Kinematic Slowing and Electrostatic Guiding of KBr Molecules Formed

Dec 16, 2009 - Here, we report the results of experiments on guiding the slow ... deduced directly from the observed time-of-flight profiles, peak at ...
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J. Phys. Chem. A 2010, 114, 3247–3255

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Kinematic Slowing and Electrostatic Guiding of KBr Molecules Formed by the Reactive Collision Process: K + HBr f KBr + H† Ning-Ning Liu and Hansju¨rgen Loesch* Fakulta¨t fu¨r Physik, UniVersita¨t Bielefeld, 33501 Bielefeld, Germany ReceiVed: September 30, 2009; ReVised Manuscript ReceiVed: NoVember 18, 2009

We have generated a beam of translationally cold KBr molecules formed by exoergic reactive collisions in counterpropagating beams of K atoms and HBr molecules. The method relies on the extreme mass ratio of the products and the proper choice of the beam velocities (Liu, N.-N.; Loesch, H. J. Phys. ReV. Lett. 2007, 98, 10300). Here, we report the results of experiments on guiding the slow molecules from the site of their creation to the detector by a linear electrostatic quadrupole field. The device enhances the total intensity by a factor of 2.3 and the intensity at 14.2 m/s (1.4K) by an order of magnitude. The density velocity distributions, deduced directly from the observed time-of-flight profiles, peak at 20 m/s (2.9K). A numerical simulation of the guiding efficiency indicates that the polarization of the nascent molecules is first altered by a sudden change of the quantization axis from parallel to the initial relative velocity to parallel to the fringing field and thereafter follows adiabatically the local field as quantization axis. Drastic differences between the velocity and rotational state distributions of the molecules entering and leaving the energized quadrupole field are predicted. The counterpropagating beams can be used to continuously load an electrostatic trap. The equilibrium density of confined molecules is estimated to 1 × 107 cm-3. 1. Introduction The generation of cold molecular gases and beams offers a unique access to experimental investigations at the yet little explored low K or even sub-K energy range. Very promising is the wide field of bimolecular collision processes, such as reactive collisions (cold chemistry) or elastic and energy transfer collisions, where at low energies quantum phenomena become dominant.1-4 High-resolution spectroscopy benefits from longer observation times, particularly if the molecules are slow enough to be confined in a trap.5,6 Fascinating are also confined molecular gases of polar molecules where at low temperatures the wide range, anisotropic dipole-dipole force dominates, which may be useful in quantum computer schemes7,8 or may lead to superfluidity and yet unknown collective properties.9-11 The prerequisite for entering these novel fields of research is the availability of cold gases or molecular beams, but owing to the more complex electronic and geometric structure, the wellestablished laser techniques for cooling atoms are not applicable to molecules and new methods have to be found. So far, a variety of techniques for cooling, slowing, or trapping molecules is already available. For a detailed description of the current state of the art, we refer to a new monograph,12 the review article of Doyle et al.,13 and a special issue of the Journal of Physics B: Atomic, Molecular and Optical Physics14 on cold molecules; complete lists of the techniques developed so far are given also in recent articles.15-18 A very interesting group of molecules are the diatomic alkali and alkali-earth halides. Their extremely large electric dipole moments of around 10 D make them an ideal object for investigations of cold dipolar gases and for experiments on guiding and trapping at moderately strong inhomogeneous electrostatic fields. The alkali-earth halides in the electronic 2Σ ground state are †

Part of the “Benoît Soep Festschrift”. * To whom correspondence should be addressed. Tel.: +49-5211065412. Fax: +49-5211066046. E-mail: [email protected].

characterized by both a magnetic and an electric dipole moment and thus can be manipulated also by an inhomogeneous magnetic field or by a superposition of inhomogeneous electric and magnetic fields. For this reason they could be applied in high-precision experiments on the search for the electron dipole moment (edm) analogous to the YbF molecule.19 Furthermore, their lonesome σ-electron leads to alkali-like properties. For example, they are chemically reactive and would allow easy access to the field of cold chemistry. Candidates for studies of reactive processes are bimolecular metal exchange collisions where a beam of cold alkaliearth halides interacts with a gas of ultracold alkali or alkali-earth atoms confined in a magneto-optical trap (beam-gas arrangement) and the metal atoms are exchanged. Furthermore, they feature simple and very intense optical spectra and thus are ideally qualified for an extremely sensitive detection by laser-induced fluorescence or resonance-enhanced multiphoton ionization. This property has been exploited in many reaction dynamics studies and could be useful for the detection of small samples of trapped molecules or weak fluxes in the fundamental edm experiments. In a previous Letter20 we have reported a novel technique for the generation of slow salt molecules that exploits bimolecular reactive collision processes in counterpropagating molecular beams. The method is applicable to reactions forming a heavy molecule and a light particle, preferentially a hydrogen atom, such as

Me + HX f MeX + H

(1)

where Me and X denote metal and halogen atoms. Alternatively, due to the large dipole moment the salt molecules could also be decelerated using a switched sequence of electrostatic field gradients. So far this technique has been applied to YbF, and a deceleration from 287 to 277 m/s has been reported.21 Much smaller velocities (e50 m/s) could be achieved using counterpropagating beams of Yb and He-seeded HF, but to date, little is known about the reaction dynamics of Yb + HF.

10.1021/jp909420n  2010 American Chemical Society Published on Web 12/16/2009

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J. Phys. Chem. A, Vol. 114, No. 9, 2010

Liu and Loesch

In this paper, we report results on guiding a flux of slow KBr molecules along a linear electrostatic quadrupole field. The molecules are formed by reactive collisions

K + HBr f KBr + H

(2)

in counterpropagating beams. A unique aspect of these experiments is that the molecules to be guided are rotationally very hot and polarized. We studied the influence of the field on the intensity of the transmitted slow molecules and rationalized the results by a Monte Carlo simulation. In section 2 we describe briefly the method of kinematic slowing of product molecules as well as the molecular beam apparatus. The experimental data and density velocity distributions of the slow molecules are presented in section 3. The basic assumptions of the Monte Carlo simulation are discussed in section 4 including a model of the reaction dynamics providing the rotational state distribution of the slow molecules. Subsequent to the conclusion (section 5) we discuss in the Appendix the prospects of using the slow particle source for loading a trap and estimate the achievable number density of confined molecules. 2. Experimental Methods a. Reaction Dynamics and Kinematic Slowing. The slow salt molecules are formed by reactive collisions of type (1). The speed uMeX of the product molecule MeX relative to a coordinate frame traveling with the center-of-mass velocity C (CM frame) is determined by energy and momentum conservation and amounts to

uMeX )

mH 2(E - Eint′)/(kJ/mol)103 m/s mH + mMeX √ tot

(3) The total energy available to the products, Etot, is the sum of the relative kinetic energy of the reagents (Etr), the internal rovibrational energy of HX (Eint), and the energy released by the process ∆D00 (positive or negative for endoergic or exoergic reactions)

Etot ) Etr + Eint - ∆D00

(4)

In the course of the reaction Etot is eventually partitioned among the corresponding degrees of freedom of the products

Etot ) Etr′ + Eint′

(5)

Crucial for the slowness of MeX is primarily the mass factor mH/(mH + mMeX) but also the degree of internal excitation. For moderately heavy metal and halogen atoms the mass factor is of the order of magnitude of 1/100. Using a typical total energy of Etot ) 30 kJ/mol and a mean energy transfer of 50% of Etot eq 3 provides as a rough estimate uMeX ) 55 m/s. In general, much higher fractions are converted and thus velocities smaller than 55 m/s even down to (near) zero can be expected. The velocity of MeX in the laboratory (LAB frame) VMeX is obtained by adding C and uMeX

VMex ) C + uMex

reagents has to be chosen such that C becomes as small as possible, preferentially zero (kinematic slowing). This can be achieved by intersecting two counterpropagating reagent beams whose velocities fulfill the relation

mHXVHX ) -mMeVMe

(8)

The respective kinematic situation is illustrated in Figure 1. As C vanishes, both the LAB and the CM frame have a common origin and the velocities in the CM frame turn into observable LAB velocities. According to eq 3 the velocity of MeX ranges between zero (all energy transferred into Eint′ and a maximal value (all energy transferred into Etr′). The points of all allowed product velocity vectors fill then the gray disk whose radius corresponds to the maximal velocity. And eventually, those products whose vectors point toward the detector positioned at a 90° angle to the beam axis form the observed slow molecule flux. In addition to the reactive processes, the Me atoms are also elastically scattered. The magnitude of the velocities of all elastically scattered atoms is equal to the one of the parent beam irrespective of the scattering angle and thus the points of the vectors are located on a circle around the common origin with radius VMe. Therefore, two different fluxes arrive at the detector: a fast one of elastically scattered Me atoms and a very slow one of MeX product molecules. So far, we have assumed that C ) 0 holds. However, in a realistic experiment the beam velocities are distributed and C ) 0 occurs only for certain velocity pairs even if the most probable velocities fulfill eq 8. The consequences of moderate deviations from an exact velocity match are discussed further below. b. Apparatus and Methods. The experimental setup is basically the same as that described in ref 20 but complemented by a quadrupole guide mounted between the center of the intersection region (SC) and the detector (Figure 2). We have studied the influence of the guide on the flux of slow KBr molecules formed by the exoergic reaction 2(∆D00 ) -24 ( 10 kJ/mol). Briefly, the pulsed valve creates a short (600 µs) HBr beam pulse that passes a skimmer and the liquid N2 cooled aperture for collimation. The continuous K beam expands through a small orifice in the front chamber of the K oven whose rear chamber contains a few grams of the metal. The beam is collimated by a skimmer and the heated aperture. Oven and skimmer are mounted within a water-cooled Cu housing. The liquid N2 cooled Cu plates A and B are cold traps to reduce the background pressure of the alkali vapor. The beams are aligned optically to guarantee counterpropagation and full overlap. Within the intersection zone two different collision processes

(6)

with

C)

mHXVHX + mMeVMe mHX + mMe

(7)

where VHX, VMe denote the velocities of the reagent particles in the LAB. To transfer the slowness of the salt molecule MeX from the CM to the LAB frame, the collision kinematics of the

Figure 1. Newton diagram of the reaction Me + HX f MeX + H for counterpropagating beams with exactly matched velocities (C ) 0). The center-of-mass (CM) and the laboratory (LAB) frames as well as the corresponding velocities in the frames are equal. The points of all product velocity vectors uMeX lie within the gray area. Only products scattered by 90° with respect to the beam axis encounter the detector.

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Figure 2. Schematic diagram of the counterpropagating molecular beams arrangement. The apparatus is the same as used in ref 20 except for the electrodes of the quadrupole guide. Potentials U are applied to the rods with alternating sign.

TABLE 1: Important Dimensions (mm), Operational Conditions, and Velocity Parameters Beams nozzle diameter nozzle-skimmer skimmer diameter nozzle-cold aperture (diameter) nozzle-heated aperture (diameter) nozzle-pulse shaper nozzle-SC SC-detector wheel diameter number of slits width of slits frequency/Hz length of flight path

K beam

HBr beam

0.15 14 1.04 61 (5) 74 (1.5)

0.12 18 1.0 60 (4)

154 259

Beam TOF Analyzer 70 2 0.3 232 260

Operational Conditions nozzle temperature/K 1073 material temperature/K 770 stagnation pressure/mbar 20 number density at SC/cm-3 1010 Velocity Parameters 0 V0 /ms-1 R /ms-1 668 most probable velocity/ms-1 818 velocity spread/ms-1 (fwhm) 780

52 147

1960 290 250-300 1013 445 Jmax

(25)

follows. The maximal impact parameter bmax, given by the reaction cross section

σr ) πbmax2

(26)

determines via eq 23 the maximal rotational state Jmax. Using the experimental value34 σr ) 31 Å2 and the most probable velocities of Table 1, Jmax ) 165 results. The corresponding maximal rotational energy of 26.2 kJ/mol is well below Etot ) 45 kJ/mol, and hence there is sufficient energy available to populate this state. The simulated guiding efficiencies are displayed in Figure 7 as a function of the rod voltage U (solid lines) together with our experimental results (circles and squares). Curves labeled a and b are the results excluding and including the induced dipole force, respectively, curves without a label include this force. The two curves marked M ) 0 have been calculated for the extremal case that only the rotational states J, M ) 0 of the molecules entering the guide are populated. This population would result if the nascent molecules would adiabatically follow the change of the quantization axis from |vrel at SC to |E inside the guiding field. According to eqs 19 and 21 all molecules are then low field seekers except for a few strong interacting small J states. This holds also if the induced dipole force (eq 22) is included only the total force weakens somewhat. The computed efficiency increases with growing rod voltage and reaches a factor 8 at U ) 8 kV. Responsible for this behavior is the increase of the harmonic force with U (eq 21). From the large number of trajectories that enter the guide and hit the rods or wall at U ) 0, an increasing fraction is bent toward the axis, starts oscillating, and eventually escapes the guide and hits the

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detector. An inspection of the trajectories shows that the deepening of the radial potential well ∝U2 (eq 21) correlates with a corresponding increase of the average kinetic energy of j tr,⊥ of the guided trajectories. Thus the mean the x, y motion, E maximal angle of incidence, defined analogous to eq 14

j tr,⊥ /mKBr)1/2 /V j KBr θ¯ ) (2E

(27)

spreads with U and the number of successful trajectories meeting j grows accordingly. The weaker forces in the condition θ j θ case b lead to somewhat smaller maximal kinetic energies of successful trajectories, and the guide becomes less efficient. The other extremal situation describes the M ) J curve where we have assumed that only the J, M ) J states are populated. The simulated guiding efficiency decreases gradually with rising U and eventually vanishes. The reason for this behavior is obvious: all molecules are high field seekers and with growing U an increasing number of molecules is pushed away from the axis and miss the detector. The strong discrepancy between experimental and theoretical results characterizes the used state distributions as unrealistic. But they are instructive as they illustrate two limiting cases that allow an interpretation of the guide’s performance also in cases of more realistic J, M state populations where both, hfs and lfs states are populated. The resulting guiding efficiencies are then just superpositions of curves similar to the J ) M and M ) 0 ones weighted by the population. Obviously, depending on the shape of the population function, the use of a quadrupole guide does not necessarily lead to a gain of intensity; a decrease of the efficiency is conceivable as well. In the following we discuss the performance of the guide for two realistic populations. The curve marked “sudden” incorporates an M state distribution that is due to the sudden change of the quantization axis from the initial direction |Vrel to the direction of the fringing field near SC that is essentially ⊥Vrel. The prerequisite for a sudden change is well fulfilled since the initial axis exists only for the collision time of about 10-12 s. The change is then by orders of magnitude faster than any oscillation period associated with ∆M transitions in the fringing field. The J, M population results from projecting the J, M ) 0 wave functions onto the new axis and with eq 25 is given by J P(J, M) ) P(J)[d M,0 (π/2)]2 J dM, 0

37,38

(28)

where the are Wigner’s d-functions. Accordingly, the full range of M states with an enhancement of the largest ones near |M| ) J is populated. Subsequent to the sudden change, the molecules encounter rotations of the field axis of maximal 90° while they slowly approach the entrance orifice within the flight time of about 0.5 ms. The change is now much slower than oscillation periods due to ∆M transitions, and hence it is justified to assume that the states follow adiabatically the local field as quantization axis. An excellent discussion of this matter is given in refs 39 and 40. The quantitative agreement between theoretical and experimental data supports strongly the assumptions made above. The insert in Figure 7 shows that the guiding efficiency continues to ascend up to 20 kV and beyond. In an attempt to improve the situation and benefit from the initial polarization, we have tried to avoid the sudden directional change and created an electric field parallel to the beam axis (buffer field) by two ring-shaped electrodes mounted symmetrically to SC and the beam axis 1 cm apart from each other.39,40 Applying the potentials (5 kV they generate near SC a buffer field of about 10 kV/cm. Now, only a change of the quantization axis during the flight time of the molecule from SC to the entrance orifice of about 0.5 ms takes place. That is,

Figure 8. Calculated flux velocity distributions of initially unpolarized molecules transmitted by the quadrupole at 0 kV (solid lines) and 8 kV (dashed line). The light histogram is the 0 kV result but normalized to unity to facilitate a comparison with the shape of the dashed histogram.

Figure 9. The same as in Figure 8 but for the rotational state population.

the adiabatic criterion is fulfilled and the states follow adiabatically the local quantization axis. The experimental result is presented in Figure 7 as open circles. The guiding efficiency is at 5 kV, a factor of 1.5 larger than those without buffer field but still by far smaller than the one for the ideal M ) 0 case. Obviously ∆M transitions (Majorana flops) do occur seriously. We blame for this the complicated structure of the buffer field near the aperture and the quadrupole. Very likely the transition field has zeros leading to a scrambling of the M states. This is supported by the simulation based on uniformly populated M states marked unpolarized that recovers these data quantitatively. Our trajectory calculation predicts a marked influence of the field on the velocity distributions and rotational state populations of the transmitted molecules. This is illustrated by the histograms shown in the Figures 8 and 9. The solid and dashed histograms represent the probability (number of trajectories) per bin that initially unpolarized molecules hit the detector at U ) 0 kV and U ) 8 kV, respectively. The U ) 0 kV histograms describe also the distributions defining the initial conditions of the trajectories such as the flux velocity distribution of the products of ref 20 (smooth curve in Figure 8) and the linear rise of the J-state population (eq 25) in Figure 9. The dashed histogram (8 kV) in Figure 8 turns out to be broader than the solid one (0 kV) and shifted toward smaller velocities. The ratio of the two probabilities at the same bin increases with decreasing VKBr indicating that at U ) 8 kV a larger fraction of the lfs trajectories is guided at smaller KBr velocities than at larger ones. The hfs trajectories need not to be considered since at 8 kV most of them are deflected away from the axis similar to the M ) J case in Figure 7. An inspection of the trajectories reveals the reason for the different shapes of the histograms: For a given j (eq 27) increases with decreasing mean j tr,⊥ is constant but θ UE

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j KBr of a bin and thus considerably more successful velocity V j for small KBr velocities trajectories meet the condition θ j θ than for large ones. It should be noted that the measured flux or density (Figure 6) distributions exhibit no significant shift toward smaller velocities with rising U. However, the marked increase of the density at very small velocities clearly indicates an enhanced efficiency of the energized guide for slower molecules in accord with the trajectory results. The linear increase of the J-state population for U ) 0 kV in Figure 9 (solid histogram) changes at 8 kV to a broad structure peaking at J ≈ 50 (dashed histogram). The ratio of the two populations at the same bin indicates that at U ) 8 kV a larger fraction of the lfs trajectories with small J are guided than with large J. This is due to the J-dependence of the forces. For given M-states they are strong at small J but weaken rapidly with growing J. j tr,⊥ and hence the mean maximal angle of Consequently, E j is larger for smaller J than for larger ones and the incidence θ fraction of successful trajectories decreases with growing J. Once trapped in a guide, the slow molecules can be conveyed to destinations much farther away from the site of generation than our surface ionization detector (259 mm) without significant loss of intensity; even bent guides are possible.17,23 In this way a beam of slow molecules could be supplied to experimental setups within extreme UHV environments for further studies such as spectroscopic investigations, slow particle reactions, and loading of three-dimensional traps. In the present study we have not measured the absolute flux of slow molecules. On the basis of the known absolute reaction cross section34 of σr ) 31 Å, the beam densities and geometry at SC (Table 1), we estimate for U ) 0 a slow particle flux at the detector of 2 × 108 s-1 cm-2. By using a beam guide with U ) 6 kV and a proper buffer field, the flux can be enhanced by a factor of 3 and by another factor of 3 or more if higher potentials are applied to the rods. In addition, the continuous K-beam oven in the present experiment could be replaced by a pulsed laser ablation source raising the beam density up to 3 orders of magnitude. Also the jet expansion of the HBr beam could be optimized providing another factor of 5-10. In summary, a flux of 1012-1013 s-1 cm-2 appears practical. The total flux of molecules scattered into the full solid angle, however, is by 3 orders of magnitude larger than the guided one. This large flux could be utilized for a continuous loading of an electrostatic quadrupole trap by letting the counterpropagating beams cross the trap’s center. In the Appendix we estimate the achievable number density of confined KBr molecules and find for the present operational conditions (Table 1) 1 × 107 cm-3. Employing the above-mentioned more intense beam sources, 1 × 1011 cm-3 can be reached. 5. Conclusion We have shown that slow KBr molecules generated by reactive collisions of counterpropagating beams can be guided to the detector by a linear electrostatic quadrupole field. TOF profiles of the guided molecules were measured for various rod potentials employing the standard method. The density velocity distributions peak at around 20 m/s (2.9 K) and extend with significant intensity to the experimental boundary of 14.2 m/s (1.4 K). The relative densities at the peak amount to 1:1.9:2.7 for U ) 0, 4, and 6 kV and near 14.2 m/s to 1:10:14. The presence of slower molecules is likely. The quadrupole guide enhances the total intensity of slow particles up to factors of 3 and 2.3 with and without buffer field. We estimate the total flux at the detector without guide to 2 × 108 s-1 cm-2. A numerical simulation of the guiding efficiency suggests that the

Liu and Loesch molecules at the entrance of the device are polarized and the M-state population results from the (sudden) projection of the J, M ) 0 wave functions of the nascent molecules with respect to vrel as quantization axis onto the fringing field at SC directed perpendicular to vrel. Subsequent to the projection the molecular states follow adiabatically the change of the field direction. The introduction of a buffer field parallel to the beam axis provides a considerably less enhancement of the flux than expected for a complete adiabatic following of the nascent J, M ) 0 states. The results suggest that the M-state population is randomized by zeros of the field occurring in the complicated transition region between buffer and quadrupole field. The trajectory calculations predict a marked effect of the energized quadrupole field on the velocity distribution and state population of the molecules. After the passage they are in the average slower and their most probable rotational state is smaller than those transmitted at zero field. The counterpropagating beams can be used to load an electrostatic trap directly and continuously. For this purpose the beams are arranged in a way that they cross the trap’s center to allow the nascent molecules to accumulate there until an equilibrium density is reached. Densities of about 1 × 107 cm-3 molecules are achievable with the present operational conditions, and by use of optimized parent beams, densities up to 1 × 1011 cm-3 are feasible. 6. Appendix In the following we attempt to estimate the maximal density of KBr molecules that can be confined in a trap using (continuous) counterpropagating beams of K and HBr. We consider an electrostatic quadrupole trap similar to the one used in the pioneering experiments of Meijer et al.41 The counterpropagating beams enter through a hole in the ring electrode (inner diameter 1 cm), cross the center of the trap perpendicular to the axis of rotation, and exit through another hole. The molecules are created inside the trap with the rate

N˙gain ) nKnHBrVrelVgainσgain

(29)

and lost by collisions at a rate of

N˙loss ) nKBrntotVVlossσloss

(30)

The KBr molecules accumulate in the trap until the total rate of KBr formation

N˙KBr ) N˙gain - N˙loss

(31)

vanishes and the rates of gain and loss become equal. The symbols n, N, N˙, V, V, σ denote number density, number, rate, velocity, volume, and cross section as indicated. Assuming that the density of the HBr beam is at least 1 order of magnitude larger than the density of the residual gases including the K beam, ntot and V can be replaced by nHBr and VHBr and one obtains the equilibrium density of KBr

Vrel Vgain σgain

〈nKBr〉 ) nK V V σ HBr loss loss

(32)

and the loading time

1/τload ) nHBrVHBrσloss

Vloss Vtrap

(33)

where we have used nKBr ) (NKBr/Vtrap) in eq 31. The loss and gain volumes are given by the beams’ cross section and the length of the beam sections within the trap (1 cm) and around the center (0.5 cm), respectively, and Vgain/Vloss

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) 0.5 holds. The trap volume is about Vtrap ) 0.4 cm3. The main loss channels are elastic and inelastic collisions between KBr and the beam gas HBr. For our estimate we use the integral elastic cross section σloss ) 3 × 10-14 cm 2 for the collision pair KBr · · · HBr based on dipole-dipole interaction. It corresponds to an interaction radius of 10 Å and should account for the majority of effective collisions. The estimate of the gain cross section is somewhat more involved as shown below. We assume that the trap is designed to stand potentials of (15 kV at the ring and cap electrodes providing a maximal field (at the ring) of 60 kV/cm. The field along the intersection volume is parallel to vrel and, except for a very small region around the center, interacts substantially with the trapped molecules. Thus it appears justified to assume that the trapped molecules remain in the initially populated J, M ) 0 state and follow the local field as quantization axis adiabatically. The potential energy well of the trap is deepest for molecules in the state J ) 9, M ) 0 with a depth of 3.6K. It decreases gradually toward larger and smaller J and reaches 2.0K and 1.3K at J ) 6, M ) 0 and J ) 15, M ) 0, respectively. Molecules in these states created at or near the trap’s center with kinetic energies smaller than the well depth are confined. According to eq 23 small J-states are correlated with near central collisions and thus with the excitation of high V-states.33 Assuming that always the highest accessible V-state is populated, the broad collision energy distribution of the parent beams allows then kinetic energies of KBr up to 2.5K. This means that for most of the molecules with 6 e J e 15 the well is sufficiently deep for trapping. The partial cross section for the formation of these states appears as a reasonable estimate for σgain. Equations 25 and 26 and the reaction cross section σr ) 31 × 1016 cm 2 eventually furnish σgain ≈ 0.2 Å. Inserting the adequate velocities, number densities (Table 1), and cross sections, eqs 32 and 33 provide the desired equilibrium density and loading time 7 -3 〈nKBr〉 ) 1 × 10 cm

(34)

τload ) 0.4 ms

(35)

and

After both beams were shut off at the same time, the confined molecules are available for further experimental studies. The short loading times suggest the use of pulsed beam sources. However, the trailing edges must be sufficiently steep to guarantee a shut off time significantly shorter than τload to avoid beam-induced loss of trapped molecules without adequate gain. If this is not practical, the pulses could be cut off by a rotating mechanical chopper synchronized to the valve analogous to the pulse shaper used in the present experiment. Acknowledgment. Support from the Deutsche Forschungsgemeinschaft is gratefully acknowledged. References and Notes (1) Hutson, J. M.; Soldan, P. Int. ReV. Phys. Chem. 2006, 25, 497. (2) Weck, P. F.; Balakrishnan, N. J. Phys. B 2006, 39, S1215. (3) Bodo, E.; Gianturco, F. A.; Dalgarno, A. J. Chem. Phys. 2002, 116, 9222. (4) Gonzalez-Sanchez, L.; Bodo, E.; Yurtsever, E.; Gianturco, F. A. Eur. Phys. J. D 2008, 48, 75. (5) Hudson, E. R.; Lewandowski, H. J.; Sawyer, B. C.; Ye, J. Phys. ReV. Lett. 2006, 96, 143004.

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