A.V. A.V. Selin

A high-order accuracy method for numerical solving of the time-dependent Schrödinger equation

Abstract A generalization of the Crank–Nicolson algorithm to higher orders for the time-dependent Schrodinger equation is proposed to improve the accuracy of the time approximation. The implicit difference schemes are obtained in terms of the Magnus expansion for the evolution operator and its further factorization with the help of diagonal Pade approximations. Stability of the schemes and conservation of the approximated solution norm are provided by the fact that the Magnus expansion of the evolution operator preserves its unitarity in any order with respect to a time step τ . As an example, a comparison between the numerical and analytical solutions of a model problem for the oscillator with an explicitly time-dependent frequency was performed for the schemes O ( τ 4 ) and O ( τ 6 ) to demonstrate accuracy, efficiency and adequate convergence of the method.

Magnus-factorized method for numerical solving the time-dependent Schrödinger equation

Abstract The method of constructing the high-order stable operator-difference schemes for solving the time-dependent Schrodinger equation are proposed as a generalization of the Crank–Nicolson scheme. The schemes are constructed in terms of the Magnus expansion for the evolution operator. The case of the non-homogeneous equation is also considered.

A semi-relativistic eikonal distorted wave model for collisions of fast highly charged ions with light atomic targets

We propose a semi-relativistic symmetric eikonal distorted wave method for treating collisions of fast projectiles with light atomic targets. The projectile interaction with target electrons is described by the Li?nard?Wiechert potential, within the impact parameter approach. Our model allows one to estimate two-centre effects in fast heavy-particle collisions. It is found that in the dipole approximation the first-order eikonal cross sections differ from the corresponding Born cross sections by a simple factor that accounts for the forward?backward asymmetry of the ejected electron with respect to the direction of the projectile motion. As an illustration of our method we have carried out calculations for single ionization in collisions of fast U92+ ions (1?GeV?u?1) with helium targets.

Single ionization of the 1 1Se and 2 1Po states of He by 1-GeV/u U92+ ions

We report calculations of the cross sections for single ionization of the ground 1 1 S and excited 2 1 P helium states by relativistic impact of a bare uranium ion of charge Z p = 92 with energy 1 GeV/u. The heavy particle collision is treated within the semirelativistic first Born approximation. The nonrelativistic initial and final two-electron correlated atomic states are obtained by numerical procedures from variational principles. The continuum final states are considered below the n=2 threshold of the He + ion The differential ionization cross section dσ/dE is obtained for electron energies E≤37 eV. This energy range includes a wide nonresonant region as well as the resonance structures due to the autoionizing helium states (2s 2 ) 1 S, (2s2p) 1 P and (2p 2 ) 1 D.

Single ionization of the [Formula Presented] and [Formula Presented] states of He by 1-GeV/u [Formula Presented] ions

We report calculations of the cross sections for single ionization of the ground 1 1 S and excited 2 1 P helium states by relativistic impact of a bare uranium ion of charge Z p = 92 with energy 1 GeV/u. The heavy particle collision is treated within the semirelativistic first Born approximation. The nonrelativistic initial and final two-electron correlated atomic states are obtained by numerical procedures from variational principles. The continuum final states are considered below the n=2 threshold of the He + ion The differential ionization cross section dσ/dE is obtained for electron energies E≤37 eV. This energy range includes a wide nonresonant region as well as the resonance structures due to the autoionizing helium states (2s 2 ) 1 S, (2s2p) 1 P and (2p 2 ) 1 D.

Single ionization of the 1 {sup 1}S{sup e} and 2 {sup 1}P{sup o} states of He by 1-GeV/u U{sup 92+} ions

We report calculations of the cross sections for single ionization of the ground 1 1 S and excited 2 1 P helium states by relativistic impact of a bare uranium ion of charge Z p = 92 with energy 1 GeV/u. The heavy particle collision is treated within the semirelativistic first Born approximation. The nonrelativistic initial and final two-electron correlated atomic states are obtained by numerical procedures from variational principles. The continuum final states are considered below the n=2 threshold of the He + ion The differential ionization cross section dσ/dE is obtained for electron energies E≤37 eV. This energy range includes a wide nonresonant region as well as the resonance structures due to the autoionizing helium states (2s 2 ) 1 S, (2s2p) 1 P and (2p 2 ) 1 D.