Protonium Research Articles

Cyclotron trap

The cyclotron trap was developed at SIN/PSI to increase the stopping density of negatively charged particle beams for the formation of exotic atoms in low pressure gases. A weak focusing magnetic field, produced by superconducting solenoids, is used. Particles are injected radially through the fringe field to a moderator, which decelerates them into orbits bound by the field. Further deceleration by moderators and/or low-pressure gases leads the particles to the centre of the device, where they can be stopped or eventually extracted. Experiments became feasible with this technique, such as those dealing with pionic hydrogen/deuterium at SIN/PSI. Muonic hydrogen laser experiments also became possible with the extraction of muons from the cyclotron trap. The formation of antiprotonic hydrogen in low pressure targets led to successful experiments at LEAR/CERN.

A typical oscillating perturbation on protonium

Protonium is a type of onium consisting of a proton (p) and an anti-proton () which is called antiprotonic hydrogen. Since the proton and the anti-particle have the same mass, and each of them is a fermion, the Hamiltonian form of this system consists of the kinetic energy terms of each particle, the potential energy, and the spin interactions of both (hyperfine structure). To simplify the analysis, the Hamiltonian is then converted into a Hamiltonian which contains the relative motion terms of the two particles. This new Hamiltonian contains their reduced mass because the two particles orbit each other towards a certain center of mass. In the initial state, t < 0, the system is in the ground state and then at 0 < t < τ, the system is given a disturbance of the form , where V 0 is a constant, V 1 is a constant and very small, is the Pauli matrix for proton, and is the three-dimensional position operator in spherical coordinates. We analyze this system using a time-dependent perturbation theory that begins by defining the initial state, then calculating the transition amplitude for the new state when the perturbation is applied to the system. From the results of this calculation, we compute the system transition probability. We find that the transition probability of this system can only occur for the following quantum number terms, namely n even positive integer, l = 2,S = 1, and with the certain combinations of m and M.

Extraction of baryonia from the lightest antiprotonic atoms

Anti-protonic hydrogen and helium atoms are analyzed. Level shifts and width are expressed in terms of $\bar{p}$-nucleon sub-threshold scattering lengths and volumes. Experimental data are compared to results obtained from the 2009 version of the Paris $N\bar{N}$ interaction potential. Comparison with 1999 version is also made. Effects of $N\bar{N}$ quasi-bound states are discussed. Atomic 2P hyperfine structure is calculated for antiprotonic deuterium and the significance of new measurements is indicated.

Influence of the p ¯ -p Nuclear Interaction on the Rate of the Low-Energy p ¯ + H μ → ( p ¯ p ) α + μ − Reaction

The influence of an additional strong p ¯ -p nuclear interaction in a three-charge-particle system with arbitrary masses is investigated. Specifically, the system of p ¯ , μ − , and p is considered in this paper, where p ¯ is an antiproton, μ − is a muon and p is a proton. A numerical computation in the framework of a detailed few-body approach is carried out for the following protonium (antiprotonic hydrogen) formation three-body reaction: p ¯ + H μ ( 1 s ) → ( p ¯ p ) α + μ − . Here, H μ ( 1 s ) is a ground state muonic hydrogen, i.e., a bound state of p and μ − . A bound state of p and its antimatter counterpart p ¯ is a protonium atom in a quantum atomic state α , i.e., P n = ( p ¯ p ) α . The low-energy cross sections and rates of the P n formation reaction are computed in the framework of coupled Faddeev-Hahn-type equations. The strong p ¯ -p interaction is included in these calculations within a first order approximation. It was found, that the inclusion of the nuclear interaction results in a quite significant correction to the rate of the three-body reaction.

Three-body resonance states just below the antiproton and hydrogen dissociation threshold

We analyze two shallow resonance states below the antiproton hydrogen dissociation threshold with a non-adiabatic three-body calculation. Rearrangement correlation between initial channel and protonium formation channel is explicitly included in the total wavefunction. The lower resonance state is in good agreement with the resonance position and width calculated with the R-matrix theory. The higher resonance state which is newly found is closer to the threshold and much narrower than the former resonance. A polarization effect of the hydrogen atom is found to be indispensable to support the resonance state. The accuracy of the present calculation is evaluated by the extended virial theorem. The resonance states calculated in the present work gives shallower relative energy below the dissociation threshold than the Born-Oppenheimer calculation, suggesting that the electron motion which is ignored in latter calculation would give positive energy because the electron is unbound inside the distance.

Antinucleon-nucleon interaction at next-to-next-to-next-to-leading order in chiral effective field theory

Results for the antinucleon-nucleon left(overline{N};Nright) interaction obtained at next-to-next-to-next-to-leading order in chiral effective field theory (EFT) are reported. A new local regularization scheme is used for the pion-exchange contributions that has been recently suggested and applied in a pertinent study of the N N force within chiral EFT. Furthermore, an alternative strategy for estimating the uncertainty is utilized that no longer depends on a variation of the cutoffs. The low-energy constants associated with the arising contact terms are fixed by a fit to the phase shifts and inelasticities provided by a phase-shift analysis of overline{p}p scattering data. An excellent description of the overline{N};N amplitudes is achieved at the highest order considered. Moreover, because of the quantitative reproduction of partial waves up to J = 3, there is also a nice agreement on the level of overline{p}p observables. Specifically, total and integrated elastic and charge-exchange cross sections agree well with the results from the partial-wave analysis up to laboratory energies of 300 MeV, while differential cross sections and analyzing powers are described quantitatively up to 200-250 MeV. The low-energy structure of the overline{N};N amplitudes is also considered and compared to data from antiprotonic hydrogen.

Differential ionization in antiproton–hydrogen collisions within the convergent-close-coupling approach

A recently developed fully quantal convergent-close-coupling (CCC) approach (Abdurakhmanov et al 2011 J. Phys. B: At. Mol. Opt. Phys. 44 075204) to ion–atom collisions is extended to differential ionization studies. An important feature of the method is that it does not have classical limitations on the relative motion of participating particles. The approach is applied to calculate fully differential, as well as various doubly and singly differential cross sections of ionization in antiproton collisions with atomic hydrogen. The CCC results for various differential cross sections agree reasonably well with the results of the semiclassical CC and the continuum-distorted-wave-eikonal-initial-state approaches, particularly at high energies. However, some discrepancies exist at low energies, where the final state interactions among colliding particles are found to be very important.

Evidence For The Production Of Slow Antiprotonic Hydrogen In Vacuum

We present evidence showing how antiprotonic hydrogen, the quasistable antiproton (p)-proton bound system, has been synthesized following the interaction of antiprotons with the molecular ion H2+ in a nested Penning trap environment. From a careful analysis of the spatial distributions of antiproton annihilation events, evidence is presented for antiprotonic hydrogen production with sub-eV kinetic energies in states around n=70, and with low angular momenta. The slow antiprotonic hydrogen may be studied using laser spectroscopic techniques.

Annihilation of antiprotonic hydrogen induced by ion collisions

In collisions of antiprotons with hydrogen atoms or molecules, antiprotonic hydrogen (protonium) is produced mostly in very high principal (n) and angular momentum (ℓ) quantum number states, which are practically stable against particle–antiparticle annihilation. However, since annihilation is very fast for the ns state, ℓ mixing induced by surrounding electric fields or by collisions has a serious influence on the stability of the produced atoms, as was first pointed out by Day et al (1959 Phys. Rev. Lett. 3 61). This paper calculates the cross sections for annihilation which stem from ℓ-changing transition by ion collisions. Because the collision time can be comparable to the lifetime against ns annihilation in the present case, collisional transition and annihilation must be treated in a coherent manner. We carry out an impact-parameter close-coupling calculation, simultaneously including the annihilation channel by means of an optical potential model. At low collision energies, the ℓ mixing due to the polarization effect makes the annihilation cross section enormously large.

Exotic Atoms

In this paper I review a number of recent results in the field of exotic atoms. Recent experiments or ongoing experiments with muonic, pionic and antiprotonic hydrogen, as well as recent measurement of the pion mass are described. These experiments provide information about nucleon-pion or nucleon-antinucleon interaction as well as information on the proton structure (charge or magnetic moment distribution).

Scattering of light exotic atoms in excited states

The differential and total cross sections for the scattering of muonic, pionic, kaonic and antiprotonic hydrogen in excited states from atomic hydrogen have been calculated for the purpose of atomic cascade calculations. The scattering problem is treated in a fully quantum mechanical framework which takes the energy shifts and, in the case of the hadronic atoms, the widths of the ns states into account. The validity of semiclassical approximations is critically examined.

On the way from thermal multifragmentation to dynamical disintegration

The strong-interaction shifts ϵ and broadenings Γ of the 2p levels in antiprotonic hydrogen and deuterium have been measured for the first time with a crystal spectrometer. In hydrogen, the 23P0 hyperfine state could be resolved from the three close-lying states 23P2, 21P1, and 23P1. The hadronic shift was determined to be ϵ23P0=+139±28 meV (attractive). The value found for Γ23P0=120±25 meV is much larger than the spin-averaged 2p-level broadening Γ̄bal2p as determined from earlier experiments measuring the intensity balance. The average shift of the three unresolved states is consistent with zero and a mean broadening of Γ̄2(3P2,1P1,3P1)=38±9 meV was measured. In deuterium, the spin-averaged hadronic shift and broadening were found to be ϵ̄2p=−243±26 meV (repulsive) and Γ̄2p=489±30 meV.

Protonium formation in collisions of antiprotons with hydrogen atoms

The formation of an antiprotonic hydrogen atom \(\{ p\bar p\} \) (protonium) in the ground state and in excited states (nlm) in collisions of 1-to 250-keV antiprotons with hydrogen atoms is considered theoretically. Partial cross sections (both differential and integrated ones) for this reaction are calculated for various values of n, l, and m up to n∼100; cross sections summed over l and m are also obtained. Statistical (polarization) tensors of the orbital angular momentum of protonium atoms are evaluated. Corrections due to strong proton-antiproton interaction in the protonium ground (1s) state are analyzed.

Balmer α transitions in antiprotonic hydrogen and deuterium

The strong-interaction shifts ϵ and broadenings Γ of the 2p levels in antiprotonic hydrogen and deuterium have been measured for the first time with a crystal spectrometer. In hydrogen, the 2 3 P 0 hyperfine state could be resolved from the three close-lying states 2 3 P 2 , 2 1 P 1 , and 2 3 P 1 . The hadronic shift was determined to be ϵ 2 3 P 0 =+139±28 meV (attractive). The value found for Γ 2 3 P 0 =120±25 meV is much larger than the spin-averaged 2p-level broadening Γ ̄ bal 2p as determined from earlier experiments measuring the intensity balance. The average shift of the three unresolved states is consistent with zero and a mean broadening of Γ ̄ 2( 3P 2, 1P 1, 3P 1) =38±9 meV was measured. In deuterium, the spin-averaged hadronic shift and broadening were found to be ϵ ̄ 2p =−243±26 meV (repulsive) and Γ ̄ 2p =489±30 meV.

Measurement of the strong interaction parameters in antiprotonic hydrogen and probable evidence for an interference with inner bremsstrahlung

The spin-averaged values of the 1s strong interaction parameters in antiprotonic hydrogen were measured with good statistics. The results are: shift (ϵ 1s) = −712.5 ± 20.3 eV and width (Γ 1s) = 1054± 65 eV . These values are compatible and have approximately the same precision as the world average before this experiment. With some additional constraints, both the triplet and singlet components could be extracted from the same spectrum. The results are: 3S 1 shift: −785 ± 35 eV , 3S 1 width: 940 ± 80 eV , 1S 0 width: 1200 ± 250 eV . In addition, precise values for the Kα Lα and Ltotal Lα yields at low pressure (20 mbar) were obtained: 0.0176 ± 0.0016 and 1.45 ± 0.05. Furthermore, the 2p mean absorption width of 30.8 ± 3.0 meV was deduced, also compatible with and of similar precision as the world average before this experiment. An indication of interference between the measured Lyman (Ki) x-ray series and the process of inner bremsstrahlung due to charged meson production after annihilation was seen because of the low background conditions of this experiment.

Measurement of the strong interaction parameters in antiprotonic deuterium

Antiprotonic deuterium K α X-rays were seen for the first time. Their analysis resulted in spin-averaged 1s strong interaction parameters, namely −1050±250 eV (repulsive) for the 1s shift and 1100±750 eV for the 1s width. The large errors are mainly due to low statistics. In addition, values for the K α /L α and L total/L α yields at low pressure (20 mbar) were obtained: 0.005±0.003 and 1.34±0.05. Furthermore, a 2p mean absorption width of 80 ≤ Γ 2p≤ 350 meV was deduced. The results for the 1s ground state are somewhat surprising, especially the narrow 1s width which is similar to the spin-averaged antiprotonic hydrogen 1s width. However, our 1s width is in agreement with low-energy scattering data [A. Zenoni et al., Phys. Lett. B 461 (1999) 413] (see preceding paper).

New results on strong-interaction effects in antiprotonic hydrogen

Lyman and Balmer transitions of antiprotonic hydrogen and deuterium have been measured at the Low-Energy Antiproton Ring LEAR at CERN in order to determine the strong interaction effects. The X-rays were detected using Charge-Coupled Devices (CCDs) and a reflection type crystal spectrometer. The results of the measurements support the meson-exchange models describing the medium and long range part of the nucleon-antinucleon interaction.

Measurement of strong interaction parameters in antiprotonic hydrogen and deuterium

In the PS207 experiment at CERN, X-rays from antiprotonic hydrogen and deuterium have been measured at low pressure. The strong interaction shift and the broadening of the Kα transition in antiprotonic hydrogen were determined. Evidence was found for the individual hyperfine components of the protonium ground state.

Protonium X-ray spectroscopy

The Lyman and Balmer transitions from antiprotonic hydrogen and deuterium were studied extensively at the Low-Energy-Antiproton Ring LEAR at CERN in order to determine the strong interaction effects. A first series of experiments was performed with semiconductor and gaseous X-ray detectors. In the last years of LEAR operation using a Bragg crystal spectrometer, strong interaction parameters in the 2p states of antiprotonic hydrogen and deuterium were measured directly. The results of the measurements support the meson-exchange models describing the medium and long range part of the nucleon-antinucleon interaction.

Protonium X-ray spectroscopy

In LEAR experiment PS207, the Balmer a radiation from antiprotonic hydrogen has been measured with a focussing crystal spectrometer. Preliminary results for strong interaction effects are reported.