Z. Papp, S. L. Yakovlev, C-. Y. Hu, J. Darai, I. N. Filikhin, B. Kónya
A novel method for calculating resonances in three-body Coulombic systems is presented. The Faddeev-Merkuriev integral equations are solved by applying the Coulomb-Sturmian separable expansion method. To show the power of the method we calculate resonances of the three-$α$ and the $H^-$ systems.
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Electron-hydrogen scattering is studied in the Faddeev-Merkuriev integral equation approach. The equations are solved by using the Coulomb-Sturmian separable expansion technique. We present $S$- and $P$-wave scattering and reactions cross sections up to the $H(n=4)$ threshold.
A novel method for calculating resonances in three-body Coulombic systems is proposed. The Faddeev-Merkuriev integral equations are solved by applying the Coulomb-Sturmian separable expansion method. The $e^- e^+ e^-$ S-state resonances up to $n=5$ threshold are calculated.
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 Green's operator has been calculated as a contour integral of two-body Coulomb Green's 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-…
The computational approach for solving the Faddeev-Merkuriev equations in total orbital momentum representation is presented. These equations describe a system of three quantum charged particles and are widely used in bound state and scattering calculations. The approach is based on the spline collocation method and exploits intensively the tensor product form of discretized operators and preconditioner, which leads to a drastic economy in both computer resources and time.
A version of the $J$-matrix method for solving numerically the three-body Faddeev-Merkuriev differential equations is proposed. This version allows to take into account the full spectrum of the two-body Coulomb subsystem. As a result, a discrete analog of the Lippmann-Schwinger equation is obtained which allows to interpret correctly the three-body wave function in two-body domains. The scheme is applied to calculations of the fully resolved absolute differential cross sections for the He$(e,2e)$He$^+$ and He$(e,3e)$He$^{++}$ reactions at small energy and momentum transfers. The results are in…
We reconsider the homogeneous Faddeev-Merkuriev integral equations for three-body Coulombic systems with attractive Coulomb interactions and point out that the resonant solutions are contaminated with spurious resonances. The spurious solutions are related to the splitting of the attractive Coulomb potential into short- and long-range parts, which is inherent in the approach, but arbitrary to some extent. By varying the parameters of the splitting the spurious solutions can easily be ruled out. We solve the integral equations by using the Coulomb-Sturmian separable expansion approach. This sol…
The potential splitting approach incorporated into the framework of Faddeev-Merkuriev equations in the differential form is used for calculations of multichannel scattering in $e^-e^+\bar{p}$ and $e^+e^-\mbox{He}^{++}$ systems. Detailed calculations of all possible S-wave cross-sections are performed %in systems $e^+e^-\bar{p}$ and $e^+e^-\mbox{He}^{++}$ in the low-energy region which supports up to seven open channels including the rearrangement channels of ground and excited states of antihydrogen, positronium and helium ion formations. All known sharp resonances of the systems obtained and …
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 apply a new highly efficient method of solving Faddeev-Merkuriev equations to multi-channel scattering calculations of the antihydrogen formation cross section for antiproton scattering off the ground and excited states of the positronium. Our results demonstrate good agreement with the known data on total and partial cross sections for all the reaction channels. Using moderate computational resources we have achieved a supreme energy resolution.
We calculate resonances in three-body systems with attractive Coulomb potentials by solving the homogeneous Faddeev-Merkuriev integral equations for complex energies. The equations are solved by using the Coulomb-Sturmian separable expansion approach. This approach provides an exact treatment of the threshold behavior of the three-body Coulombic systems. We considered the negative positronium ion and, besides locating all the previously know $S$-wave resonances, we found a whole bunch of new resonances accumulated just slightly above the two-body thresholds. The way they accumulate indicates t…
Three-body charge transfer reactions with Coulomb interaction in the final state are considered in the framework of coordinate-space integro-differential Faddeev-Hahn-type equations within two- and six-state close coupling approximations. The method is employed to study direct muon transfer in low-energy collisions of the muonic hydrogen H$_μ$ by helium (He$^{++}$) and lithium (Li$^{+++}$) nuclei. The experimentally observed isotopic dependence is reproduced.
We perform three-body calculation of direct muon-transfer rates from thermalized muonic hydrogen isotopes to bare nuclei Ne$^{10+}$, S$^{16+}$, and Ar$^{18+}$ employing integro-differential Faddeev-Hahn-type equations in configuration space with two-state close-coupling approximation scheme. All Coulomb potentials including the strong final-state Coulomb repulsion are treated exactly. A long-range polarization potential is included in the elastic channel to take into account the high polarizability of the muonic hydrogen. The transfer rates so calculated are in good agreement with recent exper…
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.
We assume all interaction to be Coulombic and solve the modified Faddeev equation for energies between the $Ps(n=2)$ and $\bar{H}(n=3)$, which involve six and eight open channels. We find that 99% of the antihydrogen are formed in $\bar{H}(n=2)$. Just above the $Ps(n=2)$ threshold the S, P, and D partial waves contribute more than 4000 square Bohr radii near the maximum. Evidences indicate that the induced long range dipole potential from the degenerate $Ps(n=2)$ targets is responsible for such a large antihydrogen formation cross section.
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