x2=r2e+r2e−2r2ecos(ϕ)=2r2e(1−cos(ϕ))
x=re√2(1−cos(ϕ))=2resin(ϕ/2)
and
rT+x=tan(θ0)
rT+tan(θ0)=2resin(ϕ/2)
ϕ=2.sin−1(rT+2retan(θ0))
This is the relationship between θ0 and ϕ, as x, the distance between the electron and the center of the T+ particle's orbit changes.
Low values of θ0 corresponds to T+ particles that are far away, (along x), from the electron. When re is finite,
θ0min=θc=tan−1(rT+√2.re)
Each orbiting T+ particle generates a E field perpendicular to it orbital plane, at an angle π/2−ϕs to the reference ϕ=0.
all these oscillations overlap at the lower values of θ0, beside θc.
But the traveling T+ particles has high velocities at these values of θ0 near θc, the center of the oscillation; the equilibrium position. The particles pass through θc quickly but dwell at the two ends of their oscillations.
If there is an uniform spread in oscillations from θc to θ0=π/2, there will be a greater concentration of E fields from higher values of θ0, due to the T+ particle longer dwell time. (A math expression is needed here.)
This could explain why higher values of θ0 has higher energy and is associated with higher frequencies and so lower wavelength.
In this case however, T+ is oscillating along the electron orbit with frequency fs, and is also revolving in its orbit perpendicular to the electron orbit at frequency fo. The concentration of E field is due to both fs and fo. The spread of energy (sum of all overlapping E fields) however is due to fs only.
If the traveling T+ particles has lower velocities (ie. lower energy oscillations), and their dwell time at higher values of θ0 is insignificant compared to the overlap, then values of lower θ0 will have higher energy and be associated with lower wavelength. The spectrum is reversed for low energy oscillations. This could explain why the emission spectrum is reversed at lower temperature.
Previously, the half angle of a light cone which give the strongest E field when at π/2, (c/f post "It's All Fluorescence Outside, Inside" dated 29 Jul 2015.), the angle also defined as θ was polarization, not wavelength (color).
Good Night...