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The “Foil-Mesh” method for measuring mean lifetimes of long-lived molecular ions
Nuclear Instruments and Methods in Physics Research B 160 (2000) 182±189
www.elsevier.nl/locate/nimb
The ``Foil-Mesh'' method for measuring mean lifetimes of long-lived molecular ions A. Bar-David a, I. Ben-Itzhak b
b,*
, J.P. Bouhnik a, I. Gertner a, Y. Levy a, B. Rosner
a
a Department of Physics, Technion, Haifa 32000, Israel J.R. Macdonald laboratory, Department of Physics, Kansas State University, 116 Cardwell Hall, Manhattan, KS 66506-2601, USA
Received 21 May 1999; received in revised form 19 July 1999
Abstract A method for measuring the mean lifetime of molecular ions undergoing unimolecular dissociation is presented. It can be used to measure molecular ions even if the beam has a large impurity fraction in it, as demonstrated by a measurement of the mean lifetime of 4 He20 Ne2 . Furthermore, this method is not limited to mean lifetimes comparable to the ¯ight time of the ions through the experimental setup as other commonly used methods. It can be used to measure mean lifetimes up to about two orders of magnitude longer than the ¯ight time, as demonstrated using 12 CD2 2 and 3 He40 Ar2 as examples. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 34.50.Gb; 36.90.+f; 34.50.ÿs Keywords: Foil-Mesh method; Molecular ions; Lifetime
1. Introduction The measurement of mean lifetimes of longlived molecular ions provides important information about the decay mechanism, and in many cases helps identify the long-lived state of the molecular ion under study. Many long-lived molecular ions have been studied, but here we focus our attention on doubly charged ions. Mean lifetime measurements have been performed for several doubly charged molecular ions, such as *
Corresponding author. Tel.: +1-785-532-6786; fax: +1-785532-6806. E-mail address: [email protected] (I. Ben-Itzhak)
HeH2 [1,2], NeAr2 [3], HeNe2 [4,5], and CO2 [6±10]. Most of these measurements were conducted using single pass experimental setups where the mean lifetime was comparable to the ¯ight time through the system. Storage devices like rings [10] and electrostatic bottles [11] enable one to measure mean lifetimes over many orders of magnitude taking advantage of the long storage time of the ions in the device, thus extending its eective length. For example, a few mean lifetimes of CO2 from tens of ls to ms were measured using a storage ring [10]. This is in contrast to mean lifetime measurements of CO2 below 1 ls, where only a narrow range of lifetimes has been measured [6±9]. This range is determined by the
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 5 8 2 - 0
A. Bar-David et al. / Nucl. Instr. and Meth. in Phys. Res. B 160 (2000) 182±189
``size'' of the experimental setup, i.e., the ¯ight time of the ions from formation to detection. Even though a wide range of lifetimes can be measured using a storage ring, it has its limitations. 1. Lifetimes can only be measured if they are longer than the stabilization time in the ring, typically a few tens of ls. 2. Many long-lived molecular ions are produced in very small amounts, a few per second, thus making their storage impractical. We have been involved in the last few years in mean lifetime measurements over a relatively wide range of times from 1 to 500 ns. This range was accessed by using experimental setups in which the ¯ight time was of the same order of magnitude as the measured mean lifetime. In Section 2 we present a method for measuring an eective mean lifetime which is longer than the ¯ight time of the ions through the setup by up to two orders of magnitude. Furthermore, using this method mean lifetimes can be measured in spite of a large fraction of beam impurities. We used the 4 He20 Ne2 dication to present the method and a couple of other examples to show that the measured mean lifetimes extend well beyond their ¯ight time through the setup. We use HeNe to denote the most common 4 He20 Ne isotope hereafter. In Section 3 we discuss the advantages and limitations of the new experimental method and some aspects of our results about the measured molecular ions.
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electrostatic de¯ector according to their energy to charge ratio, E=q. A voltage of 14.79 kV directed the doubly charged HeNe2 ions toward a photo diode detector located 824 mm downstream from the target cell at a de¯ection angle of about 7:4 , which was set using a rotatable arm (see Fig. 1, Ref. [12]). Another similar detector, placed on the beam axis, was used for normalization by monitoring the yield of neutral He fragments, thus assuring normalization to the beam current independent of the ¯ux of impurity ions in the beam. The detectors used, produce a signal proportional to the energy of the particle hitting them. The He signal is clearly distinguishable from the other peaks in the energy spectrum, as shown in Fig. 1. This is an important requirement of the new method for measuring mean lifetimes as will become clear later. The ``peak'' labeled full energy (FE) contains the HeNe2 molecular ions which survive all the way to the detector, events where
2. Experimental The doubly charged HeNe2 molecular ions were produced by charge-stripping of HeNe in fast collisions with Ar atoms in a similar way as described in our previous publications [4]. Brie¯y, the HeNe molecular ions produced in the rf ion source of the Technion 1-MV Van de Graa accelerator were accelerated to 750 keV and then directed by a 15 analyzing magnet toward the target cell where the charge-stripping reactions took place. The pressure in the dierentially pumped target cell was typically 1±5 mTorr, while the pressure in the rest of the system was kept below 2 10ÿ6 Torr. The reaction products emerging from the target cell were analyzed by an
Fig. 1. The energy spectrum when the detector is placed on the HeNe2 trajectory. (a) With a mesh and foil in front of the detector, and (b) with the mesh only. The energy spectrum in (a) is shifted to lower energies due to energy loss in the foil (see text).
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A. Bar-David et al. / Nucl. Instr. and Meth. in Phys. Res. B 160 (2000) 182±189
both He and Ne fragments of the same molecular ion are detected, the Ne fragments which are only partly resolved, and any beam impurity which has the full energy of the beam. The main impurities competing with the HeNe2 molecular ion of interest are the doubly charged C2 2 dimers and the simultaneous detection of two C fragments pro duced in C 2 Ar ! C C reactions (both with 12 the C isotope). An ``eective'' mean lifetime can be determined, assuming a single exponential decay, from the fraction of molecular ions that dissociated in ¯ight after passing the electrostatic de¯ector. In the case of a pure beam of the molecular ions of interest one can distinguish the fragment pairs from the molecular ions, for example, by using their dierent transmission through a mesh with a known transmission [12±15]. Unfortunately, this is not the case for many ``exotic'' molecular ions, and the number of molecular ions is not given by the number of ``full energy'' counts because the beam has a high level of contamination (the 4 He20 Ne2 was only 18% of the yield of doubly charged ions produced in the collisions under study). To overcome this diculty, we take advantage of our ability to detect and distinguish one fragment of the dissociating molecular ion, i.e., the He fragment in our example, and the fact that the He fragments are solely associated with the HeNe2 molecular ions of interest. This fact was used in previous measurements of the mean lifetimes of some HeNe2 isotopes [4,5]. The four dierent geometries of the experimental setup needed to conduct the mean lifetime measurements are presented schematically in Fig. 2. The narrow slit setup, shown in Fig. 2(a), is used to obtain a detailed angular distribution of the particles emerging from the de¯ector. A thin foil is placed in front of the detector to dissociate all the molecular ions before impinging on the detector, as shown in Fig. 2(b) and (c). In Fig. 2(c) and (d) we show the setups with a large acceptance angle and a mesh of transmission T placed in front of the detector. The number of analyzed HeNe2 is measured ®rst, relative to a certain number of He neutral fragments. This is done by placing a thin foil on the trajectory of these ions as shown in Fig. 2(c). It
Fig. 2. A schematic view of the experimental setup with (a) a narrow slit, (b) a narrow slit and a thin foil, (c) a large acceptance angle and both a thin foil and a mesh in front of the detector, and (d) a large acceptance angle and a mesh in front of the detector (see text).
is important to note that in addition to fragmenting the molecular ions, this foil causes signi®cant broadening of the tightly collimated beam due to multiple scattering. Thus, a large solid angle for detection must be used. A scan of the multiple scattering cone was conducted ®rst with a narrow slit on the detector, as shown in Fig. 2(b), to ensure that no signi®cant fraction of the He fragments misses the detector. Then, a 9 9 mm open area detector placed about 30 mm behind the thin carbon foil 10 lg=cm2 , as shown in Fig. 2(c), was used for the measurements described below. Note that breaking up the molecular ions is not sucient to observe the He fragments because once we have ensured that all fragments hit the detector, they will do so in pairs producing a full
A. Bar-David et al. / Nucl. Instr. and Meth. in Phys. Res. B 160 (2000) 182±189
energy signal, thus nullifying the whole purpose of the foil. This ``problem'' was used to verify that all He and Ne fragments of the HeNe2 molecular ion hit the detector after passing the carbon foil while using a wide open detector (9 9 mm aperture), i.e., no counts with the He fragment energy were detected. Now, to overcome this problem and measure the yield of the HeNe2 fragments, a ®ne mesh with 30% transmission, was placed in front of the detector, as shown in Fig. 2(c). The mesh transmission is determined from the ratio of the normalized yields, of the ions of interest, measured with and without the mesh (typically the open area fraction of the mesh). With this mesh in place, events where the Ne fragment was stopped appear as He counts in the energy spectrum (note, that these counts are unique and indicate the breakup of a HeNe2 ). The number of He fragments detected is given by Nfoil He T 1 ÿ T N0 HeNe2 ;
1
where N0 [HeNe2 is the number of HeNe2 molecular ions which passed the de¯ector exit. Events where either the He was stopped or both went through the mesh contributed to the ``full-energy'' counts (which in this case include the Ne fragments, HeNe2 , and impurities) Nfoil FE T 1 ÿ T N0 HeNe2 T 2 N0 HeNe2 2 T 2 N C2 2 T N C C
TN0 HeNe2 T 2 N C2 2 T 2 N C C ;
2
where the Ne fragments are included in the full energy peak in order to simplify the data analysis. It is possible to use a peak ®tting routine and resolve the fragments from the true full energy signals. However, the error introduced by this ®tting procedure is large, especially for the measurements with the foil. Furthermore, there is no gain from such separation because the modi®ed equations (2) and (5) lead to similar results. Note, that these equations are based on the assumption that the transmission probabilities of the two fragments of a molecular ion are independent of
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each other, which is valid if the average distance between them is much larger than the mesh unit cell. (For detailed discussions about using transmission meshes for this purpose see Refs. [12± 16].) This condition is ful®lled in our setup. Now, from Eqs. (1) and (2), the fraction of HeNe2 molecular ions out of the doubly charged ion yield is given by N0 HeNe2 N0 HeNe N C2 2 N C C TNfoil He : 3 1 ÿ T Nfoil FE ÿ Nfoil He
F HeNe2
2
Note that the fraction above is evaluated from the ratio of two peaks in the energy spectrum measured with the foil, and thus the normalization detector plays no role in these measurements. This internal normalization improves the precision of the measurements by removing the eect of instabilities in the yield of neutral fragments [12,16]. The fraction of HeNe2 out of the yield of doubly charged molecular ions produced, given by Eq. (3), varies from day to day, due to the dierent conditions mostly in the rf ion source. It was 17:9 3:5% during the measurements reported here, and fortunately, even though not constant, it varied only slightly after the beam was tuned. Once the yield of HeNe2 molecular ions produced in HeNe Ar collisions was determined, the yield of HeNe2 ions dissociating spontaneously (i.e., without the foil) was measured. The spot size due to unimolecular dissociation is smaller than the one with the foil. This was veri®ed by an angular scan with a narrow slit and without the foil, as shown in Fig. 2(a). Note that using a narrow slit limits the chances that both the He and Ne fragments are detected simultaneously. The acceptance angle of the detector, as shown in Fig. 2(d) is large enough so that all He and Ne fragments can hit the detector. Thus, the mesh is still needed for the same reason as before, i.e., in order to detect some of the events as counts of He fragments. The number of He counts measured without the foil is given by N He T 1 ÿ T N He Ne;
4
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where N He Ne denotes the number of HeNe2 molecular ions which dissociated between the exit of the de¯ector and the mesh (a small correction is needed due to those that dissociate very close to the mesh [12]; this correction, however, is very small in this case and is neglected for simplicity). Under the same conditions (shown in Fig. 2(d), i.e., no foil and with the mesh), the counts with full energy N FE include, as before, the Ne fragments, HeNe2 molecular ions, and the beam impurities, N FE TN0 HeNe2 TN C2 2 T 2 N C C :
5
Using Eqs. (4) and (1), properly normalized to the same number of neutral He fragments, the fraction of HeNe2 which dissociated in ¯ight after the de¯ector is evaluated to be R
N He Ne N He : N0 HeNe2 Nfoil He
6
Note, that the ratio above is independent of the exact transmission of the mesh, thus improving the accuracy of this method (see Ref. [12]). The ``effective'' mean lifetime of HeNe2 is then given by (assuming a single exponential decay), s
ÿx=v ; ln1 ÿ R
7
where x 503 mm is the distance from the de¯ector exit to the mesh, v 2:437 mm/ns is the beam velocity, and R is evaluated from the measurements with and without the foil using Eq. (6). The number of He counts measured with and without the foil are evaluated by ®tting a Gaussian and an exponential tail to the energy spectrum, as shown in Fig. 1. This is needed because the He peak is on the tail of the much larger C peak. Now that the method for measuring the mean lifetime of spontaneous dissociation has been described, it is important to point out that this dissociation can also be induced by collisions of the molecular ions of interest with the atoms or molecules of the residual gas. To separate these two dissociation mechanisms one has to measure the dissociation fraction, R, given in Eq. (6), as a function of the residual gas pressure, and use the
value of this ratio extrapolated to zero pressure. This measurement also allows the determination of the ``collision-induced dissociation'' cross-section. For HeNe2 the collision-induced dissociation was negligible in comparison with the relatively fast spontaneous decay rate [4]. In contrast, this was found to be an important correction in the measurement of the mean lifetime of CD2 2 [17] and the dominant decay mechanism of 3 He40 Ar2 [18]. 3. Results and discussion Using the new method described in the previous section we have measured the mean lifetime of the most abundant isotope of HeNe2 to be 126 34 ns. The error in this measurement was estimated as the standard deviation of 10 measurements. This value is in reasonable agreement with our previous measurement of 184 32 ns performed using the masked detector method [4,12]. Though the reported errors in both measurements are comparable, the new experimental method has a few advantages. First it is inherently more accurate because the main systematic error in the previous method is removed. In the masked detector method, used previously, there is a need to block the spot in which the surviving doubly charged molecular ions hit the detector. This introduces an uncertainty in the fraction of ion-pairs one can detect, i.e., how much less than half the events are measured [12]. The nice agreement between the new measurement and the previous one suggests that this factor was estimated reasonably well in the past, but it is better to avoid such problems altogether. The error in the new method in contrast is dominated by statistical errors, and thus the precision can be improved when needed beyond the one reported here. Second, in the new method the surviving molecular ions are also measured, and not only the dissociating ones as in the masked detector method. This is important when one tries to compare the measured mean lifetime to theoretically predicted ones (see discussion in Ref. [5]). Following the previous measurements [4,5] it was not clear whether states with much longer mean lifetimes are populated in the collision, because the surviving molecular ions
A. Bar-David et al. / Nucl. Instr. and Meth. in Phys. Res. B 160 (2000) 182±189
were not detected. The new results, in contrast, indicate that the population of such states is negligible. The result of the measurements reported here is in good agreement with the calculated mean lifetimes of a few possible states of 4 He20 Ne2 , explicitly the C 1 P v 8; 9, D 1 R v 9, d 3 P v 5; 6, E 1 R v 11; 12, and G 1 R v 7; 8 [5]. Note that the measurement reported here was performed for a single distance between the detector and de¯ector. Future measurements for which this distance will be varied might narrow down the number of possible states. Calculations of the most likely population of vibrational states of this isotope in vertical transitions from the parent HeNe might accomplish the same goal. Last but not the least, the new method is much simpler to apply than the previous method. Both methods allow one to measure an eective mean lifetime in spite of the large impurity of other doubly charged ions. The fraction of HeNe2 was less than half of the yield of doubly charged ions. The new method is also superior to the mesh method [12], because it does not depend on the exact knowledge of the mesh transmission, which is a main source of uncertainty in the mesh method. Furthermore, the mesh method cannot be applied when the full energy peak contains a large fraction of impurity ions. The new method, however, is limited to cases where one of the fragments of the molecular ion of interest can be uniquely identi®ed in the energy spectrum. The higher sensitivity and accuracy of the new method enables measurements of smaller fractions of unimolecular dissociation, thus extending the range of mean lifetimes well beyond the time of ¯ight of the ions of interest through the experimental setup. We have used this method recently 1:3 to measure the mean lifetime of CD2 2 to be 4:01:1 ls, about 25 times longer than its ¯ight time from the de¯ector exit to the detector [17]. This example shows that the method can be applied to polyatomic molecular ions as well. Another example is the measurement of the mean lifetime of 3 He40 Ar2 , for which only a lower limit of about 40 ls was determined [18]. This value is approximately 150 times longer than the ¯ight time of this molecular ion through the experimental setup. This limit could be further
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extended if the residual gas pressure in the apparatus were reduced below 10ÿ6 Torr. This could improve the limiting factor which is collision-induced dissociation of the HeAr2 molecular ions. The analysis of the data depends strongly on the identity of the impurities competing with the molecular ion of interest. In the case of 3 He40 Ar2 the competing impurity was 43 Ca2 . Under these conditions the full energy peak, which includes the Ar fragments, the HeAr2 or its fragments detected simultaneously, and the 43 Ca2 impurity, yields 43
N FE T fN0 HeAr2 N Ca2 g;
8
whether it is measured with or without the foil. The number of counts in the He peak measured with or without the foil are still given by Eqs. (1) and (4), respectively. The fraction of HeAr2 molecular ion in the beam is given by F HeAr2
N0 HeAr2
N0 HeAr2 N 43 Ca2 Nfoil He : 1 ÿ T Nfoil FE
9
The fraction of HeAr2 dissociating in ¯ight between the de¯ector exit and the mesh can be calculated using Eq. (6), after proper normalization of the measurements with and without the foil to the same number of neutral He fragments. However, this fraction can also be calculated by normalizing each measurement to the respective number of counts in the full energy peak. Dividing the measured ratio without the foil (i.e., Eq. (4) divided by Eq. (8)) by the ratio measured with the foil (i.e., Eq. (1) divided by Eq. (8)) yields N He Ar=fN0 HeAr2 N 43 Ca2 g 43
N0 HeAr2 =fN0 HeAr2 N Ca2 g N He=T 1 ÿ T = N FE=T : Nfoil He=T 1 ÿ T = Nfoil FE=T
10
From the equation above the fraction of molecular ions dissociating in ¯ight is evaluated to be R
N He Ar N He=N FE : 2 N N0 HeAr foil He=Nfoil FE
11
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This fraction of dissociating molecular ions is independent of the exact value of the mesh transmission as were the measurements normalized to the neutral fragments discussed previously. The mean lifetime is then calculated using Eq. (7) as was discussed before. Note that any instabilities in the neutral fragment rate which aect the normalization have no impact on such measurements. Instead, we have assumed that the fraction of HeAr2 in the beam given by Eq. (9) is not changing signi®cantly between the two measurements, with and without the foil. The HeAr2 beam fraction was stable to about 3% during the whole run [18]. It has been our experience that this internal normalization is more stable for our measurements then normalizing to the neutral fragments. 4. Summary A new method for measuring mean lifetimes of long-lived molecular ions is presented. It is based on the measurement of the yield of one molecular fragment which is solely associated with the molecular ion of interest. Two measurements are performed with and without a foil, used to induce the dissociation of all molecular ions. The measurement without the foil provides the number of molecular ions undergoing unimolecular dissociation, while the measurement with the foil is used to determine the yield of molecular ions which passed the de¯ector, i.e., N0 . An eective mean lifetime is evaluated from the normalized ratio of the two measurements. This method was applied to the 4 He20 Ne2 dication and the measured mean lifetime was determined to be 126 34 ns. This value is in agreement with a previous measurement, but has a higher accuracy because some systematic errors associated with the previous measurement were removed. Furthermore, this measurement indicates that in this collision the population of states with mean lifetimes much longer than the measured value is negligible. We have measured a 2 mean lifetime of 4:01:3 1:1 ls for CD2 , which is about 25 times longer than its ¯ight time through our apparatus. We have also determined that the mean lifetime of 3 He40 Ar2 is longer than 40 ls,
more than 150 times longer than its ¯ight time through the setup. This experimental technique is especially useful when the yield of the molecular ions of interest is small in comparison with competing beam impurities. Acknowledgements We wish to thank Prof. Kevin D. Carnes for helpful comments. This work was supported in part by the Technion V.P.R fund, the David and Miriam Mondry research fund and in part by the Division of Chemical Sciences, Oce of Basic Energy Sciences, Oce of Science, US Department of Energy.
References [1] I. Ben-Itzhak, Z. Chen, B.D. Esry, I. Gertner, O. Heber, C.D. Lin, B. Rosner, Phys. Rev. A 49 (1994) 1774. [2] I. Ben-Itzhak, J.P. Bouhnik, I. Gertner, O. Heber, B. Rosner, Nucl. Instr. and Meth. 99 (1995) 127. [3] I. Ben-Itzhak, I. Gertner, B. Rosner, Phys. Rev. A 47 (1993) 289. [4] I. Ben-Itzhak, I. Gertner, O. Heber, B. Rosner, Chem. Phys. Lett. 212 (1993) 467. [5] I. Ben-Itzhak, J.P. Bouhnik, Z. Chen, I. Gertner, C. Heinemann, W. Koch, C.D. Lin, B. Rosner, Phys. Rev. A 56 (1997) 1268. [6] C.P. Safvan, D. Mathur, J. Phys. B 26 (1993) L793. [7] T.A. Field, J.H.D. Eland, Chem. Phys. Lett. 211 (1993) 436. [8] M. Lundqvist, P. Baltzer, D. Edvardsson, L. Karlsson, B. Wannberg, Phys. Rev. Lett. 75 (1995) 1058. [9] F. Penent, R.I. Hall, R. Panajotovic, J.H.D. Eland, G. Chaplier, P. Lablanquie, Phys. Rev. Lett. 81 (1998) 3619. [10] L.H. Andersen, J.H. Postumus, O. Vahtras, H. Argen, N. Elander, A. Nunez, A. Scrinzi, M. Natiello, M. Larsson, Phys. Rev. Lett. 71 (1993) 1812. [11] A. Wolf, K.G. Bhushan, I. Ben-Itzhak, N. Altstein, D. Zajfman, O. Heber, M.L. Rappaport, Phys. Rev. A 59 (1999) 267. [12] I. Gertner, B. Rosner, I. Ben-Itzhak, Nucl. Instr. and Meth. B 94 (1994) 47. [13] O. Heber, I. Ben-Itzhak, I. Gertner, A. Mann, B. Rosner, J. Phys. B. 18 (1985) L201. [14] K.H. Berkner, T.J. Morgan, R.V. Pyle, J.W. Steams, in: J. Kistemaker (Ed.), Proceedings of the 17th International Conference on the Physics of Atomic Collisions, Amsterdam 1971, Abstracts, North-Holland, Amsterdam, 1971, p. 422.
A. Bar-David et al. / Nucl. Instr. and Meth. in Phys. Res. B 160 (2000) 182±189 [15] T.J. Morgan, K.H. Berkner, R.V. Pyle, Phys. Rev. Lett. 26 (1971) 602. [16] B. Rosner, I. Gertner, I. Ben-Itzhak, in: S.M. Shafroth, J.C. Austin (Eds.), Accelerator-Based Atomic Physics Techniques and Applications, AIP press, New York, 1997.
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[17] Y. Levy, A. Bar-David, I. Ben-Itzhak, I. Gertner, B. Rosner, J. Phys. B. 32 (1999) 3973. [18] I. Ben-Itzhak, J.P. Bouhnik, B.D. Esry, I. Gertner, B. Rosner, Chem. Phys. Lett. 307 (1999) 287.
www.elsevier.nl/locate/nimb
The ``Foil-Mesh'' method for measuring mean lifetimes of long-lived molecular ions A. Bar-David a, I. Ben-Itzhak b
b,*
, J.P. Bouhnik a, I. Gertner a, Y. Levy a, B. Rosner
a
a Department of Physics, Technion, Haifa 32000, Israel J.R. Macdonald laboratory, Department of Physics, Kansas State University, 116 Cardwell Hall, Manhattan, KS 66506-2601, USA
Received 21 May 1999; received in revised form 19 July 1999
Abstract A method for measuring the mean lifetime of molecular ions undergoing unimolecular dissociation is presented. It can be used to measure molecular ions even if the beam has a large impurity fraction in it, as demonstrated by a measurement of the mean lifetime of 4 He20 Ne2 . Furthermore, this method is not limited to mean lifetimes comparable to the ¯ight time of the ions through the experimental setup as other commonly used methods. It can be used to measure mean lifetimes up to about two orders of magnitude longer than the ¯ight time, as demonstrated using 12 CD2 2 and 3 He40 Ar2 as examples. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 34.50.Gb; 36.90.+f; 34.50.ÿs Keywords: Foil-Mesh method; Molecular ions; Lifetime
1. Introduction The measurement of mean lifetimes of longlived molecular ions provides important information about the decay mechanism, and in many cases helps identify the long-lived state of the molecular ion under study. Many long-lived molecular ions have been studied, but here we focus our attention on doubly charged ions. Mean lifetime measurements have been performed for several doubly charged molecular ions, such as *
Corresponding author. Tel.: +1-785-532-6786; fax: +1-785532-6806. E-mail address: [email protected] (I. Ben-Itzhak)
HeH2 [1,2], NeAr2 [3], HeNe2 [4,5], and CO2 [6±10]. Most of these measurements were conducted using single pass experimental setups where the mean lifetime was comparable to the ¯ight time through the system. Storage devices like rings [10] and electrostatic bottles [11] enable one to measure mean lifetimes over many orders of magnitude taking advantage of the long storage time of the ions in the device, thus extending its eective length. For example, a few mean lifetimes of CO2 from tens of ls to ms were measured using a storage ring [10]. This is in contrast to mean lifetime measurements of CO2 below 1 ls, where only a narrow range of lifetimes has been measured [6±9]. This range is determined by the
0168-583X/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 5 8 2 - 0
A. Bar-David et al. / Nucl. Instr. and Meth. in Phys. Res. B 160 (2000) 182±189
``size'' of the experimental setup, i.e., the ¯ight time of the ions from formation to detection. Even though a wide range of lifetimes can be measured using a storage ring, it has its limitations. 1. Lifetimes can only be measured if they are longer than the stabilization time in the ring, typically a few tens of ls. 2. Many long-lived molecular ions are produced in very small amounts, a few per second, thus making their storage impractical. We have been involved in the last few years in mean lifetime measurements over a relatively wide range of times from 1 to 500 ns. This range was accessed by using experimental setups in which the ¯ight time was of the same order of magnitude as the measured mean lifetime. In Section 2 we present a method for measuring an eective mean lifetime which is longer than the ¯ight time of the ions through the setup by up to two orders of magnitude. Furthermore, using this method mean lifetimes can be measured in spite of a large fraction of beam impurities. We used the 4 He20 Ne2 dication to present the method and a couple of other examples to show that the measured mean lifetimes extend well beyond their ¯ight time through the setup. We use HeNe to denote the most common 4 He20 Ne isotope hereafter. In Section 3 we discuss the advantages and limitations of the new experimental method and some aspects of our results about the measured molecular ions.
183
electrostatic de¯ector according to their energy to charge ratio, E=q. A voltage of 14.79 kV directed the doubly charged HeNe2 ions toward a photo diode detector located 824 mm downstream from the target cell at a de¯ection angle of about 7:4 , which was set using a rotatable arm (see Fig. 1, Ref. [12]). Another similar detector, placed on the beam axis, was used for normalization by monitoring the yield of neutral He fragments, thus assuring normalization to the beam current independent of the ¯ux of impurity ions in the beam. The detectors used, produce a signal proportional to the energy of the particle hitting them. The He signal is clearly distinguishable from the other peaks in the energy spectrum, as shown in Fig. 1. This is an important requirement of the new method for measuring mean lifetimes as will become clear later. The ``peak'' labeled full energy (FE) contains the HeNe2 molecular ions which survive all the way to the detector, events where
2. Experimental The doubly charged HeNe2 molecular ions were produced by charge-stripping of HeNe in fast collisions with Ar atoms in a similar way as described in our previous publications [4]. Brie¯y, the HeNe molecular ions produced in the rf ion source of the Technion 1-MV Van de Graa accelerator were accelerated to 750 keV and then directed by a 15 analyzing magnet toward the target cell where the charge-stripping reactions took place. The pressure in the dierentially pumped target cell was typically 1±5 mTorr, while the pressure in the rest of the system was kept below 2 10ÿ6 Torr. The reaction products emerging from the target cell were analyzed by an
Fig. 1. The energy spectrum when the detector is placed on the HeNe2 trajectory. (a) With a mesh and foil in front of the detector, and (b) with the mesh only. The energy spectrum in (a) is shifted to lower energies due to energy loss in the foil (see text).
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both He and Ne fragments of the same molecular ion are detected, the Ne fragments which are only partly resolved, and any beam impurity which has the full energy of the beam. The main impurities competing with the HeNe2 molecular ion of interest are the doubly charged C2 2 dimers and the simultaneous detection of two C fragments pro duced in C 2 Ar ! C C reactions (both with 12 the C isotope). An ``eective'' mean lifetime can be determined, assuming a single exponential decay, from the fraction of molecular ions that dissociated in ¯ight after passing the electrostatic de¯ector. In the case of a pure beam of the molecular ions of interest one can distinguish the fragment pairs from the molecular ions, for example, by using their dierent transmission through a mesh with a known transmission [12±15]. Unfortunately, this is not the case for many ``exotic'' molecular ions, and the number of molecular ions is not given by the number of ``full energy'' counts because the beam has a high level of contamination (the 4 He20 Ne2 was only 18% of the yield of doubly charged ions produced in the collisions under study). To overcome this diculty, we take advantage of our ability to detect and distinguish one fragment of the dissociating molecular ion, i.e., the He fragment in our example, and the fact that the He fragments are solely associated with the HeNe2 molecular ions of interest. This fact was used in previous measurements of the mean lifetimes of some HeNe2 isotopes [4,5]. The four dierent geometries of the experimental setup needed to conduct the mean lifetime measurements are presented schematically in Fig. 2. The narrow slit setup, shown in Fig. 2(a), is used to obtain a detailed angular distribution of the particles emerging from the de¯ector. A thin foil is placed in front of the detector to dissociate all the molecular ions before impinging on the detector, as shown in Fig. 2(b) and (c). In Fig. 2(c) and (d) we show the setups with a large acceptance angle and a mesh of transmission T placed in front of the detector. The number of analyzed HeNe2 is measured ®rst, relative to a certain number of He neutral fragments. This is done by placing a thin foil on the trajectory of these ions as shown in Fig. 2(c). It
Fig. 2. A schematic view of the experimental setup with (a) a narrow slit, (b) a narrow slit and a thin foil, (c) a large acceptance angle and both a thin foil and a mesh in front of the detector, and (d) a large acceptance angle and a mesh in front of the detector (see text).
is important to note that in addition to fragmenting the molecular ions, this foil causes signi®cant broadening of the tightly collimated beam due to multiple scattering. Thus, a large solid angle for detection must be used. A scan of the multiple scattering cone was conducted ®rst with a narrow slit on the detector, as shown in Fig. 2(b), to ensure that no signi®cant fraction of the He fragments misses the detector. Then, a 9 9 mm open area detector placed about 30 mm behind the thin carbon foil 10 lg=cm2 , as shown in Fig. 2(c), was used for the measurements described below. Note that breaking up the molecular ions is not sucient to observe the He fragments because once we have ensured that all fragments hit the detector, they will do so in pairs producing a full
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energy signal, thus nullifying the whole purpose of the foil. This ``problem'' was used to verify that all He and Ne fragments of the HeNe2 molecular ion hit the detector after passing the carbon foil while using a wide open detector (9 9 mm aperture), i.e., no counts with the He fragment energy were detected. Now, to overcome this problem and measure the yield of the HeNe2 fragments, a ®ne mesh with 30% transmission, was placed in front of the detector, as shown in Fig. 2(c). The mesh transmission is determined from the ratio of the normalized yields, of the ions of interest, measured with and without the mesh (typically the open area fraction of the mesh). With this mesh in place, events where the Ne fragment was stopped appear as He counts in the energy spectrum (note, that these counts are unique and indicate the breakup of a HeNe2 ). The number of He fragments detected is given by Nfoil He T 1 ÿ T N0 HeNe2 ;
1
where N0 [HeNe2 is the number of HeNe2 molecular ions which passed the de¯ector exit. Events where either the He was stopped or both went through the mesh contributed to the ``full-energy'' counts (which in this case include the Ne fragments, HeNe2 , and impurities) Nfoil FE T 1 ÿ T N0 HeNe2 T 2 N0 HeNe2 2 T 2 N C2 2 T N C C
TN0 HeNe2 T 2 N C2 2 T 2 N C C ;
2
where the Ne fragments are included in the full energy peak in order to simplify the data analysis. It is possible to use a peak ®tting routine and resolve the fragments from the true full energy signals. However, the error introduced by this ®tting procedure is large, especially for the measurements with the foil. Furthermore, there is no gain from such separation because the modi®ed equations (2) and (5) lead to similar results. Note, that these equations are based on the assumption that the transmission probabilities of the two fragments of a molecular ion are independent of
185
each other, which is valid if the average distance between them is much larger than the mesh unit cell. (For detailed discussions about using transmission meshes for this purpose see Refs. [12± 16].) This condition is ful®lled in our setup. Now, from Eqs. (1) and (2), the fraction of HeNe2 molecular ions out of the doubly charged ion yield is given by N0 HeNe2 N0 HeNe N C2 2 N C C TNfoil He : 3 1 ÿ T Nfoil FE ÿ Nfoil He
F HeNe2
2
Note that the fraction above is evaluated from the ratio of two peaks in the energy spectrum measured with the foil, and thus the normalization detector plays no role in these measurements. This internal normalization improves the precision of the measurements by removing the eect of instabilities in the yield of neutral fragments [12,16]. The fraction of HeNe2 out of the yield of doubly charged molecular ions produced, given by Eq. (3), varies from day to day, due to the dierent conditions mostly in the rf ion source. It was 17:9 3:5% during the measurements reported here, and fortunately, even though not constant, it varied only slightly after the beam was tuned. Once the yield of HeNe2 molecular ions produced in HeNe Ar collisions was determined, the yield of HeNe2 ions dissociating spontaneously (i.e., without the foil) was measured. The spot size due to unimolecular dissociation is smaller than the one with the foil. This was veri®ed by an angular scan with a narrow slit and without the foil, as shown in Fig. 2(a). Note that using a narrow slit limits the chances that both the He and Ne fragments are detected simultaneously. The acceptance angle of the detector, as shown in Fig. 2(d) is large enough so that all He and Ne fragments can hit the detector. Thus, the mesh is still needed for the same reason as before, i.e., in order to detect some of the events as counts of He fragments. The number of He counts measured without the foil is given by N He T 1 ÿ T N He Ne;
4
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where N He Ne denotes the number of HeNe2 molecular ions which dissociated between the exit of the de¯ector and the mesh (a small correction is needed due to those that dissociate very close to the mesh [12]; this correction, however, is very small in this case and is neglected for simplicity). Under the same conditions (shown in Fig. 2(d), i.e., no foil and with the mesh), the counts with full energy N FE include, as before, the Ne fragments, HeNe2 molecular ions, and the beam impurities, N FE TN0 HeNe2 TN C2 2 T 2 N C C :
5
Using Eqs. (4) and (1), properly normalized to the same number of neutral He fragments, the fraction of HeNe2 which dissociated in ¯ight after the de¯ector is evaluated to be R
N He Ne N He : N0 HeNe2 Nfoil He
6
Note, that the ratio above is independent of the exact transmission of the mesh, thus improving the accuracy of this method (see Ref. [12]). The ``effective'' mean lifetime of HeNe2 is then given by (assuming a single exponential decay), s
ÿx=v ; ln1 ÿ R
7
where x 503 mm is the distance from the de¯ector exit to the mesh, v 2:437 mm/ns is the beam velocity, and R is evaluated from the measurements with and without the foil using Eq. (6). The number of He counts measured with and without the foil are evaluated by ®tting a Gaussian and an exponential tail to the energy spectrum, as shown in Fig. 1. This is needed because the He peak is on the tail of the much larger C peak. Now that the method for measuring the mean lifetime of spontaneous dissociation has been described, it is important to point out that this dissociation can also be induced by collisions of the molecular ions of interest with the atoms or molecules of the residual gas. To separate these two dissociation mechanisms one has to measure the dissociation fraction, R, given in Eq. (6), as a function of the residual gas pressure, and use the
value of this ratio extrapolated to zero pressure. This measurement also allows the determination of the ``collision-induced dissociation'' cross-section. For HeNe2 the collision-induced dissociation was negligible in comparison with the relatively fast spontaneous decay rate [4]. In contrast, this was found to be an important correction in the measurement of the mean lifetime of CD2 2 [17] and the dominant decay mechanism of 3 He40 Ar2 [18]. 3. Results and discussion Using the new method described in the previous section we have measured the mean lifetime of the most abundant isotope of HeNe2 to be 126 34 ns. The error in this measurement was estimated as the standard deviation of 10 measurements. This value is in reasonable agreement with our previous measurement of 184 32 ns performed using the masked detector method [4,12]. Though the reported errors in both measurements are comparable, the new experimental method has a few advantages. First it is inherently more accurate because the main systematic error in the previous method is removed. In the masked detector method, used previously, there is a need to block the spot in which the surviving doubly charged molecular ions hit the detector. This introduces an uncertainty in the fraction of ion-pairs one can detect, i.e., how much less than half the events are measured [12]. The nice agreement between the new measurement and the previous one suggests that this factor was estimated reasonably well in the past, but it is better to avoid such problems altogether. The error in the new method in contrast is dominated by statistical errors, and thus the precision can be improved when needed beyond the one reported here. Second, in the new method the surviving molecular ions are also measured, and not only the dissociating ones as in the masked detector method. This is important when one tries to compare the measured mean lifetime to theoretically predicted ones (see discussion in Ref. [5]). Following the previous measurements [4,5] it was not clear whether states with much longer mean lifetimes are populated in the collision, because the surviving molecular ions
A. Bar-David et al. / Nucl. Instr. and Meth. in Phys. Res. B 160 (2000) 182±189
were not detected. The new results, in contrast, indicate that the population of such states is negligible. The result of the measurements reported here is in good agreement with the calculated mean lifetimes of a few possible states of 4 He20 Ne2 , explicitly the C 1 P v 8; 9, D 1 R v 9, d 3 P v 5; 6, E 1 R v 11; 12, and G 1 R v 7; 8 [5]. Note that the measurement reported here was performed for a single distance between the detector and de¯ector. Future measurements for which this distance will be varied might narrow down the number of possible states. Calculations of the most likely population of vibrational states of this isotope in vertical transitions from the parent HeNe might accomplish the same goal. Last but not the least, the new method is much simpler to apply than the previous method. Both methods allow one to measure an eective mean lifetime in spite of the large impurity of other doubly charged ions. The fraction of HeNe2 was less than half of the yield of doubly charged ions. The new method is also superior to the mesh method [12], because it does not depend on the exact knowledge of the mesh transmission, which is a main source of uncertainty in the mesh method. Furthermore, the mesh method cannot be applied when the full energy peak contains a large fraction of impurity ions. The new method, however, is limited to cases where one of the fragments of the molecular ion of interest can be uniquely identi®ed in the energy spectrum. The higher sensitivity and accuracy of the new method enables measurements of smaller fractions of unimolecular dissociation, thus extending the range of mean lifetimes well beyond the time of ¯ight of the ions of interest through the experimental setup. We have used this method recently 1:3 to measure the mean lifetime of CD2 2 to be 4:01:1 ls, about 25 times longer than its ¯ight time from the de¯ector exit to the detector [17]. This example shows that the method can be applied to polyatomic molecular ions as well. Another example is the measurement of the mean lifetime of 3 He40 Ar2 , for which only a lower limit of about 40 ls was determined [18]. This value is approximately 150 times longer than the ¯ight time of this molecular ion through the experimental setup. This limit could be further
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extended if the residual gas pressure in the apparatus were reduced below 10ÿ6 Torr. This could improve the limiting factor which is collision-induced dissociation of the HeAr2 molecular ions. The analysis of the data depends strongly on the identity of the impurities competing with the molecular ion of interest. In the case of 3 He40 Ar2 the competing impurity was 43 Ca2 . Under these conditions the full energy peak, which includes the Ar fragments, the HeAr2 or its fragments detected simultaneously, and the 43 Ca2 impurity, yields 43
N FE T fN0 HeAr2 N Ca2 g;
8
whether it is measured with or without the foil. The number of counts in the He peak measured with or without the foil are still given by Eqs. (1) and (4), respectively. The fraction of HeAr2 molecular ion in the beam is given by F HeAr2
N0 HeAr2
N0 HeAr2 N 43 Ca2 Nfoil He : 1 ÿ T Nfoil FE
9
The fraction of HeAr2 dissociating in ¯ight between the de¯ector exit and the mesh can be calculated using Eq. (6), after proper normalization of the measurements with and without the foil to the same number of neutral He fragments. However, this fraction can also be calculated by normalizing each measurement to the respective number of counts in the full energy peak. Dividing the measured ratio without the foil (i.e., Eq. (4) divided by Eq. (8)) by the ratio measured with the foil (i.e., Eq. (1) divided by Eq. (8)) yields N He Ar=fN0 HeAr2 N 43 Ca2 g 43
N0 HeAr2 =fN0 HeAr2 N Ca2 g N He=T 1 ÿ T = N FE=T : Nfoil He=T 1 ÿ T = Nfoil FE=T
10
From the equation above the fraction of molecular ions dissociating in ¯ight is evaluated to be R
N He Ar N He=N FE : 2 N N0 HeAr foil He=Nfoil FE
11
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This fraction of dissociating molecular ions is independent of the exact value of the mesh transmission as were the measurements normalized to the neutral fragments discussed previously. The mean lifetime is then calculated using Eq. (7) as was discussed before. Note that any instabilities in the neutral fragment rate which aect the normalization have no impact on such measurements. Instead, we have assumed that the fraction of HeAr2 in the beam given by Eq. (9) is not changing signi®cantly between the two measurements, with and without the foil. The HeAr2 beam fraction was stable to about 3% during the whole run [18]. It has been our experience that this internal normalization is more stable for our measurements then normalizing to the neutral fragments. 4. Summary A new method for measuring mean lifetimes of long-lived molecular ions is presented. It is based on the measurement of the yield of one molecular fragment which is solely associated with the molecular ion of interest. Two measurements are performed with and without a foil, used to induce the dissociation of all molecular ions. The measurement without the foil provides the number of molecular ions undergoing unimolecular dissociation, while the measurement with the foil is used to determine the yield of molecular ions which passed the de¯ector, i.e., N0 . An eective mean lifetime is evaluated from the normalized ratio of the two measurements. This method was applied to the 4 He20 Ne2 dication and the measured mean lifetime was determined to be 126 34 ns. This value is in agreement with a previous measurement, but has a higher accuracy because some systematic errors associated with the previous measurement were removed. Furthermore, this measurement indicates that in this collision the population of states with mean lifetimes much longer than the measured value is negligible. We have measured a 2 mean lifetime of 4:01:3 1:1 ls for CD2 , which is about 25 times longer than its ¯ight time through our apparatus. We have also determined that the mean lifetime of 3 He40 Ar2 is longer than 40 ls,
more than 150 times longer than its ¯ight time through the setup. This experimental technique is especially useful when the yield of the molecular ions of interest is small in comparison with competing beam impurities. Acknowledgements We wish to thank Prof. Kevin D. Carnes for helpful comments. This work was supported in part by the Technion V.P.R fund, the David and Miriam Mondry research fund and in part by the Division of Chemical Sciences, Oce of Basic Energy Sciences, Oce of Science, US Department of Energy.
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