Resonant-state solution of the Faddeev-Merkuriev integral equations for three-body systems with Coulomb potentials

Abstract

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.

Second Order Stark-Effect Induced Gailitis Resonances in e + Ps and p + 7Li

“…The average value of α 1 is 164 for 7 (14) Table 3 shows that for all 5. , which are many orders of magnitude larger than that of nuclear processes. In fact, the lifetime of the compound nuclear energy level involved in the fusion is~10 ¡23 s. Table 3.…”

“…The changing electric fields provide conditions for resonances involving all particles in the scattering system if the target has any kind of electric dipole moment [1]. In particular, we consider the two cases where the targets have no permanent electric dipole moment, such as the ground states of 7 Li and Ps. They are compared with the e + + H (n = 2) scattering system where, due to Coulomb degeneracy, the first order Stark-effect is a constant electric dipole moment [2].…”

Accumulation of Three-Body Resonances above Two-Body Thresholds

“…So, especially around thresholds it is not easy to decide whether a point is a resonance point or it belongs to the rotated continuum. Moreover, variational methods approach states from above, so resonances slightly above the thresholds may easily get lost.Recently, we have developed a method for calculating resonances in three-body Coulombic systems by solving homogeneous Faddeev-Merkuriev integral equations [1] using the Coulomb-Sturmian separable expansion approach [2]. As a test case, we calculated the resonances of the negative positronium ion.…”

“…Since our method is relatively new we briefly outline the basic concepts and the numerical techniques, specialized to the e − e − e + system (further details are in Refs. [2,4]). …”

Origin of three-body resonances

“…For completeness also the continuous non-singular background states are needed, but the singularities of the scattering matrix are very often decisive. Important examples using different methods within few-body physics are astrophysical reaction rates [18], adiabatic reaction processes arising at low energies or for large impact parameters [19], three-body decays [20], three-body resonances for Faddeev operators [21], for nucleons [22], for electrons and positrons [23] and four-body nuclear continuum states [24]. This list could be extended.…”