The photon is emitted before the particle escapes (if it escapes) as,
\(|\cfrac { d^{ 2 }x }{ dt^{ 2 } }|-\cfrac { 1 }{ m_{photon} } \psi _{ c }\lt |\cfrac { d^{ 2 }x }{ dt^{ 2 } }|-\cfrac { 1 }{ m } \psi _{ c }\)
The photon escapes the particle tangentially and the particle escape \(\psi\) tangentially. Both will be in a spin of radius, if they escape,
\( r=\cfrac{1}{\cfrac { \psi _{ c } }{ m v^2} -{ \cfrac { u }{ \psi _{ c }+u } }\cfrac { 1 }{ e^{ u }\left( { e^{ 2u }-1 } \right) ^{ 1/2 } }}\)
The ratio of energies,
\(\cfrac { \psi _{ c } }{ m v^2} \)
where
\(\psi_c=\psi _{ n }-\psi_{max}\)
\(\psi_n=\psi _{ photon }+\psi_{o}\)
\(\psi_n\) is the elevated energy level of the particle from its ground state \(\psi_o\) after receiving the photon \(\psi_{photon}\). \(\psi_{max}\) is the maximum \(\psi\) of the confining particle cloud.
is most interesting. Given a non transit (confining) particle, the term,
\({ \cfrac { u }{ \psi _{ c }+u } }\cfrac { 1 }{ e^{ u }\left( { e^{ 2u }-1 } \right) ^{ 1/2 } }\)
is fixed. It is also at maximum at the boundary of \(\psi(x)\). (To be proven...) The energy ratio, \(\cfrac { \psi _{ c } }{ m v^2} \) determines the radius of the escape spin.
This is the second way, a particle goes into a spin. The first being on head on retardation by a temperature particle that stops the particle before collision, from the post "No Temperature Particle At All, Zero" date 12 Jul 2015.
Note:
Both transit and non-transit particles are of the same type, otherwise their energy densities would not interact. The non-transit particle is considered as an extended spherical \(\psi\) cloud around the particle center. It could be the superposition of many particles of the same type. The transit particle is considered as a point particle inside \(\psi\) of the non transit particle.
