Lamb Shift in Muonic Hydrogen

The Lamb shift in muonic hydrogen continues to be a subject of experimental and theoretical investigation. Here my older work on the subject is updated to provide a complementary calculation of the energies of the 2p-2s transitions in muonic hydrogen.Comment: 15 pages, no figures. 2 small misprints corrected. Published in Phys. Rev.

Vacuum polarization in muonic and antiprotonic atoms: the fine structure at medium Z

Effects of vacuum polarization modify the energy levels in atoms with an orbiting particle heavier than an electron. The dominant effect is due to the Uehling potential. In this paper we consider the relativistic corrections to the energy levels caused by the Uehling potential and in particular the fine structure in muonic and antiprotonic atoms. We derive general expressions and consider in detail specific regions of parameters which allow simple asymptotic expansion. We take into account the recoil effects and anomalous magnetic moment in the case of an antiproton as the orbiting particle

Hyperfine Structure of S-States in Muonic Helium Ion

Corrections of orders alpha^5 and alpha^6 are calculated in the hyperfine splittings of 1S and 2S - energy levels in the ion of muonic helium. The electron vacuum polarization effects, the nuclear structure corrections and recoil corrections are taken into account. The obtained numerical values of the hyperfine splittings -1334.56 meV (1S state), -166.62 meV (2S state) can be considered as a reliable estimate for the comparison with the future experimental data. The hyperfine splitting interval Delta_{12}=(8 Delta E^{hfs}(2S)- Delta E^{hfs}(1S)) = 1.64 meV can be used for the check of quantum electrodynamics.Comment: 14 pages, 5 figure

The Uehling correction to the energy levels in a pionic atom

We consider a correction to energy levels in a pionic atom induced by the Uehling potential, i.e., by a free electron vacuum-polarization loop. The calculation is performed for circular states (l=n-1). The result is obtained in a closed analytic form as a function of $Z\alpha$ and the pion-to-electron mass ratio. Certain asymptotics of the result are also presented

Diversity of mycorrhizal plant species and arbuscular mycorrhizal fungi in evergreen forest, deciduous forest and grassland ecosystems of Southern Chile

In the Valdivian rainforest region of the Southern Chilean Andes three main ecosystems are found: Primary evergreen forests, secondary deciduous forests, and grassland areas. The secondary forest and the grasslands are habitually the result of the clearance of the primary forest some 60 years ago. The secondary forest consists mainly of the deciduous tree species Nothofagus alpina; forest management practices such as crown thinning and clearance of the understorey are applied to the secondary forest to improve its economic value. The grasslands are used by extensive cattle grazing. Soils in this region are acid Andosols with high organic matter content, high exchangeable aluminum and low levels of available phosphorus. The main objective of this study was to investigate the diversity of arbuscular mycorrhizal (AM) plant species and of arbuscular mycorrhizal fungi (AMF) in these three ecosystems. The highest diversity with 53 plant species was found in the evergreen forest with 77.4% of them AM, while in the grassland 91% of the 22 plant species were AM. The deciduous forest had 11 plant species only and the lowest proportion of AM plant species (55%). Thirty-nine AM fungal species were found in total, of which most are being reported for the first time from Southern Chile. Thirteen fungal species were of the Acaulospora genus, 10 of Glomus, 4 species each of Scutellospora and Archaeospora, 3 species each of Pacispora and Entrophospora, and one species each of Paraglomus and Diversispora. AMF species were more abundant in the grassland (29 spp.) than in the evergreen forest (20 spp.) which is likely related to a higher relative proportion of AM plant species in the grassland. Four AMF species were present in all the ecosystems, and 15 species were apparently quite specific as they were only found in one of the ecosystems. Noteworthy was the lack of Paraglomus and Scutellospora spp. in any of the forest ecosystems, and the relatively higher presence of Entrophospora spores in those ecosystems. It was concluded that the diversity of the AMF species in the ecosystems is strongly influenced by the proportion of AM plant species in each ecosystem and that their diversity is not related to soil chemical properties

Antiproton-Hydrogen annihilation at sub-kelvin temperatures

The main properties of the interaction of ultra low-energy antiprotons ($E\le10^{-6}$ a.u.) with atomic hydrogen are established. They include the elastic and inelastic cross sections and Protonium (Pn) formation spectrum. The inverse Auger process ($Pn+e \to H+\bar{p}$) is taken into account in the framework of an unitary coupled-channels model. The annihilation cross-section is found to be several times smaller than the predictions made by the black sphere absorption models. A family of $\bar{p}H$ nearthreshold metastable states is predicited. The dependence of Protonium formation probability on the position of such nearthreshold S-matrix singularities is analysed. An estimation for the $H\bar{H}$ annihilation cross section is obtained.Comment: latex.tar.gz file, 22 pages, 9 figure

Ionization Potential of the Helium Atom

Ground state ionization potential of the He^4 atom is evaluated to be 5 945 204 221 (42) MHz. Along with lower order contributions, this result includes all effects of the relative orders alpha^4, alpha^3*m_e/m_alpha and alpha^5*ln^2(alpha).Comment: 4 page