Protonium Atom Research Articles

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.

Protonium atoms generation at antiprotons channeling in a LiH crystal

The possibility of formation of moving exotic protonium atoms at channeling of antiprotons in an ionic crystal of lithium hydride is proposed and investigated. For this purpose the probability of proton capture by moving antiprotons channeling in crystallographic H−–(111) planes and H−–(110) axes in ionic LiH crystal was calculated. It has been shown that the process of formation of moving exotic pp– protonium atoms regarding antiprotons velocities has a resonance character depending on quantum states of these protonium atoms. It was shown that at the capture to higher quantum states the magnitude of resonance peaks increases and the resonance velocities decreases.

Nuclear effects in protonium formation low-energy three-body reaction: p̄ + (pμ)1s→ (p̄p)α+μ−: Strong p̄–p interaction in p̄ + (pμ)1s

A three-charge-particle system (p, μ − , p + ) with an additional matter-antimatter, i.e. p–p + , nuclear interaction is the subject of this work. Specifically, we carry out a few-body computation of the following protonium formation reaction: p + (p + μ − ) 1 s → (pp + ) 1s + μ − , where p + is a proton, p is an antiproton, μ − is a muon, and a bound state of p + and its counterpart p is a protonium atom: Pn = (pp + ). The low-energy cross sections and rates of the Pn formation reaction are computed in the framework of a Faddeev-like equation formalism. The strong p–p + interaction is approximately included in this calculation.

Three-Body Protonium Formation in a Collision Between a Slow Antiproton ( $${\bar{\rm p}}$$ p ¯ ) and Muonic Hydrogen: $${{\rm H}_{\mu}}$$ H μ —Low Energy $${\bar{\rm p} + ({\rm p} \mu^-)_{1s} \rightarrow (\bar{\rm p} {\rm p})_{1s} + \mu^-}$$ p ¯ + ( p μ - ) 1 s → ( p ¯ p ) 1 s + μ - Reaction

A bound state of a proton, p, and its counterpart antiproton, $${\bar{\rm p}}$$ , is a protonium atom $${Pn = (\bar{\rm p} {\rm p})}$$ . The following three-charge-particle reaction: $${\bar{\rm p} +({\rm p} \mu^-)_{1s} \rightarrow (\bar{\rm p} \rm{p})_{1s} + \mu^-}$$ is considered in this work, where $${\mu^-}$$ is a muon. At low-energies muonic reaction $${Pn}$$ can be formed in the short range state with α = 1s or in the first excited state: α = 2s/2p, where $${\bar{\rm p}}$$ and p are placed close enough to each other and the effect of the $${\bar{\rm p}}$$ –p nuclear interaction becomes significantly stronger. The cross sections and rates of the Pn formation reaction are computed in the framework of a few-body approach based on the two-coupled Faddeev-Hahn-type (FH-type) equations. Unlike the original three-body Faddeev method the FH-type equation approach is formulated in terms of only two but relevant components: $${{\it \Psi}_1}$$ and $${\it \Psi_2}$$ , of the system’s three-body wave function $${\it \Psi}$$ , where $${{\it \Psi}={\it \Psi}_1+{\it \Psi}_2}$$ . In order to solve the FH-type equations $${\it \Psi_1}$$ is expanded in terms of the input channel target eigenfunctions, i.e. in this work in terms of the $${(\rm{p} \mu^-)}$$ eigenfunctions. At the same time $${\it \Psi_2}$$ is expanded in terms of the output channel two-body wave function, that is in terms of the protonium $${(\bar{\rm{p}} \rm{p})}$$ eigenfunctions. A total angular momentum projection procedure is performed, which leads to an infinite set of one-dimensional coupled integral–differential equations for unknown expansion coefficients.

On the Mass Spectrum of Exotic Protonium Atom in Oscillator Representation Method

In the given paper one determines the constituent mass of the bound state and binding energy of hadronic exotic system, according to the basis investigation of the asymptotically behavior of the loop function of scalar particles in the external electromagnet field are analytically determined exploration of these states through relativistic and non-perturbative corrections. It is shown that, the mass spectrum of a relativistic bound state of protonium consisting from proton and anti-proton is differing from a mass of initial particles.

First protonium production in a nested Penning trap and related topics

After the synthesis of antihydrogen, the ATHENA collaboration has succeeded in the synthesis of protonium (a [Formula: see text] atom). The synthesis occurs at the "chemical" energy scale and we observe free protonium atoms with kinetic energies in the range 1–700 meV. We show that in the ATHENA apparatus protonium atoms with lifetime of the order of 1 µs have been produced after collisions with [Formula: see text] inside the e+ cloud in the nested Penning trap. This result could open a new scenario about measurements in fundamental physics.PACS Nos.: 36.10-k, 34.80.Lx, and 52.20.Hq

Protonium production in ATHENA

The ATHENA experiment at CERN, after producing cold antihydrogen atoms for the first time in 2002, has synthesised protonium atoms in vacuum at very low energies. Protonium, i.e. the antiproton–proton bound system, is of interest for testing fundamental physical theories. In the nested penning trap of the ATHENA apparatus protonium has been produced as result of a chemical reaction between an antiproton and the simplest matter molecule, H2+. The formed protonium atoms have kinetic energies in the range 40–700meV and are metastable with mean lifetimes of the order of 1μs. Our result shows that it will be possible to start measurements on protonium at low energy antiproton facilities, such as the AD at CERN or FLAIR at GSI.

State-Specified Protonium Formation in Low-Energy Antiproton–Hydrogen-Atom Collisions

We calculate state-specified protonium-formation cross sections in low-energy antiproton-hydrogen-atom collisions by solving the Chew-Goldberger-type integral equation directly instead of integrating the traditional differential scattering equation. Separating the incident wave from the total wave function, we calculate only the scattered outgoing wave propagated by the Green function. The scattering boundary condition is hence automatically satisfied without the tedious procedure of adjusting the wave function at the asymptotic region. The formed protonium atoms tend to be distributed in higher angular momentum l and higher principle quantum number n states as the collision energy increases. The present method has the advantage over the traditional ones in the sense that the required memory size and the computational time are much smaller, and accordingly the problem can be solved with higher accuracy.

Potential Energy Curves for Excited States of the Hydrogen-Antihydrogen System

The potential energy curves for the hydrogen-antihydrogen (HH) system in states with a leptonic orbital angular momentum projection Lambda=0, 1, 2, 6, and 30 are presented. Within the framework of the adiabatic picture, explicitly correlated Gaussians are used as basis functions which describe accurately the hydrogen-antihydrogen interaction. The critical internuclear distances where the system transforms into positronium and protonium atoms are found. Adiabatic corrections to the potential energy curves are also estimated.

Rydberg states of the hydrogen-antihydrogen quasimolecule

A description of the excited lepton states of the hydrogen-antihydrogen quasimolecule is presented. Potential energy curves and the leptonic part of the wave functions corresponding to a variety of such states are calculated within the Born-Oppenheimer approximation employing the Ritz variational principle. Nonadiabatic corrections to the leptonic potentials are also obtained. Basis functions are constructed as products of explicitly correlated Gaussians and spherical harmonics which describe correctly the motion of leptons with arbitrary orbital angular momentum projection onto the molecular (internuclear) axis. The hadronic part of the wave function for each leptonic level of the hydrogen-antihydrogen system is calculated by solving the Schr\odinger equation with the obtained leptonic potentials. Corresponding solutions are generated utilizing precise B-spline representations. Employing leptonic and hadronic parts of the wave function the electron-positron and proton-antiproton annihilation rates are computed for a number of quasimolecular states. The decay rates of the hydrogen-antihydrogen system into separate positronium and protonium atoms are also estimated for the quasimolecular levels under consideration.

Collinear study of protonium formation in collisions of antiprotons with hydrogen molecular ions

Applicability of the Born–Oppenheimer adiabatic approximation is examined for the protonium formation process p̄ + H + 2 → p̄p + H. For this purpose, a collinear configuration is assumed for the three nuclei, and a calculation using a quantum–classical hybrid (semiclassical) method is carried out. The collinear study suggests that the molecular target is much more efficient for the production of the protonium atom than the target of atomic hydrogen.

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.

The problem of Okubo–Zweig–Iizuka rule violation in nucleon–antinucleon annihilation at rest

A review of the problem of whether the violation of the OZI rule in nucleon–antinucleon annihilation at rest can be explained in the framework of conventional mechanisms is given in detail. While the vector-dominance model and the rescattering model qualitatively describe the OZI-rule violation in the reactions pp→φγ and pp→φπ 0 for the annihilation from the S state of the protonium atom, the latter model cannot explain the fact that the annihilation into φπ 0 from the P state is not seen and the OZI rule in the reaction pp→f 2 ′ π 0 is not satisfied. We also discuss what information about the OZI-rule violation can be extracted from the reaction pp→φπ + π − and decays of the J/Ψ meson.

Protonium formation in the excited state in laser assisted antiproton-hydrogen atom collisions

A detailed analysis using the Born approximation is given of protonium formation in the first excited state ( n = 2) in laser assisted antiproton hydrogen atom collisions adopting the semi-classical model. The projectile-laser-field interaction and the dressing effects on the hydrogen atom and the protonium atom have been considered to first order in the A · p gauge. The differential cross sections for protonium ( n = 2) formation have been presented for no-photon and one-photon exchange ( l = 0, ± 1) at 50, 100 and 200 keV energies with laser frequency ω = 0.043 a.u. and laser field strength E 0 = 0.002 a.u. along with the field free results. Two interesting characteristics are noted. The differential cross sections increase slowly with the scattering angle unlike the case of electron capture by heavy particles. Secondly, contributions from the entire angular region (0°–180°) are important for the calculation of cross sections, which is a familiar characteristic in light particle scattering.

Initial states and branching ratios in p [formula omitted] annihilations at rest

p p annihilations at rest occur from initial states with J PC =0 −+, 1 −−, 1 +−, 0 ++, 1 ++, 2 ++. These initial states are S- and P-wave atomic levels of protonium atoms that are populated by the atomic cascade which follows the atomic capture of the antiproton. Each of the six fractions F J PC of annihilations from initial states of protonium with quantum numbers J PC depends on the density of the target where antiprotons are brought to rest, and is not known individually at present at any target density. Here we show that the values of the six annihilation fractions F J PC can be determined by measuring at four target densities the values f J PC channel of the frequencies of annihilations for six exclusive annihilation channels. The same measurements would provide, for the channels exploited for the F J PC determination, the values B J PC channel of the branching ratios of annihilation from each J PC type of initial states from which the channels are allowed.

Protonium: From capture to annihilation

We present a model of the atomic cascade of protonium atoms. The model describe the intensities of the charactertistics lines, the fractional annihilation fo S and P states, and the cascade time. The result agree fully with recent experimental data. No free parameter is needed.

Remarks on the �pp interaction very close to the threshold

We examine possible sources for the disagreement between recent results on theρ parameter and optical potential predictions at very low energies. We find that a proper incorporation of the antineutron-neutron threshold has an extremely small effect, due to annihilation. An application to the protonium atom is discussed. The accuracy of the Bethe formula which serves to estimate the parameter from the forward differential cross-section is considered. It turns out to overestimateρ, but not enough to account for the discrepancy. We make also direct comparisons with the differential cross-sections which show in one case, a neat deviation in the interference region. In other cases the disagreement is not compelling.

Inner bremsstrahlung in low energy antiproton-proton annihilation

Photon bremsstrahlung accompanying antiproton-nucleon annihilation is examined with special regard to the experimental program at LEAR. It is shown that the bremsstrahlung continuum constitutes an important background to the photon lines emitted in radiative transitions between protonium states. Interference between lines and bremsstrahlung can yield interesting information on the protonium atom and the annihilation mechanisms, and perhaps even help in the search for baryonium states.

Baryon Symmetric Big Bang Cosmology

In a big bang cosmology in which the Universe is initially filled with thermal radiation at a very high temperature the number of nucleon-antinucleon pairs decreases exponentially with temperature when the latter falls below a value such that kT ~ 1 GeV. To explain the observed ratio η = N/Nph ~ 10-9 where N is the average baryon density and Nph the photon density, nucleons and antinucleons must have been separated in the thermal radiation at a temperature greater than 30 MeV. A mechanism has been suggested which would lead to a phase transition in thermal radiation for kT > 300 MeV resulting in two phases with opposite non zero baryon number. The interaction between nucleons and antinucleons at intermediate energy is repulsive according to the mesonic theory of nuclear forces. This can be checked experimentally by measuring with enough precision the energy of X-rays emitted by the protonium atom and this experiment is now under way at CERN. Different models have been made to investigate their consequences and in each case a phase transition has been found above a temperature of the order of 300 MeV (Omnes, 1972; Aldrovandi and Caser, 1973; Cisneros, 1973).

A possible test of matter-antimatter separation

The strong-interaction energy shift in the protonium atom is estimated and shown to be a possible test for the existence of a phase transition in the high-energy black-body radiation.