CER

N-S

PSC

-201

1-00

7/

SPSC

-SR

-079

17/0

1/20

11

Progress report on the AEGIS experiment

The AEGIS/AD-6 collaboration

1. Introduction and Overview

The primary scientific goal of AEGIS is the direct measurement of the Earth‘s localgravitational acceleration g on H. In a first phase of the experiment, a gravity measurementwith 1% relative precision will be carried out by observing the vertical displacement (usinga high-resolution position sensitive detector) of the shadow image produced by an H beam,formed by its passage though a Moire deflectometer, the classical counterpart of a matter waveinterferometer. This measurement will represent the first direct determination of the effect ofgravity on antimatter.

The essential steps leading to the production of a pulsed cold beam of H and the measurementof g with AEGIS are the following (Fig. 1):

• Production of positrons (e+) through a Surko-type source and accumulator;

• Capture and accumulation of p from the AD in a cylindrical Penning trap;

• Cooling of the p to sub-K temperatures

• Production of positronium (Ps) by bombardment of a cryogenic nanoporous material withan intense e+ pulse;

• Excitation of the Ps to a Rydberg state with principal quantum number n = 25 ∼ 35;

• Pulsed formation of H by resonant charge exchange between Rydberg Ps and cold p ;

• Pulsed formation of an H beam by Stark acceleration with inhomogeneous electric fields;

• Determination of g in a two-grating Moire deflectometer coupled with a position-sensitivedetector.

The proposal submitted to the SPSC, and which was approved in December 2008 [1], isbased on achieving these steps. The feasibility of the first two points had been conclusivelydemonstrated by the ATHENA and ATRAP collaborations (see, in particular [2, 3]), but theremaining points, while based on reasonable extrapolations of known results or calculations,remained to be validated, and only an initial technical design was available at that time.

In the following, we will discuss the remaining aspects of the proposed technique in moredetail, point out the advances achieved in 2010, and give an overview of the questions thatremain open.

1.1. Antihydrogen recombination and beam formation

An H recombination scheme based on resonant charge exchange with Ps was first proposedalmost twenty years ago [4]. The reaction proceeds according to the equation

Ps∗ + p→ H∗ + e− (1)

Ps

laser excitation

antiproton trap

positronium converter

e +

Ps

Ps*Ps*

H*

H*H beamH*

accelerating electric field

Figure 1. Proposed method for the production of a pulsed beam of cold H atoms.

where the star denotes a highly excited Rydberg state. This reaction owes its appeal to thefact that the cross-section scales approximately with the fourth power of the principal quantumnumber. In addition, it creates H in a narrow and well-defined band of final states. Mostimportantly, H formed with p at rest is created with a velocity distribution dominated by thep temperature, hence the surrounding (cryogenic) environment [5]. This is in stark contrastto the rather high H temperature observed when using the nested-well technique pioneeredby ATRAP and ATHENA [6, 7]. Our proposed technique is conceptually similar to a chargeexchange technique based on Rydberg cesium [8] which has been successfully demonstrated byATRAP [9], but offers somewhat greater control of the final state distribution of H and, moreimportantly, allows pulsed production of H.

The principle is illustrated in Fig. 1. The Ps emitted from the porous insulator material areexcited to Rydberg states. They then traverse a Penning trap region in which ∼ 105 p havebeen accumulated, stored and cooled to ∼100 mK. The low temperature requirement on theantiprotons comes from the requirement that the antihydrogen atoms that will be formed willhave a velocity that is low compared to the velocity of several 100 m/s that they will achieveafter acceleration. To reach such a low temperature, the Penning trap is coupled to a 50 mKdilution refrigerator, and the antiprotons are coupled to the low temperature environment byembedding them in an electron plasma. The later will cool through synchrotron radiation, aswell as through a tuned circuit; furthermore, evaporative cooling of the pre-cooled antiprotonsis being envisaged. The charge exchange cross-section is very large (∼ 107A2 for n = 35) andreaches a maximum when the e+ and p relative velocities are matched. Taking into account thecorresponding kinetic energy, as well as a smaller contribution due to converted internal energy,H is created at velocities of 25 ∼ 80 m s−1.

While neutral atoms are not sensitive (to first order) to constant electric fields, they doexperience a force when their electric dipole moment is exposed to an electric-field gradient.Since the dipole moment scales approximately with the square of the principal quantum number,Rydberg atoms are especially amenable to being manipulated in this way. Such so-called Starkacceleration (and deceleration) has been successfully demonstrated, among others, by one of theAEGIS groups with (ordinary) hydrogen after excitation to the n = 22, 23, 24 states [10, 11].In these experiments, accelerations of 2 × 108ms−2 were achieved using two pairs of electrodes

at right angles to each other. A hydrogen beam traveling at 700 ms−1 was stopped within 5µs over a distance of only 1.8 mm. We intend to use a similar field configuration, generatedby axially split electrodes within the cylindrical geometry of a Penning trap, to accelerate theformed H atoms to about 400 ms−1 in the direction of the deflectometer apparatus.

1.2. Gravity measurement

In matter wave interferometers of the Mach-Zehnder type [12, 13], three identical gratingsare placed at equal distances L from each other. The first two gratings produce an interferencepattern at the location of the third. That pattern has the same period d as the gratings, and itsposition perpendicular to the diffracted particle beam can be determined precisely by displacingthe third grating and recording the overall transmission with a particle detector. Under theinfluence of gravity, the interference pattern is vertically displaced (it falls) by a distance

δx = −gT 2 (2)

where g is the local gravitational acceleration and T is the time of flight L/v between each pairof gratings of a particle beam traveling at velocity v.

Contrary to such true interferometers, which place a very stringent limit on the acceptablebeam divergence (and thus antihydrogen temperature at production), the so-called Moiredeflectometer, in which diffraction on the gratings is replaced by a (classical) shadow pattern ofthose particles that converge onto the third grating, works in the classical regime. Interestingly,the gross characteristics of the interferometer are retained [14], in particular, the verticaldisplacement of the interference pattern according to Eq. (2). A three-grating Moiredeflectometer has been used to measure the local gravitational acceleration to a relative precisionof 2 × 10−4 with a beam of argon atoms traveling at an average velocity of 750 ms−1 [14]. Indeparting from the three-grating deflectometer, we intend to replace the third grating by aposition-sensitive silicon strip detector (see Fig. 2). Antihydrogen atoms impacting on thedetector plane annihilate, and the impact point can be reconstructed by means of the energydeposited locally by the annihilation products.

The value of g is extracted from two primary observables (time of flight T and verticaldisplacement of the fringe pattern δx). The periodic nature of the arrangement means thatfor a given value of T , the impact point will have dropped by a well-defined amount δx(T ),modulo the grating period. By varying the accelerating field gradient (and thus varying thevelocity of the antihydrogen atoms), or simply through the spread in velocity of the ensembleof antihydrogen atoms, the quadratic dependence of δx on T is probed.

Our simulations have shown that in order to perform a measurement of g to 1% relativeprecision, about 105 H atoms at a temperature of 100 mK will be required, equivalent to severalmonths of data taking at the AD. In these simulations, a grating period of 80 µm was used, anda finite detector resolution of 10 µm was taken into account.

2. Preparatory work and construction

2.1. Main apparatus, positron accumulator and transfer section

The AD-6 experiment is sited in the last available area of the AD hall, the ”DEM” zone. Thedimensions of the zone, but also beam and safety requirements, impose a number of constraintson the overall layout of the experiment, as well as on specific components of the apparatus.The overall layout follows a configuration in which the positron accumulator is positioned above

grating 1 grating 2

position-sensitivedetector

L Latomicbeam

Figure 2. Schematic of the principle of the Moire deflectometer consisting of two gratingscoupled to a position-sensitive detector.

the antiproton beam line; positrons are transferred through a transfer section; cryogenics forthe main magnets and the dilution refrigerator are positioned above the magnets; lasers arepositionned on a laser table immediately to the side of the central magnets; the control room issited outside the building.

In 2010, the zone and the beam line have been prepared for installation of the experimentalapparatus: gas and water pipes have been repositioned, a light-weight support structure for theATRAP positron beam line, which crosses above the DEM zone, was installed, the beam line(which supplies antiprotons also to the AD-4 experiment) has been put in place and is ready forcommissioning. A number of further modifications are still under way and will be carried outin the next months: removal of the walkway above the experiment, preparation of the rails andplatforms inside the zone, preparation of the positron accumulator support structures.

The main apparatus consists of two magnets: a 5T magnet (where field strength is importantin maximizing the trapping efficiency for antiprotons delivered from the AD), and a 1T magnetin which the antihydrogen beam will be produced (and where field homogeneity is importantin obtaining very low-temperature antiprotons). The custom design integrates the super-conducting magnets and their cryostats with the dilution refrigerator and its cryostats, as wellas allowing access from the two sides (antiproton and positron injection on the upstream sideand antihydrogen beam extraction on the downstream side) and in the region between the twomagnets (cabling and diagnostics). Laser light for Positronium excitation is injected in thecentral region and transported to the antihydrogen production region via glass fibers.

The fabrication of the coils and cryostats of the magnets and of the central structure requirepainstaking care because of the high demands on field homogeneity. The winding station forthe coils was completed early in 2010, and the two main coils (5T and 1T), as well as the smallfield-shaping coil at the exit of the 1T magnet, were wound, baked and tested for faults. Thenext step is the fabrication of the correction coils that will allow fine-tuning the field insidethe two main coils (by end of February 2011) and assembly within the cryostats and tests. Inorder to commission the trapping of antiprotons in 2011 (optimization of the degrader thicknessin order to maximize the number of trapped antiprotons), we are prioritizing the constructionof the 5T magnet, which will be completed by summer 2011, and then installed, while the 1T

Figure 3. Left: Side view of the antiproton beam line and of the accumulator above it, followedby the 5T and the 1T magnets. Right: Photo of the DEM zone with AD beam line.

Figure 4. Cross-section through (and top view of) the 5T and 1T magnets, showing the detailsof the cryostats, transfer section and electrodes.

magnet will be installed at the beginning of 2012.Achieving the sub-Kelvin antiproton temperatures required to form a slow-moving beam of

antihydrogen atoms requires, in addition to the presence of a dilution refrigerator, a very highhomogeneity of the 1T field in which the antiprotons will be stored and cooled. The design of

Figure 5. Photos of the 5T and 1T coils, during winding and after completion.

the magnet system achieves these two objectives, and provides a smoothly decreasing transitionbetween the 5T and the 1T fields, which allows a loss-free transfer of antiprotons and positronsfrom the 5T trapping region to the 1T central region. The design of the magnets, and thecare in their construction should ensure that we can reach a homogeneity in the antihydrogenproduction region of the 1T magnet of 1 part in 105, although precise field maps of the overallsetup will only be available in the beginning of 2012. While sub-Kelvin temperature antiprotonshave not yet been achieved, recent developments in evaporative cooling of charged plasmas [15]indicate that this goal is closer to being reached, but also underline the care that must be takenin the design of the electronics that determine the potentials of the electrodes.

In parallel, construction of the positron accumulator has started in the summer of 2010,and is well advanced; an order for a 22Na source has been placed and it will be delivered toCERN in May 2011. The initial source will be weaker (50 %) than the nominal source, toallow gaining experience with trapping and manipulation of positrons; a second, stronger sourcewill be ordered and delivered once the initial commissioning of the apparatus with positronsand positronium formation will have been successfully carried out. Three elements constitutethe positron accumulator: the ”RGM” (housing the source and the moderator); the ”ABPS”(housing the buffer gas trap); and the accumulator. The first two elements are being procuredfrom the First Point Scientific company, and are ready to be assembled and tested in the nextweeks, all long-lead time items having arrived there. The third element combines infrastructurefrom First Point Scientific and a high-quality (∆B/B ∼ 10−4) solenoidal magnet which iscurrently under construction in Novosibirsk. The timeline foresees delivery of all elements toCERN by the end of May of 2011, and installation in the zone over the summer.

The final element that combines the AD beam line and the positron accumulator is thetransfer section, which maintains the 0.1T magnetic field of the accumulator magnet throughout,and also allows horizontal extraction of positrons from the accumulator onto a separate positronexperimental platform situated between the accumulator and the 5T magnet. Its design wascompleted in the second half of 2010, and construction is close to completion, with a delivery

of the completed transfer section to CERN scheduled for February 2011, where it will be NEG-coated, before installation in the DEM zone in May 2011.

2.2. Positronium production

In the AEgIS experimental design, antihydrogen is produced by a charge exchange reactionbetween positronium (Ps) excited into a Rydberg state and an antiproton. To have a chargeexchange reaction cross section suitable for the experiment, it was calculated that the Ps velocitymust be equal to or lower than ∼ 104 m s−1, corresponding to a temperature of 150 K. Positronsinjected into nano-porous silica based materials efficiently form Ps with kinetic energies of 1-3eV. Ps atoms cool in the porosities, losing their kinetic energy by scattering on the walls of theporosities. Eventually, Ps can thermalize to the temperature of the sample. If porosities areconnected with the vacuum, a fraction of Ps atoms can escape. We have predicted [16] that, dueto quantum confinement, it is necessary and sufficient to tune the size of the nano-porosities forcooling down Ps to a specific temperature T. To fulfill this requirement, we have synthesizedseveral porous materials and have succeeded in producing a novel target of silicon in whichordered nano-channels were realized by electrochemical etching. The nano-channels, orientedwith their axis perpendicular to the target surface, were oxidized in air for two hours at 100◦C. This novel procedure allowed tuning the size of the nano-channels from 5 to 50 nm. Thenano-channels extend about 1.5-2 micron in depth.

Figure 6. Ortho-positronium fraction formed in nano-channels with size 4-7 nm (sample #0),8-12 nm (#1), 8-14 nm (#2), 10-16 nm (#3), 14-20 nm (#4), 80-120 nm (#5), as a function ofthe positron implantation energy (mean positron implantation depth, upper scale). 95% of theformed Ps escapes in vacuum from the nano-channels. From [17]

The resulting minimal temperature for nano-channels is then expected to lie between 116K (for 5 nm channels) and 7 K (for 20 nm channels). In Fig. 6 we show the o-Ps (orthopositronium) fraction formed in nano-channels with sizes between ∼ 5 and ∼100 nm . A fittingprocedure with the Ps diffusion equation leads to the conclusion that about 95 % of the formedPs escapes from the channel at each positron implantation energy (x axis) or mean positron

implantation depth (upper axis). It can be observed that at 10 keV positron implantationenergy, the Ps yield is about 23-25 % in all the samples.

A TOF (Time of Flight Apparatus) has been built in 2010 to measure the velocity of Psescaping into vacuum from nano-channels. This apparatus was set up at the slow positronbeam at Trento. The measurements were done in a target with nano-channels of 5-8 nm size.In Fig. 7 we show the TOF spectra at 7 keV positron implantation energy, with the targettemperature held at 300 K, 200 K, and 150 K. The average Ps energy corresponding to the Psvelocity perpendicular to the sample is 0.096 eV at 300 K, and decreases to 0.076 and 0.068eV at 200 and 150 K , respectively [18, 19]. On the right hand side in the same figure, thePs energy spectra are displayed in a semi log scale as obtained by multiplying by t3 the dataof Fig. 7. The two-exponential fits for each spectrum indicate the presence of two differentbeam Maxwellian distributions at the indicated temperature. At each temperature there is aPs fraction that escape thermalized from the target. These fractions are 5 %, 4 % and 2.5 % ofthe implanted positrons at 300 K, 200 K, and 150 K, respectively.

These results [18] are the first evidence of Ps cooling and thermalization below roomtemperature. Cooling and thermalization of Ps was possible due to the selected size of thechannels (5-8 nm) that allows avoiding Ps quantum confinement. In recent experiments [20, 21]carried out with disordered porous silica samples with pore size around 3 nm, other groups toohave reported on an absence of Ps thermalization at room temperature, confirming our previsionof quantum confinement [16]. Additionally, we have shown [22] that for specific materials, Psemission happens even for cryogenic (∼10K) targets.

Both the Ps velocity and the fraction of thermalized Ps, obtained with the silicon target withnano-channels, are suited for the AEgIS experiment. With a positron beam with a bunch of ∼109 positrons, a cloud of about 2× 107 Ps atoms could be obtained into vacuum at 150 K.

Our next steps will be:

• To assemble a TOF chamber at the high intense positron source NEPOMUC at FRMIIin Munich to look at Ps cooling below 150 K. An intense positron beam is necessary tocarry out TOF measurements in short time to avoid contamination of the surfaces at lowtemperatures. The corresponding beam time is foreseen for February 2011.

• To measure TOF spectra in target with different nano-channel sizes to select the best targetwith the best compromise between maximum yield of cooled Ps and lower temperature ofPs.

• To work on the oxidation processes of the inner walls of the nano-channels to investigateoptions to increase the Ps yield.

2.3. Laser systems and Positronium excitation

The photo-excitation of Ps to Rydberg states requires photon energies close to the bindingenergy of 6.8 eV. Laser systems at the corresponding wavelengths (180 nm) are not commerciallyavailable. We are therefore planning to perform a two-step excitation, from the ground stateto the n = 3 state (λ = 205 nm), and then to the n = 35 Rydberg band (λ ∼ 1670 nm) [23].Two pulsed-laser systems, both of which are pumped by the same Nd:YAG laser, have beendeveloped and tested in the course of 2010. Both systems must provide sufficient power toexcite the emitted Ps within a few ns and must be geometrically matched to the expandingcloud. Furthermore, the bandwidths of the lasers must be tailored to the transition line widthbroadened due to the Doppler effect as well as level splitting due to the motional Stark effectand the linear and quadratic Zeeman effect.

In 2010, we have focused our efforts on building, testing and characterizing the two systems,and verifying that we can transport the resulting power via glass fiber. The pump laser of

Figure 7. Left: Ps TOF spectra at 7 keV positron implantation energy with the target attemperature of 300 K, 200 K and 150 K. The average time between production and annihilationta of the o-Ps TOF distribution is marked by vertical dash-dotted lines. The o-Ps energycorresponding to ta is indicated. Right: Ps energy spectra in a semi log scale obtained from theleft plot. The two-exponential fits for each spectrum show the presence of two different beamMaxwellian distributions at the indicated temperature. From [18]

the whole system will be a 650 mJ Q-switched Nd:YAG laser delivering a 4 ns pulse. Theradiations are produced through second-order polarization in optical crystals (Fig. 8). The 205nm radiation for the first transition is obtained by summing in a non-linear BBO crystal the266 nm fourth harmonic of the 1064 nm Nd:YAG pulse and the 894 nm radiation generated inan optical parametric generator (OPG) by down-conversion of the second harmonic of the samelaser. The other wavelength (around 1670 nm) is generated in a single step by an OPG startingfrom the same pump laser and then amplified by an optical parametric amplifier (OPA) system.

The system has been completely designed and is partly completed: the energy of of 174 µJrequired to saturate the second transition has been exceeded, 3 mJ having been reached afteran OPA using a temporary Nd:YAG laser of only 80 mJ energy per pulse. Also for the firsttransition, we have reached (but not yet exceeded) the required 200 µJ at 205 nm. We have alsoshown that we can transport the IR laser light at the required intensity with a glass fiber overseveral meters without damaging the fiber. We intend to do the same for the UV light, havingestablished that neither attenuation, nor speckle formation are of concern. The remaining openquestion (possible solarization/damage of the fiber at full UV laser intensity) is undergoing testsin the course of January 2011.

In parallel, investigations on the quasi-continuous-wave (QCW) Lyman-alpha laser havecontinued. The scheme we are concentrating on uses a three step resonant four-wave-mixingscheme in Hg; this configuration has already been employed by the Hansch / Walz group in thecontinuous-wave regime. The wavelengths for each step are: 1) 254 - 257 nm, 2) 399 - 408 nm and3) 546 nm. For the first step, we focus on a diode-pumped Yb:GdVO4 frequency-doubled laser;we verified that the fundamental wavelength of this laser medium can be tuned over the range1012 - 1030 nm (506 - 515 nm after doubling), its thermal properties are rather good and the

Figure 8. Sketch of the set up for the laser excitation of Rydberg Ps. The wavelength of then=1 → 3 excitation is at 205 nm; the wavelength of the n=3 → 20..30 excitation is at about1670 nm.

optimization of the Yb concentration should lead to the expected high power. A QCW externaldoubling cavity has been tested with a BBO crystal to attain the UV range. Up to now, the peakpower is limited to a few watts due to the large walk-off of the crystal and to photorefractiveeffects, but other crystals will be tried (e.g. CLBO and ADP). The locking electronics system isin progress. Concerning the second step, we plan to use a frequency doubled Ti:Sapphire laser,rather than an optical parametric oscillator, for stability reasons. A crystal of Nd:GdCOB hasbeen tested for the third step; first results are encouraging, but need to be followed up.

2.4. Low temperature antiprotons

Achieving a sufficiently cold cloud of antiprotons is a central requirement of the experiment;the target antiproton temperature of 100 mK requires thermalizing the electrodes (which formthe harmonic well in which the antiprotons will be held before interacting with the excitedPositronium) to the temperature of a dilution refrigerator (50 mK), while at the same timeensuring electrical insulation. In 2010, we have continued our investigations of different optionsto achieve this thermal conduction while maintaining electrical insulation: a first solution whichputs individual electrodes into direct contact with the 3He/4He mixture within the mixingchamber (”rod solution”), and a second solution which involves coupling the electrodes to thecopper surface of the mixing chamber via a thin layer of Indium. The former solution, whileeffective, introduces a large amount of copper in the vicinity of the production region of theantihydrogen atoms, rendering diagnostics based on reconstructing the annihilation products offormed antihydrogen on the inner surfaces of the electrodes very inefficient. The later solutionhas been refined in the course of 2010, and we have converged on a design based on gold-coatedsapphire electrodes. These offer the benefit of a significant reduction of multiple scattering andfar simpler assembly without a disruptive reduction in the heat transfer between the electrodesand the mixing chamber as compared to the rod solution. Tests are under way on a completeprototype (end of March 2011), based on which a full prototype will be built and tested at the

Figure 9. Left plot: Heat transfer for Sapphire-metal-copper interfaces. Shown is the heattransfer for different combinations as a function of the temperature difference between theelectrode and the mixing chamber. Right plot: schematic design of the the electrodes andthe mixing chamber.

end of 2011.

2.5. Deflectometer

A test setup of the final deflectometer has been constructed and tested in Heidelberg in thecourse of 2010, to determine whether the individual elements could be fabricated to the requiredtolerances, and whether a sufficient stability of the set-up could be achieved, as well as to preparefor a measurement with normal atoms (Ar atoms initially). The stability was investigated via aMach-Zehnder interferometer using a support structure identical to the one that will be deployedin AEGIS. After implementing all stabilization measures, the resulting stability of the apparatusover one hour was found to be 30 nm, 1/1000th of the grating period. This stability is well inexcess of what is required for the antihydrogen measurement. A sketch of the alignment schemeis shown in Fig. 10. Fabrication of the gratings themselves has proved challenging, but it nowappears possible to fabricate 6” wafers with a thickness of a few hundred µm incorporating therequired transmission gratings, support structures and optical gratings for the Mach-Zehnderinterferometers. Also the holders that will precisely position the wafers on the support structurehave designed and are under construction. Finally, an inductively-coupled-plasma source willprovide the metastable Argon atoms with the sufficiently high flux (> 1014atoms/sec × sr)needed for a measurement of g with with a precision of ∼ 10−6. This measurement should takeplace in 2011.

Figure 10. Sketch of the set up for the alignment of the deflectometer for the Ar gravitationalmeasurement.

3. Summary and beam request

Construction is advancing well on the AEGIS experiment, whose design is based upon thebroad experience gained with the ATHENA and ATRAP experiments at the AD, a seriesof ongoing related experiments, tests and developments, as well as extensive simulationsof critical processes (charge exchange production of H, Stark acceleration and propagationthrough the Moire deflectometer, resolution of the position-sensitive detector located at theend of the deflectometer). The proposed gravity measurement merges in a single experimentalapparatus technologies already demonstrated or based on reasonable additional development.Construction, test and commissioning of the magnets is being staged, with the 5T magnetplanned to be completed in summer of 2011, and the 1T magnet a few months later. Thepositron accumulator and the positron source will arrive at CERN in early summer, and willbe installed and commissioned in situ. The apparatus will be installed in the DEM zone inthe summer of 2011 with the objective of commissioning the trapping of antiprotons in the 5Tmagnet at the end of 2011, and subsequently, the transfer and accumulation of positrons intothe main apparatus. We will focus on implementing and validating the different steps requiredto form antihydrogen in the AEgIS apparatus in 2012.

In order to optimize the trapping of antiprotons by varying the thickness of the final degrader,we request one quarter of the antiproton beam time for five weeks in 2011, at thelatest possible date to ensure that the equipment is ready.

[1] CERN-SPSC-2007-017 ( http://cdsweb.cern.ch/search?of=hd&p=reportnumber:CERN-SPSC-2007-017 )[2] L.V. Jorgensen et al., ATHENA Collaboration, Phys. Rev. Lett. 95 (2005) 025002.[3] G. Gabrielse et al., ATRAP Collaboration, Phys. Lett. B 548 (2002) 140.[4] M. Charlton, Phys. Lett. A 143 (1990) 143.[5] B.I. Deutch et al., Hyperfine Interact. 76 (1993) 153.[6] G. Gabrielse et al., ATRAP Collaboration, Phys. Rev. Lett. 93 (2004) 073401[7] N. Madsen et al., ATHENA Collaboration, Phys. Rev. Lett. 94 (2005) 033403[8] E.A. Hessels, D.M. Homan, M.J. Cavagnero, Phys. Rev. A 57 (1998) 1668[9] C.H. Storry et al., ATRAP Collaboration, Phys. Rev. Lett. 93 (2004) 263401

[10] E. Vliegen, F. Merkt, J. Phys. B 39 (2006) L241.[11] E. Vliegen et al., Phys. Rev. A 76 (2007) 023405.[12] L. Zehnder, Z. Instrumentenkunde 11 (1891) 275.[13] L. Mach, Z. Instrumentenkunde 12 (1892) 89.[14] M.K. Oberthaler et al., Phys. Rev. A 54 (1996) 3165.[15] G. B. Andresen et al., ALPHA collaboration, Phys. Rev. Lett. 105, 013003 (2010)[16] S. Mariazzi, A. Salemi and R. S. Brusa Phys. Rev. B 78, 085428 (2008)[17] S. Mariazzi, P. Bettotti, S. Larcheri, L. Toniutti and R. S. Brusa Phys. Rev. B 81, 235418 (2010)[18] S. Mariazzi, P. Bettotti, and R. S. Brusa Phys. Rev. Lett. 104, 243401(2010)[19] S. Mariazzi, R.S. Brusa 12th International Workshop on Slow Positron Beam Technique (SLOPOS12)

Magnetic Island, 1-6th August, 2010[20] D. B. Cassidy et al., Phys. Rev. A 81, 012715 (2010).[21] P. Crivelli et al. Phys. Rev. A 81, 052703 (2010).[22] R. Ferragut et al., J. Phys.: Conf. Ser. 225, 012007 (2010).[23] F. Castelli, I. Boscoli, S. Cialdi, D. Comparat, Phys. Rev. A 78 (2008) 052512.