Z. Phys. D 28, 207-214 (1993)
ZEITSCHRIFT FORPHYSIKD (~ Springer-Verlag 1993
Electron scattering with H2S and PH 3 molecules Jianmin Yuan, Zhijie Zhang CCAST (World Laboratory), P.O. Box 8730, Beijing 100080, P.R. China, and Department of Applied Physics, National University of Defense Technology, Changsha, Hunan 410073, P.R. China Received: 2 April 1992/Final version: 26 January 1993
Abstract. Calculated total, differential and momentum transfer cross sections are reported for the vibrationalty elastic scattering of electrons from H2S and PH 3 molecules in the range of energy 0.1-50 eV. The scattering process is approximated by two incoherent scatterings caused, separately, by a central field and a tong-range electric dipole interaction. The central field is calculated with a spherical approximate molecular wave function, in which the exchange interaction is treated in two ways: (i) exactly within the accuracy of the molecular wave function; (ii) approximately by a local model potential. The scattering by the central field is calculated with partial wave expansion technique, while the scattering by the electric dipole potential is calculated by using the first Born approximation for a rotating dipole model with experimental values of the dipole moments of H2S and PH 3. The total cross sections are approximated by the incoherent sum of the cross section due to the central potential and the cross section of 00--* 10 rotational transition caused by the electric dipole potential. The effects of the polarization interaction are also tested. The contribution of small-angle scattering to the integral cross section is analyzed for these weakly polar molecules with some quantitative comparison. PACS: 34.80.Bm; 34.80.Gs
I. Introduction Although there are important applications in astrophysics and plasma process for H2S and PH 3 [ 1,2], there have been only a few reported results for the scattering of electrons by these molecules. The experimental results of vibrationaUy elastic as well as inelastic differential cross sections (DCS) of H2S was given by Rohr [3] up to 10 eV. Measurements on absolute total electron scattering cross sections of HzS was made by Szmytkowski and Maciag [4] by using the linear transmission method. The earlier theoretical calculations of this collision process were per-
formed by Gianturco and Thompson [5] and Jain and Thompson [6], and only in [6] were the cross sections reported in the energy range of 0.5-10eV. The calculation of [6] was carried out by using a static potential, a local model exchange potential and a parameter-free polarization potential in the adiabatic-nuclei (AN) formalism. Most recently, Gianturco [7] calculated electron scattering from H2S molecule by using the AN approximation with different exchange and polarization potentials. Electron scattering by H2S at the energies 10-5000 eV was calculated by Jain et al. [8,9] using a local spherical model potential. The molecule PH 3 is employed in plasma processing application [2] and the scattering parameters such as the momentum transfer and excitation cross sections of electron collision with this target are important in plasma modeling, but the only one calculation was carried out by Jain and Baluja [9] from 10 to 5000eV using a spherical complex optical potential (SCOP). Farther theoretical as well as experimental studies are needed for the scattering parameters from low to intermediate energies. In our most recent calculations [10], the cross sections of low-energy scattering with H20 and N H 3 molecules were obtained with a simple approach. Reasonably good agreement was obtained between theory and experiment. In particular, the contribution of the very strong forward scattering near-zero angles to the cross sections was analyzed with quantitative comparison. This paper is an extension of our previous work to molecules with similar molecular structure but with smaller electric dipole moments, H2S and PH 3. Calculated total, differential and momentum transfer cross sections will be reported for HzS and PH 3 in the range of 0.1-50 eV. In practical measurements, the scattered electrons near-zero angles are generally very difficult to distinguish from the incident electron beam. Due to the very strong forward scattering amplitude of polar molecules, the omission of the smallangle scattering is an important source of the uncertainties of measurements on integral cross sections. The contribution of the small-angle scattering to the collision process will also be shown for these two molecules.
208
II. Theory
2.1. Spherical approximation to the molecular ,,ave function We employ the Born-Oppenheimer approximation and make a multipole expansion around the central atoms (S or P) for the coulomb interaction of electrons with nuclei. We have for the Hamiltonian
I___zzu =V
'V2-4- 1 _ ~ . ,
i rl X
- Zi j
rij
(4rcZ u']
la,i
Z
\
I
1
" < ./+1 Z Y/*m(fi) Y/m (l~u) r> m= -I
(1)
where i and/~ run, respectively, over the electrons and nuclei; Z u is the nuclear charge; r i and R u are, respectively, the ith electronic and gth nuclear coordinates centered on the central nucleus. Retaining only the first term in (1), a spherical model Hamiltonian/4o is obtained:
/ ~ o = ~ - ! V~2 +i2 L i
ij
Zu
(2)
r>
where r> is the larger of ri and R u. An argonlike onecenter-expansion (OCE) molecular wave function and electron density are obtained with the model Hamiltonian (2) using the numerical Hartree-Fock (HF) method. Equation (2) does not mean that the spherical part of the nuclear potential or the wave function is truncated inside the sphere of radius Ru. The OCE method is feasible for the special molecular structure like H2S and PH 3 [11]. The expected values of the exact Hamiltonian (1) with the argonlike spherical wave functions are - 398.15 and - 341.64 Hartrees, respectively, for H2S and PH3, which are very close to the values of -397.59 and -341.40 obtained by Moccia [ 11 ] retaining higher terms in the expansion of (1) but using analytic basis functions rather than numerical wave functions. In the most recent calculation of Gianturco [ 7], a total of 75 Slater-type orbitals (STO) centred on the S atom with maximum l of 7 was employed to obtain a total energy of -398.60335 Hartrees for HzS.
2.2. Electron scattering The interaction of the incident electron with the target molecule consists of the interactions with the electrons and nuclei in target. The electron density in molecules and the interaction between the scattered electron and the electrons in molecule are calculated using the spherically approximate molecular wave function obtained in the last subsection. Due to the spherical nature of the approximate molecular wave function, this part of interaction is in central form. A multipole expansion can be made for the coulomb interaction of the incident electron with the nuclei as in
(1). The first term in the expansion is the spherical part, the second and other higher order terms are the electric dipole and other higher order multipole interactions. For a nonpolar molecule, the electric dipole term equal zero; and if the higher order terms are negligible, a spherical model, consisting of the spherically approximated interaction of incident electron with the electrons in target molecule and the spherical part of the multipole expansion of the coulomb interaction with nuclei, works well for electron scattering. CH 4 and Sill4 are examples of such targets [12, 13]. In the present case, the electric dipole term does not equal zero for the polar molecules such as HzS and PH 3. The interactions of the scattering electron with the polar targets are approximated by a spherical part ~, (r) and a electric dipole part Voipole(r), which are written explicitly V(r) = Vs (r) -q- Vdipole(r)
(3)
V~(r)-- ~ t ( r ) + V~,,(r) + Vcp(r )
(4)
r< Vdipole(r) ~-- C ~ . P1 (COS0) r>
(5)
where V~t(r) is the electric static interaction of the scattering electron with electrons in molecule along with the spherical part, i.e. the first term, of the multipole expansion of the coulomb interaction with the nuclei; V~x(r) is the exchange interaction with the electrons in molecule; Vce(r) is the parameter-free correlation-polarization (CP) potential following Padial and Norcross [14] to account for the distortion of the molecule by incident electron. The factor C in the expression of Vaipo~e(r) is chosen so that the potential has the experimental asymptotic value,
I~ Vaipole(r) =
DP (cOs0) r < Ru ,
G
(6) Pa (cos 0)
r>
Ru
where D ( =0.384 a.u. for H2S; 0.228 a.u. for PH3) is the experimental electric dipole moment of the molecules. The dipole potential (6) is finite at r = 0. Any empirical cut-off function, generally used to remove the singularity of the point dipole potential at r = 0, is not needed in (6). The scattering of the electron is calculated separately for the spherical part and the long-range dipole potential as in the separated-atom model. The scattering amplitude for the spherical potential is calculated with partial wave technique, while the cross section associated with the dipole potential is obtained by using the first Born approximation for a rotating dipole. The two cross sections are then added incoherently to give the total cross section. It was shown by Itikawa and Takayanagi [15] for HC1 and by Jain and Thompson [6] for H2S that for the first 00-~ 10 rotational transition the first Born results agree well with Close-Coupling (CC) calculations. Therefore the Born approximation is expected to be adequate for the 00--* 10 rotational excitation of H2S and PH 3. The exchange interaction V~x(r) is treated in two different ways: (i) exactly within the accuracy of the wave
209
function by iterative calculation [10, 12], and as an argonlike OCE molecular wave function is used, the iterative calculation can be done like one does for atomic system; (ii) approximately by using the local free-electron-gas-exchange (FEGE) of Hara [16]. By comparing the results of these two exchange treatments, the effect of localizing the exchange interaction can be tested for the present molecules. The effect of switching-off of the CP potential is also displayed and the results with and without the CP potential are presented. III. Results and discussions
In Fig. 1 the total cross sections and momentum transfer cross sections of e-H2S scattering are plotted with four different sets of data obtained with different treatments of the interaction between scattering electron and target molecule: the first set of results (denoted as SEP) is obtained with static, exact exchange and the CP potential of Padial and Norcross; the second set of data (denoted as SE) is calculated with static and exact exchange but without CP potential; the third set of data (denoted as
~
~ H2S
SHP) is calculated with static, Hara's [16] FEGE model potential and the CP potential; the last set of data (denoted as SH) is obtained as the third one but without CP potential. By comparing the four different kinds of results, the localization for the exchange interaction and the effects of the CP potential on the results can be tested clearly. A few sets of other results are also shown in Fig. 1 for comparison. Actually, except for the scattering caused by the longrange electric dipole interaction, the fixed-nuclei (FN) approximation is used in our calculation of the scattering by the spherical part of the interaction. Due to the divergence of the DCS at near-zero small angles of the electric dipole scattering in FN scheme, a rotating dipole model is used in this part of calculation. For weakly polar molecules (with small electric dipole moment) the Born approximation is reasonably good for the rotational transitions caused by the long-range electric dipole interaction at the energies concerned here. At low energies, the electric dipole potential takes such an important role in the scattering processes that the spherical part of the interaction alone can not be responsible even qualitatively for the observed cross sections. The electric dipole part
H2S
a
10 2
b
10 E F
b z o O Ld 03
1
I U Ill
I
I
J
I llJ
..t [
t
~ I I [ Ill
1
I
I I t tl
[
[ [ ill
[
J _LlJt',i
_
I
[
[
[
i
t ~[
Lf) Of) 0 Q:: 0
H2S
10 2
H2S
3
< I-0
x
B \
I0
o
i
~
J L~,~,
1I
. . . . . . .
110
j
~
~ j l tl0
2
I . . L I ,11
'
'
i
i
i
I \
iiii
lo
~i
t
t i ill
10 2
INCIDENT ELECTRON ENERGY (eV)
Fig. l a - d . Total and momentum transfer cross sections of e-H2S scattering. Thefioe solid lines, from top to bottom, are respectively, the total cross sections without small-angle scattering being neglected; with 0°-1% 0o-5 °, 0°-10 ° small-angle scattering being neglected; and the scattering by the spherical interaction alone. The
dashed lines is the total momentum transfer cross section, a SEP; b SE; c SHP; d SH. Other results of total cross sections: ~ is the experimental data of [4], a is the calculated result of [6], + is the theory of [7], and × is the theory of [9]
210 and the spherical part of the interaction take the action with incoherent combination at the low energies. But at higher energies the spherical part of the interaction can approximate the real interaction adequately. From the well-known relationship between F N and AN model [17], we attribute our present results to be an approximation of the AN total vibrationally elastic cross sections. In the calculation of e-H2S scattering by Jain and Thompson [6] a local FEGE model potential and a polarization potential were used in the OCE-CC formalism. State to state rotational and vibrational transitions were calculated in this work. In the recent calculation of e-H2S scattering by Gianturco [7] the AN approximation was employed with a modified semiclassical exchange (MSCE) potential and a CP potential. Due to the differences in the exchange and polarization potentials, there were quantitative discrepancies between the results of [6] and [7]. The results of e-HzS scattering of [6, 7] exhibited the following features in integral and momentum transfer cross sections: (i) a very strong peak in the very-low energy range where the scattering is dominated by dipole force; (ii) a minimum structure around 1 eV in the momentum transfer cross section of [6]; (iii) a B2 shape resonance state in 2-5 eV; (iv) a very broad hump centered around 10 eV. The features of (i), (ii) and (iv) are reproduced well by the present simple model, but the shape resonance structure in B2 scattering state below 5 eV in their results is not predicted by our calculation. The main reason for this major discrepancy between our and their results might be that for the weakly polar molecules like H2S and PH 3 the electric dipole moments are generally small so that the 0 0 ~ 10 rotational transition scattering (caused mainly by the electric dipole interaction) can not dominate the scattering process at the shape resonance energy, and that the B 2 shape resonance state of e-H2S scattering is mainly caused by the electric dipole interaction along with other higher order interactions and the polarization potential. This important role of the electric dipole interaction in producing the B2 shape resonance state is not taken into account in our calculation, while the spherical part interaction alone is not enough for inducing such an resonance. The action of the electric dipole potential is only considered for the 0 0 ~ 10 rotational transition in our calculation, however as shown in [6] the effects of the B2 shape resonance state are pronounced for the rotationally elastic and 0---,2 excitations but are minor for the 0 0 ~ 10 excitation. Therefore the effects of this B2 shape resonance state can not be reflected in the present rotationally elastic scattering, and the B2 shape resonance peak of total and momentum transfer cross sections in 2-5 eV can not be produced. Generally, the present model will fail for the shape resonance state if it is caused mainly by the electric dipole interaction. But for the shape resonance states not absolutely related to the electric dipole or other higher order multipole interactions, the present model works well. The position and magnitude of the broad resonance peak around 10eV are predicted (SEP:6~7eV, ~50A2; SHP: 8,-~9 eV, ~- 40 A 2) in reasonably good agreement with the theoretical results in [6] and [9] and the experimental result of Szmytkowski and Maciag [4]. At
energies below 1 eV, the collision process is dominated by the 0 0 ~ 10 rotational transition for which the Born approximation works well. In the calculation of Jain and Thompson [6], minimum structures were displayed in the contributions of A1 scattering state both for the rotationally elastic cross sections and for the rotationally summed cross sections. In the result of Gianturco [7] the contribution of A1 scattering state to the rotationally summed cross sections did not go down to a deep minimum. In the present calculation, a Ramsauer-Townsend (RT) type minimum is produced in the scattering by the central part potential; and the combination of this part cross sections with the 0 0 ~ 10 transition cross sections also shows apparent minimum points in both SEP and SHP data sets. Note that the position and value of the minimum structure in momentum transfer cross sections of SEP and SHP models agree reasonable well with those of Jain and Thompson [6]. The influence of localization of the exchange interaction and the switching-off of the CP potential are also examined in Fig. 1. The localization of the exchange interaction does not induce qualitative changes in the cross sections, but does cause considerable quantitative variation below 20 eV particularly in the momentum transfer cross sections. The switching-off of the CP potential causes drastic qualitative changes in the behaviour of the cross sections below 15 eV. The RT type minimum structure in the central potential scattering will not be produced without the CP potential. Note that the present results of SH model agree well with those of Gianturco [7]. At low energies, the collision of electron with polar targets is determined to a certain extent (mainly for the very strong forward scattering) by the first rotational excitation scattering induced mainly by the electric dipole interaction with a very strong forward scattering amplitude. In experiment the very-small-angle scattering is generally very difficult to distinguish from the incident electron beam. From this point of view, at low energies the underestimated small-angle scattering in the experiment might be one important source of the uncertainties of the measurement. A possible source of the discrepancies between the theoretical predictions and the experimental results was analyzed for total cross sections in our previous calculations for H20 and N H 3 [t0] with emphasis on the difference, arising from the inclusion of smallangle scattering in total cross sections, between theory and experiment. In the present case, the molecular structures are similar to those of H20 and N H 3, but the electric dipole moments are much smaller. An analysis for the contribution of the small-angle scattering to the total cross section is also needed, if one wish to take account of the practical experimental condition in a reasonable comparison between theory and experiment. At low energies the small-angle scattering are mainly scattered from higher partial waves, where the Born approximation works well. As the present model is capable of describing the forward scattering at low energies, it is sufficient for the quantitative estimate of how many electrons being scattered into, for an example, the small angles less than I% In Fig. 1 the contributions of the small-angle scattering in
211
range from less than 1% of the total cross section at energies below 20 eV up to 2% at 70 eV impact energy. Therefore, comparisons between theory and experiment should be made with a carefull consideration for smallangle scattering in a very small solid angle in the theoretical results to fit the experimental condition in the collection of the forward scattering. For e-H2S collision process, above 5 eV, at most only a few percent uncertainties can be induced by comparing the theoretical and experimental results directly without concidering the difference between theory and experiment in the inclusion of small-angle scattering for the total cross section. The contribution of the strong forward scattering to the momentum transfer cross sections, which may have more direct significance than the total cross sections in practical appliciation, is not as significant as to the total cross sections. Special attention to small-angle scattering is not required to make a direct comparison between theory and experiment for momentum transfer cross sections. The momentum transfer cross sections of H2S is produced reasonably as shown in Fig. 1a, c compared with the calculation of Jain and Thompson [6] except the shape resonance peak near 3 eV. In Fig. 2 the total (vibrationally elastic) and momentum transfer cross sections are plotted for P H 3. The only previous results of e - P H 3 scattering was calculated by
the angle range of 0°-1% 0°-5 ° and 0°-10 ° (the corresponding solid angles are, respectively, about AO -~ 1 × 10 -3, 2 × 10 -2, and 1 × 10-1) for total cross sections are shown via the difference (dtr) between the results with and without the forward collisions in the above angle range being neglected: at 0.5 eV, dtr of about 21 A 2, 36 A 2, and 43 A 2 of the total cross section are contributed by the scattering in the above angle ranges, which are, respectively, about 30%, 50%, and 60% of the total cross section; at 1 eV, the corresponding A tr are about, respectively, 13 A 2, 20 A 2, and 24 A 2. At 5 eV less than 10% of the scattered electrons are ejected into the angles smaller than 1°. The above data illustrates that at the energies below 5 eV the forward scatterings within a solid angle of i × 10 -3 sr contribute considerable amount to the total collision process, which are comparable with the underestimated small-angle scattering in a practical linear-transmission experiment [4]. In the measurement of Szmytkowski and Maciag [4], the incomplete discrimination for the small-angle scatterings in a solid angle of At2 = 3 × 10-3 sr was compensated qualitatively, but the contribution of the small-angle scattering to the total cross section was underestimated significantly because the DCS used in their estimation (Aa~-DCS(O=O)×AO) was obtained by extrapolating the experimental DCS at finite angles to zero degree. The estimated values of dtr in [4]
1112I~,"
I~
PHs
I
PH5 a
\ \ \
I
I
I I I I I I[
I
I .L. ,L_~L.~.Lt I
I
I
L I I III
U3 U3
~D
10~i\
PH3 d
PH3
} x\
\ \ \
10-'
I
10
10
2
10
"~
I
10
10
2
iNCIDENT ELECTRON ENERGY (eV) Fig. 2. Total and m o m e n t u m transfer cross sections of e-PH 3 scattering. The present results are labeled as in Fig. 1. x is the theoretical result of [9]
212 Table 1. Total cross sections of e-PH~ scattering (in 10-16cm2)
eV
SEP
SE
SHP
SH
0.1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 5.0 6.0 8.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0
125.32 26.46 16.26 18.88 27.90 41.81 56.35 65.92 69.14 65.64 59.67 50.68 44.87 35.96 29.78 25.25 21.84 19.21 17.12 15.44 14.07
106.73 36.18 28.14 27.19 28.24 30.57 34.14 38.78 43.82 51.54 53.60 48.62 41.98 30.53 24.08 19.94 17.04 14.88 13.21 11.88 10.81
99.65 26.49 21.07 22.83 26.18 30.22 34.67 39.19 43.38 49.27 5t .25 48.48 54.65 34.46 28.33 24.06 20.91 18.47 16.53 14.96 13.69
t 17.86 50.44 44.28 42.73 41.58 40.43 39.35 38.44 37.77 37.21 37.37 37.37 35.32 27.69 22.21 18.64 16.11 14.20 12.69 11.47 10.48
Jain and Baluja [9] using a SCOP method in the range of 10-5000 eV. A few points of their results are also shown in Fig. 2. In the overlap region (10-50eV) our results agree well with those o f Jain and Baluja. F r o m the experiences of H2S and our previous results of N H 3 [10], general conclusion can be made for the present result of PH 3. The general behaviour of the energy dependence of the total and momentum transfer cross sections is similar to that of H2S molecule. The effects of the local model of the exchange interaction and the neglect of the CP potential on the result are also shown in Fig. 2. The conclusion about these effects is the same as that for HzS. Because there are not any other results below 10 eV available, it is not clear that in the actual scattering process whether there are other shape resonance states (as in the case of H2S) at lower energies except the present displayed peak near 4 eV. For the convenience of comparison, numerical values of the integral cross section of PH 3 (without small-angle scattering being omitted) are given in Table 1. The forward scattering o f PH 3 at low energies is also significant, but it is not as strong as that of H2S molecule due to the smaller electric dipole moment of PH 3. At 0.5 eV, 9 A 2 of the total cross section is attributed to the small-angle scattering within the solid angle of 1 × 10 -3, which is about 30% of the scattered electrons. While at 2.5 eV only about 7% of the total scattered electrons are ejected into the solid angle of 1 × 10 -3 sr along the incident axis. The amount of the scattering caused by the electric dipole potential at this energy is only about 10% of the total scattering, i.e., the spherical part alone can give a description of the collision process without considerable error in the total and momentum tansfer cross sections. At 2.5 eV, the calculated momentum transfer cross section is 35.95 A z in which only 0.4 A 2 are contributed by the electric dipole scattering. It is concluded that special attention to the small-angle scattering is not needed at the energies o f 0 . t - 5 0 eV if a comparison is
made for the momentum transfer cross section between theory and experiment, but the special attention should be made at the energies below 2.5 eV if a comparison is made for the total cross section, and that the spherical part of the interaction alone can work reasonably well for the total cross section above 2.5 eV and for the momentum transfer cross section above 1.5 eV. The DCS of e-HzS are plotted in Fig. 3 at a few energies from 0.5 to 50 eV. The role of the interactions (electric dipole potential, exchange interaction, and the CP potential etc.) in the collision process can be seen more clearly from DCS. As the four sets of the present results we obtained only differ in the treatment o f exchange and CP potentials in the spherical part interaction, only the total DCS of SEP is given in Fig. 3. The differencies between SEP, SE, and SHP models are shown in that part of DCS due to the spherical potential. At 0.5 eV, the present result is completely dominated by the 0 0 ~ 10 transition. It is also clear that the differences in SEP, SE and SHP models induce drastically qualitative discrepancies between the results of the spherical potential scattering of these models. The DCS o f e-H2S at 0.5 eV was given previously in the experiment of Rohr [3], but the absolute value of Rohr is much higher than our result. At 1 eV, the DCS is mainly determined by the electric dipole scattering below 150° , but the backward scattering of the electric dipole and spherical part interactions are comparable in magnitude. The disagreement between the results with different spherical potential is still significant. The DCS at 1 eV was given by Jain and Thompson [6]. The agreement between our and their results is reasonably good. The contribution of the 0 0 ~ 10 rotational transition to the DCS at 3 eV is only significant at the angles below 60 °, and considerable quantitative discrepancies exist between the results of SEP, SE and SHP. At 5 eV the dipole transition cross section is only significant below 30 °. At 10 eV the contribution of the 00--, 10 excitation cross section to the DCS can be neglected, and the agreement between the results o f SEP, SE and SHP model is improved. At the energies above 10 eV the result of 0 0 4 10 excitation cross section is not shown. The agreement between the results of SEP, SE and SHP is generally good except at the angles below 20 ° where the action of CP potential is important due to its long interaction range. The effect of CP potential is also appreciable for the backward scattering at 25 and 50 eV. Compared with the result of Jain and Thompson [6] and Gianturco [7], at a few plotted energies the minimum well near 120 ° in the DCS curve is produced too deeply due to the lost of the B 2 shape resonance state and the rotational excitation to other higher states. The DCS at 50 eV agree very well with the result of Jain et al. [8]. In Fig. 4 the DCS of e-PH 3 is plotted. Comparisons with other results can not be made. In the calculations of Jain and Baluja [9], only the integral cross sections were reported. The general features of DCS of e-PH3 collision are similar to those of e-H2S discussed in the last paragraph. The action of the electric dipole interaction is weaker than that of H2S. The contribution of the 0 0 ~ 10 transition to the collision process is appreciable at the energies below 2.5 eV, it is needed to be
213
H2S
H2S
E = 0.5eV
H2S
E = 1.0eV
E = 3.0eV
102
~
lO 10
1
10 q
.
oooo
\
,•°•%
10-1 •
10 ,2
10-2
\/ /i
10.3
10 3 i I L ~ I k , [ , ~ L i•l
10-4
H2S
I , i
1
I
co
\ \ \\\ !i"o
i
i I L I 1 i i I I ~ I i I I I E = 15.0eV
loI\
kk\
-~'o1 \
10-I
\
H2S
10.0eV
\
10
10
\\\\\
E=
H2S
\\
I 10-1 10"211
~ li~lBillllllili
10-4
E = 5.0eV
~o b
© b
;/
••,,
",.,
\
104
'\x
",x \
10.2
f
10-2
£3
I
H2S E=20,OeV
H2S
, I i j I ?~l I i L i ~ , I ~ h ! H2S E = 50,0eV
, Ill~l"~ll,lltl E = 25.0 eV
lO
10
10
\
\
1
! e',,,, I
V
10-1 10 1
0
30
60
90
120 150 180
30
60
90
120 150 180
10-1
tl
0
30
I t [l~l
60
~ t]_~llil
90
Fig. 3. The differential cross section (DCS) of e-H2S scattering. The solid line is the DCS of SEP method; the short dashed line is the part of DCS by the electric dipole interaction. The part of DCS due to the spherical potential scattering: the long dashed line is the data of SEP, o is the data of SE, • is the data of SHP
120 150 180
Scattering angle (deg)
considered below 10 ° at 2.5 eV and below 60 ° at 1 eV. The deep wells around 60 ° and 120 ° in the D C S curve are also produced at some o f the plotted energies. In conclusion, a simple model is used in the present calculation. Total, differential and m o m e n t u m transfer cross sections from 0.1 to 50 eV are provided. Although there are considerable discrepancies in D C S between the present and other results at low energies and the model fails for the B 2 shape resonance state o f e-H2S scattering in 2 - 5 eV, the values o f total and m o m e n t u m transfer cross sections are calculated in reasonably good agreement with other available results. From the experiences o f previous calculations for H 2 0 and N H 3 [10], the predictions for DCS, except the too deep minimum points around 120 ° , are generally reliable for the forward and
backward scattering amplitude. The Born approximation is suitable for the small-angle sattering, so application o f the Born approximation to the rotational transition is adequate for one o f the main purpose o f the present calculations - to demonstrate the importance of treating the small-angle scattering to fit the practical experimental condition if a comparison between theory and experiment is made for integral cross sections. Farther results of both theory and experiment o f these molecules are needed for the practical applications and the fundamental researches. This work was supported by the National Natural Science Foundation of China, under Grant. No. 9189012-06.
214 PH3
E = 0.5 eV
PH 3
PH3
E = 1.0 eV
E = 2.5 eV
lO f
10
'.°°°
:~oo OOoo00,3
1
0%
\-..,%..
1
104
!.. i0-2
\
•.
10 3
\
/
7 - ..-"
10-~
10-2
IlllllLllllill~J
PH 3
E = 5.0 eV
PH 3
E=15.0eV
10\
10 to "T O
PH 3
E=10.0eV
lO
\
,S "5
\\
10q E c-,
o \\ \k
II{ll[itI{lttlttl
10 -2
PH3
E = 20.OeV
PH 3
E = 25.0 eV
i0 q ] t i l l PH 3 E = 50.0 eV
10
\ ,
1
\
1 10-1
10-1_
V~~o, /
• .
10 -1
10 "2
/
lllllltltJ~tl[ 30
60
90
120 150 180
30
60
90 120 150 180
0
30
60
Fig. 4. Same caption as in Fig. 3, but for e-PH3 scattering
90 120 150 180
Scattering angle (deg)
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