T. K. Mukherjee

2pnp (1,3Pe) states of neutral He and Li+ ions under Debye plasma screening

The energy eigenvalues of doubly excited 2pnp (1Pe) (n = 3–8) and 2pnp (3Pe) (n = 2–7) bound states of a neutral helium atom and singly ionized lithium atom are estimated under weakly coupled plasma screening for the first time using an explicitly correlated Hylleraas-type basis in the framework of the Rayleigh–Ritz variational principle. The Debye screening model has been employed to include the effect of plasma background. Improvement over the existing approximated theoretical results has been achieved for the above-mentioned states of neutral helium under Debye plasma screening. The modified energy eigenvalues of 1,3Pe states arising from two p electrons of a Li+ ion in the Debye plasma environment are being reported for the first time.

Precise estimation of the energy levels of two-electron atoms under spherical confinement

The effect of spherical confinement on the ground state of helium-like ions (Z = 1–5) and the first four (1Se) excited states for Z = 2–5 have been analyzed in detail by using correlated Hylleraas basis sets within the variational framework. The correlated wave functions used here are consistent with the finite boundary conditions due to spherical confinement. The present energy values and the thermodynamic pressure generated for the confined ions as well as the critical values of the confining radii close to the fragmentation limit can be set as a benchmark for future references.

Variational calculation for the doubly excited state (2p{sup 2}){sup 3}P{sup e} of helium

Highly precise variational calculations of nonrelativistic energies of the (2p{sup 2}){sup 3}P{sup e} state of the helium atom are presented. We get an upper bound energy E=-0.7105 001 556 5678 a.u., the lowest yet obtained.

Effect of strongly coupled plasma on the magnetic dipolar and quadrupolar transitions of two-electron ions

Effect of strongly coupled plasma on the excitation energies and transition probabilities for the respective transitions 1s2:1Se → 1sns:3Se (n = 2, 3, 4) and 1s2:1Se → 1snp:3Po (n = 2, 3, 4) allowed by magnetic dipolar and quadrupolar excitations have been analyzed for the first time for the two-electron ions C4+, O6+, Ne8+, Mg10+, Si12+, and S14+. Time dependent Hatree-Fock theory within variational approach has been adopted for such a study. The effect of surrounding plasma has been treated through the standard Ion-Sphere (IS) model of the plasma where the plasma density is varied systematically from a low value to a pretty high value such that the respective excited states go over to continuum due to such a confinement. The effect of external pressure generated due to plasma confinement on the estimated spectral properties has been analyzed systematically.

Electronic Structure of Helium Atom in a Quantum Dot

Bound and resonance states of helium atom have been investigated inside a quantum dot by using explicitly correlated Hylleraas type basis set within the framework of stabilization method. To be specific, precise energy eigenvalues of bound 1sns (1Se) [n = 1-6] states and the resonance parameters i.e. positions and widths of 1Se states due to 2sns [n = 2-5] and 2pnp [n = 2-5] configuration of confined helium below N = 2 ionization threshold of He+ have been estimated. The two-parameter (Depth and Width) finite oscillator potential is used to represent the confining potential representing the quantum dot. It has been explicitly demonstrated that electronic structure properties become a sensitive function of the dot size. It is observed from the calculations of ionization potential that the stability of an impurity ion within quantum dot may be manipulated by varying the confinement parameters. A possibility of controlling the autoionization lifetime of doubly excited states of two-electron ions by tuning the width of the quantum cavity is also discussed here.

Structural properties of lithium atom under weakly coupled plasma environment

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.

Precise energy eigenvalues of hydrogen-like ion moving in quantum plasmas

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

Three-body negative ions under Coulomb interaction

The ground state energy eigenvalues of the symmetric three-body exotic negative ions p+π−π− and p+K−K− have been determined variationally for the first time using an explicitly correlated Hylleraas basis set. Ground state energies of Ps− and p+μ−μ− were also determined to check the accuracy of the present methodology by comparing those results to a few accurate earlier results for these systems.

Two-electron atoms under spatially compressed Debye plasma

Rayleigh–Ritz variational method has been employed to estimate precise energy-eigenvalues of spherically compressed two-electron atoms ( Z=1−10) embedded in Debye plasma with a view to modelling atom under dense plasma environment. The trial wave function is expanded in terms of explicitly correlated Hylleraas-type basis set satisfying Dirichlets boundary condition. The combined effect of decrease in the size of spatial confinement domain and increase in Debye screening parameter pushes the system towards gradual destabilization and subsequent ionization or complete fragmentation of the system. Present results are in reasonable agreement with other results existing in literature. Within finite domain, the thermodynamic pressure experienced by the ions due to the plasma electrons is also estimated.

Metastable bound D1,3o states below N=3 ionization threshold of He+

The applicability of Ritz-variational principle for 3dnf ((1,3)D(o)) states lying between N=2 and N=3 ionization threshold of singly ionized helium is discussed in this communication. Probable existence of such a state for O(6+) within the planetary atmosphere in the polar regions of Jupiter is discussed.