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Absolute differential and total cross sections for N+ formation from the interaction of N2+ with He and Ar
Nuclear Instruments and Methods in Physics Research B 241 (2005) 459–464 www.elsevier.com/locate/nimb
Absolute differential and total cross sections for N+ formation from the interaction of Nþ 2 with He and Ar H. Martı´nez a, B.E. Fuentes a
b,*
Centro de Ciencias Fı´sicas, UNAM, Apartado Postal 48-3, 62251 Cuernavaca, Morelos, Me´xico b Facultad de Ciencias, UNAM, 04510 Me´xico, D.F. Available online 19 August 2005
Abstract Differential and total cross sections for the production of N+ fragment formed by the collision of Nþ 2 on He and Ar, at projectile energies between 1.0 and 5.0 keV and for scattering angles from 4 to 4 are reported. The replotting of the angular distributions in terms of the scaled variable V0h2 as a function of (1/V0)(dr/dX), indicates the same scaling law is followed in all the study. The reduced differential cross sections show an overall increase of at least one order of magnitude and a monotonic decreasing behavior at all the collision energies studied in this work. The cross sections for þ ˚2 the Nþ 2 –He system are found to be in the range of 0.85–1.60 A , while for the N2 –Ar system are between 2.40 and ˚ 2. Both measured total cross sections for N+ formation display a slowly increasing behavior as a function of 3.90 A the incident energy. The absolute cross sections for DE (rDE) and DI (rDI) were estimated. Both cross sections for the He and Ar targets show the same behavior, with those for the Ar target slightly higher than those for the He target, while the DE process for both targets is a factor of 1.86 higher than that for DI. The measurements reported here are not found in the literature and the increasing availability of the data on these systems may stimulate work in this direction. 2005 Elsevier B.V. All rights reserved. PACS: 34.50.s; 34.70.+e Keywords: Nþ 2 ; Collision induced dissociation; Differential cross sections; Total cross section; Fragmentation mechanism
1. Introduction
*
Corresponding author. E-mail addresses: hm@fis.unam.mx, [email protected]. unam.mx (B.E. Fuentes).
The increasing interest in fields such as astrophysics, atmospheric science and material sciences has given an important impulse to the study of low energy processes. Among them we have charge
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.07.056
460
H. Martı´nez, B.E. Fuentes / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 459–464
transfer [1,2], ionization and fragmentation of small molecules [3], dissociative photoionization [4] and charge polarization [5]. Theoretical investigations have been also done, presenting a challenge to deal with multi-electron systems [6–8]. Experimentally, the cross sections for electroncapture processes by low energy ions from a neutral gas and their variation with the ion energy have been reported [9–13], many of them confined to inert and hydrogen gases. The difference in the cross section values primarily depends on the relative transition probabilities to different electronic states of molecular incident ions, and the ionization energy of the target which can well be described with the dominant mechanics of the near resonant charge exchange, including vertical transitions. In this work we report differential and total cross sections for the production of N+ fragment formed by the collision of Nþ 2 on He and Ar, at projectile energies between 1.0 and 5.0 keV and for scattering angles from 4 to 4. The measurements reported here are not found in the literature and the increasing availability of the data on these systems may stimulate work in this direction.
2. Experiment Details of the experimental arrangement have been given previously [14,15], so only a brief description will be given here. Nþ 2 ions were formed in an arc discharge source containing N2 gas (99.99% purity) at ion source pressures of 0.04–0.07 mTorr. Ions were extracted and accelerated in the energy range of 1.0 to 5.0 keV. The Nþ 2 beam was passed through an Einzel-type lens and directed to a Wien velocity filter in order to obtain an analyzed beam at the desired velocity. Next, the Nþ 2 ions were passed between cylindrical electrostatic deflection plates that were used both to steer the beam and to bend it by 10 to prevent photons in the ion source from reaching the detection system. Following that, the collimated Nþ 2 beam entered the scattering chamber, which housed a gas target cell where dissociative capture phenomena to form N+ took place. The gas target cell was a 2.54 cm long cylinder with 2.54 cm in diameter in which the target gas pressure (typically 0.4 mTorr)
was measured with a calibrated MKS capacitance manometer (model 270C). The entrance aperture was 1 mm in diameter and the exit aperture was 2 mm wide and 6 mm long. This geometry permitted the measurements of the N+ particles, the directions of which make an angle of up to ±7 with respect to the incoming beam direction. Path lengths and apertures gave an overall angular resolution of the system of 0.1. All apertures and slits have knife edges. The cell target was located at the center of a rotatable, computer-controlled vacuum chamber that moved the whole detector assembly, which was located 47 cm away from the target cell. A precision stepping motor ensured a high repeatability in the positioning of the chamber over a large series of measurements. The detector assembly consisted of a Harrower-type parallel plate analyzer with a 0.36 mm entrance aperture and two channel-electron multipliers (CEM) attached to its exit ends. The beam entered the uniform electric field of the analyzer at an angle of 45. Separation of charged particles occurred inside the analyzer, which was set to detect the N+ ions with the lateral CEM. The multiplier counting efficiencies for N+ were assumed to be the same as for H+ at the same energy [16]. A retractable Faraday cup was located 33 cm away from the target cell, allowing the measurement of the incoming Nþ 2 ion-beam current. A Keithley Instruments Electrometer model 610C was used to measure the beam current entering the Faraday cup. Vacuum base pressures in the system were 2.0 · 107 Torr without gas in the cell and 1.0 · 106 Torr with gas. Thin target conditions were used in this experiment. The differential cross sections for the formation of N+ were evaluated from the measured quantities by the expression dr IðhÞ ¼ ; dX nLI 0
ð1Þ
where I0 is the number of Nþ 2 ions incident per second on the target; n is the number of target atoms per unit volume; L is the length of the scattering chamber, and I(h) is the number of N+ particles per unit solid angle per second detected at a laboratory angle h with respect to the incident beam direction. The total cross section for the production
H. Martı´nez, B.E. Fuentes / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 459–464
-1
Care was taken when the absolute differential cross section was measured. The reported value of the angular distribution was obtained by measuring it with and without gas in the target cell with the same steady beam. Then point-to-point substraction of both angular distribution was carried out to eliminate the counting rate due to neutralization or dissociation of the Nþ 2 beam on the slits and the counts arising from background distributions. The Nþ 2 beam intensity was measured before and after each angular scan. Measurements not agreeing to within 5% were discarded. Angular distributions were measured on both sides of the forward direction to assure they were symmetric. The estimated RMS error is 15%, while the cross sections were reproducible to within 10% from day to day. Several runs were made at different gas pressures and dr/dX was determined for each run. The values were compared in order to estimate the reproducibility of the experimental results, as well as to determine the limits of the Ôsingle-collision regimeÕ since the differential and total cross sections reported are absolute. In the present work changes were not observed in the absolute values with respect to the different ion source conditions. Also, no variation in the distributions were detected over a target pressure range of 0.2–0.6 mTorr.
and h is the angle between the observed fragment and the incident beam direction. It has been shown [17] that for any fragment arising from a velocityindependent process such as electronic excitation, the left side of Eq. (3) is a universal function of V0h2. A peak in the angular distribution for a fragment can be interpreted [17] as due to a singularity in the Jacobian of the transformation. The dissociation energy can be determined from the location of the peak W = V0h2. The measured angular distributions plotted in terms of the scaled variables (reduced differential cross section) V0h2 and (1/V0)(dr/dX) are shown in Figs. 1 and 2 for He and Ar as targets, respectively. It can be seen that they follow the same scaling law. For He as a target two poorly defined humps around 2.5 and 10 eV are observed, while for the case of Ar as a target only one poor defined hump around 8.0 eV is observed. Also, the reduced differential cross sections for Ar as a target are about 2.4 times higher in magnitude than when He was used as a target. The decreasing behavior of (1/V0)(dr/dX) is almost of 2 orders of magnitude for the He target when V0h2 goes from 0 to 5.0 eV. While for Ar as a target this decreasing behavior is less than 2 orders of magnitude in the same range of V0h2. Then it is reasonable to interpret our results by stating that over this energy range, the same processes are taking place.
(1/V0)dσ/dΩ (A - sr - keV )
of the N+ particles was obtained by the integration of dr/dX over all measured angles; that is Z hmax dr sinðhÞ dh. ð2Þ r ¼ 2p dX 0
-1
3. Results and discussion
To gain more insight on the collision processes and to derive information on features of the molecular interaction involved, the angular distribution were analyzed by the relation ð1=V 0 Þðdr=dXÞ ¼ f ðV 0 h2 Þ;
+
5.0 keV 4.0 KeV 3.0 keV 2.0 keV 1.0 keV
+
N2 + He -> N 2
10
2
3.1. Angular distributions
461
1
ð3Þ
which represents a scaling law that relates the angular distributions for different incident energies V0; dr/dX is the absolute differential cross section
10
0
5
10
15
W (eV)
Fig. 1. Reduced differential cross sections for the formation of N+ ions coming from the collision of Nþ 2 ion on He.
H. Martı´nez, B.E. Fuentes / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 459–464
462
probability for the production of the N+ fragment when He is used as a target. Considering the collision systems used in this work, we note that there are at least four reactions which might result in the interaction
3
5.0 keV 4.0 keV 3.0 keV 2.0 keV 1.0 keV
-1
(1/V0)dσ/dΩ (A -sr -keV )
10
+
+
2
-1
N2 + Ar -> N
þ 0 þ Nþ 2 þ ðHe or ArÞ !N2 þ ðHe or Ar Þ
2
10
0
ð5Þ
þ
þ
ð6Þ
N þ N þ ðHe or ArÞ N þ N þ e þ ðHe or ArÞ N
1
10
0
5
10
15
W ( eV )
Fig. 2. Reduced differential cross sections for the formation of N+ ions coming from the collision of Nþ 2 ion on Ar.
3.2. Total cross sections
σ (A2)
The absolute total cross sections obtained by integration of the differential cross sections for the He and Ar targets are shown in Fig. 3. The total cross sections for both targets have the same tendency but, on average, the cross section for the He target is a factor of 2.24 lower than that for the Ar target. This fact is indicative of a weaker
+
+
N2 + He -> N +
0
+
N2 + Ar -> N
10
1
2
3 E ( keV )
4
5
Fig. 3. Absolute total cross sections for the formation of N+ ions coming from the collision of Nþ 2 ion on He and Ar.
ð4Þ
þ
2þ
0
þ N þ e þ ðHe or ArÞ; ð7Þ
which represent electron capture (EC), dissociative excitation (DE), dissociative ionization (DI) and single ionization (SI), respectively. For the molecular ions incident on He (or Ar) at low velocities, EC (Eq. (4)) is the dominant loss mechanism, analogous to the case of an incident atomic beam. On the other hand, DE (Eq. (5)) or DI (Eq. (6)) require an interaction with the tightly bound target core electrons in order to obtain the necessary energy transfer (>8.7 eV for DE and >23.3 eV for DI). It is reasonable, therefore, to suppose that for Nþ 2 molecular ions, DE and DI become important mechanisms for N+ formation. The fact that the total cross section dependence on the incident energy has different shapes, suggests that N+ arises from different excitation energy levels; it also reveals the influence of the target. It is interesting to note that the interpretation is based on electronic excitation phenomena. Since the ion source used in this work is of electron bombardment ionization, the vibrational distribution of the Nþ 2 ions is somewhat uncertain. Henri et al. [18] have estimated this distribution using the appropriate Franck–Condon factors and the electronic state distribution computed by Moran and Friedman [19]. Henri et al. estimated a vibrational distribution for Nþ 2 ðm) prepared by electron bombardment as 77% for m = 0; 14% for m = 1; 5% for m = 2; and 4% for higher levels. We have assumed that the Nþ 2 ions produced in our source have the same distribution. We derived the branching ratio from the ratio of the total cross section for the N+ production þ (Fig. 3) by Nþ 2 on He to that for N2 on Ar. From this derivation we found that rAr/rHe goes from 2.8 at 1.0 keV to 1.95 at 5.0 keV. We can infer that the cross section for the production of N+ is larger
H. Martı´nez, B.E. Fuentes / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 459–464
rDE ¼ 1.86; rDI
ð8Þ
which is consistent with the results of the electron impact dissociation and ionization of Nþ 2 obtained by Bahati et al. [21]. These authors found that the ratio of rDE and rDI goes from 1.57 to 2 in the energy range of 990 and 2499 eV. Given the fact that for all the energies studied in this work the distributions follow the same scaling law, this ratio has the same value. Therefore, the absolute cross section for DE (rDE) and DI (rDI) can be obtained by taking into account this ratio in the total cross section. The cross sections for DE and DI leading to N+ in He and Ar are shown in Fig. 4. Both cross sections for the He and Ar targets show the same behavior, with slightly higher values for Ar. While for both targets, the DE process is a factor of 1.86 higher than the DI. In conclusion, we have examined the collisional dissociation of Nþ 2 molecular ions in He and Ar. The absolute differential and total cross sections for the N+ formation at energies between 1.0 and 5.0 keV are reported. Replotting the angular distributions in terms of the scaled variables V0h2 as a
2.5
2.0
σ ( A 2)
þ for the Nþ 2 þ Ar system than for the N2 þ He system, and this ratio has a decreasing behavior as the incident energy increases. The total cross section measured in the present experiment is the sum of the cross sections of the DE and DI processes. Kaneyasu et al. [20] show that the position domains of product ions on the position-sensitive-detector for each fragmentation slightly shift to larger angle and large energy directions as the total charge (p + q) increases; p and q are final charge states of the fragment ions (that is N2 ! Np+ + Nq+). This implies that each related fragmentation process is originated in different angular regions. In Figs. 1 and 2 we can see two different contributions, which are more evident for the Nþ 2 þ He system. One of these regions is between 0 and approximately 6.0 eV, and the other between 6.0 and 16 eV (for both systems). Taking into account the experimental evidence of Kaneyasu et al. [20] DE and DI can be associated respectively to these regions. We evaluated the ratio rDE/rDI and found that for both systems
463
1.5
1.0
0.5 1
2
3
4
5
E (keV)
Fig. 4. Absolute total cross sections for DE and DI in collision of Nþ 2 ion on He and Ar. (j), rDI for He target; (d), rDE for He target; (m), rDI for Ar target; (), rDE for Ar target.
function of (1/V0)(dr/dX), it can be seen that they follow the same scaling law. This was interpreted as having the same processes over the energy range studied. The cross sections for the Nþ 2 –He system ˚ 2, while are found to be in the range of 0.85–1.60 A þ for the N2 –Ar system they are between 2.40 and ˚ 2. Both measured total cross sections for 3.90 A + N formation display a slowly increasing behavior as a function of the incident energy. The absolute cross sections for DE (rDE) and DI (rDI) were estimated. Both cross sections for both targets show the same behavior, with those for Ar slightly higher than those for He. The DE process is a factor of 1.86 higher than that for DI for both targets. The measurements reported here are not found in the literature and the increasing availability of the data on these systems may stimulate work in this direction.
Acknowledgments The authors wish to thank A. Gonza´lez, A. Bustos and Jose´ Rangel for their technical assistance and F. Castillo for useful discussions. This research was sponsored by DGAPA IN-109103-3 and CONACyT 41072-F.
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H. Martı´nez, B.E. Fuentes / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 459–464
References [1] A.T. Hasan, T.J. Gray, Int. J. Mol. Sci. 4 (2003) 284. [2] Z. Fang, V.H.S. Kwong, Phys. Rev. A 55 (1997) 440. [3] M. Ehrich, B. Siegmann, U. Werner, H. Lebius, Radiat. Phys. Chem. 68 (2003) 127. [4] C. Nicolas, A. Alcaraz, R. Thissen, M. Vervloet, O. Dutuit, J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 2239. [5] M. Ehrich, U. Werner, H.O. Lutz, Phys. Rev. A 65 (2002) 030702(R). [6] R.E. Olson, A. Salop, Phys. Rev. A 14 (1976) 579. [7] D.T. Grozdanov, R.K. Janev, Phys. Rev. A 17 (1978) 880. [8] R. Mann, F. Flokmann, H.F. Beyer, J. Phys. B 14 (1981) 1161. [9] D.R. Sieglaff, B.G. Lindsay, K.A. Smith, R.F. Stebbings, Phys. Rev. A 59 (1998) 3538. [10] W.S. Melo, M.M. SantÕAnna, A.C.F. Santos, G.M. Sigaud, E.C. Montenegro, Phys. Rev. A 60 (1999) 1124. [11] J.P. Beijers, R. Hoekstra, R.J. Morgenstern, J. Phys. B 29 (1996) 1397.
[12] P.G. Reyes, F. Castillo, H. Martı´nez, J. Phys. B 34 (2001) 1485. [13] F.W. Bliek, R. Hoekstra, R.J. Morgenstern, Phys. Rev. A 57 (1998) 221. [14] H. Martı´nez, Phys. Rev. A 63 (2001) 042702. [15] H. Martı´nez, F. Castillo, P.G. Reyes, Int. J. Mass Spectrom. 218 (2002) 161. [16] D.A. Crandall, J.A. Ray, C. Cisneros, Rev. Sci. Instr. 46 (1995) 562. [17] C. Cisneros, I. Alvarez, C.F. Barnett, J.A. Ray, A. Russek, Phys. Rev: A 14 (1976) 88. [18] G. Henri, M. Lavollee, O. Dozenne, P.M. Guyon, E.A. Gislason, J. Chem. Phys. 88 (1988) 6381. [19] T.F. Moran, L. Friedman, J. Chem. Phys. 42 (1965) 2391. [20] T. Kaneyasu, T. Azuma, M. Ehrich, M. Yoshino, K. Okuno, Nucl. Instr. and Meth. B 205 (2003) 624. [21] E.M. Bahati, J.J. Jureta, D.S. Belic, H. Cherkani-Hassani, M.O. Abdellahi, P. Defrance, J. Phys. B: At. Mol. Opt. Phys. 34 (2001) 2963.
Absolute differential and total cross sections for N+ formation from the interaction of Nþ 2 with He and Ar H. Martı´nez a, B.E. Fuentes a
b,*
Centro de Ciencias Fı´sicas, UNAM, Apartado Postal 48-3, 62251 Cuernavaca, Morelos, Me´xico b Facultad de Ciencias, UNAM, 04510 Me´xico, D.F. Available online 19 August 2005
Abstract Differential and total cross sections for the production of N+ fragment formed by the collision of Nþ 2 on He and Ar, at projectile energies between 1.0 and 5.0 keV and for scattering angles from 4 to 4 are reported. The replotting of the angular distributions in terms of the scaled variable V0h2 as a function of (1/V0)(dr/dX), indicates the same scaling law is followed in all the study. The reduced differential cross sections show an overall increase of at least one order of magnitude and a monotonic decreasing behavior at all the collision energies studied in this work. The cross sections for þ ˚2 the Nþ 2 –He system are found to be in the range of 0.85–1.60 A , while for the N2 –Ar system are between 2.40 and ˚ 2. Both measured total cross sections for N+ formation display a slowly increasing behavior as a function of 3.90 A the incident energy. The absolute cross sections for DE (rDE) and DI (rDI) were estimated. Both cross sections for the He and Ar targets show the same behavior, with those for the Ar target slightly higher than those for the He target, while the DE process for both targets is a factor of 1.86 higher than that for DI. The measurements reported here are not found in the literature and the increasing availability of the data on these systems may stimulate work in this direction. 2005 Elsevier B.V. All rights reserved. PACS: 34.50.s; 34.70.+e Keywords: Nþ 2 ; Collision induced dissociation; Differential cross sections; Total cross section; Fragmentation mechanism
1. Introduction
*
Corresponding author. E-mail addresses: hm@fis.unam.mx, [email protected]. unam.mx (B.E. Fuentes).
The increasing interest in fields such as astrophysics, atmospheric science and material sciences has given an important impulse to the study of low energy processes. Among them we have charge
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.07.056
460
H. Martı´nez, B.E. Fuentes / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 459–464
transfer [1,2], ionization and fragmentation of small molecules [3], dissociative photoionization [4] and charge polarization [5]. Theoretical investigations have been also done, presenting a challenge to deal with multi-electron systems [6–8]. Experimentally, the cross sections for electroncapture processes by low energy ions from a neutral gas and their variation with the ion energy have been reported [9–13], many of them confined to inert and hydrogen gases. The difference in the cross section values primarily depends on the relative transition probabilities to different electronic states of molecular incident ions, and the ionization energy of the target which can well be described with the dominant mechanics of the near resonant charge exchange, including vertical transitions. In this work we report differential and total cross sections for the production of N+ fragment formed by the collision of Nþ 2 on He and Ar, at projectile energies between 1.0 and 5.0 keV and for scattering angles from 4 to 4. The measurements reported here are not found in the literature and the increasing availability of the data on these systems may stimulate work in this direction.
2. Experiment Details of the experimental arrangement have been given previously [14,15], so only a brief description will be given here. Nþ 2 ions were formed in an arc discharge source containing N2 gas (99.99% purity) at ion source pressures of 0.04–0.07 mTorr. Ions were extracted and accelerated in the energy range of 1.0 to 5.0 keV. The Nþ 2 beam was passed through an Einzel-type lens and directed to a Wien velocity filter in order to obtain an analyzed beam at the desired velocity. Next, the Nþ 2 ions were passed between cylindrical electrostatic deflection plates that were used both to steer the beam and to bend it by 10 to prevent photons in the ion source from reaching the detection system. Following that, the collimated Nþ 2 beam entered the scattering chamber, which housed a gas target cell where dissociative capture phenomena to form N+ took place. The gas target cell was a 2.54 cm long cylinder with 2.54 cm in diameter in which the target gas pressure (typically 0.4 mTorr)
was measured with a calibrated MKS capacitance manometer (model 270C). The entrance aperture was 1 mm in diameter and the exit aperture was 2 mm wide and 6 mm long. This geometry permitted the measurements of the N+ particles, the directions of which make an angle of up to ±7 with respect to the incoming beam direction. Path lengths and apertures gave an overall angular resolution of the system of 0.1. All apertures and slits have knife edges. The cell target was located at the center of a rotatable, computer-controlled vacuum chamber that moved the whole detector assembly, which was located 47 cm away from the target cell. A precision stepping motor ensured a high repeatability in the positioning of the chamber over a large series of measurements. The detector assembly consisted of a Harrower-type parallel plate analyzer with a 0.36 mm entrance aperture and two channel-electron multipliers (CEM) attached to its exit ends. The beam entered the uniform electric field of the analyzer at an angle of 45. Separation of charged particles occurred inside the analyzer, which was set to detect the N+ ions with the lateral CEM. The multiplier counting efficiencies for N+ were assumed to be the same as for H+ at the same energy [16]. A retractable Faraday cup was located 33 cm away from the target cell, allowing the measurement of the incoming Nþ 2 ion-beam current. A Keithley Instruments Electrometer model 610C was used to measure the beam current entering the Faraday cup. Vacuum base pressures in the system were 2.0 · 107 Torr without gas in the cell and 1.0 · 106 Torr with gas. Thin target conditions were used in this experiment. The differential cross sections for the formation of N+ were evaluated from the measured quantities by the expression dr IðhÞ ¼ ; dX nLI 0
ð1Þ
where I0 is the number of Nþ 2 ions incident per second on the target; n is the number of target atoms per unit volume; L is the length of the scattering chamber, and I(h) is the number of N+ particles per unit solid angle per second detected at a laboratory angle h with respect to the incident beam direction. The total cross section for the production
H. Martı´nez, B.E. Fuentes / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 459–464
-1
Care was taken when the absolute differential cross section was measured. The reported value of the angular distribution was obtained by measuring it with and without gas in the target cell with the same steady beam. Then point-to-point substraction of both angular distribution was carried out to eliminate the counting rate due to neutralization or dissociation of the Nþ 2 beam on the slits and the counts arising from background distributions. The Nþ 2 beam intensity was measured before and after each angular scan. Measurements not agreeing to within 5% were discarded. Angular distributions were measured on both sides of the forward direction to assure they were symmetric. The estimated RMS error is 15%, while the cross sections were reproducible to within 10% from day to day. Several runs were made at different gas pressures and dr/dX was determined for each run. The values were compared in order to estimate the reproducibility of the experimental results, as well as to determine the limits of the Ôsingle-collision regimeÕ since the differential and total cross sections reported are absolute. In the present work changes were not observed in the absolute values with respect to the different ion source conditions. Also, no variation in the distributions were detected over a target pressure range of 0.2–0.6 mTorr.
and h is the angle between the observed fragment and the incident beam direction. It has been shown [17] that for any fragment arising from a velocityindependent process such as electronic excitation, the left side of Eq. (3) is a universal function of V0h2. A peak in the angular distribution for a fragment can be interpreted [17] as due to a singularity in the Jacobian of the transformation. The dissociation energy can be determined from the location of the peak W = V0h2. The measured angular distributions plotted in terms of the scaled variables (reduced differential cross section) V0h2 and (1/V0)(dr/dX) are shown in Figs. 1 and 2 for He and Ar as targets, respectively. It can be seen that they follow the same scaling law. For He as a target two poorly defined humps around 2.5 and 10 eV are observed, while for the case of Ar as a target only one poor defined hump around 8.0 eV is observed. Also, the reduced differential cross sections for Ar as a target are about 2.4 times higher in magnitude than when He was used as a target. The decreasing behavior of (1/V0)(dr/dX) is almost of 2 orders of magnitude for the He target when V0h2 goes from 0 to 5.0 eV. While for Ar as a target this decreasing behavior is less than 2 orders of magnitude in the same range of V0h2. Then it is reasonable to interpret our results by stating that over this energy range, the same processes are taking place.
(1/V0)dσ/dΩ (A - sr - keV )
of the N+ particles was obtained by the integration of dr/dX over all measured angles; that is Z hmax dr sinðhÞ dh. ð2Þ r ¼ 2p dX 0
-1
3. Results and discussion
To gain more insight on the collision processes and to derive information on features of the molecular interaction involved, the angular distribution were analyzed by the relation ð1=V 0 Þðdr=dXÞ ¼ f ðV 0 h2 Þ;
+
5.0 keV 4.0 KeV 3.0 keV 2.0 keV 1.0 keV
+
N2 + He -> N 2
10
2
3.1. Angular distributions
461
1
ð3Þ
which represents a scaling law that relates the angular distributions for different incident energies V0; dr/dX is the absolute differential cross section
10
0
5
10
15
W (eV)
Fig. 1. Reduced differential cross sections for the formation of N+ ions coming from the collision of Nþ 2 ion on He.
H. Martı´nez, B.E. Fuentes / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 459–464
462
probability for the production of the N+ fragment when He is used as a target. Considering the collision systems used in this work, we note that there are at least four reactions which might result in the interaction
3
5.0 keV 4.0 keV 3.0 keV 2.0 keV 1.0 keV
-1
(1/V0)dσ/dΩ (A -sr -keV )
10
+
+
2
-1
N2 + Ar -> N
þ 0 þ Nþ 2 þ ðHe or ArÞ !N2 þ ðHe or Ar Þ
2
10
0
ð5Þ
þ
þ
ð6Þ
N þ N þ ðHe or ArÞ N þ N þ e þ ðHe or ArÞ N
1
10
0
5
10
15
W ( eV )
Fig. 2. Reduced differential cross sections for the formation of N+ ions coming from the collision of Nþ 2 ion on Ar.
3.2. Total cross sections
σ (A2)
The absolute total cross sections obtained by integration of the differential cross sections for the He and Ar targets are shown in Fig. 3. The total cross sections for both targets have the same tendency but, on average, the cross section for the He target is a factor of 2.24 lower than that for the Ar target. This fact is indicative of a weaker
+
+
N2 + He -> N +
0
+
N2 + Ar -> N
10
1
2
3 E ( keV )
4
5
Fig. 3. Absolute total cross sections for the formation of N+ ions coming from the collision of Nþ 2 ion on He and Ar.
ð4Þ
þ
2þ
0
þ N þ e þ ðHe or ArÞ; ð7Þ
which represent electron capture (EC), dissociative excitation (DE), dissociative ionization (DI) and single ionization (SI), respectively. For the molecular ions incident on He (or Ar) at low velocities, EC (Eq. (4)) is the dominant loss mechanism, analogous to the case of an incident atomic beam. On the other hand, DE (Eq. (5)) or DI (Eq. (6)) require an interaction with the tightly bound target core electrons in order to obtain the necessary energy transfer (>8.7 eV for DE and >23.3 eV for DI). It is reasonable, therefore, to suppose that for Nþ 2 molecular ions, DE and DI become important mechanisms for N+ formation. The fact that the total cross section dependence on the incident energy has different shapes, suggests that N+ arises from different excitation energy levels; it also reveals the influence of the target. It is interesting to note that the interpretation is based on electronic excitation phenomena. Since the ion source used in this work is of electron bombardment ionization, the vibrational distribution of the Nþ 2 ions is somewhat uncertain. Henri et al. [18] have estimated this distribution using the appropriate Franck–Condon factors and the electronic state distribution computed by Moran and Friedman [19]. Henri et al. estimated a vibrational distribution for Nþ 2 ðm) prepared by electron bombardment as 77% for m = 0; 14% for m = 1; 5% for m = 2; and 4% for higher levels. We have assumed that the Nþ 2 ions produced in our source have the same distribution. We derived the branching ratio from the ratio of the total cross section for the N+ production þ (Fig. 3) by Nþ 2 on He to that for N2 on Ar. From this derivation we found that rAr/rHe goes from 2.8 at 1.0 keV to 1.95 at 5.0 keV. We can infer that the cross section for the production of N+ is larger
H. Martı´nez, B.E. Fuentes / Nucl. Instr. and Meth. in Phys. Res. B 241 (2005) 459–464
rDE ¼ 1.86; rDI
ð8Þ
which is consistent with the results of the electron impact dissociation and ionization of Nþ 2 obtained by Bahati et al. [21]. These authors found that the ratio of rDE and rDI goes from 1.57 to 2 in the energy range of 990 and 2499 eV. Given the fact that for all the energies studied in this work the distributions follow the same scaling law, this ratio has the same value. Therefore, the absolute cross section for DE (rDE) and DI (rDI) can be obtained by taking into account this ratio in the total cross section. The cross sections for DE and DI leading to N+ in He and Ar are shown in Fig. 4. Both cross sections for the He and Ar targets show the same behavior, with slightly higher values for Ar. While for both targets, the DE process is a factor of 1.86 higher than the DI. In conclusion, we have examined the collisional dissociation of Nþ 2 molecular ions in He and Ar. The absolute differential and total cross sections for the N+ formation at energies between 1.0 and 5.0 keV are reported. Replotting the angular distributions in terms of the scaled variables V0h2 as a
2.5
2.0
σ ( A 2)
þ for the Nþ 2 þ Ar system than for the N2 þ He system, and this ratio has a decreasing behavior as the incident energy increases. The total cross section measured in the present experiment is the sum of the cross sections of the DE and DI processes. Kaneyasu et al. [20] show that the position domains of product ions on the position-sensitive-detector for each fragmentation slightly shift to larger angle and large energy directions as the total charge (p + q) increases; p and q are final charge states of the fragment ions (that is N2 ! Np+ + Nq+). This implies that each related fragmentation process is originated in different angular regions. In Figs. 1 and 2 we can see two different contributions, which are more evident for the Nþ 2 þ He system. One of these regions is between 0 and approximately 6.0 eV, and the other between 6.0 and 16 eV (for both systems). Taking into account the experimental evidence of Kaneyasu et al. [20] DE and DI can be associated respectively to these regions. We evaluated the ratio rDE/rDI and found that for both systems
463
1.5
1.0
0.5 1
2
3
4
5
E (keV)
Fig. 4. Absolute total cross sections for DE and DI in collision of Nþ 2 ion on He and Ar. (j), rDI for He target; (d), rDE for He target; (m), rDI for Ar target; (), rDE for Ar target.
function of (1/V0)(dr/dX), it can be seen that they follow the same scaling law. This was interpreted as having the same processes over the energy range studied. The cross sections for the Nþ 2 –He system ˚ 2, while are found to be in the range of 0.85–1.60 A þ for the N2 –Ar system they are between 2.40 and ˚ 2. Both measured total cross sections for 3.90 A + N formation display a slowly increasing behavior as a function of the incident energy. The absolute cross sections for DE (rDE) and DI (rDI) were estimated. Both cross sections for both targets show the same behavior, with those for Ar slightly higher than those for He. The DE process is a factor of 1.86 higher than that for DI for both targets. The measurements reported here are not found in the literature and the increasing availability of the data on these systems may stimulate work in this direction.
Acknowledgments The authors wish to thank A. Gonza´lez, A. Bustos and Jose´ Rangel for their technical assistance and F. Castillo for useful discussions. This research was sponsored by DGAPA IN-109103-3 and CONACyT 41072-F.
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