5.3. WEAKTON MODEL OF ELEMENTARY PARTICLES 291
Layered formulas of strong interaction potentials
The layered properties of strong and weak interaction potentials are also crucial for us to
establish the weakton model. We recall briefly the strong interaction potentials in the general
form as:
(5.3.11)
Φs=gs(ρ)[
1
r−A
ρ(^1 +kr)e−kr]
,
gs(ρ) =N(
ρw
ρ) 3
gs,whereρis the particle radius,Nis the number of strong charges.
There are about five levels of strong interactions between particles:w∗-weaktons, quarks,
gluons, hadrons, atoms/molecules. Hence, based on (5.3.11) we can derive the layered for-
mulas for these five level particles as follows:
(5.3.12)
Φsw∗=gs[
1
r−
A 0
ρw( 1 +k 0 r)e−k^0 r]
,
Φsq=(
ρw
ρq) 3
gs[
1
r−
Aq
ρq( 1 +k 1 r)e−k^1 r]
,
Φsg= 2(
ρw
ρg) 3
gs[
1
r−
Ag
ρg
( 1 +k 1 r)e−k^1 r]
,
Φsn= 3(
ρw
ρn) 3
gs[
1
r−
An
ρn( 1 +knr)e−knr]
,
Φsa=N(
ρw
ρa) 3
gs[
1
r−
Aa
ρa( 1 +kar)e−kar]
.
whereρw,ρq,ρg,ρn,ρaare the radii of weakton, quark, gluon, nucleon, atom/molecule, and
gsis the strong charge ofw∗-weakton. By (4.5.70),gscan be expressed as
(5.3.13) g^2 s=
1
9
β^2(
ρn
ρw) 6
g^2 ,whereβ=
√
2 e−^1 /^4 /( 8 −e^1 /^2 )^1 /^2 andgis the Yukawa charge.Layered formulas for weak interaction potentials
The weak interaction potential for a particle with radiusρand withNweak chargesgwis
given by
(5.3.14)
Φw=gw(ρ)e−kr[
1
r−
B
ρ( 1 + 2 kr)e−kr]
,
gw(ρ) =N(
ρw
ρ) 3
gw,wherek=r^10 = 1016 cm−^1 , andr 0 = 10 −^16 cm.