Preparation of state purified beams of He, Ne, C, N, and O atoms Justin Jankunas, Kevin S. Reisyan, and Andreas Osterwalder

Citation: J. Chem. Phys. 142, 104311 (2015); doi: 10.1063/1.4914332 View online: http://dx.doi.org/10.1063/1.4914332 View Table of Contents: http://aip.scitation.org/toc/jcp/142/10 Published by the American Institute of Physics

THE JOURNAL OF CHEMICAL PHYSICS 142, 104311 (2015)

Preparation of state purified beams of He, Ne, C, N, and O atoms Justin Jankunas, Kevin S. Reisyan, and Andreas Osterwaldera) Institute for Chemical Sciences and Engineering, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

(Received 13 January 2015; accepted 25 February 2015; published online 13 March 2015) The production and guiding of ground state and metastable C, N, and O atoms in a two-meter-long, bent magnetic guide are described. Pure beams of metastable He(3S1) and Ne(3P2), and of ground state N(4S3/2) and O(3P2) are obtained using an Even-Lavie valve paired with a dielectric barrier discharge or electron bombardment source. Under these conditions no electronically excited C, N, or O atoms are observed at the exit of the guide. A general valve with electron impact excitation creates, in addition to ground state atoms, electronically excited C(3P2; 1D2) and N(2D5/2; 2P3/2) species. The two experimental conditions are complimentary, demonstrating the usefulness of a magnetic guide in crossed or merged beam experiments such as those described in Henson et al. [Science 338, 234 (2012)] and Jankunas et al. [J. Chem. Phys. 140, 244302 (2014)]. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4914332]

I. INTRODUCTION

Atomic and molecular beam experiments, be it in spectroscopy or dynamics studies, benefit from maximum control over all degrees of freedom of the particles in the beam.1 Supersonic expansions lead to internally cold atoms or molecules, and translational temperatures are normally in the range of Kelvin, even if the molecules possess high kinetic energies in the laboratory frame of reference.2 It is of great interest to control the velocity also in that reference frame, and recent advances in the translational control of polar and paramagnetic molecules nowadays allow for a complete control of the forward velocity using, for example, Stark or Zeeman decelerators.3–8 In reaction dynamics studies, an important device has been, for several decades, the electrostatic hexapole, which is used to state-select molecular beams and produce rotationally pure beams.9 Similar devices were also used as velocity filters to obtain translationally cold molecules from effusive sources.10–12 Recent efforts in reaction dynamics targeted collision energies in the few-Kelvin range.13–20 One approach was to perform a traditional crossed beam experiment, but with a very small angle between the two molecular beams. This enabled Costes and co-workers to reach collision energies below 5 K and to observe resonances in the rotational energy transfer reactions H2 + O2(v = 0, N = 1, J = 0) −→ H2 + O2(v = 0, N = 1, J = 1, 2), and H2 + CO(v = 0, N = 0) −→ H2 + CO(v = 0, N = 1).13,14 An alternative approach was chosen by Narevicius et al. and Osterwalder et al., namely, the combination of the advantages of molecular beam control and supersonic expansions. By merging two beams to reach a nominal crossing angle of zero degrees these groups reached collision energies below 1 K, or ≈ 0.1 meV.15–20 These experiments make use of magnetic and electrostatic guides to bend one or two supersonic expansions onto the same axis. In a)[email protected]

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such an experiment only the difference in forward velocities of the two expansions needs to be controlled, thus allowing to reach low collision energies also in fast beams. These merged-beam experiments were used to study several different Penning ionization reactions such as the He(3S1) + H2 −→ He + H+2 + e− reaction which was studied at collision energies as low as 0.8 µeV (≈ 10 mK).15,16 Here, the He(3S1) beam was guided and bent magnetically while a direct expansion was used for H2 molecules. In the other merged-beam setup both molecular beams are bent;17–20 paramagnetic and polar species are merged by means of a Zeeman and a Stark guide, respectively. Because of the high selectivity of the guides, Penning ionization exclusively of the upper inversion doubling component of the NH3 (J = 1, K = 1) molecule by state-selected metastable He(3S1), and Ne(3P2) atoms could be studied in the 38 mK < Ecoll < 250 K collision energy range.17–20 In all these experiments it is highly desirable to have high control over the composition of the molecular beams, both with regards to species and internal states. In the case of the Penning ionization reactions mentioned above the metastable rare gas atom in the reaction is in a single J-state. In the case of neon, for example, the metastable atoms were produced by electron bombardment which is not a selective process. One can thus assume that of the three spin-orbit components of the lowest 3P state all are statistically populated. However, because J = 1 is not metastable and J = 0 is not paramagnetic, only the J = 2 component is guided to the reaction zone, and the reaction studies are completely state-specific with regards to the atomic reactant. In the present paper it is shown that the combination of different devices for the supersonic expansion with a curved magnetic guide enables a high degree of selectivity in the production of a beam of paramagnetic atoms. Specifically, certain experimental conditions lead to atomic N(4S3/2), and O(3P2) fragments exclusively in the ground state. These conditions are characterized by high gas density, good cooling of internal and external atomic degrees of freedom and are realized experimentally by using an Even-Lavie pulsed

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valve21 (ELV) coupled to either a dielectric barrier discharge (DBD),22 or electron impact excitation (EIE) source, and a bent atom guide. Other conditions yield carbon and nitrogen atoms in electronically excited levels, in addition to ground state species. Requisite mild supersonic expansion conditions are achieved by using a general valve (GV) combined with an EIE source. The two experimental approaches are complimentary, and both showcase an inherent state filtering of a magnetic hexapole guide. The results presented here demonstrate that an appropriate combination of pulsed valve and radical source can substantially alter the composition of a molecular beam and, in favorable cases, lead to a completely state-purified beam. Additional purging is obtained by coupling the source to a magnetic guide. Similar to previous observations in Stark or Zeeman decelerators, the combination of a cold source with such a device can, in favourable cases, leads to atomic or molecular beams that are almost 100% state purified.1,4,23,24 The pure source of either ground state atoms such as N(4S3/2) and O(3P2), or metastable C(3P2) and N(2D5/2, 2P3/2) atomic fragments demonstrated here is ideally suited for applications in merged-beam experiments.

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II. EXPERIMENTAL

Two separate setups were used in the current experiments. The first one is sketched in Figure 1(d) and described in detail in Ref. 18 where this apparatus was used to perform low energy scattering experiments in merged beams. Briefly, a first differentially pumped high-vacuum chamber houses a skimmed supersonic expansion (labeled SE in Figure 1(d)). The magnetic guide, housed in the second differentially pumped chamber, captures paramagnetic particles behind the skimmer and guides them over a distance of about 1.9 m while performing an 11◦ turn. At the end of the guide, the molecular beam enters a third differentially pumped chamber that contains a time-of-flight mass spectrometer (TOF-MS in Figure 1(d)) where the guided atoms are detected by resonance enhanced multi-photon ionisation (REMPI). The SE can be produced either with a GV or an ELV. The GV can be coupled with an electron impact excitation (EIE) source where electrons with kinetic energies ≈100 V are accelerated from a ring filament into the expansion a few millimeters behind the nozzle orifice. The ELV can be operated with the same EIE source, or it can be equipped with a dielectric barrier discharge.22 In the

FIG. 1. One of two experimental apparatuses used here. Panels (a) and (b) show the magnetic field distributions in cross sections through the magnetic hexapole and quadrupole guide sections, respectively. Panel (c) shows a rendering of the guide itself. The shaded area covers the electric guide also present in that chamber, but not used in the present experiments. Panel (d) is a sketch of the high vacuum chamber (SE = supersonic expansion, TOF-MS = time-of-flight mass spectrometer).

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TABLE I. Atomic properties of helium, carbon, nitrogen, oxygen, and neon atoms probed experimentally. Landé g factors, along with maximum M = J products, are given in columns 3 and 4, the mass to µ max ratio is given in column 5, and the intermediate state character of the REMPI process and the associated wavelength are given in columns 6 and 7. State

Energy (eV)

gLSJ

µ max (µ B )

C

2s22p2, 3P0 2s22p2, 3P1 2s22p2, 3P2 2s22p2, 1D2 2s22p2, 1S0

0 0.002 0.0054 1.26 2.68

0 3/2 3/2 1 0

0 3/2 3 2 0

8 4 6

N

2s22p3, 4S3/2 2s22p3, 2D5/2 2s22p3, 2D3/2 2s22p3, 2P1/2 2s22p3, 2P3/2

0 2.38 2.38 3.58 3.58

2 6/5 4/5 2/3 4/3

3 3 6/5 1/3 2

O

2s22p4, 3P2 2s22p4, 3P1 2s22p4, 3P0 2s22p4, 1D2

0 0.02 0.028 1.97

3/2 3/2 0 1

19.8 16.6

Atom

3S 1

He

1s2s,

Ne

2p5(2P03/2)3s, 3P2

m/µ max (amu/µ B )

Intermediate state in REMPI

λ(REMPI) (nm)

2s2 2p3p, 3P0 2s22p3p, 3P1 2s22p3p, 3P2 2s22p3p, 3D2 2s22p4p, 3S0

280.2985 280.3142 280.3399 320.4199 330.0129

4.7 4.7 11.7 42 7

2s22p2(3P)3p, 4S3/2 2s22p2(3P)4p, 2D5/2 2s22p2(3P)4p, 2D3/2 2s22p2(3P)3p, 2P1/2 2s22p2(3P)3p, 2P3/2

206.7166 227.1988 227.4029 290.1441 289.9957

3 3/2 0 2

5.3 10.7 8

2s22p3(4S)3p, 3P1 2s22p3(4S)3p, 3P1 2s22p3(4S)3p, 3P1 2s22p3(4D0)3p, 1P1

225.6560 226.0594 226.2351 205.4726

2

2

2

1s4s, 3S1

656.9841

3/2

3

6.7

2p5(2P01/2)4p, 2[3/2]1

337.6618

supersonic expansions neat He, CO, N2, O2, and Ne gases are used to generate He(3S1), C(3PJ; 1D2; 1S0), N(4S3/2; 2DJ; 2 PJ), O(3PJ; 1D2), and Ne(3PJ) atoms, respectively. A backing pressure of 1-2 bars was used with the GV, and about 4 bars with the ELV. Both valves were operated without heating or cooling. While the DBD barely raises the temperature, increased temperatures must be expected when using a source in combination with the EIE. It has been observed, however, that the temperature stabilises in reasonably short time and remains steady during an experimental run. No detailed measurements were done to extract speed ratios for the expansions done here. But previous characterisations done in our lab on similar systems show that the ELV under the above conditions produces a speed ratio around v/∆v = 10 while it is somewhat worse for the GLV. The second setup is a minimalist molecular beam machine that only contains pulsed valve, skimmer, and TOF-MS. The same GV and ELV were used in both chambers, and the TOF-MSs are copies of one another. This second chamber is required to characterize the supersonic expansions alone, without the magnetic guide. The magnetic guide is shown in more detail in Figures 1(a)-1(c). Figure 1(c) is a rendering of the magnetic guide, as well as of the electric guide used in the merged-beam experiments. It was not used in the present experiment and hence it is covered under the shaded area. The magnetic guide is composed of a first section with hexapole symmetry (shown in cross section in Figure 1(b)) performing a 2-degree turn, and a second section with quadrupole symmetry that performs a 9-degree turn (Figure 1(a)). Both sections are about 0.75 T deep, and the guide has an inner diameter of 8 mm and a total length of about 1.9 m. All ground state and electronically excited atoms, with the exception of Ne(3P2), were probed by [2+1] REMPI. In

addition, He(3S1), and Ne(3P2) atoms were also detected by [1+1] REMPI. The wavelengths and REMPI transitions used in this work are summarized in Table I. The second harmonic of a Nd:YAG laser (20 Hz repetition rate, ≈5 ns pulse duration) was used to pump a dye laser operating with DCM dye. Doubling the output of this dye laser yielded 7 mJ–10 mJ of 310 nm–325 nm laser radiation. Tripling the output the dye laser resulted in up to 4 mJ of 205 nm–216 nm radiation. The third harmonic of a second Nd:YAG laser pumped a second dye laser operated with Coumarin 460 or Coumarin 540 A dyes. Doubling the output of this dye laser resulted in pulse energies of ≈ 1 mJ of 224–235 nm, and up to 2 mJ in the 280–290 nm range. In all cases, the laser beam was focused with 50 cm and 30 cm spherical lenses in the first and second chamber, respectively. All pertinent atomic energy levels, and atomic REMPI lines used in this work have been obtained from the NIST Atomic Spectra Database.25 III. RESULTS AND DISCUSSION

Figure 2 shows representative results of this study, using the nitrogen expanded from the GV atom as an example. Typical REMPI signals measured behind the magnetic hexapole guide and in the chamber without guide are displayed in Figures 2(a) and 2(b), respectively. The traces were recorded by parking the laser on a particular REMPI transition and averaging the TOF-MS trace for 3000–5000 shots. Each of the traces is color coded for the probing of a particular initial state. The colors are as follows: blue: 2D5/2; green: 2P3/2; red: 4S3/2; black: 2D3/2; purple: 2P1/2; gray: EIE switched off. The dashed red line in Figure 2(b) shows the N(4S3/2) signal obtained when using the ELV. All other N-atom transitions had no intensity under these conditions. The mass peaks shown in Figs. 2(a) and 2(b) have been corrected for laser power.

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FIG. 2. Experimental [2 + 1] REMPI signals of five low-lying nitrogen atom states from a GV expansion. (a) Before the guide, and (b) after the guide. The colors in both panels are as follows: blue: 2D5/2; green: 2P3/2; red: 4S3/2; black: 2D3/2; purple: 2P1/2; gray: no ionizer. The red dashed line shows the 4S 3/2 state but after expansion from an ELV. All traces have been corrected for laser power fluctuations only. (c) Typical REMPI line: ionisation of atomic nitrogen via the 2s22p2(3P)3p(4S3/2)← 2s22p3(4S3/2) transition.

For this, the power dependencies I(N+)REMPI ∝ P1.62±0.03 , and laser I(C+)REMPI ∝ P1.10±0.11 (I(X) is signal intensity, P is laser laser laser power) were used, where the exponent in each case was determined experimentally. The value of the exponents for these scalings demonstrate that the REMPI was done under conditions of partial saturation, since otherwise p = 2 would be expected for a [2 + 1] REMPI process. The present interpretation is not compromised by the saturation since conditions are the same for all pairs of data sets that are being compared. Figure 2(c) shows the 2s22p2(3P)3p(4S3/2) ←− 2s22p3(4S3/2) transition in nitrogen as a representative

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example for a REMPI line. For each of the signals shown in Figs. 2(a) and 2(b), the laser position was carefully adjusted to probe the most intense part of the molecular beam pulse. All results obtained for C, N, and O atoms are shown in Figure 3. For each of the atoms, separated in individual panels, the bars show the relative intensities for different electronic states. Each of the panels shows the relative statistical weights, the REMPI signals without guide, using the GV, the REMPI signal for the guided molecules produced either with the GV or the ELV, and the calculated transmission through the guide (see below). The REMPI signals for each atom are normalized to one state. All experimental data were recorded like the ones detailed above, and the ratios were calculated by integration of the peak in the TOF trace and normalization. All data without guide were obtained using the GV, and all data with the GV used EIE for atom production. The ELV produced the same results with the DBD and the EIE, and it was not used without guide. It should be noted that a weak REMPI signal from O(1D2) atoms is observed without, but not with, the magnetic guide, but it is too week to be included in the present analysis. Furthermore, the REMPI transition used for O(1D2) is associated with the auto-ionizing 2s22p3(2D0)3p, 1P1 intermediate state,26 thus rendering it difficult to relate the relative peak intensities to relative particle densities (see below). To understand the observed relative intensities shown in Figure 3 one has to consider the three steps between production and detection of the atoms: (1) the supersonic expansion and atom production, (2) the guiding, and (3) the REMPI process. Each of these steps affects, by different mechanisms, the observed composition of the beam. The relative intensities observed in the non-guided beams are determined by points 1 and 3. The first step contains the statistical weights of each state, which are given on the left in each of the panels in Figure 3, as well as the state-dependent production efficiency that is more difficult to quantify. The experimental results determined for non-guided nitrogen atoms shown in Figure 3 are reasonably close to the statistical weights. In carbon the ratio of ground and electronically excited states deviates more markedly from this ratio. Nitrogen and carbon atoms were produced by bombarding N2 or CO molecules with ≈ 100 eV electrons, respectively. The observed relative densities in the beams do not only depend on the statistical weights but also on the branching ratio of the EIE process. In the present experiment, the sources were optimized in order to maximize the total dissociation efficiency.27,28 The branching ratio for production of different electronic states in C appears to depend more strongly on the electron kinetic energy than in N, but this was not further investigated here. One of the most striking results in Figure 3 is the different outcome of GV and ELV used in the production of atomic fragments. An ELV expansion produces O, N, and C exclusively in the ground state while an expansion from the GV also shows atoms in excited states. The results suggest that the high number densities and high collision rate that exist in the supersonic expansion of an ELV suffice to quench electronically excited atomic C, N, and O fragments.29 It is remarkable that under these conditions even the C(3P2) state of carbon, lying only 5.4 meV above the 3P0 ground state is completely absent from the beam. This stands in

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FIG. 3. Relative contributions for (top to bottom) carbon, nitrogen, and oxygen atoms in different electronic states. Each panel shows (left to right) the relative statistical weights, the relative experimental REMPI intensities for different experimental conditions (to a good approximation proportional to the ratios of atomic densities), and the relative transmissions extracted from trajectory simulations. Experimental ratios shown in columns 2, 4, and 5 have an associated error of ≈15%, arising primarily from laser power correction.

stark contrast to high intensity He(3S1) and Ne(3P2) beams produced from 100% He and 100% Ne in the ELV, coupled to either DBD or EIE source. One might think that the high collision rate in the ELV eliminates all population from the metastable states. Presumably, the difference comes from the presence of molecules in the expansion used for C, N, or O atom production. Two-body collisions between excited He or Ne atoms and ground state atoms can only lead to resonant energy transfer or transfer of electronic to translational energy. This latter process, however, is known to have an exceedingly small cross section.22 In the presence of molecules, transfer to internal degrees of freedom (vibration or rotation) by inelastic collisions is possible, and likely has a larger cross section than collisions wherein internal energy is transferred to translational degrees of freedom. In the expansions from the GV fewer collisions are taking place because the particle density is substantially lower. Consequently, electronically excited C, N, and O atoms have a higher probability to survive, and they remain in the molecular beam. The observed ratios also depend on the REMPI efficiency, point 3 above. In order to make the connection between the observed signal intensity and the relative densities in the beam, a few approximations are required. The number of ions A formed per time interval ∆t can be written as p A N A+m (∆t) = N A m σabs Flaser ∆t,

(1)

A where N A i is the number density of species Ai , σabs is the p two photon absorption cross section, Flaser is the photon flux density, and p is the power dependence of the REMPI signal. No attempt was made at measuring absolute N A m densities and only the ratios are reported here. Of particular interest in the present context are relative ratios for different experimental conditions because this treatment eliminates several theoretical complications. This shall be demonstrated using the example of the five states of N atoms, as shown in Figs. 2(a) and 2(b). Having comparable experimental conditions the photon flux density Flaser can be replaced by the laser power Plaser which eliminates the necessity to exactly know the focusing conditions of the laser. All ions are collected p for the same amount of time ∆t, and all Plaser factors are known. Hence, p An N A+n Plaser N A n σabs (m) NAn = ≈ . p A N A+m Plaser(n) NAm N A m σabsm

(2)

The approximation made in Eq. (2) is that the REMPI cross sections of atomic species An and Am , being the same atom in two different ground state electron configurations, e.g., N(4S3/2) and N(2D5/2) for N: 2s22p3, are similar. While this assumption is not critical for the final result of this paper it shall nevertheless be rationalized here. Carbon and nitrogen atoms, being the species of the most interest here because

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all five low-lying electronic states are observed, are probed exclusively on ∆J = 0 transitions. In the [2 + 1] REMPI process the bound-bound two-photon absorption cross section from level i to level f via virtual state j is proportional to 2  ⟨ f |⃗ϵ · ⃗µ| j⟩ ⟨ j|⃗ϵ · ⃗µ|i⟩ ,   (3) σabs ≈ Eji − E j where ϵ⃗ and ⃗µ are the laser field and the transition dipole moment, respectively. E and Ei j are the laser energy and transition energy, respectively. For a rigorous calculation, one would therefore have to evaluate the integrals in Eq. (3). For the present purpose, however, it is sufficient to make the following, rough estimates. In the case of nitrogen atom REMPI, the dominant virtual state is characterized by the 2s22p2(3P)3s electron configuration. Absorption of the first photon by N atoms in 4S3/2, 2DJ, and 2PJ states results in a 4.67 eV, 2.84 eV, and 2.83 eV detuning from the 2s22p2(3P)3s state; hence the denominator in Eq. (3) differs only by a factor of ≈ 1.65 for 4S3/2, and 2DJ, 2PJ states. The ground state 4S3/2, and excited 2PJ states are probed via electronic states associated with a 3p electron (see Table I). One would therefore expect the numerator of Eq. (3) to be similar for a two-photon absorption cross section from 4S3/2 and 2PJ states. The two 2DJ states are probed through electronic states associated with a 4p electron. In order to compare the integrals associated with 2p → 3s → 3p and 2p → 3s → 4p transitions, we make another rough approximation: we assume that the wavefunctions associated with a given electronic N atom configuration, i.e., 2s22p3, 2s22p2(3P)3s, 2s22p2(3P)3p, and 2s22p2(3P)4p can be approximated by hydrogen-like 2p, 3s, 3p, and 4p eigenfunctions. The integrals (see Eq. (3)) associated with 2p → 3s → 3p and 2p → 3s → 4p transitions are then computed to examine if the two differ significantly. It is found that ⟨3p |⃗ϵ · ⃗µ| 3s⟩ ⟨3s |⃗ϵ · ⃗µ| 2p⟩ ≈ 0.87. (4) ⟨4p |⃗ϵ · ⃗µ| 3 s⟩ ⟨3s |⃗ϵ · ⃗µ| 2p⟩ These estimates demonstrate that the approximation made in Eq. (2) is correct to within a factor of approximately 2. By comparing ratios of transition intensities of an atom in a given electronic state obtained with and without the magnetic guide, the approximation is no more required. The state distribution measured behind the magnetic guide is also shown in Figure 3. These relative contributions contain, in addition to the production and the detection efficiency, the state-dependent probability for any atom to be guided through the magnetic guide.11 Atoms follow the bend in the magnetic hexapole only if they possess a magnetic moment that permits to compensate the centrifugal force. An electronic state with total angular momentum quantum number J is split into (2J + 1) sublevels by the Zeeman effect.4 The field dependent energy is, to first order, given by W (B, J, M) = µB = gLSJ µ B M B,

their usual meaning. The guiding force for the particles is generated by the position-dependent Zeeman energy in the inhomogeneous magnetic field of the guides. It is apparent from Eq. (5) that M = 0 (and hence all states with J = 0) levels have no first-order Zeeman effect and are not guided, nor are high-field-seeking (M < 0) states, for which the energy is reduced with increasing field magnitude, and which are pushed out of the guide. For any given (J, M > 0) state, the Zeeman effect is essentially determined by the Landé g factor. In summary, consider as an example the (J = 3/2, M = 3/2) and (J = 5/2, M = 3/2) states. Both have M = 3/2, but the former has gLSJ = 2 while the latter has gLSJ = 6/5. The resulting magnetic moments µ = MgLSJ thus are µ = 3 µ B and µ = 9/5 µ B, respectively. With this information at hand, it is straightforward to explain the absence of C(3P0, 1S0), and O(3P0) atoms behind the magnetic guide (see Figure 3). The three atomic species are in a J = 0, M = 0 level, for which the first order Zeeman effect vanishes (Eq. (5)), hence these atoms are not guided. The results shown in Figure 3 can be further rationalized using the Landé factors for different states of C and O. For example, µ(3P2, M = 2) = 3 µ B, and µ(3P1, M = 1) = 3/2 µ B (see Table I). In addition to the magnetic moment, the total transmission for any given state also depends on the number of guidable M components, and the initial population of each of these. In the above case, for example, the 3P2 state is split into five components (−2 ≤ M ≤ 2) that, assuming a completely isotropic initial distribution, all have the same population. Of these, the M = 1 and M = 2 are guidable, having µ = 3 µ B and µ = 3/2 µ B, respectively. In contrast, the 3P1 state only has one guidable component, with µ = 3/2 µ B. Assuming that µ = 3/2 µ B is sufficient (see below) to guide C and O this means that 40% of the 3P2 are guided but only 33% of the 3P1. A more quantitative comparison requires trajectory simulations, shown in Fig. 4. For the simulations, the hexapole part of the magnetic guide was modeled as an analytical two-dimensional harmonic potential with a depth of 0.75 T, whereas a simulated potential, fitted to the measured, true potential, is used for the quadrupole section of the guide. Particle trajectories are calculated by numerically solving Newton’s equations of motion using a home written code.30 Input parameters consist of the number of particles (3 × 105 for each run), particle mass and its magnetic moment, and the initial velocity distribution. Transmission curves are obtained by assuming a flat initial probability distribution for

(5)

where µ is the state-dependent magnetic moment, gLSJ = 1 is the Landé g-factor, µ B = 9.27 + J (J +1)−L(L+1)+S(S+1) 2J (J +1) × 10−24 J/T is the Bohr magneton, and B the magnetic field strength. L, S, J, and M are atomic quantum numbers with

FIG. 4. Theoretical transmission curves for various N atom states, as a function of beam speed in the laboratory frame. All curves have been normalized such that the maximum transmission is set to one.

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longitudinal speeds of 100 m/s–1000 m/s. Figure 4 shows transmission curves for the N atom as an example, each curve representing the result for a different state, as labeled in the figure. The transmission probability is plotted on the y-axis as a function of longitudinal particle velocity. Each curve is normalized to set the maximum transmission to unity and offset vertically for readability. It should be kept in mind, however, that the real transmission deviates from 1 for all states because in the transverse velocity distribution is not considered explicitly while in reality high transverse velocities can compromise the guidability for any particle even at low longitudinal velocities. The dips in the transmission (observed, for example, around 500 m/s in the top trace and moving towards lower velocities in the lower traces) are stop bands that stem from the dynamics of the atoms in the segmented guide.31 Since under the conditions used in the present study it always is outside the range of interest it was of no concern here. No particles are transmitted through the magnetic guide above a certain threshold velocity vmax. This threshold is given by the longitudinal velocity where the centrifugal and Zeeman forces become equal. Since the centrifugal force is mass dependent and the Zeeman force depends on the magnetic moment, vmax is largely determined by the ratio m/µ which is listed in the fifth column of Table I, in each case for the M = J component of the particular state. Only a small part of the molecular beam is probed by REMPI. Given the atomic beam parameters, i.e., ≈ 60 µs pulse duration, v/∆v ≈ 10, the spread in forward velocities that has been probed here is 686 ± 7 m/s, and 737 ± 8 m/s for N and C atom beams, respectively. The nitrogen atom speed range probed is indicated by vertical bars in Fig. 4. The theoretical transmission curves for the N(2D3/2 and 2P1/2) states suggest that these states should not be guided in the experimentally relevant ≈ 686 m/s speed range. This is confirmed experimentally: there is no signal from N(2D3/2) and N(2P1/2) states, see Figs. 2(b) and 3. Calculations predict that only 4S3/2, 2D5/2, and 2P3/2 states of nitrogen should be guided. More precisely, it is only the highest M sublevel of each state that is guided; for N atom only the 4S3/2 (M = 3/2), 2D5/2 (M = 5/2), and 2P3/2 (M = 3/2) components are guided. (Note that at ≈ 650 m/s the M = 3/2 sublevel of 2D5/2 state could also be guided. This would correspond to a N(2D5/2) REMPI signal increase at vbeam < 650 m/s, provided the appropriate REMPI transition is used.) The two lowest states in nitrogen, 4S3/2, and 2 D5/2 have the same Landé g factor, and the M = J levels are therefore predicted to have the same transmission efficiency through the magnetic guide. But because of the different J-values (and thus the different number of M components) this means that of the 4 sublevels of the 4S3/2 state one is guided, while the 2D5/2 has 6 sublevels and thus 2/3 the total transmission probability of the 4S3/2 state. This estimate predicts that the 4S3/2 : 2D5/2 ratio of 1:1.34 from before the guide should become ≈ 1.00 : 0.89 behind the guide. The ratio of the areas under the transmission curves for 4S3/2 and 2P3/2 in the 679 m/s to 693 m/s speed range is 2.57. Starting from the ratio measured without guide, trajectory simulations predict a 4 S3/2 : 2P3/2 ratio of 1.00 : 0.31, versus the measured ratio of 1.00 : 0.22. Analogous calculations for C atoms yield a 3P0 : 3 P1 : 3P2 : 1D2 : 1S0 ratio of 0 : 0 : 1.00 : 0.06 : 0, compared to the

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measured one of 0 : 0 : 1.00 : 0.17 : 0. The 3P1 state of oxygen has vmax ≈ 570 m/s, and is therefore predicted to be lost from the beam moving at ≈ 686 m/s. Experiment corroborates this, as no REMPI signal from O(3P1) is observed. Due to the required approximations for the comparison of the REMPI intensities, the available data cannot be the basis of a fully quantitative analysis and comparison between theory and experiment. In addition, several experimental factors render a fully quantitative comparison between results from the two chambers used here difficult. For example, the background atomic carbon signal was higher in the test chamber. Different lenses, having focal lengths of 30 cm and 50 cm, respectively, were used in the two chambers. The distance between the GV orifice and EIE ring filament was not exactly the same when mounted in the two chambers (due to different mounts used in the two chambers); the distance is about 3 mm in the straight chamber, and roughly 1 mm in the chamber containing the guide. Due to the strong dependence of the collision dynamics in a supersonic expansion on the distance from the nozzle this may have an effect on the propensities to form different states in particular atoms. Furthermore, certain processes in atomic nitrogen have been neglected in the analysis. The 2D5/2 – 2D3/2 separation is 8.713 cm−1, whereas the 2P1/2 – 2P3/2 energy gap is only 0.386 cm−1. The magnetic field mixes, particularly in case of the 2P doublet, states with the same M value.32 This, in turn, will change the values of the Landé g factors and thus the dynamics in the guide. We neglected this mixing because the 2 P3/2 (M = 3/2) state remains pure since there is no M = 3/2 component in the 2P1/2 state. The magnetic moment of the 2P1/2 (M = 1/2) state, on the other hand, will deviate significantly from that given in Table I. In fact, coupling to 2P3/2 (M = 1/2) is strong at B ≈ 0.75 T, and the resultant wavefunction will be an almost equal mixture of 2P1/2 and 2P3/2 states. We have also ignored complications arising due to the hyperfine structure of atomic nitrogen, even though it is known that the coupling of the nuclear spin angular momentum and the total electronic angular momentum changes g. Nevertheless, the overall agreement between experimental and theoretical ratios of atomic populations is satisfactory and permits the demonstration of the main point of this paper. Namely, the appropriate combination of supersonic expansion, radicals source, and curved guide can produce atomic beams in which a very low number of states is populated. This result is comparable to that obtained when using a straight hexapole in combination with beam block and pinhole.33 The non-statistical distribution in the supersonic expansion can be further modified to, in the extreme case, end up with a single state populated. Conditions as those obtained in an ELV in combination with a curved magnetic guide yield beams of N, O, He, or Ne atoms that are, within our error bars, 100% pure. For applications in reaction dynamics studies, it often is sufficient to reduce the number of populated states to only a few, namely, if only one of those is reactive. IV. CONCLUSION

The use of a bent magnetic guide as a device to purge supersonic expansions of atoms has been demonstrated. The

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combination of different initial populations of certain atomic states with different guiding probabilities leads to purified beams that in favorable cases can be composed of only one single state. It has furthermore been shown that the use of an appropriate valve can dramatically affect the composition of an atomic beam. The high particle density, and consequently the high collision rate, when using an Even-Lavie valve leads to considerably colder atomic beams in which, in the case of atomic oxygen, carbon, and nitrogen only a single state remains populated. In the case of carbon this means that, when using an Even-Lavie valve no guiding occurs because the ground state has a 3P0 configuration and is not paramagnetic. As will be shown in a forthcoming paper, the guided states of these atoms in several cases are also oriented and retain their orientation for sufficiently long times to perform collision studies with oriented atoms.34 These results, in combination with previous measurements using metastable He and Ne atoms show how magnetic guides can be used as a powerful tool in reaction dynamics studies where the highest possible control over the reactant beam composition is desired. ACKNOWLEDGMENTS

We thank Dr. Katrin Dulitz for helpful discussions. Support from the Swiss National Science Foundation (Grant No. PP0022-119081) and EPFL is acknowledged. 1J.

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