Large mass expansion in two-loop QCD corrections of para-charmonium decay

We calculate the two-loop QCD corrections to paracharmonium decays $eta_{c} rightarrow gamma gamma$ and $eta_{c} rightarrow g g$ involving light-by-light scattering diagrams with light quark loops. Artificial large mass expansion and convergence improvement techniques are used to evaluate these corrections. The obtained corrections to the decays $eta_{c} rightarrow gamma gamma$ and $eta_{c} rightarrow g g$ account for $-1.25$ and $-0.73$ of the leading order contribution, respectively.Comment: 24 pages, 10 figures; REVTeX version; Version to appear in Phys. Rev. D, 9 pages, 4 figure

Rockets, magnetics and spin: a theoretical perspective

The theoretical part of the Dissertation addresses various problems of calculating molecular properties related to the electron spin density at the nuclei. The formalism for analytic evaluation of restricted Hartree-Fock indirect spin-spin coupling constants is reviewed and various aspects of including solvent effects in the calculation of spin-spin coupling are discussed. Suitability of Gaussian basis sets for calculations of properties related to Fermi contact interaction, as well as the electron correlation treatment requirements for such properties are investigated. It is demonstrated, although for the particularly difficult cases of boron and carbon atoms, that very large basis sets and accounting at least to some extent for excitations to all orbitals in the complete space of basis functions may be required to correctly describe spin density at the nuclei. An original derivation of analytic hyperfine coupling tensors for MCQDPT theory is suggested. The derivation is based on the response functions formalism and incorporates some of the earlier results by other authors for analytic MCQDPT energy gradients. Once computed, the hyperfine coupling tensors can be numerically differentiated to obtain indirect spin-spin coupling constants.;The computational part of the Dissertation is a multi-configurational study of mechanisms of reactions of aluminum atoms with oxygen. This study is motivated by potential use of aluminum to improve energetic properties of solid H2 used as a rocket fuel. Our results indicate that the reaction of Al with O2 initially leads to the formation of the AlO2 molecule. A multi-configurational analysis of the PES for AlO2 shows that the linear form of this molecule is considerably lower in energy than the cyclic isomer. AlO2 can dissociate to AlO and atomic oxygen without any barrier beyond the endothermicity of this reaction. There is also no barrier for the reaction of AlO2 with AlO to form Al2O3, and this reaction is highly exothermic. While an additional study of the AlO2 + AlO 2 reaction is still necessary to make the final conclusion, most of our results suggest that Al2O3, may indeed be the main product of the Al combustion

A note on the breathing mode of an elastic sphere in Newtonian and complex fluids

Experiments on the acoustic vibrations of elastic nanostructures in fluid media have been used to study the mechanical properties of materials, as well as for mechanical and biological sensing. The medium surrounding the nanostructure is typically modeled as a Newtonian fluid. A recent experiment however suggested that high-frequency longitudinal vibration of bipyramidal nanoparticles could trigger a viscoelastic response in water-glycerol mixtures [M. Pelton et al., "Viscoelastic flows in simple liquids generated by vibrating nanostructures," Phys. Rev. Lett. 111, 244502 (2013)]. Motivated by these experimental studies, we first revisit a classical continuum mechanics problem of the purely radial vibration of an elastic sphere, also called the breathing mode, in a compressible viscous fluid, and then extend our analysis to a viscoelastic medium using the Maxwell fluid model. The effects of fluid compressibility and viscoelasticity are discussed. Although in the case of longitudinal vibration of bipyramidal nanoparticles, the effects of fluid compressibility were shown to be negligible, we demonstrate that it plays a significant role in the breathing mode of an elastic sphere. On the other hand, despite the different vibration modes, the breathing mode of a sphere triggers a viscoelastic response in water-glycerol mixtures similar to that triggered by the longitudinal vibration of bipyramidal nanoparticles. We also comment on the effect of fluid viscoelasticity on the idea of destroying virus particles by acoustic resonance

Semi-Leptonic b-decay at Intermediate Recoil

We compute the O(\alpha_s^2) corrections to the differential rate of the semileptonic decay b -> clv at the "intermediate recoil" point, where the c-quark mass and the invariant mass of the leptons are equal. The calculation is based on an expansion around two opposite limits of the quark masses m_{b,c}: m_c ~ m_b and m_c << m_b. The former case was previously studied; we correct and extend that result. The latter case is new. The smooth matching of both expansions provides a check of both. We clarify the discrepancy between the recent determinations of the full NNLO QCD correction to the semileptonic b -> c rate, and its earlier estimate.Comment: 9 pages, 6 figures, Replaced figures, small format and typo corrections, added appendix and reference

Unitarity of the tree approximation to the Glauber AA amplitude for large A

The nucleus-nucleus Glauber amplitude in the tree approximation is studied for heavy participant nuclei. It is shown that, contrary to previous published results, it is not unitary for realistic values of nucleon-nucleon cross-sections.Comment: 15 pages, 1 figure, 1 table. Submitted to Yad. Fi