Electronic structure, spectroscopy, cold ion-atom elastic collision properties and photoassociation formation prediction of (MgCs)+^+ molecular ion

Studies on the interactions between an alkali atom and an alkaline earth ion at low energy are important in the field of cold chemistry. In this paper we, extensively, study the structure, interactions, and dynamics of (MgCs)$^+$ molecular ion. We use an ab initio approach based on the formalism of non-empirical pseudo-potential for Mg$^{2+}$ and Cs$^+$ cores, large Gaussian basis sets and full valence configuration interaction. In this context, the (MgCs)$^+$ cation is treated as an effective two-electron system. Potential energy curves and their spectroscopic constants for the ground and the first 41 excited states of $^{1,3}\Sigma^+$, $^{1,3}\Pi$ and $^{1,3}\Delta$ symmetries are determined. Furthermore, we identify the avoided crossings between the electronic states of $^{1,3}\Sigma^+$ and $^{1,3}\Pi$ symmetries. These crossings are related to the charge transfer process between the two ionic limits Mg/Cs$^+$ and Mg$^+$/Cs. In addition, vibrational-level spacings, the transition and permanent dipole moments are presented and analysed. Using the produced potential energy data, the ground-state scattering wave functions and elastic cross sections for a wide range of energies are performed. Furthermore, we predict the formation of translationally and rotationally cold molecular ion (MgCs) + in the ground state electronic potential energy by stimulated Raman type process aided by ion-atom cold collision. In the low energy limit (< 1 mK), elastic scattering cross sections exhibit Wigner law threshold behaviour; while in the high energy limit the cross sections as a function of energy E go as E$^{-1/3}$. A qualitative discussion about the possibilities of forming the cold (MgCs)$^+$ molecular ions by photoassociative spectroscopy is presented

Multichannel quantum defect theory with numerical reference functions: Applications to cold atomic collisions

We develop a method for the calculation of multichannel wavefunctions in the spirit of quantum defect theory using numerically calculated reference functions. We first verify our method by calculating cold collisional properties of $^{85}$Rb and $^6$Li in the presence of external magnetic fields tuned across specific $s$-wave Feshbach resonances and thereby reproducing known results. We then calculate recently discovered $d$-wave Feshbach resonance [Phys. Rev. Lett. {\bf 119}, 203402 (2017)] in $^{87}$Rb-$^{85}$Rb cold collisions by our method. Our numerical results on this $d$-wave resonance agree reasonably well with the experimental ones. Our method is applicable to any arbitrary form of potentials and any arbitrary range of energies around threshold. The implementation of our method to any multichannel two-body scattering problem is straightforward.Comment: 16 pages, 8 figures, new results on $d$-wave Feshbach resonance are adde

Estimating above Ground Tree Biomass of Semi-Arid Bundelkhand Region Using Satellite Data, Regression Modelling and ANN Technique

Remotely sensed satellite imagery can be used to classify and monitor vegetation dynamics (Tucker, 1979). The Normalized Difference Vegetation Index (NDVI) computed from satellite data is a good measure of photosynthetic activity at landscape scales, and can be used to estimate vegetation biomass and Net Primary Production (NPP) (Tucker, 1979; Myneni et al., 1995, Nemani et al., 2003). As in the present environmental condition the climate change has adversely affected the ecosystem and the forest cover, NDVI has an important role to play to track and quantify the change taking place in plant ecosystem process (Myneni et al., 1995, Nemani et al., 2003). Biomass estimation using NDVI is easy to implement, harvesting of trees is not required and also effectively reduce the time and cost required in case of any other estimation process. In this study regression models and ANN (Artificial Neural Network) model were tried to simulate and predict total biomass production from different districts of Bundelkhand region. NDVI values collected from remote sensing images at particular season of the year to characterize above ground biomass of the study area. The performance of the ANN model was compared with several other commonly used linear and nonlinear models and validation was done based on the model’s stability