## Conclusions

Experimentalists have made an almost negligible contribution to our knowledge of antimatter compounds despite the existence of suitable beams for almost two decades. A set of interesting experiments which can be performed now are discussed. The authors are pleased to acknowledge the help of D. W. Gidley, A. P. Mills, Jr., J. Mitroy, Patricia S. Schaefer, J. L. Schrader, and K. Varga. 1 G. G. Ryzhikh and J. Mitroy, Phys. Rev. Lett. 79, 4124 (1997). 2 D. Bressanini, M. Mella, and G. Morosi, J....

## WoTV

In the case of a target belonging to the group for example, the interaction potential which appears in the transition from the vibrationally ground state of, say, the H2O molecule to one of its excited states of the antisymmetric stretching mode belongs to the B2 symmetry, and only the equations with (p,po,p') AUB2,B2), (A2,B2,Bi), (Bi,B2,A2) and (B2,B2,Ai) are therefore possible (see table 1). 3.4. The Annihilation Rates in Gases As mentioned in the introduction, the parameter is a measure, at...

## Positron Beams And Related

What we are capable of doing, from an experimental perspective, with low energy positrons is very much dependent upon the quality of the beams we use. To this end our science has been instrument-led, with often extraordinary effort put into machine development before physics investigations can begin. In this section we describe three possible methods of manipulating beams to achieve spatial and temporal compression. The use of a voltage pulse quadratically distributed along the axis of a beam...

## Centrifugal Separation

Due to the plasma rotation, ion species with different charge-to-mass ratios tend to centrifugally separate in a Penning trap 30, 31 . If ions with different q m rotate about the trap axis at the same radius, they will tend to rotate with different rates because of different centrifugal forces. Collisional drag will cause a radial drift of the lighter ions inward, and the heavier ions outward, if the ions have the same charge. The different species will separate and the whole plasma will come...

## Summary

We have demonstrated sympathetic cooling of positrons by laser-cooled 9Be+ ions. We observed centrifugal separation of the positrons and the 9Be+ ions, and are able to use this observation to place an upper limit on the positron temperature for motion parallel to the magnetic field of approximately 5 K. The positron perpendicular temperature presumably did not cool below 10 K because the perpendicular and par- Figure 9. (a) Calculated radial variation of the Be+ ion density for different...

## DP Positron Annihilation Lifetime Spectroscopy

Schematic of the Depth-Profiled Positron Spectrometer used at the University of Michigan. Figure 1. Schematic of the Depth-Profiled Positron Spectrometer used at the University of Michigan. The pick off annihilation channel of ortho Ps is strongly dependent on the density of electrons and, thereby, the size and distribution of pores in a sample. With increasing electron density, the natural lifetime in vacuum of 142 ns is reduced. In beam based PALS, the positron beam forms Ps...

## Positron Attachment To Atoms

Whether a positron can form a bound state with atoms has been thoroughly investigated by Mitroy's group 3 by using the stochastic variational method, and in their most recent attempt, they have found that for most of the alkaline and alkaline-earth atoms, a positron can indeed attach and form a stable bound state. For example, a positron can form a bound state with Li and Na atoms with corresponding binding energy of 1.52 eV, and 1.86 eV, respectively, thus forming Li e+ , and Na e+ . It was...

## Zeff For Atoms And Molecules

The most accurate values have been obtained in calculations for simple systems like H and He 5, 6 , and in experiments for He 7 . For other systems experimental values are more reliable, although there is a good theoretical understanding of Zeff for noble-gas atoms 8, 9 , and there have been several calculations for simple molecules 10, 11, 12 , A collection of for the hydrogen and noble-gas atoms, simple inorganic molecules and alkanes and their perhalogenated substitutes is presented in...

## Scattering Cross Sections

2.1.1 Grand Total Scattering Cross Sections Perhaps more than any other, this particular facet of positron scattering physics has been well exploited over the past 20 years. As the total cross section represents a sum over all energetically available scattering channels, and an integral over all positron scattering angles within each of these channels, it provides minimal information about the dynamics of the collision process. However, it is a measurement that can be performed with high...

## Positron Binding To Neutral Atoms

It has been suggested 45, 46, 47 that the structure of any positronic atom can be heuristically written as tf a (Atom)< p(e+) + bn(Atom+)w Ps) . (15) The first of these terms represents a positron moving in the field of a polarized atom while the second term represents a Ps cluster attached to the residual ion (or atom). The relative strength of these two configurations is determined by the ionization potential (or electron affinity) of the atomic (or ionic) parent. When the ionization...

## Ps Formation Cross Section

Ps formation is one of the most important processes in positron scattering. The Ps formation cross section is obtained by the measurement of 3yphotons 17 or 2yphotons 18 from the annihilation of Ps, or the measurement of all positrons scattered, i.e. those not involved in the formation of Ps 19 . These methods are orthodox, and the range of the impact energy is from the threshold energy up to 100 or several hundreds eV. Although these data are very important, the types of target gases measured...

## Closed Pore Systems And Pore Size Distribution

A system with closed pores with a distribution of sizes results in a distribution of Ps lifetimes since there is a singular relationship between pore size and z based on the extension of the Tao-Eldrup model. In principle an inverse Laplace transformation of the lifetime data can be performed to obtain the pore size distribution. However, exponentially decaying functions do not form an orthogonal set of basis functions and statistical noise further complicates the situation. Several methods...

## Intense Radioisotope Sources For Spin Polarized Positron Beams

Kurihara, N. Suzuki, 1Y. Itoh, and 1A. Goto 1rThe Institute of Physical and Chemical Research, 2-1, Hirosawa, Wako-shi, Saitama 351-0198, Japan 2Institute of Physics, Graduate School of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo 53-8902, Japan 3Institute of Material Structure Science (IMMS), High Energy Accelerator Research Organization (KEK), - , Oho, Tsukuba, Ibaraki 305-0801, Japan Abstract Radioisotopes are convenient sources for spin...

## Brightness Enhancement by Controlled Extraction

Another technique for brightness enhancement using traps exploits the space charge of the positron plasma itself. If sufficient positrons are accumulated in a Penning trap, there is a significant space charge depression in the center of the trap. Thus, if only a fraction of the positron charge is released from the trap, positrons nearest the axis are ejected first. Therefore, a beam created by the partial release of positrons from a trap is narrower than the initial plasma. The plasma remaining...

## Summary And Outlook

Ideas outlined in this paper provide a solid framework for the description and understanding of positron annihilation on molecules. The two basic annihilation mechanisms, direct and resonant, should be capable of describing the whole variety of phenomena associated with this pro cess, such as large values of Zeg, their rapid increase with the size of the molecule, and strong chemical sensitivity. Complete understanding of resonant annihilation will require solving several difficult problems,...

## Positron Trapping

Positrons can be accumulated in Penning traps using a variety of techniques 3 . However, the only method that has been demonstrated to have sufficiently high efficiency for the applications under discussion is the buffer gas method 8, 19, 3 . For this method, moderated positrons from a radioactive source are accumulated in a modified Penning-Malmberg trap by means of inelastic collisions with a buffer gas such as nitrogen. The electrode structure of the trap, illustrated in Fig. 1 forms three...

## Twocomponent

The DFT reduces the quantum-mechanical many-body problem to a set of manageable one-body problems 21 , It solves the electronic structure of a system in its ground state so that the electron density is the basic quantity. The DFT can be generalized to positron-electron systems by including the positron density n+(r) as well it is then called a 2-component DFT 22, 23 , The enhancement factor is treated as a function of the electron density n(r) in the local density approximation (LDA) 22 ....

## Annihilation Cross Sections And Rates

The process of electron-positron annihilation is described by quantum electrodynamics. In the non-relativistic Born approximation the annihilation cross section averaged over the electron and positron spins is given by 1 where v is the relative velocity, c is the speed of light, and ro is the classical electron radius defined by e2 ro mc2, e and m being the electron charge and mass. The cross section (1) obeys a pure l v-law, which characterises the near-threshold behaviour of inelastic...

## Introduction

When positrons are present at a high enough density near a solid surface, they will interact significantly with each other and the solid, revealing the new physics of the many positron-many electron system. As envisioned in 1946 by Wheeler 22 , the polyelectron states having several positrons and electrons are known to form stable bound states up to the positronium molecule Ps2 23 . Positronium was first observed in 1951 24 and the positronium negative ion in 1981 25 . Due to advancing...

## Positronium Atom Scattering

The development of monoenergetic Ps beams at University College London 17, 18, 19, 20 has led to growing interest in Ps - atom collisions. Ps is the lightest neutral atomic projectile, being like a hydrogen atom but only l 1000th of its mass, Ps collisions are therefore of considerable fundamental interest. The normalized spatial wave functions, 4> nlm t)> of Ps are simply related to those of atomic hydrogen, i jnim re), by In addition, it is important to specify the total spin state of the...

## LINAC Target

The first step in making slow positrons is to make a shower by irradiating a high-Z converter target with 150 MeV electrons from the LINAC 13 . For this energy of primary electrons, the target should be about three radiation lengths of a material such as tungsten or a high-Z liquid metal. A relatively non-toxic alloy such as the binary eutectic 55.5 Bi-44.5 Pb with a melting point of 124 C might be a good choice for the latter if it is necessary. We assume a LINAC power of 10 kW and a pulse...

## Rearrangement Collisions

We consider the rearrangement process where NL and nl are the principal and angular momentum quantum numbers of the bound states of protonium and positronium respectively. Figure 1. Scattering thresholds with Pn principal quantum number N 22-24, and positronium principal quantum number n. The lines show the sum of protonium and positronium binding energies. Any final state with energy below -1 a.u., corresponding to zero collision energy, can be formed in zero-energy hydrogen-antihydrogen...

## Positronium Formation In The Alkali Atoms

As mentioned earlier, the formation of ground-state positronium in single ionization of the alkali atoms is an exothermic process, so that the parameter Er ( Eps) in equation 7 is negative. A naive assumption Figure 3. (a) Cross sections for atom formation in positronium collisions with singly ionized alkali atoms, (b) Ground state positronium formation cross sections in positron collisions with alkali atoms. The data are from 16 for Rb and Cs, 17 for Na, 18 for K and 19 for Li. < 7pg(ls) for...

## References

Bardsley, Phys. Rev. Lett. 28,127 (1972). 2 D.L. Morgan and Hughes, Phys. Rev. A 7, 1811, (1973) Phys. Rev. D 2, 1389 (1970). 3 W. Kolos, D.L. Morgan, D. M. Schrader and L. Wolniewicz, Phys. Rev. A11, 1792 (1975). 4 E.A.G. Armour and C. Chamberlain, this volume. 5 S. Jonsell, A. Saenz, P. Froelich, B. Zygelman and A. Dalgarno, Phys. Rev. A in press (2001). 6 P. Froelich, S. Jonsell, A. Saenz, B. Zygelman and A. Dalgarno, Phys. Rev. Lett. 84, 4777 (2000). 7 B. Zygelman,...

## Positronium Behavior In Porous Films

Positronium formation in porous materials. The shape of a typical positron implantation profile is depicted in the lower panel. The most important process a positron can undergo in an insulator is electron-capture to form the bound state of Ps. Ps formation in a porous insulator is depicted in Figure 3. The positron slows down through collisions in the material from its initial beam energy of several keV to several eV. It can either capture a bound molecular electron or recombine with...

## Conclusion And Outlook

The existence of positron-atom bound states and the ability to calculate their wave functions give unique insights into how positrons interact with complex electronic systems. For the last two decades the theoretical emphasis has been on scattering calculations. However, the theoretical uncertainties inherent in bound state calculations are smaller than those associated with scattering calculations and this allows for better understanding of the dynamics of positron-atom interactions. The...

## Positronium Formation In The Noble Gases

We became interested in correlations between ionization cross sections and ionization energies in the course of investigating positronium formation in the double ionization of the noble gases. Experimental studies by Bluhme et al. 4 and Moxom et al. 5 had revealed the almost complete absence of transfer ionization in the second Ore gap for helium and neon, but not for argon, krypton and xenon. These findings led us to develop a model of positronium formation, the basis of which is as follows....

## Antimatter Compounds

(a) Chemistry Department, Marquette University, P.O. Box 1881, Milwaukee, WI 53201-1881, U.S.A., david.schrader marquette.edu (b) Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831-6142, U.S.A., moxomj ornl.gov Abstract This chapter is about chemical compounds containing both matter and antimatter, the latter in the form of positrons. Most of our knowledge of such compounds comes from quantum mechanical calculations. Our discussion includes some issues relating to calculating...

## Info

When the ionization potential of the neutral atom is less than 0.250 Hartree, the addition of the extra electron and the two positrons leads to formation of a Ps2 molecule which is then bound to the residual ion core. The Ps2 dominates because the two most weakly bound electrons are each more strongly attracted to a positron and therefore b 1. Similarities of the Ps2, Li+Ps2 and Na+Ps2 annihilation rates provides a good indicator of Ps2 cluster formation (inter-particle correlations also...

## Fundamental Studies Involving Positrons And Positronium

There continues to be interest in fundamental aspects of positronium physics, including lifetime measurements and spectroscopy. The recent observation of magnetized Rydberg positronium 28 has added a measure of excitement to the field. Many experiments of this type can be performed using a rapid cycle pulsed positron beam, as described above, coupled to a pulsed laser system. In addition, there continues to be interest in the production of systems containing more than one positron 29 , despite...

## Total Cross Section

The contribution of the interaction potential in positron and electron scattering by atoms and molecules is summarized in Table 1. This effect of the contribution is revealed in the total cross section (TCS). The total cross-section for positron scattering is given by Q+t Q+ela + Q+ex + Qps + Q+ion + Q+dis + Qa where Q+eu is the elastic scattering cross-section, Q+e, is the sum of all contributions from rotational, vibrational and electronic excitations, is the Ps Table . Positron and electron...

## Calibration Of Pore Size And Open Pore Systems

It is critically important for PALS to calibrate Ps lifetimes with pore sizes. The 3y Ps annihilation parameter, which measures the convoluted effect of pore size and density, will also benefit from such calibration. In the very large pore (classical) regime (pores with mean free paths on the order of 100 nm), a calibration was performed using high porosity (90-98 ) silica powders 18 . In the other extreme (sub-nm pores), the quantum mechanical model 13 first developed by Tao and Eldrup has...

## Annihilation On Atoms And Molecules

The annihilation rate is a sensitive measure of short-range correlations between the positron and the bound electrons. We follow the convention of expressing the annihilation rate r in terms of the parameter Zeg, which is the annihilation rate relative to that for positrons in a gas of uncorrelated electrons (i.e., the Dirac annihilation rate). where r0 is the classical electron radius, c is the speed of light, and nm is the number density of atoms or molecules. For large molecules, it is well...

## Positron Annihilation

To conserve energy and momentum, electrons and positrons usually annihilate by a second order process in which two photons are emitted 3, 4 . The process is shown in Fig. 1. At the first vertex the electron emits a photon, at Figure 1. Feynman diagram for the electron positron annihilation. Figure 1. Feynman diagram for the electron positron annihilation. the second vertex it emits a second photon and jumps into a negative energy state (positron). This phenomenon is analogous to Compton...

## E H Ise H2s 2 p

Atomic hydrogen would clearly be an ideal candidate for such a search of positron scattering resonances, given the considerable amount of theoretical work which already exists. Similar resonances in electron scattering have been revealed in a beautiful series of measurements by Williams 86 . However, given the considerable experimental difficulties posed by atomic hydrogen sources, in combination with those posed by high resolution positron beams and scattering experiments, H may not be the...