232 CHAPTER 4. UNIFIED FIELD THEORY
whereβ=
√
2 /
√
8
√
e−e,gis the Yukawa charge,r 1 = 10 −^13 cm, and the modified Yukawa
force is
(4.5.68) Fn=β^2 g^2
[
1
r^2−
8 e^1 /^2
r^21r
r 1
e−r/r^1]
.
- The nucleon strong interaction constantAnis given by
(4.5.69) An= 8 e^1 /^2 × 10 −^3 , e= 2. 718.
- By (4.5.66), the strong chargegsis given by
(4.5.70) g^2 s=
2
9
e−^1 /^2
8 −e^1 /^2(
ρn
ρw) 6
g^2 ,whereρwis thew∗-weakton radius andρnthe nucleon radius.
- The largest attraction force ofFnis achieved atr= 1. 5 r 1 , and the force is given by
(4.5.71) Fmax=−
8 e−^1 /^2
8 −e^1 /^2
g^2
r^21[
3 e^2 −1
9
]
.
- By (4.5.68), the attractive and repulsive regions of the strong nucleon forceFnare as
follows
(4.5.72) Fn
>0 for 0<r<r 1 / 2 ,
<0 forr 1 / 2 <r< 9 r 1 ,
>0 for 9r 1 <r.- Based on (4.5.67), the theoretical curve of the strong interaction potential energy for
two nucleons is as shown in Figure4.4, where we see that the theoretical result is in agreement
with the experimental curve shown in Figure4.2.
Figure 4.4: Theoretical curve of nucleon potential energy.