Another Resonance Hollow

There is another resonance applicable to all $\psi$ particles where $\psi$ is made to oscillate through the particle center, across a diameter.  From the post "$T^4$ Strikes Again!" dated 18 Jul 2015,

$\left(f_{osc}\right)^4=\cfrac{2c^2G^2}{m}$

but,

$\cfrac{G}{\sqrt{2mc^2}}\left(a_{\psi}\right)=\pi$

which is a point valid on all $\psi$ vs $a_x$ plots.  We have,

$\cfrac{G^2}{{2mc^2}}=\left(\cfrac{\pi}{a_{\psi}}\right)^2$

so,

$\left(f_{osc}\right)^4=4c^4\cfrac{G^2}{2mc^2}$
$\left(f_{osc}\right)^4=\left(2c^2\cfrac{\pi}{a_{\psi}}\right)^2$
$\left(f_{osc}\right)^2=2c^2\cfrac{\pi}{a_{\psi}}$
$f_{osc}=c \sqrt{\cfrac{2\pi}{a_{\psi}}}$ --- $(***)$

This is different from

$f_{res}=0.061\cfrac{c}{a_{\psi}}$

from the posts "A Shield" and "A $\Psi$ Gun" both dated 31 May 2016, where the particle is oscillating at the boundary $x$, given by,

$\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } }  }x=\pi$ --- $(*)$

not necessarily $x=a_{\psi}$.  The particle stores oscillatory energy at the boundary defined by $(*)$.

Resonance using $(***)$ however crosses the center of the particle and if $\psi$ reaches light speed around the center, the particle is hollowed out as in the post "Hollow Particle, Driving Miss
$\psi$" dated 07 Jul 2016.  $\psi$ is "recycled" to the surface of the particle and is possibly freed as photons.  This is the resonance that makes metals glow.

Good night zzz