Dipankar Chattarji

Electron shake-off in neon and the interaction of continuum states

Abstract Transition probabilities for shake-off of a 2 p electron in a neon atom into the continuum following the creation of a vacancy in the 1 s shell by an energetic electron or photon are calculated in the sudden approximation and include the electrostatic interaction between the shake-off electron and the residual ion core. The calculations is based on nonrelativistic Hartree-Fock-Slater wave functions, the residual interaction resulting from the electrostatic term being treated as a perturbation. In the first Born limit as well as in a complete calculation results for the ratio I ( 3 P )/ I ( 1 P = transition probability to continuum states with 3 P core transition probability to continuum states with 1 P core are lower than the value 3: 1 predicted by statistics in the independent particle limit .

Some applications of time‐dependent canonical transformations to nonlinear nonconservative classical systems

The recently proposed time‐dependent canonical transformation method of Leach for the quadratic Hamiltonian has been extended to deal with nonlinear nonconservative classical systems. It is observed that the linear time dependent canonical transformations are not adequate to remove the time dependence of any arbitrary time‐dependent nonlinear Hamiltonian. Alternatively, we propose that such a Hamiltonian may be transformed to a quadratic form by means of successive nonlinear canonical transformations. It is also shown that the canonical method is useful to obtain solutions for differential equations governing certain dissipative classical systems.

Off‐shell Jost function and T matrix for the Woods–Saxon potential

The s‐wave van Leeuwan and Reiner equation for the Woods–Saxon potential is solved. Analytical expressions for the off‐shell Jost solution and Jost function are derived. The results are used to obtain the T matrix.

Off-shell t-matrix for an exponential potential with non-local core interaction

Abstract The wave function approach of Van Leeuwen and Reiner to the t -matrix is generalized to the case of a non-local potential. The transition matrix element for this potential is obtained. The results are used to compute the s-wave part of the t -matrix for a non-local square well potential combined with an outside exponential potential.

Angular correlation theory for double photoionization in a rare-gas atom: Ionization by polarized photons

This is a sequel to an earlier article on the theory of angular correlation for double photoionization. Here we consider the two-step double photoionization of a rare gas atom under the influence of a polarized photon beam described by appropriate Stokes parameters. Cylindrical mirror analysers (CMA) are used to detect the outgoing electrons. Theoretical values of the correlation functions are obtained for linearly polarized light. Two different situations is handled. Once, the value of the correlation function is obtained keeping the photo-electron in a fixed direction. The other case the direction of the Auger electron is kept fixed. Comparison with experiments on xenon shows excellent agreement for the case of (4d_{5/2}) photoionization followed by a subsequent (N_{5}-O_{23}O_{23} ^{1}S_{0}) Auger decay for a polarized incident photon of energy (94.5eV) {[}J. Phys.B,

An angular correlation function for double photoionization in atoms

Abstract We consider the successive emission of two electrons following the absorption of a photon by an atom. An expression for the angular correlation between the emitted electrons is derived in terms of the angle between their directions of propagation, following the generalized approach of Biedenharn and Rose (Rev. Mod. Phys. 25 (1953) 729). Our theory treats double photoionization as a two-step process and does not refer to perturbation theory. The dynamics of the process are embodied in the reduced matrix elements. It is clear that angular correlation is closely related to the coupling of the angular momenta. A sample computation is made for double photoionization in argon leading to the 3p −2 1 D e final ionic state.

The jost function and bound state solution for the hulthén potential

Abstract The parameters of the attractive Hulthen potential are obtained in terms of the parameters of effective range theory by using the Jost function for the potential. The bound state solution for 1 + 0 is found from the corresponding Jost solution. The possibility of extending the present treatment to higher angular momentum states is discussed.

On K-shell internal conversion coefficients

Abstract K-shell internal conversion coefficients have been obtained for E1 and M1 transitions in the point nucleus limit by using solutions of the Biedenharn symmetric Dirac-Coulomb Hamiltonian. Numerical results obtained for atoms having Z values between 20 and 65 with γ-ray energies from 0.15 MeV to 2.5 MeV are compared with results of earlier calculations.