Exotic systems under screened Coulomb interactions: a study on Borromean windows

Abstract

An extensive calculation of Borromean windows (BWs) for 22 different configurations of three-body exotic systems have been done using an explicitly correlated Hylleraas type basis set. From the variation of BWs with mass relation parameter (q) as observed from our calculations, a physical argument is being placed to interpret the existence of a BW for only q < 1 configurations.

Critical Stability of the Negatively Charged Positronium-Like Ions with Yukawa Potentials and Varying Z

“…As stated earlier in Section 1, basic idea of the three-body Borromean binding states that the three-body Yukawa system can be defined as Borromean when it supports bound states for a fixed range of screening parameters (called the Borromean window) while none of their two-body subsystems are bound in such a range of screening parameter. From the Table S1 (Supplementary Materials), it is clear that the upper critical screening parameter for each Z is similar to the critical screening of the respective two-body subsystem and so from this study, we can only find the range for the Borromean binding [33,34] close to the upper critical screening parameter of the three-body Yukawa system under study. However, the present calculations show that the Borromean window, if it existed for certain Z, would be too narrow and very close to µ U .…”

“…The critical charge Z C denotes a cut-off for which the system under study does not support any bound state for Z < Z C , but supports at least one bound state for Z ≥ Z C . The critical parameter µ C also indicates cut-off points those are responsible for the determination of bound states, quasi-bound states [32], or Borromean states [33][34][35]. Suppose the critical screening µ C admits two values µ L (the lower critical screening parameter) and µ U (the upper critical screening parameter) for a given Z, the proposed three-body Yukawa system supports bound states for µ L ≤ µ ≤ µ U , subject to the condition that its two-body subsystem (Ze + , e − ) (or the Ps like system) is stable for µ L ≤ µ ≤ µ U .…”

Electronic structure calculations of compressed Li atom using composite technique under Ritz variational framework

“…By suitably tuning the geometrical ratio γ c , we can control the radial space in a flexible manner. Such type of basis set has successfully been used in structure calculations for both free and plasma embedded two‐electron atoms [46–58]. The linear variational parameters, that is, C i 's (Equation ) along with the energy eigenvalues of the core electrons E c are obtained by solving the generalized eigenvalue equation where is the Hamiltonian matrix, is the overlap matrix and is the column matrix consisting of linear variational parameters.…”

Ritz variational method for the high‐lying nonautoionizing doubly excited 1,3Fe states of two‐electron atoms

“…In this communication, we have made an attempt to estimate the energy eigenvalues of 2pnf F e states ( ) of two‐electron systems ( ) using trial wave function expanded in multiexponent Hylleraas type basis set. We have already used such type of wavefunction to determine the structural parameters of different S, P, and D states of free and confined two‐electron systems . It is worthwhile to mention that using Hylleraas basis the energy values of 2pnf F e states of two electron atoms with Z > 10 are being reported for the first time.…”