An extensive calculation of Borromean windows (BWs) for 22 different configurations of three-body exotic systems have been done using an explicitly correlated Hylleraas type basis set. From the variation of BWs with mass relation parameter (q) as observed from our calculations, a physical argument is being placed to interpret the existence of a BW for only q < 1 configurations.

The Rayleigh-Ritz variational technique with a Hylleraas basis set is being tested for the first time to estimate the structural modifications of a lithium atom embedded in a weakly coupled plasma environment. The Debye-Huckel potential is used to mimic the weakly coupled plasma environment. The wave functions for both the helium-like lithium ion and the lithium atom are expanded in the explicitly correlated Hylleraas type basis set which fully takes care of the electron-electron correlation effect. Due to the continuum lowering under plasma environment, the ionization potential of the system gradually decreases leading to the destabilization of the atom. The excited states destabilize at a lower value of the plasma density. The estimated ionization potential agrees fairly well with the few available theoretical estimates. The variation of one and two particle moments, dielectric susceptibility and magnetic shielding constant, with respect to plasma density is also been discussed in detail.

The ground state energy and structural properties of a model two‐electron system (Zee), bound via screened Coulomb interaction with nuclear charge Z, have been studied under the variational framework. Hylleraas type basis has been adopted for explicit incorporation of the electron–electron correlation. Critical nuclear charges (Zc) of Zee system have been reported for different screening parameters (μ). Expectation values of different structural properties have been estimated to predict the internal structure of the Zee system. The variation of the structural properties with respect to Z for different μ reveals the signature of quantum phase transition (QPT) in the vicinity of Zc. Moreover, the nature of variation of these properties with respect to Z in case of bare Coulomb or free system (μ = 0) is completely opposite to those of screened system (μ ≠ 0). Radial two‐particle density (TPD) confirms the symmetry breaking of the electronic structure and therefore QPT in the vicinity of Zc.

The analytic form of the electrostatic potential felt by a slowly moving test charge in quantum plasma is being derived. It has been shown that the potential composed of two parts: Debye-Huckel screening term and near-field wake potential which depends on the velocity of the test charge and the number density of the plasma electrons. Rayleigh-Ritz variational calculation has been done to estimate precise energy eigenvalues of hydrogen-like ion under such plasma environment. A detailed analysis shows that the energy levels are gradually moves to the continuum with increasing plasma electron density while level crossing phenomenon have been observed with the variation of ion velocity.

Energy eigenvalues of nonautoionizing doubly excited 1,3Fe states originating from 2pnf ( n=4−20) configuration of two‐electron atoms Z=3−18 have been calculated by expanding the basis set in explicitly correlated Hylleraas coordinates under the framework of Ritz variational method. A detailed discussion on the evaluation of correlated basis integrals is given. The energy eigenvalues of a number of these doubly excited states are being reported for the first time especially for the high lying states. The effective quantum numbers ( n∗) for the states mentioned above have been calculated by using the theory of quantum defect.