310 CHAPTER 5. ELEMENTARY PARTICLES
γ,γ 0 ,gk,gk 0 ,ν, is given by
Fw=−gw(ρm)gw(ρe)∂
∂r[
1
r
e−kr−B ̃
ρ ̃
( 1 + 2 kr)e−^2 kr]
(5.4.37) ,
=gw(ρm)gw(ρe)e−kr[
1
r^2+
1
rr 0−
4 B ̃
̃ρr
r^20e−kr]
,
wherek= 1 /r 0 = 1016 cm−^1 ,gw(ρm)andgw(ρe)are the weak charges of mediators and the
naked electron, expressed as
gw(ρm) = 2(
ρw
ρm) 3
gw, gw(ρe) = 3(
ρw
ρe) 3
gw,andB ̃/ ̃ρis a parameter determined by the naked electron and mediators.
By the weak force formula (5.4.37), there is an attracting shell region of weak interaction
between naked electron and mediators
(5.4.38) ρ 1 <r<ρ 2
as shown in Figure5.13, with small weak force, whereρj(j= 1 , 2 )are the zero points of
(5.4.37). Namely, they satisfy that
e−kρjρ^3 j=̃ρ
4 B ̃(
1 +
ρj
r 0)
for 1≤j≤ 2.In the region (5.4.38), the weak force is attracting, and outside this region the weak force is
repelling:
(5.4.39) Fw
{
<0 forρ 1 <r<ρ 2 ,
>0 forr<ρ 1 andρ 2 <r.Since the mediatorsγ,γ 0 ,gk,gk 0 andνcontain two weak chargesQw= 2 gw, by (5.4.39)
they are attached to the electron in the attracting shell region (5.4.38), forming a cloud of
mediators. The irregular triangle distribution of the weaktonsνe,w 1 ,w 2 generate a small
moment of force on the mediators. Meanwhile there also existweak forces between them.
Therefore the bosons will rotate at a speed less than the speed of light, and generate a small
mass attached to the naked electronνew 1 w 2.
5.4.6 Mechanism of bremsstrahlung
It is known that an electron emits photons as its velocity changes, which is called the bremsstrahlung.
The reasons why bremsstrahlung can occur is unknown in classical theories. Based on the
electron structure theory established in the last subsection, we present here a mechanism of
this phenomenon.
In fact, if an electron is situated in an electromagnetic field, then the electromagnetic
field exerts a Coulomb force on ithe naked electronνew 1 w 2 , but not on the attached neutral