We should mention that the four-body system similar to the case of two-body system in [24] (that was solved analytically for the massless mediating field case) may suggest a critical value of the coupling constant around ( alpha sim 1).
Moreover, The two-body system in Ref. [24] could be solved analytically for the massless mediating field case and also the results suggest a critical value of the coupling strength around (alpha sim 1).
(chi (x)) designates the mediating field which can be massless (i.e., (mu =0)), (cf. [3]), or massive ( (mu ne 0)).
Binding energy ({mathbf {B}}_{4}) is: ({mathbf {B}}_{4}=E_{4}-4) in units of m (i.e., (m=1)); the binding energy augments when we increase the coupling ( alpha.) This is because of the fact that for present scalar mediating field, the dominant one-quantum exchange interactions are attractive.
Approximate ground-state solutions of the two-, four-, and six-body systems have been presented for different strength of coupling, for both massive and massless scalar mediating field to compare the effects of virtual annihilation interaction terms and retardation effects in the relativistic equations.
Moreover, the mediating fields which act between particles antiparticles are also scalar mediating fields.
Approximate ground-state solutions have been studied for different strengths of coupling, for both massive and massless mediating fields where the virtual annihilation terms or retardation effects in the wave equations have been included or eliminated.
The equations have the Schrödinger non-relativistic limit, with Yukawa potentials in the event of a massive mediating scalar field or Coulombic interparticle potentials on condition of having a massless mediating scalar field.
might play a mediating role within Ukraine.
In the next book, "I Married a Communist," Zuckerman's not just a mediating presence.
"He was a consensus element; he played a mediating role in many reconciliations," Mr. Abdulal said.
