall agreement with the experiment has been improved (see fig. 4b). The total cross section calculated at 64 meV with V; is 503.5 ai, i.e. rather close to that calculated with V,. Actually V; represents an effective potential equivalent to the several (coupled) potentials 8 which describe the real collision, at least in an experiment in which neither prepration nor analysis of Zeeman sublevels are made.
[ 1] T. Fukuyama
’
”
modified
[4]
potential
-P(R-&)I
1 +exp[ -P(R-R,)]
_-
[ 51
I’; is of the form:
[6[
c6
R6+6
’ [ 71
with V2=(a,,+a,R+a2R2+a3R3+a,R4)
exp(-aR)
.
collisions
[8]
and P.E. Siska, Chem Phys Letters 39 (1976) 418. S. Saoudi, C. Lerminiaux and M. Dumont, Phys Rev. Letters 56 (1986) 2164. P.E. Siska, J. Chem. Phys. 73 (1980) 2372. D. Hennecart and F. Masnou-Seeuws, J. Phys B 18 (1985) 657. V. Bocvarski, J. Robert, 1. Colomb, J. Reinhardt and J. Baudon, J. Phys. (Paris) 46 (1985) L13. V. Bocvarski, J. Robert, I. Colomb, M. Dumont, J. Reinhardt and J. Baudon, 2nd ECAMP, Amsterdam 1985, Book of Abstracts, p. 275. N. Courtier and M. Dumont, Rev. Phys. Appl. I6 (198 I ) 601. R. Campargue, J. Chem. Phys. 73 (1970) 1773.