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The compton defect in ammonia as observed using 35 keV incident electrons
PEJYSICS LETTERS
c;IEMIcAL
Volume6O,number3
THE COMPTON DEFECT IN AMMONIA
AS OBSERVED USING 35 keV INCIDENT
1.5 Janualy 1979
ELECTRONS
Azzedine LAHMAM BENNANI, Alsin DUGUET and H.F_ WELLENS’IFlN* tiborntoire de ColiYrionrAtomiques et Mohkires (Difi’mction i?~ectronique), Utim-t6
de Pan% Sud, 9140.5 Onay, Frunce
Received 24 ApriI 1978 Revised manuscript received 21 September 1978
Using a 35 keV electron beam incident on NHa, precision m easurements of the energy loss position of the Compton peak have been performed. The observed Compton peak is found to be at larger energy losses than predicted fox an electron scattered through the same angle from a stationary unbound electron. This defect has been studied for the momentum transfer range 0.5 au < K < 11 au, and is shown to be nonzero even at large K values. A sudden krease in the magnitude of the defect is observed when the inner ekctrons start contributing to the maximum of tke Compton profite. This couId suwt the possibility that the defect is related to the binding energies of the target electrons.
1. Introduction Within the framework of the binary encounter .@E) approximation, the dens@ of generalized oscillator strength [ 1] df(K, E)IdE per unit of energy loss (GOS) is directly connected [Z] to the Compton profile (CP) of the target:
df(K, Eli=
= (E12K3)J@)
,
(1)
where E is the energy lost by the incident electron and transferred to the target, K is the momentum transfer and J(q) is the CP as usuelly defined in X-ray scattering by J(q) = 2m i dp p p(p) 3 141
(2)
with p the target electron momentum, p(p) the atomic or molecular momentum density averaged over all orientations in space, and Q = (E - K2)/2K in the nonrelativistic treatment. It should be noted that relativistic expressions were used thou&out thiswork, see Wellenstein et al. [3] for the exact relations. In this BE, the scattering of the incident electron * Permanent address: Physics Department, Brandeis University,
involves only one electron of the target, this electron being considered as free. The profile J(q) is then symmetrically centered around 4 = 0, i.e_ around the energy loss EBE = K2 corresponding to the knock out of an electron initially free and at rest. However, a double disagreement has been found with this prediction: (i) the position in the energy loss scale of the maximum of the observed profile is shifted by an amount AJ!? with respect to E = K2 (or & with respect to Q = 0) 14-63 ; (ii) this profile is not symmetric around its maximum, i.e. J(Aq - (I) is different from J(Aq + (I)
171-
It is to be noted that all the experimental CP measured up to now using high energy electron impact were not precise enough to show off this so-called ‘Tompton defect”, except the very recent meassrements of Barlas et al. [4] on H2 and He concerning the above point (i). And although this defect has been observed as early as 1934 [S] by X-ray scattering from beryllium and graphite, it is only recently that Weiss _et al. [6] have established it firmIy_ In a previous communication [7], we have reported for the first time a quantitative study of the asymmetry mentioned in point (ii) above. It is the purpose of this note to present and discuss our measurements on the shift M as observed in ammonia.
walth.am. IbfaSsachusetts02154, USA.
411
Volume 60, number 3
CIB%KXLPHYSICS
2. Experiment The apparatus used as well as the technique of measurement and the data analysis method have been descrikd elsewhere [8], and we will only note here the most si@cant improvements: the residual magnetic fie1d.shave been reduced to less than f mG in the collision phrne by completely mumetal shielding the apparatus; aho a powerfki rontroi on the spatial stability of the electron beam was mtroduced f9] : these improvements allowed the scattering angle to be determined to within f: 0.003” by taking two symmetrical measurements on both sides of a preliminary roughly determined zero angle_ Rence it was not necessary anymore to readjust the szattering angle so as to force the CP to peak at 4 = 0, as one would rather have ftith in the experiment than in the BE. Energy loss spectra were obtained at scattering an@es from OS0 to 12Ousing 35 keV incident electrons and NH3 as a target. Several measurements were also carried on He in order to compare our results wi*“rh those of Barks et al_ [4]_ The position of the peak of the CP was found using the same method as previously described [‘I], and the Compton defect A.Z?was then defined by A.Z?= ,Qs - EBE where Eobs is the posZtion in the energy loss scale of the observed Compton peak and EBE is defined above. Numerous tests have been conducted to ascertain that the defect was not of experimental origin. Special care was paid to the reduction cf mtdtipk sCattering which would shift the Compton peak to higher energy kxrsesand would make the profile nonsymmetric: the target density was varied from 0.04 to 25 times the nominai density ?ro used in the present experiment, and it was only above 16no that a change in AI? could be detected, excluding so any multiple scattering effect.
3. Resnits and discmsbn Fig. 1 gives, as a function of momentum transfer K (or scattering angle 6) 0~ measurements for NH, of the shift eE expressed in eV together with the esf&u&d uncertainties fkom all error sources_ In the same $&me are also shown two results obtained for He at 0 = 1So and 8 = 3O_The agreement between our measurements and the very recent ones obtained by Barlas et al. [4] is very good. At small K values, the 4X2
LElTERS
15 J2lnuary 1979
t AE t&I
E, ,35-V
-5J
Fa. 1. The Compton defect, ie- ffie shift in the energy loss tie of the observed peak from the &%?ak predicted for the scatte&g from a stationary unbound electron, versus scattering aa@e B and momentum tran&er K using 35 keV intideat dectrons. FuIl circles: our measure ments on NH3 induding some typical error bus. ‘lbingles: our mezkvrrements on He. Crosses: measurements of Bark et at. f4] on He. The full and dotted c=zves are eye intupoIations respectively to the NH3 &ta and to the He data. The da?&ed line is the sin 8 function predkted by Weiss et aL [6j, normalized to our NH3 data at e=s”.
BE model fails very badly, the r&at&e defect AE/& for NH3 being 135% at lo and >SOO% at 0.5”. This was to be expected since in the BE theory the neglect of the binding energy of the target electron is not jus%ed at such small angles, as the binding energy is here comparable to the energy loss suffered by the incident electron. But even for large K values the shift AZT of the observed peak from the BE prediction is not zero but reaches a constant vahre of about 5 eV_ However, the relative shift at 6 = 10” is only =O.S%_ A sudden step increase in the magnitude of AJ? is observed at about 5O, corresponding to the scattering angle for which the max&mm of the CP passes through the uitrogen K shell threshold. This means that the BE conditions, which improved as 8 increased to 5” (AJT[J!!& = 05% at 4_5”), are suddenly less satisfied above 5O, This is expIained by the contribution of the more bound inner electrons to the CP, which increase the average binding energy. Such-a behaviour should be met at each ionization threshoId of the molectie, but we have only observed it distinctly for the inner shells. ‘khe theoretical interpretation of this Compton defect is still an open problem: Ross and Kirkpatrick in 1934 IS], using sem.icIassicalarguments for energy and
Volume 60. number 3
CHEMICAL
PHYSICS LETTERS
momentum conservations, and Bloch [lo] using the broader basis of wave mechanical theory, deduced in the case of X-ray scattering, the following relation for the shift:
Ax=-Dg, where b is the wavelength of the incident radiation, AX is the shift expressed in the wavelength scale, and
D is a target dependent “constant” in which the mean electron binding energies enter in a rather complicated way. In this treatment, AX is always a negative quantity. Other calculations have appeared in the literature in the last few years [l l-131 and are reviewed by Weiss et al. [6 J , but none of these theories is directly comparable to the experiment. More recently, Tavard et al. 1141 have proposed a correction to the BE taking into account the acceleration effects in the field of the nucleus which act on the target electrons during the collision. They have also evaluated the influence of the other electrons on the target electron, and showed that, in the case of He, the shift of the Compton peak due to the nuclear field is dominant compared to the one due to the electronic field. But Tavard’s calculations are only concerning the asymptotic behaviour of the shift AE in the limit of large K values, and not its variation with K. Nevertheless, good agreement was obtained in this limit with the measurements of Barks et al. [4] on He. Unfortunately, no calculations were done for molecules like NH3. Also recently, Weiss et al. [6], using qualitative arguments, attempted to explain the Compton defect by means of the recoil momentum transferred to the other el&trons considered as free and interacting through their Coulomb forces (spectator electrons model). They showed that, for the electron case, the relative defect AE/EBE should be proportional to sinW18, the constant of proportionality beiag a function of the electron-electron distance and of the incident energy. And as EBE is simply given by E. sin38, AE should be proportional to sin 8. Bark et al. [4], using this
15
January1979
qualitative prediction normalized to their He and H, data at 0 = 4.5”, found it to reasonably describe the experiment above = 3O. This function was also normalized to our measurements at 0 = 5” and is shown in fig. 1: because of the scattering of the data, it is not in disagreement with our observations for 8 > 5” but fails completely at smaller angles. This work has shown the shortcomings of the BE approximations to describe the inelastic scattering of fast electrons by NH, _ However, in spite of this situation, the relative defect is o_nly about 0.5% at a momentum transfer K = 10 au, allowing at large K values the determkration of the target Compton profile with reasonable accuracy_ This analysis for NH3 CP is discussed elsewhere [9] and will be published later.
References Ill hf. Inokuti, Rev. Mod. Phys. 43 (1971) 297. 121R-k Bonham and ii-F_ Wellenstein, in: Compton scat-
tering, ed. B. WiEiams (Ascot Press, 1976) ch. 8. I31 H.F. WelIenstein, RA. Bonham and RC. ULsh, Phys. Rev. A8 (1973) 304. 141 A.D. Barlas, W. Rueckner and H.F. Wellenstein, PhiL hfag. 36 (1977) 201. ES1 P-k Ross and P- Kirkpatrick, Phys. Rev. 45 (1934) 221. f61 RJ. Weiss, M.J. Cooper and R. Holt, PhiL hfag. 36 (19771 93. [71 A. Lahmam Bennard, k Duguet and hf. Rowult, PhiL Msg. (1978), to be published. 181A. Lahmam Bennani, H.F. Wellenstein, A. Duguet, B. Nguyen and AD. Badas, Chem. Phys. Letters 41 (1976) 470. 191 A. Lahmam Bennani, Th&e de Doctorat, Orsay (1978) I101 F. Bloch, Phys. Rev. 46 (1934) 674. illI B.J. Bloch and L.B. hfendelsohn, Phys. Rev_ A9 (1974) 129. WI L.B. Mendelsohn and B.J. Bloch, Phys. Rev. Al2 (1975) 552. 1131 R Cur-rat, P.D. de Cicco and R.J. Weiss, Phys. Rev. B84 (1971) 4256_ 1141 C. Tavard, F. Gasser and C. dal Capello (1978), to be published.
413
c;IEMIcAL
Volume6O,number3
THE COMPTON DEFECT IN AMMONIA
AS OBSERVED USING 35 keV INCIDENT
1.5 Janualy 1979
ELECTRONS
Azzedine LAHMAM BENNANI, Alsin DUGUET and H.F_ WELLENS’IFlN* tiborntoire de ColiYrionrAtomiques et Mohkires (Difi’mction i?~ectronique), Utim-t6
de Pan% Sud, 9140.5 Onay, Frunce
Received 24 ApriI 1978 Revised manuscript received 21 September 1978
Using a 35 keV electron beam incident on NHa, precision m easurements of the energy loss position of the Compton peak have been performed. The observed Compton peak is found to be at larger energy losses than predicted fox an electron scattered through the same angle from a stationary unbound electron. This defect has been studied for the momentum transfer range 0.5 au < K < 11 au, and is shown to be nonzero even at large K values. A sudden krease in the magnitude of the defect is observed when the inner ekctrons start contributing to the maximum of tke Compton profite. This couId suwt the possibility that the defect is related to the binding energies of the target electrons.
1. Introduction Within the framework of the binary encounter .@E) approximation, the dens@ of generalized oscillator strength [ 1] df(K, E)IdE per unit of energy loss (GOS) is directly connected [Z] to the Compton profile (CP) of the target:
df(K, Eli=
= (E12K3)J@)
,
(1)
where E is the energy lost by the incident electron and transferred to the target, K is the momentum transfer and J(q) is the CP as usuelly defined in X-ray scattering by J(q) = 2m i dp p p(p) 3 141
(2)
with p the target electron momentum, p(p) the atomic or molecular momentum density averaged over all orientations in space, and Q = (E - K2)/2K in the nonrelativistic treatment. It should be noted that relativistic expressions were used thou&out thiswork, see Wellenstein et al. [3] for the exact relations. In this BE, the scattering of the incident electron * Permanent address: Physics Department, Brandeis University,
involves only one electron of the target, this electron being considered as free. The profile J(q) is then symmetrically centered around 4 = 0, i.e_ around the energy loss EBE = K2 corresponding to the knock out of an electron initially free and at rest. However, a double disagreement has been found with this prediction: (i) the position in the energy loss scale of the maximum of the observed profile is shifted by an amount AJ!? with respect to E = K2 (or & with respect to Q = 0) 14-63 ; (ii) this profile is not symmetric around its maximum, i.e. J(Aq - (I) is different from J(Aq + (I)
171-
It is to be noted that all the experimental CP measured up to now using high energy electron impact were not precise enough to show off this so-called ‘Tompton defect”, except the very recent meassrements of Barlas et al. [4] on H2 and He concerning the above point (i). And although this defect has been observed as early as 1934 [S] by X-ray scattering from beryllium and graphite, it is only recently that Weiss _et al. [6] have established it firmIy_ In a previous communication [7], we have reported for the first time a quantitative study of the asymmetry mentioned in point (ii) above. It is the purpose of this note to present and discuss our measurements on the shift M as observed in ammonia.
walth.am. IbfaSsachusetts02154, USA.
411
Volume 60, number 3
CIB%KXLPHYSICS
2. Experiment The apparatus used as well as the technique of measurement and the data analysis method have been descrikd elsewhere [8], and we will only note here the most si@cant improvements: the residual magnetic fie1d.shave been reduced to less than f mG in the collision phrne by completely mumetal shielding the apparatus; aho a powerfki rontroi on the spatial stability of the electron beam was mtroduced f9] : these improvements allowed the scattering angle to be determined to within f: 0.003” by taking two symmetrical measurements on both sides of a preliminary roughly determined zero angle_ Rence it was not necessary anymore to readjust the szattering angle so as to force the CP to peak at 4 = 0, as one would rather have ftith in the experiment than in the BE. Energy loss spectra were obtained at scattering an@es from OS0 to 12Ousing 35 keV incident electrons and NH3 as a target. Several measurements were also carried on He in order to compare our results wi*“rh those of Barks et al_ [4]_ The position of the peak of the CP was found using the same method as previously described [‘I], and the Compton defect A.Z?was then defined by A.Z?= ,Qs - EBE where Eobs is the posZtion in the energy loss scale of the observed Compton peak and EBE is defined above. Numerous tests have been conducted to ascertain that the defect was not of experimental origin. Special care was paid to the reduction cf mtdtipk sCattering which would shift the Compton peak to higher energy kxrsesand would make the profile nonsymmetric: the target density was varied from 0.04 to 25 times the nominai density ?ro used in the present experiment, and it was only above 16no that a change in AI? could be detected, excluding so any multiple scattering effect.
3. Resnits and discmsbn Fig. 1 gives, as a function of momentum transfer K (or scattering angle 6) 0~ measurements for NH, of the shift eE expressed in eV together with the esf&u&d uncertainties fkom all error sources_ In the same $&me are also shown two results obtained for He at 0 = 1So and 8 = 3O_The agreement between our measurements and the very recent ones obtained by Barlas et al. [4] is very good. At small K values, the 4X2
LElTERS
15 J2lnuary 1979
t AE t&I
E, ,35-V
-5J
Fa. 1. The Compton defect, ie- ffie shift in the energy loss tie of the observed peak from the &%?ak predicted for the scatte&g from a stationary unbound electron, versus scattering aa@e B and momentum tran&er K using 35 keV intideat dectrons. FuIl circles: our measure ments on NH3 induding some typical error bus. ‘lbingles: our mezkvrrements on He. Crosses: measurements of Bark et at. f4] on He. The full and dotted c=zves are eye intupoIations respectively to the NH3 &ta and to the He data. The da?&ed line is the sin 8 function predkted by Weiss et aL [6j, normalized to our NH3 data at e=s”.
BE model fails very badly, the r&at&e defect AE/& for NH3 being 135% at lo and >SOO% at 0.5”. This was to be expected since in the BE theory the neglect of the binding energy of the target electron is not jus%ed at such small angles, as the binding energy is here comparable to the energy loss suffered by the incident electron. But even for large K values the shift AZT of the observed peak from the BE prediction is not zero but reaches a constant vahre of about 5 eV_ However, the relative shift at 6 = 10” is only =O.S%_ A sudden step increase in the magnitude of AJ? is observed at about 5O, corresponding to the scattering angle for which the max&mm of the CP passes through the uitrogen K shell threshold. This means that the BE conditions, which improved as 8 increased to 5” (AJT[J!!& = 05% at 4_5”), are suddenly less satisfied above 5O, This is expIained by the contribution of the more bound inner electrons to the CP, which increase the average binding energy. Such-a behaviour should be met at each ionization threshoId of the molectie, but we have only observed it distinctly for the inner shells. ‘khe theoretical interpretation of this Compton defect is still an open problem: Ross and Kirkpatrick in 1934 IS], using sem.icIassicalarguments for energy and
Volume 60. number 3
CHEMICAL
PHYSICS LETTERS
momentum conservations, and Bloch [lo] using the broader basis of wave mechanical theory, deduced in the case of X-ray scattering, the following relation for the shift:
Ax=-Dg, where b is the wavelength of the incident radiation, AX is the shift expressed in the wavelength scale, and
D is a target dependent “constant” in which the mean electron binding energies enter in a rather complicated way. In this treatment, AX is always a negative quantity. Other calculations have appeared in the literature in the last few years [l l-131 and are reviewed by Weiss et al. [6 J , but none of these theories is directly comparable to the experiment. More recently, Tavard et al. 1141 have proposed a correction to the BE taking into account the acceleration effects in the field of the nucleus which act on the target electrons during the collision. They have also evaluated the influence of the other electrons on the target electron, and showed that, in the case of He, the shift of the Compton peak due to the nuclear field is dominant compared to the one due to the electronic field. But Tavard’s calculations are only concerning the asymptotic behaviour of the shift AE in the limit of large K values, and not its variation with K. Nevertheless, good agreement was obtained in this limit with the measurements of Barks et al. [4] on He. Unfortunately, no calculations were done for molecules like NH3. Also recently, Weiss et al. [6], using qualitative arguments, attempted to explain the Compton defect by means of the recoil momentum transferred to the other el&trons considered as free and interacting through their Coulomb forces (spectator electrons model). They showed that, for the electron case, the relative defect AE/EBE should be proportional to sinW18, the constant of proportionality beiag a function of the electron-electron distance and of the incident energy. And as EBE is simply given by E. sin38, AE should be proportional to sin 8. Bark et al. [4], using this
15
January1979
qualitative prediction normalized to their He and H, data at 0 = 4.5”, found it to reasonably describe the experiment above = 3O. This function was also normalized to our measurements at 0 = 5” and is shown in fig. 1: because of the scattering of the data, it is not in disagreement with our observations for 8 > 5” but fails completely at smaller angles. This work has shown the shortcomings of the BE approximations to describe the inelastic scattering of fast electrons by NH, _ However, in spite of this situation, the relative defect is o_nly about 0.5% at a momentum transfer K = 10 au, allowing at large K values the determkration of the target Compton profile with reasonable accuracy_ This analysis for NH3 CP is discussed elsewhere [9] and will be published later.
References Ill hf. Inokuti, Rev. Mod. Phys. 43 (1971) 297. 121R-k Bonham and ii-F_ Wellenstein, in: Compton scat-
tering, ed. B. WiEiams (Ascot Press, 1976) ch. 8. I31 H.F. WelIenstein, RA. Bonham and RC. ULsh, Phys. Rev. A8 (1973) 304. 141 A.D. Barlas, W. Rueckner and H.F. Wellenstein, PhiL hfag. 36 (1977) 201. ES1 P-k Ross and P- Kirkpatrick, Phys. Rev. 45 (1934) 221. f61 RJ. Weiss, M.J. Cooper and R. Holt, PhiL hfag. 36 (19771 93. [71 A. Lahmam Bennard, k Duguet and hf. Rowult, PhiL Msg. (1978), to be published. 181A. Lahmam Bennani, H.F. Wellenstein, A. Duguet, B. Nguyen and AD. Badas, Chem. Phys. Letters 41 (1976) 470. 191 A. Lahmam Bennani, Th&e de Doctorat, Orsay (1978) I101 F. Bloch, Phys. Rev. 46 (1934) 674. illI B.J. Bloch and L.B. hfendelsohn, Phys. Rev_ A9 (1974) 129. WI L.B. Mendelsohn and B.J. Bloch, Phys. Rev. Al2 (1975) 552. 1131 R Cur-rat, P.D. de Cicco and R.J. Weiss, Phys. Rev. B84 (1971) 4256_ 1141 C. Tavard, F. Gasser and C. dal Capello (1978), to be published.
413