Elastic and Inelastic Collisions in Ultracold and Astrophysical Environments

We explore collisions of atomic particles in two different regimes. In the first part of this work, we study atom-atom collisions of alkali metals at ultracold temperatures and conditions typically found in modern experiments. Feshbach resonances induced by external magnetic fields present a way to change collisional properties and exhibit control over cold collisions. We perform a fully quantum coupled-channel calculation in molecular orbital formalism to calculate collisional properties and characterize Feshbach resonances in ultracold Li+Na and Li+Rb systems. Furthermore, we use the results of these calculations as a foundation to propose a novel scheme for formation of stable ultracold molecules in their lowest rovibrational level. The formation scheme relies on the fact that the photoassociation rate becomes greatly enhanced in the vicinity of a Feshbach resonance, resulting in a large increase of the number of produced excited molecules. Efficient production of stable ultracold molecules is a prerequisite for realization of various proposed platforms for quantum computing with neutral atoms and molecules. In addition, we suggest a way to exploit specifics of the photoassociation rate behavior near its minimum for a precision measurement experiment to detect hypothetical variation of the electron-proton mass ratio in time. ^ The second part of this study examines ion-atom collisions in our solar system. Highly charged ions present in the solar wind collide with neutrals, capture one or more electrons into high excited states and deexcite, radiating energetic X-ray and UV photons. In particular, we study X-ray emissions charge-exchange collisions between fully stripped C6+, N7+ and O8+ solar wind ions and heliospheric hydrogen. We analytically solve the two-center Schrödinger equation and construct electronic potential curves for the aforementioned molecular ions. Subsequently, we compute polarization of the X-rays emitted in a single-step deexcitation following charge-exchange collisions and construct a polarization map for the ecliptic plane, as observed from Earth. Our analysis indicates that the heliospheric charge-exchange X-rays are slightly polarized, with the polarization P close to ten percent for the optimal line-of-sight.