Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThree-potential formalism for the atomic three-body problem
302
0
0.0
(
0
)
Authors
Z. Papp
Ask ChatGPT about the research
No Arabic abstract
Based on a three-potential formalism we propose mathematically well-behaved Faddeev-type integral equations for the atomic three-body problem and descibe their solutions in Coulomb-Sturmian space representation. Although the system contains only long-range Coulomb interactions these equations allow us to reach solution by approximating only some auxiliary short-range type potentials. We outline the method for bound states and demonstrate its power in benchmark calculations. We can report a fast convergence in angular momentum channels.
rate research
Read More
A three-body scattering process in the presence of Coulomb interaction can be decomposed formally into a two-body single channel, a two-body multichannel and a genuine three-body scattering. The corresponding integral equations are coupled Lippmann-Schwinger and Faddeev-Merkuriev integral equations. We solve them by applying the Coulomb-Sturmian separable expansion method. We present elastic scattering and reaction cross sections of the $e^++H$ system both below and above the $H(n=2)$ threshold. We found excellent agreements with previous calculations in most cases.
We propose a three-potential formalism for the three-body Coulomb scattering problem. The corresponding integral equations are mathematically well-behaved and can succesfully be solved by the Coulomb-Sturmian separable expansion method. The results show perfect agreements with existing low-energy $n-d$ and $p-d$ scattering calculations.
Three-body resonances in atomic systems are calculated as complex-energy solutions of Faddeev-type integral equations. The homogeneous Faddeev-Merkuriev integral equations are solved by approximating the potential terms in a Coulomb-Sturmian basis. The Coulomb-Sturmian matrix elements of the three-body Coulomb Greens operator has been calculated as a contour integral of two-body Coulomb Greens matrices. This approximation casts the integral equation into a matrix equation and the complex energies are located as the complex zeros of the Fredholm determinant. We calculated resonances of the e-Ps system at higher energies and for total angular momentum L=1 with natural and unnatural parity
Although the convergent close-coupling (CCC) method has achieved unprecedented success in obtaining accurate theoretical cross sections for electron-atom scattering, it generally fails to yield converged energy distributions for ionization. Here we report converged energy distributions for ionization of H(1s) by numerically integrating Schroedingers equation subject to correct asymptotic boundary conditions for the Temkin-Poet model collision problem, which neglects angular momentum. Moreover, since the present method is complete, we obtained convergence for all transitions in a single calculation. Complete results, accurate to 1%, are presented for impact energies of 54.4 and 40.8 eV, where CCC results are available for comparison.
The three-body energy-dependent effective interaction given by the Bloch-Horowitz (BH) equation is evaluated for various shell-model oscillator spaces. The results are applied to the test case of the three-body problem (triton and He3), where it is shown that the interaction reproduces the exact binding energy, regardless of the parameterization (number of oscillator quanta or value of the oscillator parameter b) of the low-energy included space. We demonstrate a non-perturbative technique for summing the excluded-space three-body ladder diagrams, but also show that accurate results can be obtained perturbatively by iterating the two-body ladders. We examine the evolution of the effective two-body and induced three-body terms as b and the size of the included space Lambda are varied, including the case of a single included shell, Lambda hw=0 hw. For typical ranges of b, the induced effective three-body interaction, essential for giving the exact three-body binding, is found to contribute ~10% to the binding energy.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
