Kinetic energy distributions in pionic hydrogen

A framework for analyzing the Doppler broadening of the X-ray lines in pionic hydrogen is proposed. It is shown that the kinetic energy distributions at the instant of the (n = 2-4) radiative transitions are related to each other. In order to establish the connection, the collisional processes for pionic hydrogen scattering from hydrogen atoms and molecules have been calculated in different models. The proposed method can be used to determine reliably the strong interaction width of the ground state of pionic hydrogen from the X-ray line profiles measured recently at the Paul-Scherrer-Institut.Received: 6 August 2004, Published online: 28 September 2004PACS: 34.50.-s Scattering of atoms and molecules - 36.10.Gv Mesonic atoms and molecules, hyperonic atoms and molecules     

Ground-state energy of uranium diatomic quasimolecules with one and two electrons

Ground-state energies of the one- and two-electron uranium dimers are calculated for internuclear distances in the range D=40–1,000 fm and compared with the previous calculations. The generalization of the dual-kinetic-balance approach for axially symmetric systems is employed to solve the two-center Dirac equation without the partial-wave expansion for the potential of two nuclei. The one-electron one-loop QED contributions (self-energy and vacuum polarization) to the ground-state energy are evaluated using the monopole approximation for the two-center potential. Interelectronic interaction of the first and second order is taken into account for the two-electron quasimolecule. Within the QED approach, one-photon-exchange contribution is calculated in the two-center potential, whereas the two-photon-exchange contribution is treated in the monopole approximation.     

The pionic hydrogen experiment at PSI

A new high-precision determination of the strong-interaction shift (∈_1s) and broadening (Γ_1s) of the ground state in pionic hydrogen (πH) has been started at PSI. This constitutes a direct measurement of the πN scattering lengths and is an important test of the methods of chiral perturbation theory.The experiment will be conducted in two steps. In the first step we aim for a precision of 0.2% for ∈_1s and 3% for Γ_1s. A new method of energy calibration is used: by measuring πH simultaneously with pionic oxygen (πO), systematic errors are suppressed. The goal for the second step is an accuracy of 1% for Γ_1s.     

Electromagnetic corrections to the s-wave scattering lengths in pionic hydrogen

Motivated by the recently performed X-ray precision experiments on pionic hydrogen (preceding paper), we reconsider the problem of electromagnetic corrections to the π - N scattering lengths. Based on a relativistic two-channel approach, we find corrections to the π⁻p elastic and single-charge-exchange (SCE) scatering lengths due to the point-Coulomb interaction, the finite-size Coulomb interaction (including the pion size), the first-order vacuum polarization (Uehling potential) and the (π⁻p) - (π⁰n) mass difference (mass difference effect). We also estimate the contribution due to the (γ,n) decay channel. The total corrections to the elastic and the SCE scattering lengths are found to be δ_ε = −(2.1 ± 0.5) × 10⁻² and δ_Γ = −(1.3 ± 0.5) × 10⁻². Previously published values for the corrections are critically compared with our results.     

Ground-state energy of quantum liquids

The kinetic (K ₄ ⁰ (n) and K ₃ ⁰ (n)) and potential (V ₄ ⁰ (n) and V ₃ ⁰ (n)) energies of ⁴He and ³He atoms have been found from the law of corresponding states and the experimental data on the dependence of the ground-state energies E ₄ ⁰ (n) and E ₃ ⁰ (n) on the density of the isotopes ⁴He and ³He. In the approximation of structureless quantum liquid, the potential energies are equal, V ₄ ⁰ V ₃ ⁰ (n) = (n), and the kinetic energies are inversely proportional to the atomic mass, $K_4^0 (n) = \frac{3} {4}K_3^0 (n)$ . The potential energy given by the expression V ⁰ = 4E ₄ ⁰ ? 3E ₃ ⁰ to a high accuracy is linear in the density n, which is associated with nearly an absence of short-range order in liquid helium. The kinetic energy of liquid ⁴He is given by the expression K ₄ ⁰ = 3(E ₃ ⁰ ? E ₄ ⁰ ), which agrees with the experimental data on neutron scattering in liquid ⁴He. The quantities K ₄ ⁰ (n) and K ₃ ⁰ (n) determine the scale of all thermodynamic characteristics in the temperature range where the effects of the particle statistics can be neglected.     

Ground-state structures of atomic metallic hydrogen

Ab initio random structure searching using density functional theory is used to determine the ground-state structures of atomic metallic hydrogen from 500 GPa to 5 TPa. Including proton zero-point motion within the harmonic approximation, we estimate that molecular hydrogen dissociates into a monatomic body-centered tetragonal structure near 500 GPa (r(s)=1.23) that remains stable to 1 TPa (r(s)=1.11). At higher pressures, hydrogen stabilizes in an …ABCABC… planar structure that is similar to the ground state of lithium, but with a different stacking sequence. With increasing pressure, this structure compresses to the face-centered cubic lattice near 3.5 TPa (r(s)=0.92).     

The new pionic hydrogen experiment at PSI

A new high-precision determination of the strong-interaction shift (_1s) and broadening (Γ_1s) of the ground state in pionic hydrogen (πH) has been started at PSI [1]. This constitutes a direct measurement of the πN scattering lengths a⁺ and a⁻ and is an important test of the methods of chiral perturbation theory.     

Observation of double radiative capture on pionic hydrogen

We report the first observation of double radiative capture on pionic hydrogen. The experiment was conducted at the TRIUMF cyclotron using the RMC spectrometer and detected gamma-ray coincidences following pi(-) stops in liquid hydrogen. We found the branching ratio for double radiative capture to be [3.05+/-0.27(stat)+/-0.31(syst)]x10(-5). The measured branching ratio and angle-energy distributions support the theoretical prediction of a dominant contribution from the pipi-->gammagamma annihilation mechanism.     

Solid hydrogen. Ground-state energy,pressure, compressibility and phase transition at high densities

The ground-state energy, the pressure and the compressibility of solid molecular hydrogen is calculated by means of a modified Brueckner theory. The Bethe-Gold-stone equation is solved to give the reaction matrix or the effective interaction in coordinate space, and the ground-state energy for hcp and fcp hydrogen is calculated. Also, the pressure and the compressibility is estimated from the dependence of the ground-state energy on density or molar volume. The possibility of a phase transition from solid molecular hydrogen into a metallic atomic phase is also considered. The ground-state energy and pressure for bcc atomic hydrogen is calculated, and a phase transition is found to occur at a pressure of 1.2·10⁶ atm.     

Ground-state properties of the one dimensional electron liquid

We present a theory of the pair distribution function g(z) and many-body effective electron-electron interaction for the one dimensional (1D) electron liquid. Our approach involves the solution of a zero-energy scattering Schrödinger equation for where we implemented the Fermi hypernetted-chain approximation including the elementary diagram corrections. We present numerical results for g(z) and the static structure factor S(k) and obtain good agreement with data from diffusion Monte Carlo studies of the 1D system. We calculate the correlation energy and charge excitation spectrum over an extensive range of electron density. Furthermore, we obtain the static correlations in good qualitative agreement with those calculated for the Luttinger liquid model with long-range interactions.     

Behavior of pionic hydrogen atoms in liquid organic compounds

Negative pion transfer from pionic hydrogen to other heavier atoms was studied in some liquid organic compounds. The pion capture probability on hydrogen at a particular site in the molecules was obtained using deuterated compounds for alcohols and carboxylic acids. The transfer process to carbon atoms in different chemical states was also studied in the mixtures of C₆ H₁₂ or C₆ H₆+ CCl₄. These methods revealed that the pionic hydrogen atoms originating from hydrogen in different chemical environments showed different behavior. The transfer process was discussed using a large mesomolecular model combined with an external transfer process. This revised version was published online in August 2006 with corrections to the Cover Date.     

Ground-state energy of strongly correlated electronic systems

We calculate the ground-state energy of strongly correlated electrons by using a twodimensional (CuO₂)_N system as an example. It constitutes the most important structural element of the high-T _c superconducting materials. The strong correlations are treated by projection technique. For that purpose a new form of the free energy is derived, which allows for applying that method. The ground-state energy for the half-filled band case is calculated by using a Padé approximation which agrees with series expansions up to order (t/( _p – _d ))⁶. Heret is thep-d hopping matrix element and _p , _d are the orbital energies of the O(2p _x(y)) and electrons.     

Ground-state energy of a classical artificial molecule

We study the ground-state energy of a classical artificial molecule formed by two-dimensional clusters (artificial atoms) of N/2 charged particles separated by a distance d. For the small molecules of N = 2 and 4, we obtain analytical expressions for this energy. For the larger ones, we calculate the ground-state energy using molecular dynamics simulation for N up to 128. From our numerical results, we are able to find out a function to approximate the ground-state energy of the molecules covering the range from atoms to molecules for any inter-atom distance d and for particle number from N = 8 to 128 within a difference less than one percent from the MD data.