• S N Datta

Articles written in Pramana – Journal of Physics

• Relativistic extension of the Hohenberg-Kohn theorem

Using the configuration-space HamiltonianH+ which is derivable within the framework of quantum electrodynamics, we extend the Hohenberg-Kohn theorem to the relativistic theory of electrons in atoms or molecules.

• Quenching of excitations in an impure molecular crystal

The rate of quenching of excitons in a one-dimensional molecular crystal by an impurity is quantum-mechanically calculated.

• The minimax technique in relativistic Hartree-Fock calculations

Using the set of trial spinors$$\left\{ {N_i \left( {_{\hat \Omega _i u_i }^{u_i } } \right), i = 1, \ldots , N} \right\}$$ and the Dirac-Coulomb Hamiltonian (HDC) we discuss the role of the minimax theorem in relativistic Hartree-Fock calculations. In principle, the minimax theorem guarantees the occurrence of an upper bound. We also consider a scaling of the functionsui and discuss the condition to derive the relativistic hypervirial theorem; the variational procedure represented by the condition serves as an example of the minimax technique. Single zeta calculations onH2+,H2 and He are analysed. The effect of enlarging the basis is investigated for the He atom. The “upper bound” obtained by usingcoherent basis spinors differs from the result of the (random) linear variation using the kinetically balanced basis set by an amount which is at most of orderc−4. Use of thecoherent basis set is advocated.

• The minimax technique in relativistic Hartree-Fock calculations

• Bound state solutions of the two-electron Dirac-Coulomb equation

We present a variational method for solving the two-electron Dirac-Coulomb equation. When the expectation value of the Dirac-Coulomb Hamiltonian is made stationary for all possible variations of the different components of a well-behaved trial function one obtains solutions representative of the physical bound state wave functions. The ground state wave function is derived from the application of a minimax principle. Since the trial function remains well-behaved, the method remains safe from the twin demons of variational collapse and continuum dissolution.

The ground state wave function thus derived can be interpreted as a linear combination of different configurations. In particular, the admixing of intermediate states having one (two) electron(s) deexcited to a negative-energy orbital (orbitals) contributes a second-order level shiftE0−(2) which can be identified with the second-order shift due to the Pauli blocking of the production of one (or two) virtual electron-positron pair(s). Thus the minimax solution corresponds to the renormalized ground state in quantum electrodynamics, with deexcitations to negative-energy orbitals taking the place of the avoidance of virtual pairs.

If one extends the relativistic configuration interaction (RCI) treatment by additionally including negative-energy and mixed-energyeigenvectors of the Dirac-Hartree-Fock hamiltonian matrix in the two-electron basis, the calculated energy will be shifted from the conventional RCI value by an amount that is much smaller thanE0−(2). For two-electron atoms, we have derived expressions for the all-spinor limit (δE) and thes-spinor limit (δEs) of this shift in leading orders. The all-spinor limit (δE) is of orderα4Z4 1/3 whereas thes-spinor limit (δEs) is of orderα4Z3 2/3. leading components are related to the 1-pair component ofE0−(2) in a simple way, and the relationships offer the possibility of computing energy due to virtual pairs. Numerical results are discussed.

• Examples of the minimax technique in relativistic atomic one-electron calculations

Several examples of the application of the minimax technique to relativistic calculations on one-electron atoms are given here. Normalizable eigenfunctions corresponding to the ground states of one-electron atoms with various angular momenta are derived analytically.

• # Pramana – Journal of Physics

Volume 95, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019