The role of impacting processes in the chemical evolution of the atmosphere of primordial Earth

The role of impacting processes in the chemical evolution of the atmosphere of primordial Earth is discussed. The following subject areas are covered: (1) Earth's initial atmosphere; (2) continuous degassing; (3) impact processes and the Earth's protoatmosphere; and (4) the evolution of an impact-generated atmosphere

Measurement of helium-3 and deuterium stopping power ratio for negative muons

The measurement method and results measuring of the stopping power ratio of helium-3 and deuterium atoms for muons slowed down in the D/$^3$He mixture are presented. Measurements were performed at four values of pure $^3$He gas target densities, $\phi_{He} = 0.0337, 0.0355, 0.0359, 0.0363$ (normalized to the liquid hydrogen density) and at a density 0.0585 of the D/$^3$He mixture. The experiment was carried out at PSI muon beam $\mu$E4 with the momentum P$\mu =34.0$ MeV/c. The measured value of the mean stopping ratio $S_{^3He/D}$ is $1.66\pm 0.04$. This value can also be interpreted as the value of mean reduced ratio of probabilities for muon capture by helium-3 and deuterium atoms.Comment: 7 pages, 6 figure

Spin Asymmetry and Gerasimov-Drell-Hearn Sum Rule for the Deuteron

An explicit evaluation of the spin asymmetry of the deuteron and the associated GDH sum rule is presented which includes photodisintegration, single and double pion and eta production as well. Photodisintegration is treated with a realistic retarded potential and a corresponding meson exchange current. For single pion and eta production the elementary operator from MAID is employed whereas for double pion production an effective Lagrangean approach is used. A large cancellation between the disintegration and the meson production channels yields for the explicit GDH integral a value of 27.31 $\mu$b to be compared to the sum rule value 0.65 $\mu$b.Comment: 4 pages, 5 figures, revtex

Pion Form Factor in Chiral Limit of Hard-Wall AdS/QCD Model

We develop a formalism to calculate form factor and charge density distribution of pion in the chiral limit using the holographic dual model of QCD with hard-wall cutoff. We introduce two conjugate pion wave functions and present analytic expressions for these functions and for the pion form factor. They allow to relate such observables as the pion decay constant and the pion charge electric radius to the values of chiral condensate and hard-wall cutoff scale. The evolution of the pion form factor to large values of the momentum transfer is discussed, and results are compared to existing experimental data.Comment: 21 page, 7 figures. Short comparison with NJL predictions for pion radius and new references added. To be published in Phys.Rev.

Towards Integrability of Topological Strings I: Three-forms on Calabi-Yau manifolds

The precise relation between Kodaira-Spencer path integral and a particular wave function in seven dimensional quadratic field theory is established. The special properties of three-forms in 6d, as well as Hitchin's action functional, play an important role. The latter defines a quantum field theory similar to Polyakov's formulation of 2d gravity; the curious analogy with world-sheet action of bosonic string is also pointed out.Comment: 31 page

3-D orbital evolution model of outer asteroid belt

The evolution of minor planets in the outer part of the asteroid belt is considered. In the framework of the semi-averaged elliptic restricted three-dimensional three-body model, the boundary of regions of the Hill's stability is found. As was shown in our work, the Jacobian integral exists

Liouville Type Models in Group Theory Framework. I. Finite-Dimensional Algebras

In the series of papers we represent the ``Whittaker'' wave functional of $d+1$-dimensional Liouville model as a correlator in $d+0$-dimensional theory of the sine-Gordon type (for $d=0$ and $1$). Asypmtotics of this wave function is characterized by the Harish-Chandra function, which is shown to be a product of simple $\Gamma$-function factors over all positive roots of the corresponding algebras (finite-dimensional for $d=0$ and affine for $d=1$). This is in nice correspondence with the recent results on 2- and 3-point correlators in $1+1$ Liouville model, where emergence of peculiar double-periodicity is observed. The Whittaker wave functions of $d+1$-dimensional non-affine ("conformal") Toda type models are given by simple averages in the $d+0$ dimensional theories of the affine Toda type. This phenomenon is in obvious parallel with representation of the free-field wave functional, which is originally a Gaussian integral over interior of a $d+1$-dimensional disk with given boundary conditions, as a (non-local) quadratic integral over the $d$-dimensional boundary itself. In the present paper we mostly concentrate on the finite-dimensional case. The results for finite-dimensional "Iwasawa" Whittaker functions were known, and we present their survey. We also construct new "Gauss" Whittaker functions.Comment: 47 pages, LaTe

Generalized sum rules of the nucleon in the constituent quark model

We study the generalized sum rules and polarizabilities of the nucleon in the framework of the hypercentral constituent quark model. We include in the calculation all the well known $3^*$ and $4^*$ resonances and consider all the generalized sum rules for which there are data available. To test the model dependence of the calculation, we compare our results to the results obtained in the harmonic oscillator CQM. We furthermore confront our results to the model-independent sum rules values and to the predictions of the phenomenological MAID model. The CQM calculations provide a good description of most of the presented generalized sum rules in the intermediate $Q^2$ region (above $\sim0.2$ GeV$^2$) while they encounter difficulties in describing these observables at low $Q^2$, where the effects of the pion cloud, not included in the present calculation, are expected to be important.Comment: 26 pages, 10 figure