VbvNeuE-001

22 CHAPTER 3. IS NEUTRON AN ELEMENTARY PARTICLE?
Where α = e2
c
is the fine structure constant.
Thus, we obtain that the energy associated with magnetic flux is almost
exactly compensates the spin-orbit interaction described by the Larmor field:
δ ≡ E Φ + E L
γm e c 2
α
= −
2(1 + ϑ) . (3.11)
The balance of forces in the proton-electron system.
In a stable bound state, the Coulomb attraction between electron and proton
and the Lorentz force acting from the proton magnetic moment on moving
electron should be differently oriented that the total energy of their interaction
was less.
In equilibrium state, these forces are compensated by the centrifugal force:
γm e c 2
R e
− γ e2
R 2 + γ eµ p
R 3 + δ · γm ec 2
= 0. (3.12)
R
After simple transformations we obtain the equation
Where r c =
m ec
(1 + ϑ) − X + ξ p
m e
αM p
X 2 + δ = 0. (3.13)
is the Compton radius and
X = αr c
R
= αM p
m e
ϑ
(1 + ϑ) √ 1 − ϑ 2 . (3.14)
From these equations we obtain the solution
and
ϑ ∼ = 0.2 (3.15)
R = αr c
X ∼ = 1.235 · 10 −13 cm (3.16)
3.2 Main properties of neutron
3.2.1 Spin of neutron
The spin of neutron is the sum of spin of proton, the generalized moment of
momentum of the e-current ring and the generalized moment of momentum of
proton.
Moment of the generalized electron momentum can be written as
[ {
S 0e = R e × γ m e c − e ( e
c R − µ p
Re
2 − δ · m ec 2 )}]
. (3.17)
e