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Collision-induced dissociation of 10 keV H2+ ions
Physica 35 258-272
Gibson, D. K. Los, J. 1967
COLLISION-INDUCED
DISSOCIATION
by D. K. GIBSON FOM-Instituut
voor Atoom-
OF 10 keV HZ+ IONS
and J. LOS
en Molecuulfysica,
Amsterdam*)
synopsis Measurements of the angular and velocity distributions of the protons obtained by passing a beam of 10 keV Ha+ ions through hydrogen or helium gases are described. The angular distribution is in agreement with that previously measured by McClure. The velocity distribution has been accounted for in terms of collision - induced electronic excitations leading to dissociative states of the He+ ion. The agreement between theory and experiment indicates that this theory is essentially correct, the greatest unknown being the dependence of the excitation cross section upon the length and orientation of the Hz+ internuclear axis. This dependence is found to be different for the two target gases (Ha and He).
Introduction. The simple structure of the Hz+ ion and the consequent wealth of accurate theoretical data relating to it have led to this ion being the object of many investigations of collision-induced dissociation. It has been shown by Purser et aliil) that the mutual recoiling of the two nuclei with a repulsive energy of about 5 eV causes very large energy spreads in the laboratory system**). Two studies in particular have led directly to the work described in this paper. Firstly, the Aston band caused by the dissociation of Hz+ in a mass spectrometer has been studied by McGowan and Kerwins), who have investigated the effects of vibrational states on the shape of this band. The second work is McClure’sa) measurement and theoretical description of the angular distribution of the dissociation fragments Hf and H. We have extended the work in these two studies by measuring both the velocity and angular distribution of the protons resulting from Hz+ dissociation. In effect we have measured the shape of the Aston band, but have refined the experiment by measuring the same band many times, each time altering the angle through which the particles must scatter in order to pass through the mass spectrometer. Or, from another *) Formerly:
Laboratorium
voor
Massascheiding.
**) where Eo is the Laboratory
energy
of the Ha + and e is the centre
dissociation.
-
258 -
of mass energy
liberated
during
COLLISION-INDUCED
DISSOCIATION
OF
10keV Hz+ IONS
259
point of view, we have measured the differential cross section but have gained further information by using a momentum analyser in front of our detector. Our results can be explained by an extension of McClure’s theory. He accounted for the observed angular distribution of the protons on the hypothesis that the Hz+ ions are excited from the ground electronic state to the first excited state, 2fio,, which is dissociative. Interaction
McClure assumed the
Energy (eV)
lo-
R, Intornuchar
Separation
(a,)
Fig. 1. Energy level diagram of Hz+.
electronic excitation to follow the Franck-Condon principle and thus the mutual repulsion after excitation to be strongly dependent on the Hz+ internuclear spacing, R, at the moment of excitation. Therefore, in the centre of mass system, the magnitude of the dissociation velocity was held to depend on R, and its direction on the angle, q3,between the internuclear axis and the directionof motion of the Hs+ion. In order to calculate the angular distribution of protons arising from the dissociation of Hz+ ions McClure needed to know the cross section for excitation of the 2fi0, state due to collision with the target atom as a function of both R and 4, and also the probability, D(R), of finding an Hz+ ion with internuclear spacing R. The cross section for excitation, a(R, +), has been calculated by P eek4) at 10 keV for a hydrogen atom target, using the first Born approximation. McGowan and Kerwin have shown that the expression D(R) approaches that given by the Franck-
260
D.
K. GIBSON
AND
J. LOS
Condon overlap integrals between ground state Hz and the nineteen vibrational states of Hz+ if the ionization is caused by electrons with more than 20 eV energy. We have followed McClure in using these data, except that we have used the Franck-Condon factors recently calculated by Dunns) in place of those of McGowan and Kerwin. McClure’s calculation included an integration which gave the angular distribution averaged over all velocities, whereas we have calculated both the angular and velocity distributions of the dissociated particles. Moreover, we have found it necessary to calculate the intensity near zero deflection by a different method. Ex#erimental procedure. The apparatus is shown schematically in figure 2. Ions produced in the unoplasmatron source are accelerated to 10 keV and focussed through the 0.4 mm diameter apertures, which are spaced 30 cm apart. The beam intensity is naturally very small (10-T amp) after this stringent collimation, but, in view of the angular resolution required, such collimation is necessary. The beam traverses the collision chamber and, after passing between a pair of condenser plates which are used for the angular analysis, enters the magnetic analyser through a 5 mm diameter hole. As far as geometrical calculations of the scattering angle are concerned this aperture can be considered as the detector. In the range between f 2” the angular resolution is of the order f 1/IO”; the divergence of the initial beam, the finite length of the target chamber and the finite size of the collection aperture all cantribute in approximately equal parts to the uncertainty in angle. The angular analysis is performed by means of a transverse voltage between the condenser plates. Within our small angular range, and provided that the energy spread of the beam is not very great, this simple method of angular analysis is not very much in error. For, although the spread in energies of protons resulting from collision-induced dissociation at 10 keV is some 500 eV, the variation in angle from the slowest to the fastest particle is only 5%. The deflection voltage was calibrated in terms of angle with the aid of two Faraday cups placed either side of the beam axis. The transverse voltages required to deflect the beam through a known angle into these cups were measured for a series of beam energies. We found that
e=
188p
a
degrees
where I’t and Va are the transverse and acceleration potentials respectively. The constant of proportionality agreed to within 3% with the value calculated from the geometry of the plates and we assumed, therefore, that the relation between 8 and vt was linear over our small angular range.
COLLISION-INDUCED
DISSOCIATION
10keV
OF
Hz+ IONS
261
The momentum analyser consists of an inhomogeneous field magnetic mass spectrometere), so arranged that the object point (the centre of the collision chamber) is focussed onto a slit in front of the electron multiplier. The halfwidth of the primary
beam is about
5 eV, this being a sum of the energy
i 1 ,%I * ::
T
Fig. 2. Apparatus
1
A
Ion source
B
Collimators
C
Collision chamber
D
Deflection plates
(0.4 mm)
E
Undisturbed
beam
F
Scattered beam
G
Collimators
(5 mm)
H
Magnet
I
Detector
spread of the ion beam and the aberrations of the analyser. In view of the broad energy distribution of the protons (500 eV) this primary beam width is satisfactory. The velocity distributions were measured with the help of an XY recorder. The X signal was provided by a differential gaussmeter (RFL Model 1965) which measured the magnetic field between the pole faces of the analyser
262
D. K. GIBSON AND J. LOS
by means of a Hall probe. Thus the X scale was proportional
to the magnetic
field and hence to the velocity of the protons. The Y signal was the amplified output of the electron multiplier detector. Thus the velocity distribution at one fixed scattering angle could be directly recorded by slowly scanning the magnetic field. A trace made without collision gas gave the contribution due to dissociations induced by the background gas. The beam intensities have always been expressed in arbitrary units as the gain of the electron multiplier was not measured. The velocity scale was calibrated by measuring the shift in a peak position corresponding to a known change in the acceleration voltage. We wished to establish the relation between the velocities of the protons and the velocity of the H s+ beam from which they were formed. We were able to do this by using the protons issuing directly from the ion source as a marker peak. In order to give these protons the same velocity as the Proton Intensity tArbitrary
units)
Proton velocity
IlO’cm
s-‘1
Fig. 3. Experimental curve, 10 keV Hz+ on Hz. a) Proton velocity distribution at 8 = 0”. b) Background signal. c) 5keV proton marker peak. Inset shows proportionality between mass and acclerating voltage. d) 5000 eV Hf e) 2500 eV HZ+ f) 1666.7 eV Hsf.
original Hz+ ions, the accelerating potential was reduced to exactly one half of its original value. In this way the primary proton peak was superimposed upon the broad distribution which was yielded by the protons formed by collision-induced dissociation (figure 3). An inset on figure 3 shows successive traces of H+, Ha+ and Ha+, with the acceleration voltage respectively l/2, l/4 and l/6 of its original value. The fact that these three
COLLISION-INDUCED
DISSOCIATION
OF
IOkeV Hz+ IONS
263
peaks occur at the same magnetic field strength shows that the potential of the arc of the ion source differs from the acceleration voltage by a negligible amount. We have also measured the angular distribution of the protons by means of integrating the velocity distributions at several angles. The results of these measurements
are in very good agreement
with those of McClure, as
can be seen from figure 4. Differential
Cross Section
lU’*crr?
Steradim~
20 -
/
lo-
i b-
2
1
i 4
8
-2
,
-
I
I
0
-1
Fig. 4. Differential on Hz target. normalized
cross section
for protons
Solid line shows McClure’s
to McClure’s
2
Angle (Degrees1
produced
by dissociation
of 10 keV
Hz+
results. The crosses denote our measurements
at 8 = 0”. The deviations
as the scatter
I
1 Scattering
of McClure’s
of our points are of the same order measurements.
Disczlssiorz. From figure 3 it is clear that many protons are travelling faster than the Hz+ ions from which they originated. This phenomenon can be explained only by assuming that the Hz+ ions dissociate in such a way that the two nuclei are thrown apart by some considerable repulsive force. Thus the basis of McClure’s explanation of the dissociation is strongly supported. Before describing the calculations we will discuss various basic points.
264
D. K. GIBSON AND J. LOS
(i) We assume that the angular scattering
is entirely
due to the transverse
component of the disssociation velocity. Thus we neglect the angular deviation of the Hz+ C. of M. due to the collision. This assumption is to some extent justified by the work of McClure. However, the intensity he measured at scattering angles above 1” is larger than he calculated; attributed to scattering of the Hz+ ion. Our calculations at small angles will be very little affected
this
could be
by scattering,
which will lead only to reduction in intensity. However, at larger angles the scattering could bring about discrepancies between the theory and experiment. (ii) McClure assumes that the number of excitations to the 2pu, state overshadows the number to all higher states. From figure 3 it appears that this may bot be correct, for there is a slight displacement of the secondary protons towards lower energies. The displacement corresponds to about 7 eV energy loss on the part of the H s+ ion, which can be easily accounted for if about 70% of the Hz+ ions are excited to the 2+nU state, or higher, with a 10 eV inelastic energy loss. Excitation to the 2@cU state mostly leads to dissociation with the subsequent emission of Lyman-a radiation. However, this argument is not conclusive, for Peeka) has shown that simultaneous excitation of the target is rather probable and this would also explain the energy defect. Approaching the problem from another angle, one can 104"cm2 /atom 1.5 i
Fig. 5. Cross sections for Hs+ in He. Total cross section for proton production (Williams and Dunbar). Cross section for Lyman - oc production plus metastable 2s formation. The excited atoms arise from reaction Hz+ + He + Hf + H” + He as, in the case of helium target, the alternative process, charge exchange, is very small (Jaecks and Tynan) .
COLLISION-INDUCED
compare
the total dissociation
cross section for excitation
DISSOCIATION
OF 10 keV Hz+ IONS
265
cross section of Hz+ ions in helium7) with the
to the six excited states of Hz+ which lead to the
emission of Lyman+ radiation*) 9) (figure 5). In the energy range 1-l 0 keV these two cross sections are of the same order of magnitude and hence dissociation through excitation to the 2@cu and higher states should be appreciable. We have made calculations for both states, the calculations being semiquantitative because of the unknown R and 4 dependence of the excitation cross section. We are attempting to clarify further the relative importance of the various excitation processes. (iii) The length of the internuclear axis of each Hz+ ion is taken to be constant throughout the collision. This is equivalent to assuming that the electronic transition obeys the Franck-Condon principle. A comparison of the collision time (1 O-15 second) with the vibrational time (1 O-14second) supports this view. (iv) The internuclear axis is assumed to maintain a constant inclination to the direction of motion during the dissociation process. Again this is justified by a comparison of the dissociation time (lo-14 second) with the rotational time (1 O-12 second). (v) The relative population of each vibrational state of the incident Hz+ ions is taken to be given by the Franck-Condon overlap integrals. If the Hz+ ions are formed by a single fast electron impact (> 20 eV) this assumption would be well founded. However, arguments against a constant vibrational distribution are provided by various experiments in which variations in dissociation cross sections with ion source conditions are observed and attributed to varying vibrational distributions7) 10) ii). On the other hand there are also experimenters who have failed to detect this ion source effect is) 13). Now in all sources in normal use the ionizing electrons have energies well above 20 eV (in our case the potential drop across the arc was 100 volts). Therefore, a modification of the relative populations of the vibrational states would have to occur by means of vibrational deactivation of the ions, rather than by alteration of the electron energy. Thus sources in which transverse magnetic fields are applied, causing some trapping of the ions, seem to give a cross section dependent on operating conditions. However, if the ions are quickly ejected from a source the population distribution should be independent of the operating conditions and should, therefore, be given by the Franck-Condon factors. In our experiments we found the ratio of centre to side peaks (a fairly sensitive measure of the relative populations of respectively the high and low vibrational statess)) to be insensitive to the mode of operation of the ion source. We therefore feel justified in using the Franck-Condon distribution *). *) We are grateful to Dr. J. M. Peek for providing us with a table of the probability over R based on Dunn’s Franck-Condon factors.
distribution
266
D. K. GIBSON
AND
J. LOS
(vi) For the probability of excitation to the 2p0, state as a function of R and I$ we have followed McClure in the use of the function cr(R, 4) calculated by Peek. This cross section is the result of a Born approximation for Hz+ incident at 10 keV upon H. For our calculation of the excitation to the 2p7rU state we had no figures available and have therefore taken the interaction to be independent of both R and 4. The purpose of this calculation is to show that the experimental results can be approximately accounted for by both processes; it also shows that a very rough approximation to a(R, +) suffices for a semiquantitative calculation of both excitation processes. We can now proceed with the calculation of the distributions of the protons, first considering excitations to the 2@, state. The number of excitations, N(R, 4) dR d4, occurring at particular R and 4 values per unit incident Hz+ flux, per unit target gas density and per unit collision path length is given bY
N(R, 4) dR d4 = 2&(R)
a(R, rj) sin rj dR d+
where D(R) gives the number of ions at spacing R, and o(R, 4) their probability of excitation. These Hz+ ions dissociate, both fragments attaining a velocity v in the centre of mass system, the relationship between R and v being given by the 2@, potential energy curve of Hs+r4). Hence N(R, 4) can be transformed into an expression in v and + as follows:
2&(R) The new expression
a(R, 4) dR d$ sin 4 = 2nN(v, 4) dv d4 sin 4. is therefore
WV>4) = D(R) o(R,4)
$
N(v, 4) is the dissociation probability expressed in centre of mass coordinates. The function must now be transformed into the laboratory coordinates I’ and 0; the relationship between these four variables is shown in figure 6. The transformation requires that N(v, 4) dv d+ sin 4 = P(V,
0) dI’ df3 sin 13.
Therefore P(V, e) =
qcos4, 4
qcos8,V) NV, 9)
where a(cos $7 v) a(cos is the Jacobian
of the transformation.
8, v)
COLLISION-INDUCED DISSOCIATION OF 10 keV HZ+ IONS
267
Fig. 6. Vector diagram of Hz+ dissociation. Vo is initial Hz+ ion velocity; 4 is inclination of internuclear axis to I/O; is the dissociation velocity V of the nuclei, w.r.t. their C. of M.; V is resultant proton velocity, and 8 the laboratory scattering angle.
Using the vector relationships
(fig. 6) we can easily show that
and therefore
( )2
P(V, e) = N(v, 4) +
=
WY Qw
(-g(G)
Now P(V, 19)is the expression we require giving the distribution of the protons in the laboratory velocity and angular co-ordinates. For the calculations we treated v as a parameter and calculated Pv(8) for 10 values of v. The shape of the velocity distribution at 8 = 0” was obtained by graphical integration of the ten curves Pv(B) sin 0 between 8 = 0 and 0 = a, where a is the half opening angle of the apparatus. For angles other than zero the values of PO(V) were simply read from the graphed Pv(8) values. However, there is one complication relating to the velocity distribution at 0 = 0 which must now be discussed. We have up till now assumed that the 2$a, state is completely dissociative, but in fact the potential curve does have a minimum, albeit extremely shallow (“A eV) and at large internuclear spacing of 12.5 a 014). We do not imagine that stable ions can exist in this shallow well, but accounting for the dissociations occurring at large values of R is, with the above formula, no longer possible. For, at a certain point (10.7 a~), the dissociation velocity becomes zero and the
268
D.
K. GIBSON
AND
J. LOS
Jacobian infinite. In reality what must happen is that all such particles dissociate with a small velocity derived from vibrational energy. Therefore, we must cut off our calculation of P(V, 19) at a certain R value before the dissociation energy given by the repulsive potential curves becomes so small that the vibrational energy is significant. Then all Hz+ ions excited at R values above this limit (Re) must be dealt with in another manner. The total number
of dissociations PZ= { rD(R)
occurring
at R > R, is given by
a(R, 4) sin C#d$ dR.
0 R.
These particles dissociate with very small centre of mass velocities, and the angular spread in thus very small. The maximum angle is given by v,/Ve, where ZI, is the dissociation velocity pertaining to R,. This angle is smaller than the acceptance of the energy analyser and so all the particles appear within the nominal 8 = 0 distribution. From a similar argument it can be seen that the particles would have velocities between T/s -& zle. We have therefore represented them by a triangular distribution on a base 2v, and centred about Va on the 8 = 0” velocity distribution. The area of the triangle must correspond to the number of particles, rt, for which the formula was given. The results of these calculations are shown in figure 7. We have taken two values of R, (8.2 a0 and 6.8 UO) and there is no difference in the calculated distribution. The results at two other angles are also shown in figure 7.
Proton Intensity 15
/
I
Proton Velocity
Fig.
7a
llO1cm
s-‘1
COLLISION-INDUCED
DISSOCIATION
OF
10keV Hz+ IONS
269
\ Fyy.$ \
l-
‘1
‘\ \
0
95
99
‘.
‘\
A
-.
-\
101 100 Proton VIlocity(10‘cm s-‘)
Fig. 7b ProtonIntensity
\
100
99 Protm
Velocity
\ I
I
I
101 (10’
cm
5-O
Fig. 7c Fig. 7. Velocity distribution
----
of protons from 10 keV dissociation angles.
at three different
Experimental Theoretical, using o(R, 4) for H atom target from Peek. The same arbitrary intensity units apply to all three angles.
In order to give an idea of the sensitivity of our calculations to a(R, c$), we shall now carry out the calculation for 8 = 0 taking o(R, 4) = 1. Putting o(R, 6) = 1 in our formula for P(V, fl) we obtain P(V, e) = VT(v)
D. K. GIBSON AND J. LOS
270 where
dR
1
Writing ZIin terms of VO and V we have P(V, e) = vsF([v;
+ vs -
2vav
= V2F(]Va -
VI).
cos e]*)
and for the case of 13= 0 P(V)
We have calculated this function for both the 2#a, and 2finu states (figure 8). The centre peak is difficult to add in the case of the 2+cu state Proton Intensity (Arbitrary units)
I
04
99
I
99
100 Proton
- - - -. -. -
Velocity
101 IlO
cm 5-O
Fig. 8. Proton velocity distribution at 0 = 0”. Experimental, Hz target. Theoretical, excitation to 2@cU state, cr(R, 4) = 1. Theoretical, excitation to 2@, state, o(R, 4) = 1.
because this state has a far deeper well (& eV) 15) and hence some of the excitations could lead to excited Hz+ ions, which de-excite by radiation rather than by dissociation. From these calculations it can be seen that the essential shape of the velocity distribution is not strongly dependent on a(R, +), and furthermore that it can also be explained in terms of excitations to states other than the 290,. On the other hand if one looks for good agreement between the calculations and measurements over the whole range of angle and velocity the function c (R, 4) must be well defined. Conclusion. We have measured the angular and velocity distributions of the protons resulting from collisions of 10 keV Hz+ ions with hydrogen
COLLISION-INDUCED
molecules
or helium atoms.
we have obtained
DISSOCIATION
By integrating
the angular distribution
OF
10keV
Hz+ IONS
271
these results over the velocity, and found it to be in very good
agreement with the measurements of McClure. McClure’s explanation of collision-induced dissociation in terms of electronic excitation has been extended to describe our results. From the good agreement between theory and experiment it is clear that the theory is essentially correct. In particular the high central peak previously observed in Aston band measurementsrs) is shown to arise from electronic excitation of those Hz+ ions which have very large internuclear separations at the moment of impact. This central peak has sometimes been wrongly attributed to a second dissociation process, that of excitation into the vibrational continuum17) 18). Our interpretation of this central peak is supported by the fact that the ratio of its height to that of the side peaks remains approximately constant over a collision energy range from 25 eV19) to 70 keVr*). The dissociation of the HZ+ ions with widely separated nuclei must also be taken into account in order to explain the observed maximum at zero scattering angle. McClure neglected these particles and hence obtained a narrow minimum at zero deflection angle. The calculation of the proton distribution requires knowledge of the relative population of the 19 vibrational states of the Hz+ ion. We have found that the distribution given by Dunn’s calculations of the FranckCondon factors gives a good ratio of the intensities of the side peaks (R small) to the central peak (I? large). The factors of McGowan and Kerwin overestimate the large R values by a factor of about three. We have used both hydrogen and helium as target gas and have observed a clear difference between the distributions of the protons for these two cases. This difference can only be due to a dependence of the function a(R,4)on the nature of the target gas. Our results indicate that the measurement of both the velocity and angular distributions of the fragments of dissociation could be a rather sensitive method for determining the dependence of the excitation cross sections on R, c#, the collision velocity and the nature of the target particle. Acknowledgements. The authors wish to express their thanks to Professor J. Kistemaker, Dr. A. J. H. Boerboom and Dr. D. Jaecks for the interest they have taken in this work. They are also grateful to all those who have made the project possible by their technical assistance. This work is part of the research programme of the Stichting voor Fundamenteel Onderzoek der Materie (F.O.M.) and was made possible by financial support of the Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek (Z.W.O.). Received 11-2-67
272
COLLISION-INDUCED
DISSOCIATION
OF
10 keV Hz+ IONS
REFEREN’CES
1) Purser,
4 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)
13) 14) 15) 16) 17) 18) 19)
K. H., Rose, P. H., Brooks, N. B., Bastide, R. P. and Wittkower, A. B., Phys. Letters 6 (1963) 176. McGowan, J. Wm. and Kerwin, Larkin, Can. J. Phys. 42 (1964) 972. McClure, G. W., Phys. Rev. 140 (1965) A 769. Peek, J. M., Phys. Rev. 140 (1965) All. Dunn, Gordon, H., J. Chem. Phys. 44 (1966) 2592. Tasman, H. A., Advances in Mass Spectrometry, Pergamon Press, London, Vol. I (1959), p. 36. Williams, J. F. and Dunbar, D. N. F., Phys. Rev. 149 (1966) 62. Van Zyl, B., Jaecks, D., Pretzer, D. and Geballe, R., Phys. Rev. 13GA (1964) 1951. Jaecks, D. and Tynan, E., IVth International Conference on the Physics of Electronic and Atomic Collisions, Quebec (1965), Science Bookcrafters, p. 315. McClure, G. W., Phys. Rev. 130 (1963) 1852. Chambers, E. S., Phys. Rev. 139 (1965) A 1068. Barne t t, C. F. and Ray, J. A., Proceedings of the Third International Conference on the Physics of Electronic and Atomic Collisions (London, 1963) edited by M. R. C. McDowell (NorthHolland Publishing Co., Amsterdam), p. 743. Riviere, A. C. and Sweetman, D. R., Proc. Phys. Sot. (London), 78 (1961) 1215. Peek, James M., TID-4500 (39th Ed) UC-34 Physics SC-RR-65-77. Bates, D. R., Ledsham, Kathleen and Stewart,A. L., Phil. Trans. Roy. Sot. London, 246 (1953) 215. McGowan, J. Wm and Kerwin, Larkin, Can. J. Phys. 41 (1963) 316. Caudano, R., Delfosse, J. M. and Steyaert, J., Ann. de la Sot. Scientifique de Bruxelles, 76, III, (1963) 127. Verveer, P., Euratom report EUR 2767.f, Brussels (1966). Champion, R. L., Doverspike, L. D. and Bailey, T. L., J. them. Phys. 45 (1966) 4377.
Gibson, D. K. Los, J. 1967
COLLISION-INDUCED
DISSOCIATION
by D. K. GIBSON FOM-Instituut
voor Atoom-
OF 10 keV HZ+ IONS
and J. LOS
en Molecuulfysica,
Amsterdam*)
synopsis Measurements of the angular and velocity distributions of the protons obtained by passing a beam of 10 keV Ha+ ions through hydrogen or helium gases are described. The angular distribution is in agreement with that previously measured by McClure. The velocity distribution has been accounted for in terms of collision - induced electronic excitations leading to dissociative states of the He+ ion. The agreement between theory and experiment indicates that this theory is essentially correct, the greatest unknown being the dependence of the excitation cross section upon the length and orientation of the Hz+ internuclear axis. This dependence is found to be different for the two target gases (Ha and He).
Introduction. The simple structure of the Hz+ ion and the consequent wealth of accurate theoretical data relating to it have led to this ion being the object of many investigations of collision-induced dissociation. It has been shown by Purser et aliil) that the mutual recoiling of the two nuclei with a repulsive energy of about 5 eV causes very large energy spreads in the laboratory system**). Two studies in particular have led directly to the work described in this paper. Firstly, the Aston band caused by the dissociation of Hz+ in a mass spectrometer has been studied by McGowan and Kerwins), who have investigated the effects of vibrational states on the shape of this band. The second work is McClure’sa) measurement and theoretical description of the angular distribution of the dissociation fragments Hf and H. We have extended the work in these two studies by measuring both the velocity and angular distribution of the protons resulting from Hz+ dissociation. In effect we have measured the shape of the Aston band, but have refined the experiment by measuring the same band many times, each time altering the angle through which the particles must scatter in order to pass through the mass spectrometer. Or, from another *) Formerly:
Laboratorium
voor
Massascheiding.
**) where Eo is the Laboratory
energy
of the Ha + and e is the centre
dissociation.
-
258 -
of mass energy
liberated
during
COLLISION-INDUCED
DISSOCIATION
OF
10keV Hz+ IONS
259
point of view, we have measured the differential cross section but have gained further information by using a momentum analyser in front of our detector. Our results can be explained by an extension of McClure’s theory. He accounted for the observed angular distribution of the protons on the hypothesis that the Hz+ ions are excited from the ground electronic state to the first excited state, 2fio,, which is dissociative. Interaction
McClure assumed the
Energy (eV)
lo-
R, Intornuchar
Separation
(a,)
Fig. 1. Energy level diagram of Hz+.
electronic excitation to follow the Franck-Condon principle and thus the mutual repulsion after excitation to be strongly dependent on the Hz+ internuclear spacing, R, at the moment of excitation. Therefore, in the centre of mass system, the magnitude of the dissociation velocity was held to depend on R, and its direction on the angle, q3,between the internuclear axis and the directionof motion of the Hs+ion. In order to calculate the angular distribution of protons arising from the dissociation of Hz+ ions McClure needed to know the cross section for excitation of the 2fi0, state due to collision with the target atom as a function of both R and 4, and also the probability, D(R), of finding an Hz+ ion with internuclear spacing R. The cross section for excitation, a(R, +), has been calculated by P eek4) at 10 keV for a hydrogen atom target, using the first Born approximation. McGowan and Kerwin have shown that the expression D(R) approaches that given by the Franck-
260
D.
K. GIBSON
AND
J. LOS
Condon overlap integrals between ground state Hz and the nineteen vibrational states of Hz+ if the ionization is caused by electrons with more than 20 eV energy. We have followed McClure in using these data, except that we have used the Franck-Condon factors recently calculated by Dunns) in place of those of McGowan and Kerwin. McClure’s calculation included an integration which gave the angular distribution averaged over all velocities, whereas we have calculated both the angular and velocity distributions of the dissociated particles. Moreover, we have found it necessary to calculate the intensity near zero deflection by a different method. Ex#erimental procedure. The apparatus is shown schematically in figure 2. Ions produced in the unoplasmatron source are accelerated to 10 keV and focussed through the 0.4 mm diameter apertures, which are spaced 30 cm apart. The beam intensity is naturally very small (10-T amp) after this stringent collimation, but, in view of the angular resolution required, such collimation is necessary. The beam traverses the collision chamber and, after passing between a pair of condenser plates which are used for the angular analysis, enters the magnetic analyser through a 5 mm diameter hole. As far as geometrical calculations of the scattering angle are concerned this aperture can be considered as the detector. In the range between f 2” the angular resolution is of the order f 1/IO”; the divergence of the initial beam, the finite length of the target chamber and the finite size of the collection aperture all cantribute in approximately equal parts to the uncertainty in angle. The angular analysis is performed by means of a transverse voltage between the condenser plates. Within our small angular range, and provided that the energy spread of the beam is not very great, this simple method of angular analysis is not very much in error. For, although the spread in energies of protons resulting from collision-induced dissociation at 10 keV is some 500 eV, the variation in angle from the slowest to the fastest particle is only 5%. The deflection voltage was calibrated in terms of angle with the aid of two Faraday cups placed either side of the beam axis. The transverse voltages required to deflect the beam through a known angle into these cups were measured for a series of beam energies. We found that
e=
188p
a
degrees
where I’t and Va are the transverse and acceleration potentials respectively. The constant of proportionality agreed to within 3% with the value calculated from the geometry of the plates and we assumed, therefore, that the relation between 8 and vt was linear over our small angular range.
COLLISION-INDUCED
DISSOCIATION
10keV
OF
Hz+ IONS
261
The momentum analyser consists of an inhomogeneous field magnetic mass spectrometere), so arranged that the object point (the centre of the collision chamber) is focussed onto a slit in front of the electron multiplier. The halfwidth of the primary
beam is about
5 eV, this being a sum of the energy
i 1 ,%I * ::
T
Fig. 2. Apparatus
1
A
Ion source
B
Collimators
C
Collision chamber
D
Deflection plates
(0.4 mm)
E
Undisturbed
beam
F
Scattered beam
G
Collimators
(5 mm)
H
Magnet
I
Detector
spread of the ion beam and the aberrations of the analyser. In view of the broad energy distribution of the protons (500 eV) this primary beam width is satisfactory. The velocity distributions were measured with the help of an XY recorder. The X signal was provided by a differential gaussmeter (RFL Model 1965) which measured the magnetic field between the pole faces of the analyser
262
D. K. GIBSON AND J. LOS
by means of a Hall probe. Thus the X scale was proportional
to the magnetic
field and hence to the velocity of the protons. The Y signal was the amplified output of the electron multiplier detector. Thus the velocity distribution at one fixed scattering angle could be directly recorded by slowly scanning the magnetic field. A trace made without collision gas gave the contribution due to dissociations induced by the background gas. The beam intensities have always been expressed in arbitrary units as the gain of the electron multiplier was not measured. The velocity scale was calibrated by measuring the shift in a peak position corresponding to a known change in the acceleration voltage. We wished to establish the relation between the velocities of the protons and the velocity of the H s+ beam from which they were formed. We were able to do this by using the protons issuing directly from the ion source as a marker peak. In order to give these protons the same velocity as the Proton Intensity tArbitrary
units)
Proton velocity
IlO’cm
s-‘1
Fig. 3. Experimental curve, 10 keV Hz+ on Hz. a) Proton velocity distribution at 8 = 0”. b) Background signal. c) 5keV proton marker peak. Inset shows proportionality between mass and acclerating voltage. d) 5000 eV Hf e) 2500 eV HZ+ f) 1666.7 eV Hsf.
original Hz+ ions, the accelerating potential was reduced to exactly one half of its original value. In this way the primary proton peak was superimposed upon the broad distribution which was yielded by the protons formed by collision-induced dissociation (figure 3). An inset on figure 3 shows successive traces of H+, Ha+ and Ha+, with the acceleration voltage respectively l/2, l/4 and l/6 of its original value. The fact that these three
COLLISION-INDUCED
DISSOCIATION
OF
IOkeV Hz+ IONS
263
peaks occur at the same magnetic field strength shows that the potential of the arc of the ion source differs from the acceleration voltage by a negligible amount. We have also measured the angular distribution of the protons by means of integrating the velocity distributions at several angles. The results of these measurements
are in very good agreement
with those of McClure, as
can be seen from figure 4. Differential
Cross Section
lU’*crr?
Steradim~
20 -
/
lo-
i b-
2
1
i 4
8
-2
,
-
I
I
0
-1
Fig. 4. Differential on Hz target. normalized
cross section
for protons
Solid line shows McClure’s
to McClure’s
2
Angle (Degrees1
produced
by dissociation
of 10 keV
Hz+
results. The crosses denote our measurements
at 8 = 0”. The deviations
as the scatter
I
1 Scattering
of McClure’s
of our points are of the same order measurements.
Disczlssiorz. From figure 3 it is clear that many protons are travelling faster than the Hz+ ions from which they originated. This phenomenon can be explained only by assuming that the Hz+ ions dissociate in such a way that the two nuclei are thrown apart by some considerable repulsive force. Thus the basis of McClure’s explanation of the dissociation is strongly supported. Before describing the calculations we will discuss various basic points.
264
D. K. GIBSON AND J. LOS
(i) We assume that the angular scattering
is entirely
due to the transverse
component of the disssociation velocity. Thus we neglect the angular deviation of the Hz+ C. of M. due to the collision. This assumption is to some extent justified by the work of McClure. However, the intensity he measured at scattering angles above 1” is larger than he calculated; attributed to scattering of the Hz+ ion. Our calculations at small angles will be very little affected
this
could be
by scattering,
which will lead only to reduction in intensity. However, at larger angles the scattering could bring about discrepancies between the theory and experiment. (ii) McClure assumes that the number of excitations to the 2pu, state overshadows the number to all higher states. From figure 3 it appears that this may bot be correct, for there is a slight displacement of the secondary protons towards lower energies. The displacement corresponds to about 7 eV energy loss on the part of the H s+ ion, which can be easily accounted for if about 70% of the Hz+ ions are excited to the 2+nU state, or higher, with a 10 eV inelastic energy loss. Excitation to the 2@cU state mostly leads to dissociation with the subsequent emission of Lyman-a radiation. However, this argument is not conclusive, for Peeka) has shown that simultaneous excitation of the target is rather probable and this would also explain the energy defect. Approaching the problem from another angle, one can 104"cm2 /atom 1.5 i
Fig. 5. Cross sections for Hs+ in He. Total cross section for proton production (Williams and Dunbar). Cross section for Lyman - oc production plus metastable 2s formation. The excited atoms arise from reaction Hz+ + He + Hf + H” + He as, in the case of helium target, the alternative process, charge exchange, is very small (Jaecks and Tynan) .
COLLISION-INDUCED
compare
the total dissociation
cross section for excitation
DISSOCIATION
OF 10 keV Hz+ IONS
265
cross section of Hz+ ions in helium7) with the
to the six excited states of Hz+ which lead to the
emission of Lyman+ radiation*) 9) (figure 5). In the energy range 1-l 0 keV these two cross sections are of the same order of magnitude and hence dissociation through excitation to the 2@cu and higher states should be appreciable. We have made calculations for both states, the calculations being semiquantitative because of the unknown R and 4 dependence of the excitation cross section. We are attempting to clarify further the relative importance of the various excitation processes. (iii) The length of the internuclear axis of each Hz+ ion is taken to be constant throughout the collision. This is equivalent to assuming that the electronic transition obeys the Franck-Condon principle. A comparison of the collision time (1 O-15 second) with the vibrational time (1 O-14second) supports this view. (iv) The internuclear axis is assumed to maintain a constant inclination to the direction of motion during the dissociation process. Again this is justified by a comparison of the dissociation time (lo-14 second) with the rotational time (1 O-12 second). (v) The relative population of each vibrational state of the incident Hz+ ions is taken to be given by the Franck-Condon overlap integrals. If the Hz+ ions are formed by a single fast electron impact (> 20 eV) this assumption would be well founded. However, arguments against a constant vibrational distribution are provided by various experiments in which variations in dissociation cross sections with ion source conditions are observed and attributed to varying vibrational distributions7) 10) ii). On the other hand there are also experimenters who have failed to detect this ion source effect is) 13). Now in all sources in normal use the ionizing electrons have energies well above 20 eV (in our case the potential drop across the arc was 100 volts). Therefore, a modification of the relative populations of the vibrational states would have to occur by means of vibrational deactivation of the ions, rather than by alteration of the electron energy. Thus sources in which transverse magnetic fields are applied, causing some trapping of the ions, seem to give a cross section dependent on operating conditions. However, if the ions are quickly ejected from a source the population distribution should be independent of the operating conditions and should, therefore, be given by the Franck-Condon factors. In our experiments we found the ratio of centre to side peaks (a fairly sensitive measure of the relative populations of respectively the high and low vibrational statess)) to be insensitive to the mode of operation of the ion source. We therefore feel justified in using the Franck-Condon distribution *). *) We are grateful to Dr. J. M. Peek for providing us with a table of the probability over R based on Dunn’s Franck-Condon factors.
distribution
266
D. K. GIBSON
AND
J. LOS
(vi) For the probability of excitation to the 2p0, state as a function of R and I$ we have followed McClure in the use of the function cr(R, 4) calculated by Peek. This cross section is the result of a Born approximation for Hz+ incident at 10 keV upon H. For our calculation of the excitation to the 2p7rU state we had no figures available and have therefore taken the interaction to be independent of both R and 4. The purpose of this calculation is to show that the experimental results can be approximately accounted for by both processes; it also shows that a very rough approximation to a(R, +) suffices for a semiquantitative calculation of both excitation processes. We can now proceed with the calculation of the distributions of the protons, first considering excitations to the 2@, state. The number of excitations, N(R, 4) dR d4, occurring at particular R and 4 values per unit incident Hz+ flux, per unit target gas density and per unit collision path length is given bY
N(R, 4) dR d4 = 2&(R)
a(R, rj) sin rj dR d+
where D(R) gives the number of ions at spacing R, and o(R, 4) their probability of excitation. These Hz+ ions dissociate, both fragments attaining a velocity v in the centre of mass system, the relationship between R and v being given by the 2@, potential energy curve of Hs+r4). Hence N(R, 4) can be transformed into an expression in v and + as follows:
2&(R) The new expression
a(R, 4) dR d$ sin 4 = 2nN(v, 4) dv d4 sin 4. is therefore
WV>4) = D(R) o(R,4)
$
N(v, 4) is the dissociation probability expressed in centre of mass coordinates. The function must now be transformed into the laboratory coordinates I’ and 0; the relationship between these four variables is shown in figure 6. The transformation requires that N(v, 4) dv d+ sin 4 = P(V,
0) dI’ df3 sin 13.
Therefore P(V, e) =
qcos4, 4
qcos8,V) NV, 9)
where a(cos $7 v) a(cos is the Jacobian
of the transformation.
8, v)
COLLISION-INDUCED DISSOCIATION OF 10 keV HZ+ IONS
267
Fig. 6. Vector diagram of Hz+ dissociation. Vo is initial Hz+ ion velocity; 4 is inclination of internuclear axis to I/O; is the dissociation velocity V of the nuclei, w.r.t. their C. of M.; V is resultant proton velocity, and 8 the laboratory scattering angle.
Using the vector relationships
(fig. 6) we can easily show that
and therefore
( )2
P(V, e) = N(v, 4) +
=
WY Qw
(-g(G)
Now P(V, 19)is the expression we require giving the distribution of the protons in the laboratory velocity and angular co-ordinates. For the calculations we treated v as a parameter and calculated Pv(8) for 10 values of v. The shape of the velocity distribution at 8 = 0” was obtained by graphical integration of the ten curves Pv(B) sin 0 between 8 = 0 and 0 = a, where a is the half opening angle of the apparatus. For angles other than zero the values of PO(V) were simply read from the graphed Pv(8) values. However, there is one complication relating to the velocity distribution at 0 = 0 which must now be discussed. We have up till now assumed that the 2$a, state is completely dissociative, but in fact the potential curve does have a minimum, albeit extremely shallow (“A eV) and at large internuclear spacing of 12.5 a 014). We do not imagine that stable ions can exist in this shallow well, but accounting for the dissociations occurring at large values of R is, with the above formula, no longer possible. For, at a certain point (10.7 a~), the dissociation velocity becomes zero and the
268
D.
K. GIBSON
AND
J. LOS
Jacobian infinite. In reality what must happen is that all such particles dissociate with a small velocity derived from vibrational energy. Therefore, we must cut off our calculation of P(V, 19) at a certain R value before the dissociation energy given by the repulsive potential curves becomes so small that the vibrational energy is significant. Then all Hz+ ions excited at R values above this limit (Re) must be dealt with in another manner. The total number
of dissociations PZ= { rD(R)
occurring
at R > R, is given by
a(R, 4) sin C#d$ dR.
0 R.
These particles dissociate with very small centre of mass velocities, and the angular spread in thus very small. The maximum angle is given by v,/Ve, where ZI, is the dissociation velocity pertaining to R,. This angle is smaller than the acceptance of the energy analyser and so all the particles appear within the nominal 8 = 0 distribution. From a similar argument it can be seen that the particles would have velocities between T/s -& zle. We have therefore represented them by a triangular distribution on a base 2v, and centred about Va on the 8 = 0” velocity distribution. The area of the triangle must correspond to the number of particles, rt, for which the formula was given. The results of these calculations are shown in figure 7. We have taken two values of R, (8.2 a0 and 6.8 UO) and there is no difference in the calculated distribution. The results at two other angles are also shown in figure 7.
Proton Intensity 15
/
I
Proton Velocity
Fig.
7a
llO1cm
s-‘1
COLLISION-INDUCED
DISSOCIATION
OF
10keV Hz+ IONS
269
\ Fyy.$ \
l-
‘1
‘\ \
0
95
99
‘.
‘\
A
-.
-\
101 100 Proton VIlocity(10‘cm s-‘)
Fig. 7b ProtonIntensity
\
100
99 Protm
Velocity
\ I
I
I
101 (10’
cm
5-O
Fig. 7c Fig. 7. Velocity distribution
----
of protons from 10 keV dissociation angles.
at three different
Experimental Theoretical, using o(R, 4) for H atom target from Peek. The same arbitrary intensity units apply to all three angles.
In order to give an idea of the sensitivity of our calculations to a(R, c$), we shall now carry out the calculation for 8 = 0 taking o(R, 4) = 1. Putting o(R, 6) = 1 in our formula for P(V, fl) we obtain P(V, e) = VT(v)
D. K. GIBSON AND J. LOS
270 where
dR
1
Writing ZIin terms of VO and V we have P(V, e) = vsF([v;
+ vs -
2vav
= V2F(]Va -
VI).
cos e]*)
and for the case of 13= 0 P(V)
We have calculated this function for both the 2#a, and 2finu states (figure 8). The centre peak is difficult to add in the case of the 2+cu state Proton Intensity (Arbitrary units)
I
04
99
I
99
100 Proton
- - - -. -. -
Velocity
101 IlO
cm 5-O
Fig. 8. Proton velocity distribution at 0 = 0”. Experimental, Hz target. Theoretical, excitation to 2@cU state, cr(R, 4) = 1. Theoretical, excitation to 2@, state, o(R, 4) = 1.
because this state has a far deeper well (& eV) 15) and hence some of the excitations could lead to excited Hz+ ions, which de-excite by radiation rather than by dissociation. From these calculations it can be seen that the essential shape of the velocity distribution is not strongly dependent on a(R, +), and furthermore that it can also be explained in terms of excitations to states other than the 290,. On the other hand if one looks for good agreement between the calculations and measurements over the whole range of angle and velocity the function c (R, 4) must be well defined. Conclusion. We have measured the angular and velocity distributions of the protons resulting from collisions of 10 keV Hz+ ions with hydrogen
COLLISION-INDUCED
molecules
or helium atoms.
we have obtained
DISSOCIATION
By integrating
the angular distribution
OF
10keV
Hz+ IONS
271
these results over the velocity, and found it to be in very good
agreement with the measurements of McClure. McClure’s explanation of collision-induced dissociation in terms of electronic excitation has been extended to describe our results. From the good agreement between theory and experiment it is clear that the theory is essentially correct. In particular the high central peak previously observed in Aston band measurementsrs) is shown to arise from electronic excitation of those Hz+ ions which have very large internuclear separations at the moment of impact. This central peak has sometimes been wrongly attributed to a second dissociation process, that of excitation into the vibrational continuum17) 18). Our interpretation of this central peak is supported by the fact that the ratio of its height to that of the side peaks remains approximately constant over a collision energy range from 25 eV19) to 70 keVr*). The dissociation of the HZ+ ions with widely separated nuclei must also be taken into account in order to explain the observed maximum at zero scattering angle. McClure neglected these particles and hence obtained a narrow minimum at zero deflection angle. The calculation of the proton distribution requires knowledge of the relative population of the 19 vibrational states of the Hz+ ion. We have found that the distribution given by Dunn’s calculations of the FranckCondon factors gives a good ratio of the intensities of the side peaks (R small) to the central peak (I? large). The factors of McGowan and Kerwin overestimate the large R values by a factor of about three. We have used both hydrogen and helium as target gas and have observed a clear difference between the distributions of the protons for these two cases. This difference can only be due to a dependence of the function a(R,4)on the nature of the target gas. Our results indicate that the measurement of both the velocity and angular distributions of the fragments of dissociation could be a rather sensitive method for determining the dependence of the excitation cross sections on R, c#, the collision velocity and the nature of the target particle. Acknowledgements. The authors wish to express their thanks to Professor J. Kistemaker, Dr. A. J. H. Boerboom and Dr. D. Jaecks for the interest they have taken in this work. They are also grateful to all those who have made the project possible by their technical assistance. This work is part of the research programme of the Stichting voor Fundamenteel Onderzoek der Materie (F.O.M.) and was made possible by financial support of the Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek (Z.W.O.). Received 11-2-67
272
COLLISION-INDUCED
DISSOCIATION
OF
10 keV Hz+ IONS
REFEREN’CES
1) Purser,
4 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)
13) 14) 15) 16) 17) 18) 19)
K. H., Rose, P. H., Brooks, N. B., Bastide, R. P. and Wittkower, A. B., Phys. Letters 6 (1963) 176. McGowan, J. Wm. and Kerwin, Larkin, Can. J. Phys. 42 (1964) 972. McClure, G. W., Phys. Rev. 140 (1965) A 769. Peek, J. M., Phys. Rev. 140 (1965) All. Dunn, Gordon, H., J. Chem. Phys. 44 (1966) 2592. Tasman, H. A., Advances in Mass Spectrometry, Pergamon Press, London, Vol. I (1959), p. 36. Williams, J. F. and Dunbar, D. N. F., Phys. Rev. 149 (1966) 62. Van Zyl, B., Jaecks, D., Pretzer, D. and Geballe, R., Phys. Rev. 13GA (1964) 1951. Jaecks, D. and Tynan, E., IVth International Conference on the Physics of Electronic and Atomic Collisions, Quebec (1965), Science Bookcrafters, p. 315. McClure, G. W., Phys. Rev. 130 (1963) 1852. Chambers, E. S., Phys. Rev. 139 (1965) A 1068. Barne t t, C. F. and Ray, J. A., Proceedings of the Third International Conference on the Physics of Electronic and Atomic Collisions (London, 1963) edited by M. R. C. McDowell (NorthHolland Publishing Co., Amsterdam), p. 743. Riviere, A. C. and Sweetman, D. R., Proc. Phys. Sot. (London), 78 (1961) 1215. Peek, James M., TID-4500 (39th Ed) UC-34 Physics SC-RR-65-77. Bates, D. R., Ledsham, Kathleen and Stewart,A. L., Phil. Trans. Roy. Sot. London, 246 (1953) 215. McGowan, J. Wm and Kerwin, Larkin, Can. J. Phys. 41 (1963) 316. Caudano, R., Delfosse, J. M. and Steyaert, J., Ann. de la Sot. Scientifique de Bruxelles, 76, III, (1963) 127. Verveer, P., Euratom report EUR 2767.f, Brussels (1966). Champion, R. L., Doverspike, L. D. and Bailey, T. L., J. them. Phys. 45 (1966) 4377.