Borromean bindings in muonic molecular ions with screened Coulomb potentials

Abstract

We have investigated the stability of muonic molecular ions interacting with screened Coulomb potentials of various strengths. Particular emphasize has been given to study the Borromean bindings in these ions. Two types of screened potentials are considered, namely, static screened Coulomb potentials and exponential cosine-screened Coulomb potentials. Making use of extensive correlated variational wavefunctions, Borromean windows for these ions are determined accurately. The possibility of existence of Borromean binding for other three-body systems has also been explored. Moreover, the results for ground state energies, excited states energies and several expectation values associated with ppμ, ddμ and tdμ molecular ions are reported for various values of the screening parameter.

Properties of hydrogen molecular ion with static screened coulomb and exponential cosine screened coulomb potentials

“…Such a binding is called a Borromean binding, and the range of the screening parameter for which Borromean binding exists is called Borromean window. A detail discussion about Borromean binding has been made in our previous article [2]. Using extrapolation formulas we obtain the following values of the critical screening parameter λ c (the value of λ for which the system becomes unbound) for the ground state ( J = 0, ν = 0) and excited state ( J = 0, ν = 1) of hydrogen molecular ion:…”

“…(11) and (12), we note that that size of a Borromean window in ECSCP is broader than the corresponding size in SSCP, as weaker potentials produce broader windows [2]. But in the case of hydrogen molecular ion, the size of the Borromean window in ECSCP is much broader than those of ppµ, ddµ, tdµ, and ttµ molecular ions [2]. The mass relation parameter q (ratio of the mass of the particle attracting the other two to the mass of one of the repelling-each-other particles) is much less for H + 2 .…”

“…of hydrogen molecular in pure Coulomb potential (λ = 0). λ (a as obtained in our previous article [2], we get the critical screening parameter for the ground state of atomic hydrogen as…”

“…Here λ is related to the plasma frequency ω p by means of the relation λ = ω p /( ω p /m) 1/2 . Moreover, screened Coulomb potentials are also important to understand Borromean bindings [2].…”

“…The applications of SSCP to physical and chemical phenomena are well-known in the literature. ECSCP also find various applications in different areas of physics, such as, plasma physics [1][2][3][4][5], solid-state physics [6][7][8][9][10][11], nuclear physics [12,13]. From Eqs.…”