2 state of In atom at small scattering angles

Nuclear Instruments and Methods in Physics Research B 267 (2009) 279–282

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Electron impact excitation of the 6s 2S1/2 state of In atom at small scattering angles M.S. Rabasovic´ a,*, S.D. Tošic´ a, D. Ševic´ a, V. Pejcˇev a,b, D.M. Filipovic´ a,c, B.P. Marinkovic´ a a b c

Institute of Physics, Pregrevica 118, 11080 Belgrade, Serbia Faculty of Natural Sciences, University of Kragujevac, Radoja Domanovic´a 12, 34000 Kragujevac, Serbia Faculty of Physics, University of Belgrade, P.O. Box 368, 11001 Belgrade, Serbia

a r t i c l e

i n f o

Available online 25 October 2008 PACS: 34.80.Dp Keywords: Differential cross sections Generalized oscillator strength

a b s t r a c t We measured the differential cross sections (DCSs) for the electron-impact excitation of the resonance transition 5p2P1/2–6s2S1/2 of In atom at small scattering angles using a crossed electron–atom beam technique. The incident electron energies were E0 = 10, 20, 40, 60, 80 and 100 eV, while the small scattering angles ranged from 1° to 10° in steps of 1°. The forward scattering function method has been used for normalizing the generalized oscillator strengths (GOS) to the known optical oscillator strength and obtaining the absolute DCS values. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction The results of differential cross sections for excitation processes of indium atom are needed in different applications. Indium is technologically attractive especially in the fields of semi-conductors and optoelectronics. The indium excited spectral lines are of an interest in the plasma spectroscopy and in astrophysical research. The abundance of indium in the solar spectrum was determined by the identification of the resonance line of In at k = 451.13 nm (5p2P3/2 ? 6s2S1/2). That line is one component of the resonance dublet, 5p2P1/2,3/2 ? 6s2S1/2, while the other component at k = 410.1765 nm is positioned in the wing of the strong Balmer Hd line and is not quite recognizable [1]. The indium atom belongs to the metals, its atomic number is 49 and the ionizaion energy IP = 5.7864 eV. That atom has an open shell structure. It is the first of a series of the 5p-elements with a small value of the dipole static polarizability ad ¼ 30:4 a30 [2]. Indium has two stable isotopes 115In and 113In with an abundance of 95.7% and 4.3%, respectively. The 115In+ stored in a radio-frequency trap and laser cooled has been investigated as a possible optical frequency standard with high stability and accuracy. The narrow 5s21S0–5s5p3P0 transition in In+ at a wavelength of 236.5 nm could be used as a reference clock transition [3,4]. We have recently published the paper with measured and calculated results on differential cross sections (DCSs), integral (rel ), momentum-transfer (rm ) and viscosity (rv ) cross sections for elastic electron scattering by indium atom [5]. However, the resonant

excitation is much more pronounced than the elastic DCS. The electron-atom collision cross section is of specific importance due to the possibilities of excitation of optically forbidden states in atoms. To the best of our knowledge, the number of experimental and theoretical data related to electron scattering by indium atom are very limited. So far published investigations have been related to scattering of spin-polarized electrons from indium atom which were unpolarized [6,7]. The experimental investigation [6] covered the influence of the atomic structure of Indium on spin-dependent electron scattering. They concluded that in open-shell indium atom (L = 1) the angular momentum orientation effects, so called ‘fine structure’ effects, dominate over Mott scattering effect (spin–orbit interaction) causing significant polarization (left–right assymetry). Bartschat [7] gave the theoretical confirmation of that by performing the R-matrix (close-coupling) calculations in both approximations, without and with relativistic effects. He concluded that the inclusion of the spin-orbit interaction between electron and indium atom does not change the polarization dramatically. Differential cross sections (DCSs) for resonant transitions in metal atoms are generally very forward peaked. DCSs increase rapidly with decreasing the scattering angle, especially at high impact energies. For higher electron impact energies and the smallest scattering angles, i.e. zero momentum change, the generalized oscillator strengths (GOS) approach to the optical oscillator strength (OOS):

f 0 ¼ lim f ðKÞ; K 2 !0

* Corresponding author. E-mail address: [email protected] (M.S. Rabasovic´). 0168-583X/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2008.10.056

ð1Þ

where the optical oscillator strength (OOS) is denoted as f 0 and f ðKÞ is the generalized oscillator strength (GOS). That conclusion is

M.S. Rabasovic´ et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 279–282

named ‘‘Lassettre limit theorem” and it gives the estimation of the reliability of extrapolated GOS [8]. That fact has been used in many experimental and theoretical approaches for the normalization and evaluation of the reliability of DCSs at small scattering angles. GOS values could be fitted by straight lines with ending on the forward scattering function (FSF) as is described in [9]. For heavy multi-electron atoms Ozimba et al. [10] have introduced the universal extrapolation function which is used for the examination and corrections of other experimentally and theoretically obtained DCSs. The reliability of the measured DCS for resonance transitions in Cd in near-zero scattering angle (presented in [11]) has been estimated by this procedure. The latter theoretical calculations [12,13] have introduced a new approach to fitting procedure for the GOS around K2 = 0. In this work, we derived the FSF curve using the OOS value of 0.125 ± 0.013 given in [14]. That OOS value is in good agreement to the previously measured OOS = 0.12 given with uncertainty less than 20% [15]. In the present paper, we investigated the electron impact excitation of the resonant state 6s2S1/2 and a normalization procedure to obtain the absolute DCS values at small scattering angles. We performed measurements for the electron-impact energies at 10, 20, 40, 60, 80 and 100 eV and at small scattering angles from 1° to 10°. In Section 2, the apparatus and experimental procedure are described. Our results are shown and discussed in Section 3.

2. Experimental techniques and procedures The apparatus used for the present measurements is the same as in our earlier experimental investigations [16,17]. This is a conventional spectrometer (ESMA) with crossed electron-atom beams. A short description of experimental procedure will be given here. The electron beam is emitted from a hairpin cathode, with the current at the end of the hemispherical monochromator of the order of 1–10 nA. The monochromator is fixed and the analyzer can be positioned from 30° to 150° with respect to direction of the electron beam around the atomic beam. The indium vapor beam was produced by heating the oven crucible and effused through a 20 mm long channel in the cap of the oven crucible that has an inner diameter of 2.5 mm, so the aspect ratio was c = 0.125. Working temperature was approximately 1300 K and the metal-vapor pressure was about 10 Pa (0.07 Torr). The spectrometer could be operated in three different modes: energy loss mode, angular distribution mode and incident energy mode. The energy-loss scale was calibrated by measuring the positions of the elastic feature and the excitation threshold of the 6s2S1/2 resonant state of indium at 3.022 eV according the value from Tables given by Moore [18] and NIST. This resonance structure is clearly resolved with an overall system energy resolution (FWHM) of about 180 meV. The impact energy scale was calibrated by recording the resonance at the 3.022 eV. The uncertainty in the impact energy was estimated to be 100 meV. The real zero position was determined before each run by checking the symmetry of the inelastic (excitation of the 2S1/2 state) scattering at positive and negative scattering angles between 10° and +10° around the mechanical zero. The angular resolution of the spectrometer was estimated to be 1.5°. The measured angular distribution of the scattered electrons was converted to relative differential cross sections (DCS) by using the adequate correction factor procedure. The approach of Brinkmann and Trajmar is adopted for our experimental conditions (p = 0.07 Torr and gas kinetic cross section of 12.56 Å2 derived from atomic radius data [19]) to determine the effective path correction factor [20]. So obtained correction factor is consistent with the assumption of molecular flow conditions.

The errors at small scattering angles come from the influence of finite angular and energy resolution, uncertainty of applied volume correction and the normalization to the optical oscillator strength. The statistical errors are calculated at each particular angle as the square root of the number of counts at that angle. The contribution to the error from the angular uncertainty is less than 0.15 and it depends on the slope of the differential cross section. The contribution to the error arising from the uncertainty of the energy scale is estimated to be 0.03 at 1° and is less than 0.07 at 10°. Total errors of DCSs are obtained as the square root of the sum of squared particular errors. 3. Results and discussion We used the theoretical procedure suggested in [13,21] in order to put our experimental relative DCSs on an absolute scale. The formula:

f ðK; E0 Þ ¼

xki 2kf

K2



 dr dX

ð2Þ

  is used for converting the measured relative DCSs ddXr to the generalized oscillator strengths (GOS), where ki and kf are the electron momenta before and after the collision, x is excitation energy given in a.u. (x = 3.022 eV) for resonant transition 5p2P1/2–6s2S1/2 in indium atom), E0 is impact energy and K is the momentum transfer given as follows:

" 2

K ¼ 2E 2 

x E

#

rffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1

x E

cosðhÞ :

ð3Þ

We normalized the relative DCSs by using the FSF method. The theoretical results obtained from the 1s–2p transition of the hydrogen can be used to obtain the forward scattering function (FSF) /ðxÞ for resonant or any other known transition of any element [21]. In our case, we have obtained /ðxÞ curve from the knowledge of the OOS values for both, the 1s–2p transition in hydrogen atom (fHo =0.415) and for the resonant transition of indium atom(fIno =0.125):

10

10

0

-1

GOS

280

10

-2

FSF(φIn (x)) 10eV 20eV 40eV 60eV 80eV 100eV

e/In 2 6s S1/2

ω=3.022eV 10

-3

10

-2

10

-1

K2 (a. u.) Fig. 1. Generalized oscillator strengths (GOS) for the 62S1/2) state of the indium atom versus momentum transfer squared (K2) at 10 (open up triangle), 20 (filled up triangle), 40 (filled down triangle), 60 (open circles), 80 (filled circles) and 100 eV (open squares) electron-impact energies. Stars show the appropriate minimal values of K2 and the solid line represents the forward scattering function (FSF) /ðxÞ generated by using the experimental optical oscillator strength (OOS) value of 0.125 [14].

M.S. Rabasovic´ et al. / Nuclear Instruments and Methods in Physics Research B 267 (2009) 279–282

0:125 / ðxÞ: 0:415 H

ð4Þ

In Fig. 1 we presented the absolute GOS values versus K2 on a log–log graph together with the FSF for the resonant transition 52P1/2–62S1/2 in indium atom. The all impact energies satisfy the necessary condition that the FSF method is applicable for the values E0 P 2.5x [21]. Then, we normalized the measured relative DCSs through the GOSs for all measured impact energies. First, we calculated relative GOS values by the Eq. (1) from the measured relative DCS values. At each impact energy, we calculated the K 2min for zero scattering angle by the Eq. (3). That point lies on the FSF curve and corresponds to the absolute GOS value for zero scattering angle. The absolute GOS values are obtained by normalizing the relative GOS values to the FSF curve. The absolute GOSs rapidly decrease with increasing momentum transfer (see Fig. 1). The minimal values of squared momentum transfer slide down the /In ðxÞ curve as the incident energy decreases, from 0.001704 at 100 eV to 0.019927 at 10 eV. Finally, the normalized-to-relative GOS quotients have been used as normalization factors for putting our relative DCSs on the absolute scale. The present absolute DCSs for the resonant excitation of indium are tabulated in Table 1 and shown in Fig. 2(a) and (b) together with the absolute errors. As one can see from Fig. 2, DCSs decrease from 1° to 10° and the slope of DCSs increase with the increasing incident energy. As seen from Fig. 2(a), DCS at 10 eV is about three times less relating to DCS at 20 eV at all measured angular region. Note also that DCS at 20 eV and 1° is 2.3 times larger, but at 10° is 1.4 times less than the DCS at 40 eV. Fig. 2(b) presents the results of DCSs at other three energies: 60 eV, 80 eV and 100 eV. So, at 100 eV the DCS value at 1° amounts 310.7 m2 sr1, but at 10° DCS reaches the value 1.37 m2 sr1 and that is the largest variation in measured DCS values at small scattering angle range. To compare In with other atoms studied in our laboratory it could be interesting to use the results for Zn [22] and Pb [17]. The similar FSF procedure is used for the normalization of relative experimental DCS values at small scattering angles for Zn atom at all measured impact energies except at 10 eV where the excitation energy for Zn (x = 5.79 eV) does not satisfy the necessary condition E0 P 2.5x. In that work a linear fit of the log(GOS) as a function of log(K2) has been used for the obtaining the absolute GOS values. In the normalization procedure described in [9] it was pointed out that the linear variation of the GOS with K2 is extensive for impact energy values close to the x, but it covers fewer and fewer scattering angles as energy increases. In our recent published paper for Pb atom [17] it can be seen that the shape of the GOS values is similar to our results for In atom. For both of these atoms we used nonlinear fit instead of the linear one. This is supported by the relativistic distorted wave calculations [17]. The GOS values for Pb decrease fastly with the increase of the impact en-

a 10

10

2

10eV 20eV 40eV

1

e/In

DCS (10-20m2sr-1)

/In ðxÞ ¼

281

6s 2S1/2 ω=3.022eV 10

0

b 10

10

2

60eV 80eV 100eV

1

e/In 6s 2S1/2 ω=3.022eV 10

0

0

1

2

3

4

5

6

7

8

9

10

11

Scattering Angle (deg.) Fig. 2. Differential cross sections for excitation of the resonant 6s2S1/2 state of the indium atom at: (a) 10 eV, 20 eV and 40 eV; (b) 60 eV, 80 eV and 100 eV electronimpact energies and at small scattering angles (in units of 1020 m2 sr–1). The experimental results at all energies are presented with error bars. Notations are the same as in Fig. 1.

ergy, while in the case of indium the GOS values show the maxima around 3° and tend to decrease both at smaller and larger scattering angles. 4. Conclusion We have obtained absolute values for generalized oscillator strengths and differential cross-sections for the excitation from

Table 1 Differential cross sections in units of 1020 m2 sr1, for electron excitation of the 62S1/2 state of the indium atom. The numbers in parentheses are the absolute errors. Angle (deg)

Electron energy (eV) 10

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10

13.9(1.8) 12.5(1.6) 10.9(1.4) 9.2(1.2) 7.59(1.01) 6.10(0.83) 4.80(0.66) 3.73(0.52) 2.90(0.40) 2.32(0.35)

47.0(6.0) 41.0(5.2) 34.7 (4.5) 28.7(3.7) 23.0(3.0) 18.0(2.4) 13.7(1.9) 10.3(1.5) 7.7(1.1) 5.88(0.85)

109(14) 86.8(11.5) 65.4(9.0) 46.8(6.7) 32.2(4.8) 21.4(3.2) 13.9(2.2) 9.0(1.4) 5.98(0.91) 4.20(0.64)

155(20) 117(17) 80(12) 51.5(8.0) 32.2(5.1) 20.0(3.2) 12.5(2.0) 8.0(1.3) 5.14(0.82) 3.29(0.56)

233(31) 169(25) 108(18) 62(11) 33.5(6.2) 17.5(3.3) 9.10(1.70) 4.88(0.92) 2.80(0.50) 1.88(0.32)

310(41) 217(34) 124(23) 62(12) 29.0(6.0) 13.6(2.8) 6.74(1.27) 3.64(0.64) 2.17(0.37) 1.37(0.24)

282

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the ground 5p2P1/2 to the 6s2S1/2 state of indium atom in the intermediate electron energy range from 10 to 100 eV, at small scattering angles up to 10°. All impact energies satisfy the necessary condition given by Emin ¼ 2:5x which is needed for the applicability of given normalization procedure. So far as we know, there are no other available experimental data until our present measurements. Our future work will be concentrated to the larger scattering angles of the resonance state that would be a challenging task due to low signal intensities. Acknowledgement This work has been carried out within Project 141011 financed by Ministry of Science and Technology of Republic of Serbia. References [1] N. Vitas, I. Vince, M. Lugaro, O. Andriyenko, M. Gosic, R.J. Rutten, Mon. Not. R. Astron. Soc. 384 (2008) 370. [2] T.M. Miller, B. Bederson, in: D.R. Bates, B. Bederson (Eds.), Advances in Atomic and Molecular Physics, Vol. 13, Academic, New York, 1977, p. 1. [3] J.A. Sherman, W. Trimble, S. Metz, W. Nagourney, N. Fortson, arxiv:/ arXiv:physics/0504013.

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