This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

IP Address: 131.114.129.125

This content was downloaded on 29/07/2014 at 13:21

Please note that terms and conditions apply.

A high-density collimated metastable He beam with population inversion

View the table of contents for this issue, or go to the journal homepage for more

1992 J. Phys. D: Appl. Phys. 25 1408

(http://iopscience.iop.org/0022-3727/25/10/005)

Home Search Collections Journals About Contact us My IOPscience

J. Phys. D: Appl. Phys. 25 (1992) 140e-1417. Printed in the UK

A high-density collimated metastable He beam with population inversion

0 Tommasi, G Bertuccellit, M Francesconi, F Giammanco, D RomaniniS and F Strumia Dipattimento di Fisica-UniversitA di Pisa, Piazza Torricelli 2, I-56126-Pisa, Italy

Received 20 January 1992, in final form 1 June 1992

Abstract. A method for obtaining an intense source of transversally excited helium atoms in the 2?S1 and 2'S0 metastable states (He') is described. As a consequence of the particular kinematics of electron-He atom collisions. the metastable beam is deflected 12" from the gfound state beam, with a suitable choice of experimental parameters such as electron beam energy and geometry of the excitation apparatus. The maximum measured value of the flux intensity is 1OI6 atoms si-l s-'. Due to a fairly narrow electron energy distribution of the electron beam, the velocity distribution of metastable atoms remains almost as sharp as that of the ground state atoms. As a consequence, the average velocities of the metastable beam and of the ground state atoms, scattered along the same direction, are separated from each other by more than 2 FWHM. The excitation apparatus shows a bistable behaviour, due to space charge effects, which strongly influences the He' formation efficiency.

1. Introduction

Metastable beams of noble gases, in particular of He, are used for spectroscopic purposes [l, 21, surface spectroscopy [3,4], differential scattering experiments [5], isotope separation experiments [6 ] , trace analysis [7], and laser velocity manipulation [8]. An intense population-inverted beam of metastable H e atoms can be used to obtain nonlinear generation of coherent xuv radiation by means of Raman scattering [9]. In this process, an incident photon of frequency vL is scattered into a photon of frequency v,, with hv, = Eo + hv,, where Eo is the energy of the metastable level. This scheme was proposed in the past as a method to con- vert visible or infrared radiation into a xuv coherent emission [10-12]. In fact, in the presence of a popu- lation-inverted medium, the xuv photons, emitted by spontaneous Raman scattering, can be single-pass amplified by stimulated Raman scattering.

In this paper we present a scheme to realize an intense, well collimated beam of metastable He with a population inversion obtained in an original way. The basic idea is to use the kinematic effects of the elec- tron-He collision at right angles to separate the meta- stable beam from the ground state beam. Owing to the large excitation energy of He metastable states (19.8 and 20.6 eV) and to the small He atomic mass, excited

t Present address: Institute de Fisica, Universidad de Tandil, Tandil, Argentina. t Present address: Frick Laboratory. Princeton University, New Jersey, USA.

0022.3727/921101408+ 10 $04.50 @ 1992 IOP Publishing Ltd

atoms experience a significant deflection from their initial direction, because of the momentum transfer in the collision with the exciting electrons. In the exci- tation apparatus elastic collisions between electrons and ground state He atoms are also possible, but these ground state atoms spread out over a larger angle when elastically scattered, owing to the different momentum transfer experienced by each atom. A spatial sep- aration of the atomic species can therefore be expected. A description of the resultant spatial dis- tribution is given in section 2 .

An efficient spatial separation, as well as the col- limation and the intensity of the metastabie beam, dep- end critically on the atomic velocity distribution of the main He beam. The choice of a supersonic He beam allows us to achieve an optimum performance with respect to beam intensity, collimation and population inversion, in agreement with predictions based on the kinematics of the collision (section 2).

To separate the beam of metastable atoms spatially, we have chosen a transverse electron excitation, although a longitudinal excitation would give meta- stable beams with better velocity resolution [ 2 , 5 ] . In any case, the estimated velocity resolution is good enough to introduce an additional separation from atoms in the ground state, due to the different vel- ocities of the two groups of atoms.

In principle, a longitudinal excitation could produce a metastable beam with a different velocity, from that of the ground state beam. Unfortunately, most meta- stable sources with longitudinal excitation, in which the

High-den$ity collimated metastable He beam

differential pumping

Flgure 1. Diagram of the experimental arrangement,

metastable atoms remain in the main beam, are affec- ted by the resonant energy transfer reaction

He* + He- He + He’

which leads to a significant velocity exchange between metastable and ground state atoms [SI. This type of source presents two groups of metastable atoms: one of them directly excited by electron impact, and the other, with a different velocity distribution, consisting of atoms which have undergone an excitation transfer collision with ground state atoms. The densities of the first and second groups of atoms depend linearly and quadratically on the main beam density respectively. Hence, in intense longitudinally excited sources, the velocity separation is rather poor. In our source, the resonant energy transfer is negligible because of the low density of the ground state atoms along the direc- tion of the metastable beam.

2. Kinematics of e--He collisions

Figure 1 shows the experimental apparatus in the final optimized configuration. The following discussion refers to this schematic.

It is convenient to analyse the collision problem both in the centre-of-mass frame (CM) and in the laboratory frame (LAB). The relationships between the velocities measured in both frames are shown in figure

The threshold energy for triplet and singlet meta- stable state production is 19.8 eV and 20.6 eV respect- ively. If the initial kinetic energy in the CM (practically the electron energy E.) is equal to the threshold energy Eo, after the collision atom and electron are at rest in the CM, whilst in the LAB they move with a centre-of- mass velocity VcM. Assuming an initial He beam vel- ocity uHc = 1700 m s-l and E. = Eo, the resultant angle between VcM and uHc is about 12”.

If E, > E,, the atom and electron have a residual velocity in the CM; therefore the energy conservation principle imposes that dHe (He final velocity in the CM) must lie within a sphere whose radius is

W.

The probability of a certain scattering angle is given by a differential cross section depending on the energy of the incoming electron. The relationship (131 between the metastable formation cross sections, au,/asL in the LAB and au,,,/aw in the CM, is

a”,=%ld”l asz a w d Q

where dw/dQ = a(0, q)/d(O, ‘D) is the Jacobian of the transformation; Q = (0, @) and w = (0, q) are

ve

He -b

a)

\

\ \

“H.

Figure 2. Collision e--He at 90” (a) Pictorial representation 01 the relationships between the velocities in LAB and in CM: the vectors v, and U, are measured in the LAB and in the CM respectively; the apices indicate velocities after the collision. (b) Limit angles ObseNed from the LAB (not to scale). (c) Plot of 0, and Om, against electron energy.

1409

0 Tommasi et a/

the angles in the LAB and in the CM respectively. Such a Jacobian has two singularities at Omax and Omin, which are the limit angles observed in the collision plane of the LAB (see figure 2(bj):

1 - 7 5 tan Omi, = ~

and

where 5 = MHeuHe/meus and 7 = (1 - Eo/E,)'/2. These singularities are integrable, leading to a very sharp metastable atom distribution if observed in the LAB. In addition, the differential cross sections [14-171 are larger at these limit angles, especially at Om,,.

At an electron energy of about 20eV, the total elastic cross section is about 100 times the cross section of metastable atom production [16,18]. However, elas- tically scattered atoms are distributed over a solid angle much larger than inelastic atoms. Because of kinetic energy conservation in an elastic collision, in the CM the atom velocity modulus does not change; thus, in the LAB the allowed scattering directions are within a cone whose V,, is the axis and uHe (the He velocity before the collision) is a generatrix. In this case, the limit angles are 0" and 23" (for E, = E& so that. due to the wide dispersion of the elastically scattered atoms, a region of inverted density of population can be expected in spite of the much smaller value of the inelastic cross section.

The results of a computer simulation confirm that a weak population inversion can be achieved under our choice of experimental parameters. Figure 3 shows the computed flux of metastable atoms minus the flux of

A€ = 0.30 SV rr - 0.60 cv

Flgure 3. Simulation of the electron-He atom collision at right angles. Figure shows the computed flux "-No (metastable minus fundamental) on a plane orthogonal to the main beam, 38 cm away from the centre of the excitation apparatus. Simulation parameters: Mach number of the fundamental beam, 40; FWHM of the electron energy distribution (assumed Gaussian), 0.6 eV; average electron energy, 0.3 eV above threshold.

1410

1 5 0 2 5 30 35 40

electron energy (ev) 2 0

b )

Figure 4. iaj Compurea veiociry aisrriburions aiong the He- flight direction. Simulation parameters as in figure 3. (b) Plot of velocity difference between metastable and fundamental atoms against electron energy.

elastically scattered ground state atoms through a plane orthogonal to the main beam.

Along the He* flight direction, metastable and ground state atoms have different velocities, whose difference is a function of the electron energy, namely

If this difference is greater than the widths of the vel- ocity distributions (see figure 4j, both species can be optically separated, i.e. a photon emitted by the excited atom cannot be absorbed by the atoms in the ground state. Thus, in the case of fluxes with com- parable intensities along the He* flight direction, an effective population inversion may also occur as a consequence of the Doppler shift.

From the above analysis it turns out that the efficiency of this separation strongly depends on the electro'n kinetic energy, which must be close to the excitation threshold, and on the width of the electron velocity distribution. In fact, over-energetic electrons or electrons with a broad energy distribution, destroy collimation by spreading out the velocity distribution of the He beam and mixing metastable and ground state atoms both in position and in velocity space.

High-density collimated metastable He beam

3. Experimental apparatus

The supersonic source of ground state helium atoms consists of a pulsed valve with a nozzle of 0.3 mm in diameter. The valve is a commercial LPV (Laser- technics), where pulsed outflow of He is obtained by a voltage pulse applied to a piezoelectric bimorph disc. The pulse duration is adjustable from 150 ps to several milliseconds. The maximum operating pressure Po of the LPV valve is 12 bar, above which a prompt opening becomes difficult. Using a 200 w s pulse, the 0.3 mm nozzle and Po = 12 bar, at the maximum voltage (200V), about 2 X 10" atoms per pulse can be produced.

The nozzle chamber is evacuated by a diffusion pump whose pumping speed limits the repetition rate to 2Hz. The beam passes into the second chamber through a 1.0 mm diameter skimmer placed 4 cm away from the nozzle. This chamber is pumped by a trapped diffusion pump (3200 I S K I ) . When the source is oper- ating, the background pressure is lower than 4 mTorr and 7 x mTorr in the first and second chambers respectively.

The density and collimation characteristics of the ground state beam were investigated by means of a microphone detector. Figure 5 shows a typical beam profile at 237" downstream from the skimmer entrance, for different values of the stagnation press- ure. The beam collimation can give'us a crude estimate of the Mach number -50. Time-of-flight (TOF) measurements furnish a Mach number >36, in agree- ment with the previous estimate.

The proportionality between the intensities of the metastable and fundamental beams is conserved until multiple scattering takes place, whose probability is given by a%&, where no is the ground state beam density, d the transverse beam dimension and U* the

4 1 r 3

- 0 - 1 5 - 1 0 - 5 0 5 10 1 5

x (mm)

Figure 5. Fundamental beam profile for different values of stagnation pressure Po in atm. Nozzle diameter, 0.3 mm; nozzle-skimmer distance, 40 mm; skimmer-detector (microphone) distance, 237 mm. Collimation (FWHM), 0.01 7 rad (0.97").

cross section for the elastic collision He*-He. The value of U* depends on the relative velocity, which, in our case, is about 350 m s-' . Experimental values of U* were given by Rothe and Neynaber [19] for the relative velocity range 100&3000 m s-'. The dep- endance of U* as the relative velocity was found to be small in the observed range, thus allowing an extrapo- lated value at 350ms-' of 0*(350) = 1.4 ? 0.2 x cmZ. To avoid multiple scattering the following relation must be verified:

u*nods 1.

For a beam diameter of 2mm, one obtains no s 4 x 10'' atoms C I I - ~ . The density of the main beam in the electron gun region is a factor of two below this value and multiple scattering effects are still weak.

In order to fulfill the requirements of section 2, the electron beam energy must be close to the metastable excitation threshold. Moreover, to obtain a high-inten- sity metastable beam, a large current is required.

A method to obtain high currents in transverse elec- tron guns is to increase the length of the emitting areas. Since metastable atoms are deflected from the original flight direction, the electrode spacing must be large enough to avoid intercepting a fraction of the deflected metastable atoms, in particular those excited at the entrance of the interaction region. Hence, an increase of the apparatus length requires an increase of the electrode distance, with a consequent decrease of cur- rent intensity, especially due to space charge effects which are enhanced by the relatively low energy of the electrons.

The electron gun consists of four electrodes (see figure 6), i.e. a cathode, two grids and an anode. The cathode is heated indirectly to obtain an equipotential surface, while the emitting area of 25 X 5 mm is coated by barium-strontium carbonate. Its activation needs special care in following the procedure indicated by Freund [20]. The grids are identical, both consisting of 50 wires (of diameter 60 pm) spaced by 0.60 mm. The anode consists of 10 thin (0.15 mm) tantalum plates. Electrons reach the anode surface travelling along the channels formed by the plates, thus reducing secondary electron emission and overheating. The inter-electrode distances can be varied and the best values are given in figure 6.

The gun operates continuously, in a voltage con- figuration which keeps the cathode at ground potential, and the grids and anode at positive potentials. A static transverse (to the main beam) magnetic field (= 200 gauss) improves the confinement of the electrons, and deflects the ions produced by too energetic elec- trons and/or by multiple collisions, out of the direction of the metastable beam.

The ground state beam passes between the equi- potential grids in a configuration which should yield almost monoenergetic electrons. The first grid is close to the cathode to produce an intense electric field on its surface, which extracts and injects the electrons in

1411

0 Tommasi et a/

I i ..... .... . . 5 o r~ ...................................................................... v2 ~ ...,.......... ", ,I

30

20

0 1 0 20 30 4 0 50 6 0

v, (VI

10

Fmni view

Side view

Flgure 6. The electron gun. K, cathode; G, , first grid; GZ, second grid: A, anode; W, tungsten wire. The cathode-first grid and the second grid-anode distances are 1 mm and 2 mm respectively. The inter-grid distance is 11 mm.

the field-free region between the grids. In principle, the grid potential determines the interation energy with the atoms.

The anode ib at higher volhge V, (some hundreds ot volts) to remove electrons from the second grid efficiently and, therefore, to reduce space charge effects. Nevertheless, in spite of the high-voltage anode, a space charge influence on the inter-grid field has been observed. The current-voltage characteristic curve of the electron gun exhibits an interesting bi- stability, which strongly affects the efficiency of meta- stable atom formation.

Figure 7(a) shows a typical hysteresis in the exper- imental curve of the anode current against the grid potential. The system can choose between two station- ary states in a grid voltage range limited by the values V , and V,. The preferred state depends on the initial value of the grid potential. For instance, if the grid voltage V, increases from 0 at VI, the anode current 1, undergoes a steep increase. When V, decreases, the anode current follows the upper curve until V, = V2, with V2<V1, and then suddenly drops. In cor-

1412

' I

0 2 4 6 8 1 0 1 2 ( 4

x (cm) b)

Flgure 7. (a) Typical bistability cuwe IA against VG. The figure shows the transition points V, and V,. (b) Intensities of the He' spatial distributions for the same value of grid voltage but in different bistable conditions (points A and B in (a)). Detector position is located 38cm from t h e excitation apparatus.

respondence with this fact, in the interval [V2, VI], two differeiii He' flux inzensities can be observed for ihe same value of grid potential VG. Whereas the current ratio between upper and lower curve is about 1.2, a noticeable difference arises in the metastable forma- tion. In fact, the ratio of metastable production efficiency between upper and lower values of current, is larger by two orders of magnitude or more (figure

We observed that the bistability does not depend on the presence of the helium beam. In fact the same phenomenon was discovered in 1925 in a thermoionic vacuum tube [21]. The interpretation of the effect was discussed in several papers [22-261 as a general feature of the space charge effects in valves with a large inter- electrode distance. The calculated characteristics show two or three possible values of the anode current over certain ranges of the anode voltage.

These theories may be applied to our excitation apparatus and may explain the difference in the meta-

7).

High-density collimated metastable He beam

stable atom formation shown in figure 7. Two different potential distributions correspond to the two stationary solutions of the anode current. In both cases a potential minimum is created between the two equipotential grids, so that the kinetic energy of the exciting elec- trons in the interaction region is lower than eV,, where e is the electron charge and V , the grid voltage. In one case, in the lower curve of the bistability, the potential minimum is so deep that the electrons are always below the metastable excitation threshold. In the other case, in the upper curve, the potential reduction is of only a few volts.

The values of the critical potentials V , and V , dep- end on several parameters, such as the cathode tem- perature, the inter-electrode distances and the anode voltage V,. Some observed features of the influence of these parameters are shown in figures 8 and 9. As an example, Vl moves toward lower values if V , increases. Both V1 and V , shift toward higher values if the cathode temperature, i.e. the injected current, increases.

The critical potential V , is very important. It must be kept below the He* excitation threshold and as close as possible to it. Only in this case a well collimated and intense beam was obtained. Otherwise the beam was much worse both in intensity and collimation.

4. Results

The metastable atoms are detected by an electron mul- tiplier in which the cathode is constituted by the first dynode. The detector is mounted on a moveable arm and it is equipped with a 4 mm diaphragm in front of the first dynode to resolve the spatial distribution of the He* flux on a plane perpendicular to the axis of the main beam. This plane is located 38 cm from the centre of the gun. In the detection plane, profiles are recorded scanning the detector position along the x axis (in the electron-atom collision plane) and the orthogonal w axis which crosses the x axis where the metastable beam encounters the detection plane (see

-v -1mv ---" i lsuv -1 .-.-.v -3mv -Y =6wv

z E 7 1

Flgure 10. Axes x and w in the detection plane

Figure 8. Dependence of the characteristic curve anode current la against grid voltage V, on the anode voltage. Heating power, 15 W.

160

E 140 z P , a w -

120 Y 3 100

5 80 c

60

1 0

20

0

P,.t7 w

P,-14 w

O E l o 2 0 30 4 0 P.11 5 0 w BO 7 0 80 L P.11 w

arid potential (VI

Figure 9. Dependence of the characteristic cuwe cathode current IC against grid voltage VG on the temperature. Anode voltage V,, 450 V. Pt represents the heating power in W.

Figure 11. Metastable beam profile ObSeNed near the lower critical point on the upper curve of bistability: VG = 26 V, lA = 25 mA, V, = 400 V. Heating power, 16 W.

1413

0 Tommasi et a/

8

0

% 5 10 1 5

-v = 2 4 v

2 4 6 6 10 1 2 14 16 x (cm)

Figure 12. Beam profile of the He* flux for low values of VG. The detection plane is located 38 cm from the excitation apparatus. Trace A, VG = 23 V; la = 20 mA, V, = 550v 8, V, = 24V. I,= 21 mA. VA= 550v C. VG = 25 V. I, = 450 V. Heating power is 15 W.

figure 10). Figures 11-14 show the recorded profiles along these axes.

We assume a value of 0.17 for the detection

emission) determined by Borst [26], induced by meta- stable atoms of rare gas into a dynode surface exposed to the air (also by Kohlhase and Kita [2]).

As noted previously, in order to maintain the criti- cal point V, at a value near the metastable excitation threshold, it is necessary to limit the injected current by controlling the cathode temperature. In spite of this, very high current could be obtained (>100mA). In addition, the fluctuations of the cathode emission can influence the stability of the system, e.g. by inducing transition to the lower curve near the critical points.

effiriency (which ccrrespnnds tn the secondary e k c t m n

5 10 d,n: ,1:, , , , R i ! ! ! ! ! ! ! ! . , . . . , . , ! ! t

2 4 6 8 10 12 14 16 (cm)

Figure 13. Beam profile of the He" flux under different conditions: A, VG = 25 V, I, = 22 mA, V, = 450 V; B, VG = 30 V. la = 28 mA, V, = 450 V; C, V, = 40 V, /, = 36 mA, V, = 400 V. Heating power, 15 W.

1414

8

? 5 m

ii - , * - s 4 II I

2

0 - 8 - 6 - 4 - 2 0 2 4 6 6

Y ("

Flaure 14. Beam Drofile of the He* flux alono the w axis: A , V G = ~ ~ V , 1~= '18mA. V,=45OV; B, V,29V, / A = 25 mA, V, = 450 V.

Figure 11 shows the profile of a very intense metastable beam, obtained by optimizing current and grid voltage in such a way that the critical point V , corresponds to an electron energy close to the threshold of metastable excitation. Continuous monitoring of current is required in order to maintain these optimal conditions. In this case, the measured flux was larger than loL6 He* atomssr-'s-', corresponding to a density of ?h"?l! 4 x 108 atems rm-3 at the exit nf the ercitatinn apparatus. It turns out that at such a density the loss of metastable atoms due to the He* + He* + He+ + e + He reaction is negligible. Compared with previous experiments (see table I), we obtained a flux almost one order of magnitude greater. Compared with experiments [20,27] in which electron- He collision at right angles is used, our improvement is even larger. This result is due to the capability to produce metastable atoms where the excitation cross section is maximum (close to the threshold) and to contain the spread after the collision.

4.1. Spatial distributions of the metss!ab!e beam

In order to obtain stable operation, the cathode tem- perature must be reduced until the lower critical point is below the excitation threshold, which implies a loss of about 30% in the metastable production. Figures 12-14 show the metastable beam profiles recorded in the stable regime to investigate the dependence on the grid voltage.

Figures 12 and 13 show the flux intensities as a function of the detector position along the x axis, for different values of the electron energy.

Figure 12 shows the He* distribution for values of VG just above the metastable excitation threshold. The beam profiles have the same shape and position but different intensities. When the value of VG is helow the excitation threshold only a fraction of electrons can produce metastable atoms. A further increase of V, does not improve the metastable flux, hut only induces a spread of the spatial distribution, when the over-

High-density collimated metastable He beam

Table 1. Comparison of the intensity and velocity resolutions of different metastable helium beams for longitudinal and right angles excitations (values with an asterisk have been estimated by Brutschy and Haberland [51).

~

Authors

~

He’ flux Velocity resolution (atoms sr-’ s-’) FWHM (%)

Longitudinal excitation Johnson and Delchar [3] Brutschy and Haberiand [5] 3 x 1 0 4 4 3 Kohlhase and Kita [Z] (pulsed beam) 10’5 3.8

Chen et a/ [27] 10’3 -30’ This work (pulsed beam) 10’6 7

4 x 1 0 ’ 4

Right angles excitation Freund [ZO] 5 x IO” -60’

lapping of the excitation cross section and the electron energy distribution is complete (in our conditions for V, = 25) (see figure 13).

Figure 13 shows important features of the beam profile which are in agreement with the predictions of section 2 . Trace A in the figure (V, = 25 V) shows one peak centred at the deflection angle of the He* atoms for an electron energy close to the excitation threshold. It turns out that the space charge field reduces the effective electron kinetic energy of about 4 eV. Profile B (V, = 30 V) shows two peaks whose narrow and broad features are due to the metastable He atoms deflected at the minimum and at the maximum angles respectively (see figure 2 ) . In profile C (V, = 40V) electrode screening prevents the observation of atoms deflected at the maximum angle.

The width of the beam profile A in figure 13, measured in a plane located at a distance of 38cm from the electron gun centre, is 3 cm full-width-half- maximum (FWHM). In this detection plane, but along

2.0 - - m - .? 1.5 - ... . ... m ol c

0

- ._

1.0 - ._ 5 .- H

H

t -I 0.0

20 30 4 0 50 60 70 grid voltage (V)

Figure 15. Singlet to triplet ratio as a function of the grid potential V, above cathode potential.

the transverse w axis, the beam width for V, = 25 V is about the same (figure 14). Taking into account the He* beam dimensions at the exit of the excitation apparatus, a beam divergence of less than 2” half- width-half-maximum (HWHM) can be calculated.

The width of the spatial distribution allows us to estimate the spread of the transverse velocity distri- bution, which can be related to the longitudinal vel- ocity distribution. For electron energies near the metastable excitation threshold, the electron-atom col- lision does not introduce noticeable modifications of the longitudinal and transverse atomic velocity dis- tribution. Hence, the width of the velocity distribution of the metastable beam can be assumed to be approxi- mately the same in the longitudinal and transverse directions. It turns out that the longitudinal velocity spread is less than 0.07 of the average velocity (FWHM).

Taking into account the velocity distribution of the elastically scattered atoms along the direction of the metastable beam (section 2), we obtain a result similar to that shown in figure 4(a), where the average vel- ocities of both beams are separated by more than twice the RNHM value of the distribution.

4.2. Singlet and triplet metastable contents

The metastable beam contains atoms in the singlet and triplet states. The singlet level is 0.8eV above the triplet-a triplet content is therefore unavoidable. Hence an experimental investigation of the relative population of 2’S0 and z3SI states is necessary.

The simplest method consists in quenching the atoms in the singlet state by means of a helium lamp and observing the detector signal difference when the lamp is turned on and off. Depopulation of singlet states is caused by helium lamp light excitation to the upper n’P levels, which decay preferentially towards the ground state. Depopulation of triplet metastable states does not occur, since transitions to the ground state are forbidden, and multiphoton ionization is neg- ligible because of the insufficient spectral lamp bright- ness.

Figure 15 shows the observed ratio as a function of grid voltage V,. As seen in section 4.2, the large space

1415

0 Tommasi et a/

Figure 16. Calculation of the metastable atom flux through the detection plane of figure 10. Parameters of the calculation: Mach number of the main beam, 50; average electron energy, 22.5 eV; electron energy resolution (HWHM) 0.5eV. (a) Singlet atom flux. (b) Triplet atom flux.

charge value in the interaction region reduces the effec- tive potential and then the electron energy. So the metastahle signal appears only at V , = 23 V. At this grid voltage the lamp does not affect the signal because the electron energy is below the singlet excitation threshold, so that the singlet to triplet ratio is 0. At V , = 24 V the metastable beam begins to show a singlet content and the ratio is about 1. By increasing the electron energy, the ratio also increases. At V , = 70 V the ratio is favourable to the singlet atoms at 2 to 1. Unfortunately, too energetic electrons destroy collimation, causing a decrease in the flux intensity. In addition, the electron energy must be as near as poss- ible to the singlet threshold for producing the popu- lation inversion. Thus the useful operation is when the ratio is about 1 and the flux of the 2'So atoms, under optimum conditions, is about 3 x l O I 5 atoms sr-' s-'.

Finally, we show how the profile B of figure 13 can be related to the measured singlet to triplet ratio. Taking into account the differential scattering cross sections [14,28], the singlet and triplet metastable atom fluxes through the detection plane were inde-

1416

1 8 16 1 4 1 2 10 8 6 4 2 distance from the main beam (cm)

Figure 17. Comparison between experimental and theoretical profiles. The experimental is profile B of figure 13; the theoretical trace is obtained by adding the two fluxes of figure 16 with a relative weight determined by the ratio experimentally found for V, = 30 V (figure 15).

pendently calculated, as shown in figure 16(a) and (b) respectively.

We performed a computer simulation similar to that for figure 3. The calculation of the singlet and triplet

shown in figures 16(a) and (b) respectively. The par- ticular distribution of the triplet atoms along the y direction is a consequence of the Jacobian of the trans- formation from the CM to the LAB. The differential scattering cross section for the singlet atoms has two maxima at 0" and NO", whereas the triplet has a maxi- mum at 90" [28], leading to two peaks where the con- tribution, due to the Jacobian and to the cross section, is maximum. The fluxes of figure 16 can be summed with the relative weight determined by the exper- imental ratio and superimposed to the experimental data (figure 17) showing a good agreement.

--+-*-hl- -e-- A th- dP?4~tinn d 2 n e I------ --- ,,.b,a~Lc,"'L. YLY.L. LI"..cy >..

5. Concluslons

In this paper we have investigated an original scheme to achieve an intense, collimated beam of metastable He atoms. Compared with previous experiments (see table I), we obtained a flux almost one order of mag- nitude larger without too great a reduction in the vel- ocity resolution (about a factor of two). The bistable behaviour of our electron gun makes large excitation currents with a relatively narrow energy distribution available. As a consequence, the spread of the deflec- tion angle and of the velocity are rather small.

Our experimental results are in good agreement with the kinematics of electron-He atom collisions described in section 2, so that a population inversion between metastable and ground state atoms is achieved. A possible application is the generation of XUV radiation by stimulated Raman scattering from the

High-density collimated metastable He beam

atoms in the 2’S, state. In fact we have observed the emission of coherent radiation at 53.7nm when the beam of metastable atoms is illuminated by a pulsed dye laser at 501.6 nm. Measurements are in progress and will b e reported in a forthcoming paper.

Acknowledgment

We thank Professor G Scoles for helpful discussions and for his critical reading of the manuscript.

References

[l] Rundel R D, Dunning F B and Stehhings R F 1974 Rev. Sci. Instrum. 45 116

[2] Kohlhase A and Kita S 1987 Reu. Sci. Instrum. 57, 2925

[3] Johnson P D and Delchar T A 1977 J. Phys. E: Sci. Inshum. 10428

[4] Riddle T W, Onellion M, Dunning F B and Walters G K 1981 Rev. Sci. Instrum. 25 797

[5] Brutschy B and Haberland H 1977 1. Phys. E: Sci. Instrum. 10 90

[6] Kudryavtsev Yu A, Petrunin V V, Sitkin V M and Lethokov V S 1989 Appl. Phys. B 48 93

[7] Bekov G I and Lethokov V S 1986 Laser Analytical Spectrochemistry ed V S Lethokov (Bristol: Adam Hilger)

and Cohen-Tannoudji C 1988 Phys. Reu. Len. 61 826

[8] Aspect A, Arimondo E, Kaiser R, Vansteenkiste N

[9] Goeppert-Mayer M 1931 Ann. Phys., Lpz 9 23

[lo] Braulich P and Lambropoulos P 1970 Phys. Rev. Lett. 25 986

[ l l ] Fornaca G, Giammanco F, Giulietti A and Vaselli M 1974 Nuovo Cimento Len 9 395

[12] Rothenberg J E, Young J F and Harris S E 1983 IEEE J . Quant. Electron. 19 1795

1131 Fahrikant I I, Shpenik 0 B, Zavilopulo A N and Snegurskii A V 1983 Opt. Spectrosc. 55 370

[14] Fon W C, Berrington K A and Kingston A E 1980 1. Phys. E: At. Mol. Phys. 13 2306

[15] Fon W C, Betrington F A , Burke P G and Kingston A E 1981 1. Phys. E: At. Mol. Phys. 14 2921

[16] Zetner P W, Westerveld W B, King G C and McConkey J W 1986 J. Phys. B: At . Mol. Phys. 19 4205

Mol. Phvs. 16 613 [17] Johnston A R and Burrow P D 1983 J. Phys. B: At.

[le] Buckman S’J and Lohmann B 1986 J . Phys. E: At . Mol. Phvs. 19 2547

[19] Rothe E W-and Neynaber R H 1965 J . Chem. Phys. 42 3306

[20] Freund R S 1970 Reu. Sci. Instrum. 41 1213 [21] Gill E W B 1925 Phil. Mag. 49 993 [22] Plato G, Kleen Wand Rothe H. 1936 Z. Phys. 101

<no ””, Kleen Wand Rothe H 1937 Z. Phys. 104 711

[23] Fay C E, Samuel A L and Shockley W 1938 Bell System Technol J 17 49

Strutt M J 0 and Van der Ziel A 1937 Physica 6 977 1241 Walker G B 1945 Wireless Enc. 22 157 . > .

Rodda S 1946 Wireless Eng. 2 j 140 [25] Bull C S 1947 1. IEE 95 17 [26] Borst W L 1971 Rev. Sci. Instrum. 42 1543 [27] Chen C H, Haherland H and Lee Y T 1974 1. Chem.

Phvs. 61 3095 [28] Pichou F, Huetz A, Joyez G, Landau M and Mazeau J

J . Phys. E : At. Mol. Phys 9 933

1417