- Email: [email protected]
The compton defect in neon and argon as observed using 25 kev incident electrons
Volume 74, number
THE
1
COMF-ION
AS OBSERVED Azzeddine
CHEMICAL
IN NEON
DEFECT
and
LETTERS
AND ARGON
USING 25 keV INCIDENT
LAHhIAhl-BENNAN
PHYSICS
ELECTRONS
AIain DUGUET
Laboratowe des Collmons Atomrques et Mol&ulaues assoc6 au CNRS. Unirersitb de Pars-Sud, F 91405 Orsay France Received
17, December
1979.
m final form 13 hlay 1980
Electron energy-loss spectra. obtamrd for Ne and Ar, are analysed tn terms of Compton profiles (CPs). The euperimental CPs do not peak at q = 0, nor are they symmetrtcal as to theu maxImum value, as predlcted withm the framework of the lmpulsc approuunatlon. Thus Yompton defect” IS charactertsed by a shaft parameter w and an asymmetry parameter 69, and IS mvcstlgated as a function of momentum transfer K. A quahtahve comparison IS made with theoretical predicsons for the Compton defect We also emphasize the K range where partial or total K-Independent CPs of the w=et may be detcrmtned
I_ Introduction
units” used in previous pubhcatlons related to this work. The quanhty Jw(q) defined by
It has recently been demonstrated [ 1,2] that hrgh energy electron unpact spectroscopy IS a pow2rful tecbmque m mvestigatmg the vahdlty of the bmary encounter or unpulse approuunahon (IA). In this approxlmatlon, the incident electron interacts with only one electron of the target considered as free, the melastic (or Compton) Intensity scattered mto a fixed duectlon IS then sunply related to the momentum dlstnbutlon p(p) of the target elzctron by
$0 _ 47Tki dmTdQko”’
=
J
dpp p(P),
Iq,
where d?-o/tidQ IS the melastlc differential cross section with respect to scattering angle and energy, ko and kf are respectively the uutlal and final momenta of the projectlle electron, K is the momentum transfer under coibnon, K = ko - k,, p the target electron momentum and 4 a reduced vanable defined by 4 = (215 - K’)/X in the non-relativistic treatment. It should be noted that throughout t&s work we use (1) relatrvistlc expressions, see ref. [3] for the exact relatrons, and (in) Hartree atomic units (1 unit of energy = 2 rydberg) instead of the “rydberg atomic
(2) and to which we shall refer as the impulse approximation Compton profile (IACP), is a function of only one vanable 4, and IS symmetrically centered around q = 0 corresponding to the collision with a stationary electron. However, the experimental Compton profile (CP), J(q, K), as determined through the relation J(q. K) = (koK5/2kf)
d*aldEdS22.
(1) is found to be a function of both variables q and K, and (li) is neither centered on q = 0 nor is it symmetrical as to its maximum value. The above point (h) constitutes the so-called Compton defect. As part of a program pursued by our group to study tl12 fdure of the IA and to understand the mechanism of the colbsion leading to the Compton defect, we have recently reported and discussed results for the NH3 molecule [ 1,4-6]_ In this note we present new measurements of the Compton defect in neon and argon. Rueckner et al. [7J have 85
Volume 74, number
previously
reported
1
CHEMICAL
a smgle data pomt
PHYSlCS
for neon.
2. Experiment The apparatus and experimental techmque have been described m detail elsewhere [ 1,5,6] . A 25 keV, 0.25 mm fwhm electron beam crosses a gaseous target beam of 1 mm diameter. The scattermg mtenslty IS observed m the angular range 0 2” to aZOo, with an acceptance angle of O.Ol” and an angular precislon of 0 003” The scattered electrons are anafysed by means of a 127” electrostatic energy anaiyser, wth ii resolution of 2- 1 S eV i3ver an enerw 10s~ range up to 7500 eV, depending on the scattermg angle tmder invrstigatton. The cahbrstton of the energy loss spectra IS obtained by displaymg the elastic hne across the multlchnnnel analyser wlule the energy of the mcidznt electrons IS vaned by known amounts. This cahbratton IS checked agamst mnershell iontsatlon potent&s of various targets. Eutensave tests have been carrled out [6] m order to reduce the effects of energy resolution, multlple scattenng, nozzle scattering and other extraneous scattenng.
LETTERS
15 August 1980
64, however, can only be defined if the centres of gravrty of the different sectrons are more or less on a smgle stra&t hne. This conditron is not satisfied when the energy loss at the maximum of the CP (ELhtCP) is close to an romsation threshold of the target. A more complete and ngorous representatxon of the asymmetry of the CP IS given in a separate paper
PI-
Figs. la and lb give, as a fun&Ion of momentum transfer K (or scattering angle 8 ), our measurements for neon of the shift M (or b) and the asymmetry parameter 6q, together with some typical error bars representing ihe total estimated uncertmntres. The 22 eV absolute uncert~nty III s shown at large scat-
I”““““““’ NEON-25
he’.‘
-06
3. Results and discussion To charactense the Compton defect for a given momentum transfer K value, two parameters could be used The most “natural” ones are (I) the shrft * (or -1E in the energy scale) of the maximum of the observed profile from the posltion of the maximum of the IACP, i e from 9 = 0 (or from EM = r\;‘/Z), and (11)the asymmetry parameter 6q (or 6.45 in the energy scale) defined [-I] at half the maximum of the CP by the distance between the vertrcal axes going through Its maxunum and the 8x1s of the profde (see f2g. I of ref. [4] )_ This latter BYISis found dividmg the CP into ten parts, each one tenth of the maxunum he&t. then computmg the centre OF gravtty for each sectlon and fmally drawmg a stra&t line through these pomts. Obviously. thus parameterlsatton of the Compton defect is not the only one possible, but it offers two sunple parameters whose variation with momentum transfer can be represented graphically The parameter 86
‘
-02,
0 , 0 r1t.1
, 2
,
, 1
,,,,,,‘,,* I
0 20 so
,
, , ; 6 8 8
200
,111 LOO
,
12 too0
, , , , 10 Klauf
* ‘
@(deg.)
I
2000 EEA [eV)
.16
20
.
s
3GOO
Ftp t The Ne Compton defect as a functron ot momentum transfer R. (a) The shirt &!Z (0). or Aq (+), oi the mawmum of the observed CP from the IACP Also shown IS one data pomt c-1 obtamed by Ruecknrr ct at. 171. (b) The asymmetry parameter 6q (0) The bottom scalcsglve respectwely the scattcrmg ande 0 and the energy loss, ErAI at the mawmum of the IACP. The arro\is mdlcntc the K values where the cncrs> loss at the mawmum of the measured CP 1s equal to the iontsatron energies of the successwe shelis
CHEhfiCAL
Volume 71, number 1
I
lfS
I!
3
4
i ARGON-25 keV
1 I
,
PHYSICS
LETTERS
and 29.3 eV for Ar 3p and 3s energy of the eJected electron the scattering interaction can as taking place during a short
LS AugustE%0
electrons). The kinetic is then so small that no longer be regarded time (as assumed in the
IA iSI)As K increases, the maximum of the CP moves to higher energy losses, and consequently passes through the successive iomsation energies of the electronic orbit& of the target. The K values for which the ELMCP coincides with an ronisation energy are marked by arrows in figs. 1 and 2. Note that arrows cormsponding to the outermost orbit&s (2p of Ne and 3p of Ar) are missrng because the CP cannot reach its
lughest point for the first ionisation energy of the target. Each of those particular
-02
0
2
FIB. 2 Same
L
1s
m fig.
6
8 $5 K fa.u 1
17
1, but for Ar.
tering angles corresponds to a relattve uncertainty of less than 0.15, emphasizing the hrgh precision needed and achreved m thrs work. Fig. la shows also the only other existmg data point for neon, obtamed by Rueckner et al. [7] usmg 25 keV electrons. These authors did not report the asymmetry parameter gq, but their &5 value is m good agreement with ours. Frgs. 2a and 2b show the shrft .&E and the asymmetry parameter 6q as determined for argon. As prevrously observed rn Hz [7], He [5,7] and NH, [5], the Ar and the Ne data are characterised m the range of small K values (K < 2-3 au) by the strong shortcoming of the IA. In neon, the relative defect at K = 1 au is about 200% for AEJEm and about 100% for SEJEm , where Em = K2J2 IS the most probable energy loss as predrcted within the framework of the IA. (Ew is shown rn the bottom scale of fig. 1 ) This shortcoming is due to the fact that the target electron 1s not free as it IS assumed to be m the IA. but has a bmdrng energy EB comparable to EM (EB is equal to 2 1.6 and 48 5 eV for Ne 2p and 2s electrons and 15.8
K values corresponds
to a noticeable increase in AE (or dq), Followed by a more or less rapid decrease_ Plateau regions with almost constant & are reached for neon and argon in the respective K ranges 4 5 au
Volume 74, number 1
CHEMICAL PHYSICS LETTERS
6q in Ne and Ar, occurrmg at about K = 3.5 au and K = 5.5 au, respectively No simple explanation could be found for this result. A particular note here IS concemmg the K range 2.5 to 4 au wl1ere the ELWCP lies between the lorusauon energies of the Ar 3s and 2p shells. While the tift SY 1s almost zero, 6q varies and hence the shape of the experunental CP IS still strongly dependent upon I\‘. Consequently, the partial CP previously defined for N1. Ne and Ar [9] and ior NH3 161, cannot be deduced from the experiment for the argon hl shell. Wong et al. [9 ] , who based themselves on only two measurements at K = 3.1 au and K = 3.8 au, also reported that “the Ar hl shell CP appears still not quite independent of K”. The Ne L shell and the Ar L-plus-M shell may be consIdered as R mdependent, withm the experimental uncertamr1es. m the K ranges 4 5 to 7 au and 6 to 7 5 au, respectrvely. In these ranges (1) both Aq and 6q are almost constant, and (ii) the relative magmtude of the Compton defect as measured by AE/EW and 6E;Ew 1s smaller than 2%. The Ne total CP IS only slightly dependent on K (&Y/EL4 < 1%) for K values larger than 11 au. Thus the detemunatlon of these three expemnental CPs may be meaningfully considered_ The theory of the Compton defect has recently been summarized by Rueckner et al. [7] and by Lahman-Brnnnm et al. [S] . hlendelsohn and Bloch [lo], using ‘*exact” hydrogeruc (EH) bound- and contmuumstat2 wavefunctlons, have calculated neon and argon L-shcil CR for a typical X-ray scattering evperunent corrzspondmg to a momentum transfer of about 9 au. Thrlr results yield a posrt1ve shift (a > 0) for the 3_p6 subshell and a negatwe one for the 2s’ subshell. so that both shifts largely compensate each other, and a very small shift IS left for the L shell. No indlcatlon 1s g1vzn as to the magnrtude and the sign of this Lshell shift. Howlver, for neon. WC find oy comparing with fig. 7 of ref. [lo] that their quoted values of J(q) (versus q appearing in table 1) most hkely were obtain2d from the posltlve q side of then asymmetnc EHCP The L-shell smft for neon can then be ascertam2d within the hm1ts 0 < &I < 0.1 au No sirmlar evaluation could be made for argon, nor was 1t possable to obtam any mformatlon about the asymmetry param2ter 6q Recently, Gasser and Tavard [l l] pr\iposed a cor-
88
15 August 1980
rection to the IA takmg mto account the acceleration effects WI the field of the nucleus wmch act on the target electrons during the collision_ They derived a simple expression for the Compton defect for hydrogemc ns orbitals. In a quahtative extension to this work, Tavard [ 121 predmted, for large K values, negatlve Jq shifts for tts and tzp* hydrogenic orbltals, and positive ones for trpO orbnals. This 1s not in contradlcuon with Mendelsohn and Bloch’s results smce Tavard states that for neon, the 2po correction may be larger than the 2p, corrections. thus leading to a positive shrft for the 2p6 subshell. From the above, we see that only a qualitative comparison with experiment can be made for the sign of &I 1n the high momentum transfer limit The comparison 1s further complicated since figs. 1 and 2 show that tlus limit 1s not completely reached for all cases m the expenment. However, this limit may be considered as sufficrently approached In the plateau regions wth K ranges 4.5-7 au and 6-7.5 au. for the Ne L-shell and the Ar L-plus-hl-shell CR, respectively In these ranges, 1t is possible to estimate the “large R” defect by averaging over the whole experunental data One thus obtains. Ne L sh2U X=(7.6-C
I)eV.
SE = (13.5 + 2) eV,
*
= (0.049
6q = (0.086
+ 0.005)
au.
+ 0 009) au,
Ar L + hl shell ;1E = -(6 6E=-(11.45
3 +- 0.3) eV, l)eV,
Jr7 = -(0.035
-C0.005)
au,
6q = -(0.063
* 0.00-l)
au,
where the quoted uncertamties are the standard dewations from the average values. The Ne L-shell shift IS thus posltlve. m agreement with Mendelsohn and Bloch’s predlctlon [IO] _ No sumlar sm1ple conclusion can be drawn for argon smce (1) the expenment cannot reach the large-K hmit of the &ft of the hi-shell CP. and (u) the theoretical calculations are hmlted to the L shell. For the Ne total CP, it is only possible to fix an upper bound to the large-K hm1t of th2 tift &, & s 0.015 au (or ti s 6 eV), and a lower one to the large-K lunit of the asymmetry parameter 6q, 6q > -0.06 au (or 6E > -25 ev). Subtracting the L-shell contnbutlon aven above, it is then found that the shift rlq (or &) of the ls2-21ectron CP is nega-
Volume 74. number
1
15 August 1980
CHEMICAL PHYSICS LETTERS
trve, in agreement with Tavard’s prediction [ 123. However, it should be noted that this shift is posnive for smaller K values, i.e. closer to the Is t.hreshoId.
Acknowledgement The authors thank Professor hl. Rouault for his constant mterest m this work, and Mrs. D. Cord& for her help m the preparation of the manuscript.
4. Conclusion On the basrs of the above comparison, we state that the exact bydrogemc calculations of hlendelsohn and Bloch, as well as the Casser-Tavard mode1 account qualitattvely for the shift of the maximum and predict rn the large-K limrt a posirrve shift for the Ne L-shell CP in accordance with the measurements. Tavard’s predrctron also agrees with expenment as to the srgn of the Ne K-shell shift. The MendelsohnBloch calculations for the Ar and Ne L shell coutd profitably be extended to other shells and may then gwe quantltatwe values of the Aft Neither theory gives any Information on the K dependence of the
nor on the asymmetry of the CP. We feel thus mformatlon to be unportant for the detailed description of the complete prolile, particularly in K ranges
defect
where the shape of the profile 1s stabibzed. Hence, in spite of the promlsmg prospects of these theones, more theoretical work IS needed, with an accuracy comparable to that of the present measurements
References Th&e de Doctorat d’Etat, Universi(11 A. Lehman-Bennam. tg de PG.+Sud, Orsay (1978). 121A D Barias, W H.E. Rueckner and H.F. Wellenstein. J. Phys
Bll
(1978) 3381. and C. Tavard,
[31 R A. Bonham
1691. (41 A. Lahman-Bennani, hlag 38B (1978) 95. ISI A. Lahman-Bennam, Chcm. Phys Letters t61 A. Lahman-Bennani.
[71 181 191 1101
J_ Chem. Phys. 59 (1973)
A. DuBuct and hl. Rouault,
Phd.
A. Duguet and H.F. WeBemtein. 60 (1979) 411. A. Duguct, H F. Wellensteiu and hl. Rouault, J Chem. Phys. (19801, to be pubbsbed. W.H E. Rueckner, A.D Barlas and H-F. Wellenstein, Phys Rev. A18 (1978) 895. P. Etsenberger and P U. Phtzmann, Phys. Rev. A2 (1970) 415 T.C. Wang. J S. Lee, H.F WeUenstem and R A. Bonham. Phys Rev A12 (1975) 1846. L.B. Xfendelsohn and 6-l. Bloch, Phys. Rev. AL2 (1975)
551
(111 F Gasser and C. Tavard, Compt.
Rend.
386B (1978) 13. [I31 C Tavard, Seminar on Electron Umversui de hlrtz (Nov. 1978)
Compton
Au&
Sa.
<.“aris~
Scattering,
89
THE
1
COMF-ION
AS OBSERVED Azzeddine
CHEMICAL
IN NEON
DEFECT
and
LETTERS
AND ARGON
USING 25 keV INCIDENT
LAHhIAhl-BENNAN
PHYSICS
ELECTRONS
AIain DUGUET
Laboratowe des Collmons Atomrques et Mol&ulaues assoc6 au CNRS. Unirersitb de Pars-Sud, F 91405 Orsay France Received
17, December
1979.
m final form 13 hlay 1980
Electron energy-loss spectra. obtamrd for Ne and Ar, are analysed tn terms of Compton profiles (CPs). The euperimental CPs do not peak at q = 0, nor are they symmetrtcal as to theu maxImum value, as predlcted withm the framework of the lmpulsc approuunatlon. Thus Yompton defect” IS charactertsed by a shaft parameter w and an asymmetry parameter 69, and IS mvcstlgated as a function of momentum transfer K. A quahtahve comparison IS made with theoretical predicsons for the Compton defect We also emphasize the K range where partial or total K-Independent CPs of the w=et may be detcrmtned
I_ Introduction
units” used in previous pubhcatlons related to this work. The quanhty Jw(q) defined by
It has recently been demonstrated [ 1,2] that hrgh energy electron unpact spectroscopy IS a pow2rful tecbmque m mvestigatmg the vahdlty of the bmary encounter or unpulse approuunahon (IA). In this approxlmatlon, the incident electron interacts with only one electron of the target considered as free, the melastic (or Compton) Intensity scattered mto a fixed duectlon IS then sunply related to the momentum dlstnbutlon p(p) of the target elzctron by
$0 _ 47Tki dmTdQko”’
=
J
dpp p(P),
Iq,
where d?-o/tidQ IS the melastlc differential cross section with respect to scattering angle and energy, ko and kf are respectively the uutlal and final momenta of the projectlle electron, K is the momentum transfer under coibnon, K = ko - k,, p the target electron momentum and 4 a reduced vanable defined by 4 = (215 - K’)/X in the non-relativistic treatment. It should be noted that throughout t&s work we use (1) relatrvistlc expressions, see ref. [3] for the exact relatrons, and (in) Hartree atomic units (1 unit of energy = 2 rydberg) instead of the “rydberg atomic
(2) and to which we shall refer as the impulse approximation Compton profile (IACP), is a function of only one vanable 4, and IS symmetrically centered around q = 0 corresponding to the collision with a stationary electron. However, the experimental Compton profile (CP), J(q, K), as determined through the relation J(q. K) = (koK5/2kf)
d*aldEdS22.
(1) is found to be a function of both variables q and K, and (li) is neither centered on q = 0 nor is it symmetrical as to its maximum value. The above point (h) constitutes the so-called Compton defect. As part of a program pursued by our group to study tl12 fdure of the IA and to understand the mechanism of the colbsion leading to the Compton defect, we have recently reported and discussed results for the NH3 molecule [ 1,4-6]_ In this note we present new measurements of the Compton defect in neon and argon. Rueckner et al. [7J have 85
Volume 74, number
previously
reported
1
CHEMICAL
a smgle data pomt
PHYSlCS
for neon.
2. Experiment The apparatus and experimental techmque have been described m detail elsewhere [ 1,5,6] . A 25 keV, 0.25 mm fwhm electron beam crosses a gaseous target beam of 1 mm diameter. The scattermg mtenslty IS observed m the angular range 0 2” to aZOo, with an acceptance angle of O.Ol” and an angular precislon of 0 003” The scattered electrons are anafysed by means of a 127” electrostatic energy anaiyser, wth ii resolution of 2- 1 S eV i3ver an enerw 10s~ range up to 7500 eV, depending on the scattermg angle tmder invrstigatton. The cahbrstton of the energy loss spectra IS obtained by displaymg the elastic hne across the multlchnnnel analyser wlule the energy of the mcidznt electrons IS vaned by known amounts. This cahbratton IS checked agamst mnershell iontsatlon potent&s of various targets. Eutensave tests have been carrled out [6] m order to reduce the effects of energy resolution, multlple scattenng, nozzle scattering and other extraneous scattenng.
LETTERS
15 August 1980
64, however, can only be defined if the centres of gravrty of the different sectrons are more or less on a smgle stra&t hne. This conditron is not satisfied when the energy loss at the maximum of the CP (ELhtCP) is close to an romsation threshold of the target. A more complete and ngorous representatxon of the asymmetry of the CP IS given in a separate paper
PI-
Figs. la and lb give, as a fun&Ion of momentum transfer K (or scattering angle 8 ), our measurements for neon of the shift M (or b) and the asymmetry parameter 6q, together with some typical error bars representing ihe total estimated uncertmntres. The 22 eV absolute uncert~nty III s shown at large scat-
I”““““““’ NEON-25
he’.‘
-06
3. Results and discussion To charactense the Compton defect for a given momentum transfer K value, two parameters could be used The most “natural” ones are (I) the shrft * (or -1E in the energy scale) of the maximum of the observed profile from the posltion of the maximum of the IACP, i e from 9 = 0 (or from EM = r\;‘/Z), and (11)the asymmetry parameter 6q (or 6.45 in the energy scale) defined [-I] at half the maximum of the CP by the distance between the vertrcal axes going through Its maxunum and the 8x1s of the profde (see f2g. I of ref. [4] )_ This latter BYISis found dividmg the CP into ten parts, each one tenth of the maxunum he&t. then computmg the centre OF gravtty for each sectlon and fmally drawmg a stra&t line through these pomts. Obviously. thus parameterlsatton of the Compton defect is not the only one possible, but it offers two sunple parameters whose variation with momentum transfer can be represented graphically The parameter 86
‘
-02,
0 , 0 r1t.1
, 2
,
, 1
,,,,,,‘,,* I
0 20 so
,
, , ; 6 8 8
200
,111 LOO
,
12 too0
, , , , 10 Klauf
* ‘
@(deg.)
I
2000 EEA [eV)
.16
20
.
s
3GOO
Ftp t The Ne Compton defect as a functron ot momentum transfer R. (a) The shirt &!Z (0). or Aq (+), oi the mawmum of the observed CP from the IACP Also shown IS one data pomt c-1 obtamed by Ruecknrr ct at. 171. (b) The asymmetry parameter 6q (0) The bottom scalcsglve respectwely the scattcrmg ande 0 and the energy loss, ErAI at the mawmum of the IACP. The arro\is mdlcntc the K values where the cncrs> loss at the mawmum of the measured CP 1s equal to the iontsatron energies of the successwe shelis
CHEhfiCAL
Volume 71, number 1
I
lfS
I!
3
4
i ARGON-25 keV
1 I
,
PHYSICS
LETTERS
and 29.3 eV for Ar 3p and 3s energy of the eJected electron the scattering interaction can as taking place during a short
LS AugustE%0
electrons). The kinetic is then so small that no longer be regarded time (as assumed in the
IA iSI)As K increases, the maximum of the CP moves to higher energy losses, and consequently passes through the successive iomsation energies of the electronic orbit& of the target. The K values for which the ELMCP coincides with an ronisation energy are marked by arrows in figs. 1 and 2. Note that arrows cormsponding to the outermost orbit&s (2p of Ne and 3p of Ar) are missrng because the CP cannot reach its
lughest point for the first ionisation energy of the target. Each of those particular
-02
0
2
FIB. 2 Same
L
1s
m fig.
6
8 $5 K fa.u 1
17
1, but for Ar.
tering angles corresponds to a relattve uncertainty of less than 0.15, emphasizing the hrgh precision needed and achreved m thrs work. Fig. la shows also the only other existmg data point for neon, obtamed by Rueckner et al. [7] usmg 25 keV electrons. These authors did not report the asymmetry parameter gq, but their &5 value is m good agreement with ours. Frgs. 2a and 2b show the shrft .&E and the asymmetry parameter 6q as determined for argon. As prevrously observed rn Hz [7], He [5,7] and NH, [5], the Ar and the Ne data are characterised m the range of small K values (K < 2-3 au) by the strong shortcoming of the IA. In neon, the relative defect at K = 1 au is about 200% for AEJEm and about 100% for SEJEm , where Em = K2J2 IS the most probable energy loss as predrcted within the framework of the IA. (Ew is shown rn the bottom scale of fig. 1 ) This shortcoming is due to the fact that the target electron 1s not free as it IS assumed to be m the IA. but has a bmdrng energy EB comparable to EM (EB is equal to 2 1.6 and 48 5 eV for Ne 2p and 2s electrons and 15.8
K values corresponds
to a noticeable increase in AE (or dq), Followed by a more or less rapid decrease_ Plateau regions with almost constant & are reached for neon and argon in the respective K ranges 4 5 au
Volume 74, number 1
CHEMICAL PHYSICS LETTERS
6q in Ne and Ar, occurrmg at about K = 3.5 au and K = 5.5 au, respectively No simple explanation could be found for this result. A particular note here IS concemmg the K range 2.5 to 4 au wl1ere the ELWCP lies between the lorusauon energies of the Ar 3s and 2p shells. While the tift SY 1s almost zero, 6q varies and hence the shape of the experunental CP IS still strongly dependent upon I\‘. Consequently, the partial CP previously defined for N1. Ne and Ar [9] and ior NH3 161, cannot be deduced from the experiment for the argon hl shell. Wong et al. [9 ] , who based themselves on only two measurements at K = 3.1 au and K = 3.8 au, also reported that “the Ar hl shell CP appears still not quite independent of K”. The Ne L shell and the Ar L-plus-M shell may be consIdered as R mdependent, withm the experimental uncertamr1es. m the K ranges 4 5 to 7 au and 6 to 7 5 au, respectrvely. In these ranges (1) both Aq and 6q are almost constant, and (ii) the relative magmtude of the Compton defect as measured by AE/EW and 6E;Ew 1s smaller than 2%. The Ne total CP IS only slightly dependent on K (&Y/EL4 < 1%) for K values larger than 11 au. Thus the detemunatlon of these three expemnental CPs may be meaningfully considered_ The theory of the Compton defect has recently been summarized by Rueckner et al. [7] and by Lahman-Brnnnm et al. [S] . hlendelsohn and Bloch [lo], using ‘*exact” hydrogeruc (EH) bound- and contmuumstat2 wavefunctlons, have calculated neon and argon L-shcil CR for a typical X-ray scattering evperunent corrzspondmg to a momentum transfer of about 9 au. Thrlr results yield a posrt1ve shift (a > 0) for the 3_p6 subshell and a negatwe one for the 2s’ subshell. so that both shifts largely compensate each other, and a very small shift IS left for the L shell. No indlcatlon 1s g1vzn as to the magnrtude and the sign of this Lshell shift. Howlver, for neon. WC find oy comparing with fig. 7 of ref. [lo] that their quoted values of J(q) (versus q appearing in table 1) most hkely were obtain2d from the posltlve q side of then asymmetnc EHCP The L-shell smft for neon can then be ascertam2d within the hm1ts 0 < &I < 0.1 au No sirmlar evaluation could be made for argon, nor was 1t possable to obtam any mformatlon about the asymmetry param2ter 6q Recently, Gasser and Tavard [l l] pr\iposed a cor-
88
15 August 1980
rection to the IA takmg mto account the acceleration effects WI the field of the nucleus wmch act on the target electrons during the collision_ They derived a simple expression for the Compton defect for hydrogemc ns orbitals. In a quahtative extension to this work, Tavard [ 121 predmted, for large K values, negatlve Jq shifts for tts and tzp* hydrogenic orbltals, and positive ones for trpO orbnals. This 1s not in contradlcuon with Mendelsohn and Bloch’s results smce Tavard states that for neon, the 2po correction may be larger than the 2p, corrections. thus leading to a positive shrft for the 2p6 subshell. From the above, we see that only a qualitative comparison with experiment can be made for the sign of &I 1n the high momentum transfer limit The comparison 1s further complicated since figs. 1 and 2 show that tlus limit 1s not completely reached for all cases m the expenment. However, this limit may be considered as sufficrently approached In the plateau regions wth K ranges 4.5-7 au and 6-7.5 au. for the Ne L-shell and the Ar L-plus-hl-shell CR, respectively In these ranges, 1t is possible to estimate the “large R” defect by averaging over the whole experunental data One thus obtains. Ne L sh2U X=(7.6-C
I)eV.
SE = (13.5 + 2) eV,
*
= (0.049
6q = (0.086
+ 0.005)
au.
+ 0 009) au,
Ar L + hl shell ;1E = -(6 6E=-(11.45
3 +- 0.3) eV, l)eV,
Jr7 = -(0.035
-C0.005)
au,
6q = -(0.063
* 0.00-l)
au,
where the quoted uncertamties are the standard dewations from the average values. The Ne L-shell shift IS thus posltlve. m agreement with Mendelsohn and Bloch’s predlctlon [IO] _ No sumlar sm1ple conclusion can be drawn for argon smce (1) the expenment cannot reach the large-K hmit of the &ft of the hi-shell CP. and (u) the theoretical calculations are hmlted to the L shell. For the Ne total CP, it is only possible to fix an upper bound to the large-K hm1t of th2 tift &, & s 0.015 au (or ti s 6 eV), and a lower one to the large-K lunit of the asymmetry parameter 6q, 6q > -0.06 au (or 6E > -25 ev). Subtracting the L-shell contnbutlon aven above, it is then found that the shift rlq (or &) of the ls2-21ectron CP is nega-
Volume 74. number
1
15 August 1980
CHEMICAL PHYSICS LETTERS
trve, in agreement with Tavard’s prediction [ 123. However, it should be noted that this shift is posnive for smaller K values, i.e. closer to the Is t.hreshoId.
Acknowledgement The authors thank Professor hl. Rouault for his constant mterest m this work, and Mrs. D. Cord& for her help m the preparation of the manuscript.
4. Conclusion On the basrs of the above comparison, we state that the exact bydrogemc calculations of hlendelsohn and Bloch, as well as the Casser-Tavard mode1 account qualitattvely for the shift of the maximum and predict rn the large-K limrt a posirrve shift for the Ne L-shell CP in accordance with the measurements. Tavard’s predrctron also agrees with expenment as to the srgn of the Ne K-shell shift. The MendelsohnBloch calculations for the Ar and Ne L shell coutd profitably be extended to other shells and may then gwe quantltatwe values of the Aft Neither theory gives any Information on the K dependence of the
nor on the asymmetry of the CP. We feel thus mformatlon to be unportant for the detailed description of the complete prolile, particularly in K ranges
defect
where the shape of the profile 1s stabibzed. Hence, in spite of the promlsmg prospects of these theones, more theoretical work IS needed, with an accuracy comparable to that of the present measurements
References Th&e de Doctorat d’Etat, Universi(11 A. Lehman-Bennam. tg de PG.+Sud, Orsay (1978). 121A D Barias, W H.E. Rueckner and H.F. Wellenstein. J. Phys
Bll
(1978) 3381. and C. Tavard,
[31 R A. Bonham
1691. (41 A. Lahman-Bennani, hlag 38B (1978) 95. ISI A. Lahman-Bennam, Chcm. Phys Letters t61 A. Lahman-Bennani.
[71 181 191 1101
J_ Chem. Phys. 59 (1973)
A. DuBuct and hl. Rouault,
Phd.
A. Duguet and H.F. WeBemtein. 60 (1979) 411. A. Duguct, H F. Wellensteiu and hl. Rouault, J Chem. Phys. (19801, to be pubbsbed. W.H E. Rueckner, A.D Barlas and H-F. Wellenstein, Phys Rev. A18 (1978) 895. P. Etsenberger and P U. Phtzmann, Phys. Rev. A2 (1970) 415 T.C. Wang. J S. Lee, H.F WeUenstem and R A. Bonham. Phys Rev A12 (1975) 1846. L.B. Xfendelsohn and 6-l. Bloch, Phys. Rev. AL2 (1975)
551
(111 F Gasser and C. Tavard, Compt.
Rend.
386B (1978) 13. [I31 C Tavard, Seminar on Electron Umversui de hlrtz (Nov. 1978)
Compton
Au&
Sa.
<.“aris~
Scattering,
89