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On the non-symmetry of the cross section for collision-induced excitation of HD+ to the 2pσ2 state
Volume 5,’ number
CHEMIC.4LPHYSICSLETTERS
6
ON THE
NON-SYMMETRY
COLLISION-INDUCED
OF
EXCITATION
THE OF
1 May 1970
CROSS HD+
TO
SECTlON THE
2~0,
FOR STATE
PHAM DbNG and JEAN DURUP
Received 13 February
1970
The 1~~~4. Ppou collisionnl excitation of fast HD- is unsymmetrical as regards forward or bncknnrd ejuction of n gown fragment at zero scattering angle. The branching ratio (J(D- ~ H,/OCH+ _ Dj is equal in both cases to 2.0 k 0.1.
From the measurement bution
of protons+arising
of the velocity from
distri-
collision-induced
dissociation of H2 ions in the keSTenergy range it was shown by several workers that a large part of the dissociation occurred through electronic excitation of the Hi ions from the lsog ground state to the repulsive 2~0, state [l-S]. In the case of the collision-induced dissociation of HD+ ions it is expected that the 2p CT,state will dissociate either into H++ D or into Df+ H with some branching ratio: when the protondeuteron distance becomes large enough the electron will oscillate between the quasi-degenerate H+ + D and Df + H states (which at short distances mix into the 1s ug and 2pau states). A branching ratio u(D++H)/u(H++D) = 2.3 to 2.5 was obtained in total collision-induced dissociation cross section measurements at 3 keV incident energy by Kuprijanov et al. 1’71. At lower energies 18.91 the observed phenomena are essentially adiabatic processes [6,8] which we shall not consider in the present paper. We measured the velocity distributions of H+ and D+ from the dissociation of HDi on coiiision with He atoms at 4 000 eV incident energy, using the apparatus which was described in a previous paper @I. The product ions were collected at zero scattering angle, the aperture solid angle being 2.5 x 10-5 steradian. The distributions of the proton and deuteron laboratory energy V were transformed into distributions of the total excess energy W with respect to the center-of-mass of the HD+ ion after the collision, using the apparatus function which was earlier calculated and prepared as computer program by Fournier and one ?Assscinted with the C.N.R.S. 340
of US [6. lo]. This apparatus function takes into account the geometry of the apparatus, and the efficiency of detection by the particle multiplier as a function of ion energy and mass as estimated from Schram et al.‘s data for noble gas atoms [ll]$. A further slight correction takes into account the energy loss of the HDf ion which is practically equal to its electronic excitation energy E* ; we estimate it as the vertical excitation energy needed for a 1s ug- 2~0, transition leading to the point of the potential curve of the upper state lying at an energy TVabove threshold; E* and W are thus computed from the laboratory energy V by iteration. The results appear as distribution functions doubly differentiated with respect to I.Vand to the scattering solid angle in the center-of-mass system of reference. The ordinates are arbitrary units but the absolute ratio of the D+ curve to the H+ curve is known. Figs, 1 and 2 show such distributions obtained for D+ and H’, respectively, at incident ion energy 4000 eV. ionizing electron energy 19 eV, scattering angle O”, and helium as target. The maxima are observed at IV = 3.2* 0.1 eV (on the D+ curve) and 3.5*0.1 eV (on the Hf curve). The distributions obtained are clearly unsymmetrical with respect to forward or backward scattering of a given fragment (in contrast with the distributions obtained for H+ from !if under similar conditions [6. lo]): whichever be the charged fragment, the deuterated one (D or Df) is preferentially forward scattered and the protonated one (H or Hi) preferentially backward scattered. Thus the cross section for Isag $ The szwne law applies within a few percent uncertainty to H-'and D’ [12].
Volume
5, number 6
I May 1970
CHEMICAL PHYSICS LETTERS
Fig. 2. Distribution
of the total kinetic
energy
W of
H-- D fragments with respect to the c. m. of HD. (same conditions as fig. 1). 1’ is the Iahoratorv energy
of H-. Fig. 1. Distribution of the total kinetic energy W of D‘ --H fragments with respect to the c. m. of HD* (target:
He: incident ion energy: 4000 eV: ionizing electron cnergv: 19 eV: scattering angle: O”). V is the lnborntory energy of D .
The ratio of the ordinates actual ratio of differential
example
ref.
[16]
p. 804)
of fiRs. I and 2 is the cross sections.
which
are
unaffected
by
time reversal. cross sections
The observed unsymmetrical can therefore be accounted for
- 2p Uu excitation of HDf on collision with He, the molecule ion being oriented parallel to its flight
only by higher
than first-order
direction,
molecule ion is electronically symmetrical. Thus a theoretical description leading to the observed
appears
to be higher
when the deuteron
is in forward position than when it is in backward position. This statement of course rests on the assumption that the smearing of the angular distribution of the relative momentum of the fragments, arising from the small rotation taking place during the dissociation, is independent of the forward or backward position of the deuteron. This assumption appears to be realistic since the dissociation time (ca half a vibrational period) is much longer than the collision time. Similar unsymmetries have been observed in the collision-induced dissociation of electronically non-symmetrical ions: NO+ and CO* [13], and
non-symmetrical not only a second
I
HeH+ [14,15]. They cannot be explained in the usual approximations of the atomic collision theory based on a small perturbation, viz. the first Born approximation or the semi-classical first-order perturbation theory: the first Born approximation yields differential cross sections (see for example refs. [16,17]) which are unchanged by a reflection of all vectors about the plane perpendicular to the incident wave directiont; again, the semi-classical first-order perturbation theory leads to transition probabilities (see for 7 For s.vmmetrical molecule ions it has been shown by Green and Peek [18] that the collision-induced dissociation corss section in the first Born appro.ximation was unsymmetrical with respect to such a reflection, because of the interference between the g and u states: this effect was mostly apparent at 900 scattering angle (center-of-mass system) and low W (where the adiabatic dissociation is important). It does not seem to be re-
lated to the present effect.
approximations.
in the present case in addition the incident cross
section would require
or higher-order quantummechanical treatment but also the introduction of the coupiing between the electronic states of tine whole (HDHejf quasi-moiecule and the vibrationalrotational states of the HE)+ moiety of this complex. More precisely. if 5 (cy.0) is the differential cross section for an HD+ ion with initial orienta-
tion angle u (with respect to the flight direction) to be excited to the 2 pu,, state and simultaneously deflected from CYto 0 as a result of the collision $, the total cross
section
for production
of frag-
ments which are detected at 0 scattering angle (within an accepted aperture angIe dcr) wiL1be proportional
to ii
/
2i; sinrY.a(cz, Ojda
Thus the observed
.
non-symmetry
of the cross
section reflects the fact that the function (I(u, 0) has different values for forward or backward position of the deuteron. The value of the branching ratio o(D+ + ~),‘u(Hf + D). as may be seen on figs. 1 and 2. is independent of TV in the range of 2.5 to 9 eV; this range covers the region where the Yi In fact the HD- internuclear a..is does not need to rotate from (Y to 0 during the collision. hut the nuciei may undergo momentum changes equivnlent to (and undistinguishable from) such a rotation.
341
Volume 5, number 6
dissociation may be considered as taking place mainly from the 2puu state, the excitation of higher states being unimportant at the relatively low incident velocity used (5 X lo7 cm/set) [5]; on the other hand the adiabatic dissociation becomes important only at lower W [l, 4-61. The mean values of this branching ratio in the abovementioned range of W are: o(l)+ + H)$H++ for-forward
hw-ier
D)
= 2.04 zt 0.08 and 1.90 * 0.12
and backward
scattering
fragment, respectively;
of the
the difference
between these values is within the uncertainties, so that it appears most likely that this branching ratio is actually a constant, equal to 2.0 f 0.1 for dissociation from any state of the vibrational continuum of the 2~0, state of RDf. REFERENCES J.M.Delfosse and J.Steyaert, Ann. Soc.Sci.Bruxelles 76 (1962) 127; R.Caudano and J.M.Delfosse. Proc.Phys.Soc. (London) 2 (1968) 813. [2) F.P.G.Valckx and P.Verveer. J.Phys.27 (1966) [l] R.Caudnno.
[5] B.Meierjohann
and W.Seibt.
Z.Physik
225 (1969)
[6] ?Durup P Fournier end D Pham. Intern. J-Mass. Spectry.ion-Phys.2 (1969) 311. [7] S. E. Kuprijanov zmd V.K. Potapov. Zh. Eksperim. i Teor.Fiz.33 (1957) 311. [a] A.P.Irsa and L-Friedman, J.Chem.Phys.34 (1961) 330. [9] R.W.Rozett and W.S.Koski. J.Chem.Phys.49 (1968) 2691. [lo] P. Fournier. These. Orsay (1969). Fill A.J.H.Boerboom. M.Kleine and . . B.L.Schram. J.Kistemaker. Proc.Vth conf. ionization phenomena of gases. Belgrade 1 (1966) 170. [ 121 J. Appell. private communication. rl31 . - W.Seibt. 6th Intern. Conf.Phys. Electron Atom. Molec. Coil., Cambridge. Mass. (1969): W.Schulz. B.Meierjohann. W.Seibt and H.Eaald. Intern. Conf. Mass. Spectry.. Kyoto (1969), [ 141 J. Schopman and J. Los. Phys. Letters 3iA (1970) 79. [15] J-C.Houver. J.Baudon. M.Abignoli, M.Barat. P.Fournier and J.Durup. Intern.J.Mass.Spectry. Ion Phys.. to be published. [IS] N.F.Mott and H.S.W.Massey. The theory of atomic collisions, 3rd Ed. (Clarendon Press, Oxford. 1965) p.331. [17] J.M.Peek, Phys.Rev.140 (1965) All: J.M.Peek, T.A.Green and W. H. Weihofen. Phys. Rev. 160 (1967) 117: T.A.Green and J.M.Peek, Phys.Rev.183 (1969) 166.
480.
[3] D.K.Gibson and J.Los. -. [+I iV.Vogler and W.seibr.
342
1 May 1970
CHEMICAL PHYSICS LETTERS
Physica 35 (19671 258.
Z. Physik 210 (1968) 337.
[18] T.A.Green and J-M-Peek, (1968) 1732.
Phya.Rev.Letters
21
CHEMIC.4LPHYSICSLETTERS
6
ON THE
NON-SYMMETRY
COLLISION-INDUCED
OF
EXCITATION
THE OF
1 May 1970
CROSS HD+
TO
SECTlON THE
2~0,
FOR STATE
PHAM DbNG and JEAN DURUP
Received 13 February
1970
The 1~~~4. Ppou collisionnl excitation of fast HD- is unsymmetrical as regards forward or bncknnrd ejuction of n gown fragment at zero scattering angle. The branching ratio (J(D- ~ H,/OCH+ _ Dj is equal in both cases to 2.0 k 0.1.
From the measurement bution
of protons+arising
of the velocity from
distri-
collision-induced
dissociation of H2 ions in the keSTenergy range it was shown by several workers that a large part of the dissociation occurred through electronic excitation of the Hi ions from the lsog ground state to the repulsive 2~0, state [l-S]. In the case of the collision-induced dissociation of HD+ ions it is expected that the 2p CT,state will dissociate either into H++ D or into Df+ H with some branching ratio: when the protondeuteron distance becomes large enough the electron will oscillate between the quasi-degenerate H+ + D and Df + H states (which at short distances mix into the 1s ug and 2pau states). A branching ratio u(D++H)/u(H++D) = 2.3 to 2.5 was obtained in total collision-induced dissociation cross section measurements at 3 keV incident energy by Kuprijanov et al. 1’71. At lower energies 18.91 the observed phenomena are essentially adiabatic processes [6,8] which we shall not consider in the present paper. We measured the velocity distributions of H+ and D+ from the dissociation of HDi on coiiision with He atoms at 4 000 eV incident energy, using the apparatus which was described in a previous paper @I. The product ions were collected at zero scattering angle, the aperture solid angle being 2.5 x 10-5 steradian. The distributions of the proton and deuteron laboratory energy V were transformed into distributions of the total excess energy W with respect to the center-of-mass of the HD+ ion after the collision, using the apparatus function which was earlier calculated and prepared as computer program by Fournier and one ?Assscinted with the C.N.R.S. 340
of US [6. lo]. This apparatus function takes into account the geometry of the apparatus, and the efficiency of detection by the particle multiplier as a function of ion energy and mass as estimated from Schram et al.‘s data for noble gas atoms [ll]$. A further slight correction takes into account the energy loss of the HDf ion which is practically equal to its electronic excitation energy E* ; we estimate it as the vertical excitation energy needed for a 1s ug- 2~0, transition leading to the point of the potential curve of the upper state lying at an energy TVabove threshold; E* and W are thus computed from the laboratory energy V by iteration. The results appear as distribution functions doubly differentiated with respect to I.Vand to the scattering solid angle in the center-of-mass system of reference. The ordinates are arbitrary units but the absolute ratio of the D+ curve to the H+ curve is known. Figs, 1 and 2 show such distributions obtained for D+ and H’, respectively, at incident ion energy 4000 eV. ionizing electron energy 19 eV, scattering angle O”, and helium as target. The maxima are observed at IV = 3.2* 0.1 eV (on the D+ curve) and 3.5*0.1 eV (on the Hf curve). The distributions obtained are clearly unsymmetrical with respect to forward or backward scattering of a given fragment (in contrast with the distributions obtained for H+ from !if under similar conditions [6. lo]): whichever be the charged fragment, the deuterated one (D or Df) is preferentially forward scattered and the protonated one (H or Hi) preferentially backward scattered. Thus the cross section for Isag $ The szwne law applies within a few percent uncertainty to H-'and D’ [12].
Volume
5, number 6
I May 1970
CHEMICAL PHYSICS LETTERS
Fig. 2. Distribution
of the total kinetic
energy
W of
H-- D fragments with respect to the c. m. of HD. (same conditions as fig. 1). 1’ is the Iahoratorv energy
of H-. Fig. 1. Distribution of the total kinetic energy W of D‘ --H fragments with respect to the c. m. of HD* (target:
He: incident ion energy: 4000 eV: ionizing electron cnergv: 19 eV: scattering angle: O”). V is the lnborntory energy of D .
The ratio of the ordinates actual ratio of differential
example
ref.
[16]
p. 804)
of fiRs. I and 2 is the cross sections.
which
are
unaffected
by
time reversal. cross sections
The observed unsymmetrical can therefore be accounted for
- 2p Uu excitation of HDf on collision with He, the molecule ion being oriented parallel to its flight
only by higher
than first-order
direction,
molecule ion is electronically symmetrical. Thus a theoretical description leading to the observed
appears
to be higher
when the deuteron
is in forward position than when it is in backward position. This statement of course rests on the assumption that the smearing of the angular distribution of the relative momentum of the fragments, arising from the small rotation taking place during the dissociation, is independent of the forward or backward position of the deuteron. This assumption appears to be realistic since the dissociation time (ca half a vibrational period) is much longer than the collision time. Similar unsymmetries have been observed in the collision-induced dissociation of electronically non-symmetrical ions: NO+ and CO* [13], and
non-symmetrical not only a second
I
HeH+ [14,15]. They cannot be explained in the usual approximations of the atomic collision theory based on a small perturbation, viz. the first Born approximation or the semi-classical first-order perturbation theory: the first Born approximation yields differential cross sections (see for example refs. [16,17]) which are unchanged by a reflection of all vectors about the plane perpendicular to the incident wave directiont; again, the semi-classical first-order perturbation theory leads to transition probabilities (see for 7 For s.vmmetrical molecule ions it has been shown by Green and Peek [18] that the collision-induced dissociation corss section in the first Born appro.ximation was unsymmetrical with respect to such a reflection, because of the interference between the g and u states: this effect was mostly apparent at 900 scattering angle (center-of-mass system) and low W (where the adiabatic dissociation is important). It does not seem to be re-
lated to the present effect.
approximations.
in the present case in addition the incident cross
section would require
or higher-order quantummechanical treatment but also the introduction of the coupiing between the electronic states of tine whole (HDHejf quasi-moiecule and the vibrationalrotational states of the HE)+ moiety of this complex. More precisely. if 5 (cy.0) is the differential cross section for an HD+ ion with initial orienta-
tion angle u (with respect to the flight direction) to be excited to the 2 pu,, state and simultaneously deflected from CYto 0 as a result of the collision $, the total cross
section
for production
of frag-
ments which are detected at 0 scattering angle (within an accepted aperture angIe dcr) wiL1be proportional
to ii
/
2i; sinrY.a(cz, Ojda
Thus the observed
.
non-symmetry
of the cross
section reflects the fact that the function (I(u, 0) has different values for forward or backward position of the deuteron. The value of the branching ratio o(D+ + ~),‘u(Hf + D). as may be seen on figs. 1 and 2. is independent of TV in the range of 2.5 to 9 eV; this range covers the region where the Yi In fact the HD- internuclear a..is does not need to rotate from (Y to 0 during the collision. hut the nuciei may undergo momentum changes equivnlent to (and undistinguishable from) such a rotation.
341
Volume 5, number 6
dissociation may be considered as taking place mainly from the 2puu state, the excitation of higher states being unimportant at the relatively low incident velocity used (5 X lo7 cm/set) [5]; on the other hand the adiabatic dissociation becomes important only at lower W [l, 4-61. The mean values of this branching ratio in the abovementioned range of W are: o(l)+ + H)$H++ for-forward
hw-ier
D)
= 2.04 zt 0.08 and 1.90 * 0.12
and backward
scattering
fragment, respectively;
of the
the difference
between these values is within the uncertainties, so that it appears most likely that this branching ratio is actually a constant, equal to 2.0 f 0.1 for dissociation from any state of the vibrational continuum of the 2~0, state of RDf. REFERENCES J.M.Delfosse and J.Steyaert, Ann. Soc.Sci.Bruxelles 76 (1962) 127; R.Caudano and J.M.Delfosse. Proc.Phys.Soc. (London) 2 (1968) 813. [2) F.P.G.Valckx and P.Verveer. J.Phys.27 (1966) [l] R.Caudnno.
[5] B.Meierjohann
and W.Seibt.
Z.Physik
225 (1969)
[6] ?Durup P Fournier end D Pham. Intern. J-Mass. Spectry.ion-Phys.2 (1969) 311. [7] S. E. Kuprijanov zmd V.K. Potapov. Zh. Eksperim. i Teor.Fiz.33 (1957) 311. [a] A.P.Irsa and L-Friedman, J.Chem.Phys.34 (1961) 330. [9] R.W.Rozett and W.S.Koski. J.Chem.Phys.49 (1968) 2691. [lo] P. Fournier. These. Orsay (1969). Fill A.J.H.Boerboom. M.Kleine and . . B.L.Schram. J.Kistemaker. Proc.Vth conf. ionization phenomena of gases. Belgrade 1 (1966) 170. [ 121 J. Appell. private communication. rl31 . - W.Seibt. 6th Intern. Conf.Phys. Electron Atom. Molec. Coil., Cambridge. Mass. (1969): W.Schulz. B.Meierjohann. W.Seibt and H.Eaald. Intern. Conf. Mass. Spectry.. Kyoto (1969), [ 141 J. Schopman and J. Los. Phys. Letters 3iA (1970) 79. [15] J-C.Houver. J.Baudon. M.Abignoli, M.Barat. P.Fournier and J.Durup. Intern.J.Mass.Spectry. Ion Phys.. to be published. [IS] N.F.Mott and H.S.W.Massey. The theory of atomic collisions, 3rd Ed. (Clarendon Press, Oxford. 1965) p.331. [17] J.M.Peek, Phys.Rev.140 (1965) All: J.M.Peek, T.A.Green and W. H. Weihofen. Phys. Rev. 160 (1967) 117: T.A.Green and J.M.Peek, Phys.Rev.183 (1969) 166.
480.
[3] D.K.Gibson and J.Los. -. [+I iV.Vogler and W.seibr.
342
1 May 1970
CHEMICAL PHYSICS LETTERS
Physica 35 (19671 258.
Z. Physik 210 (1968) 337.
[18] T.A.Green and J-M-Peek, (1968) 1732.
Phya.Rev.Letters
21