3.4. Radius of force reach of particles, calculation of velocities, frequencies, and mass of particles, "mass defect" notion

The electron radius can be determined provided the whole electron mass m_e has electromagnetic nature, i.e. potential energy W_p is determined by charge e distributed on the surface of a ball of the radius of r_e, see [7]. In contemporary physics for the electric potential energy on the surface of the ball the following equation is valid (see [8])

Fig. 3.10. The dependence of T_kin on W_curr

Fig. 3.11. The dependence of T_kin on , W on and T_c on

which according to the present theory - see part. 3.3 will be substitued by

(3.23)

From the derivation T_kin in part 3.2 it follows at the same time

(3.24)

By comparison (3.23) and (3.24) we get

(3.25)

(v₁=v).

Analogically for proton

(3.26)

m_p - the proton mass

Similarly for quark, prequark, or - particle we get

(3.27)

where m_i - is the mass of prequark, quark, proton,

- particle, or electron respectively, e_i - is the charge of prequark, quark, proton,

- particle, electron.

Table 6 of the dependence of or respectively d on and gives possible radii and diameters of subparticles, and particles, calculated according to the equation (3.27) for speeds from the interval 10^-11c trough c and the value .

Table 6.

v/c			d_p [fm]
10^-11 10^-10 10^-9 10^-8 10^-7 10^-6 10^-4 10^-3			3.06.10¹⁹ 3.06.10¹⁷ 3.06.10¹⁵ 3.06.10¹³ 3.06.10¹¹ 3.06.10⁹ 6.12.10⁵ 6.12.10³
0.03 0.04 0.06 0.07	3.0719 1.66934 0.6917 0.49045	3.75224 2.1798 1.0324 0.78267	6.824 3.8491 1.7241 1.27312
0.1			0.6361
0.11 0.19	0.1716 0.0421	0.35832 0.1516	0.5299 0.1937
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1			0.17719 0.09223 0.06261 0.04895 0.04165 0.0373 0.03458 0.0328 0.03168

For the diameter of the particle d_i it holds approximately true:

(3.28)

see fig. 3.12.

Fig. 3.12. The diameter of the particle d_i

Fig. 3.13 gives the dependence of d_i on while the "comb" ...is shown for one of the possible values of the relation of the particle and subparticle diameters:

Fig. 3.13. The dependence of d_i on

Table 7.

		p	k	pk
d	4.1262 fm	1.5103 fm	0.552 fm	0.2023 fm
v	0.04c	0.065c	0.11c	0.19c
d_circle	7.149 fm	2.6168 fm	0.958 fm	0.35 fm
V_edge	5.34.10²⁰ Hz	2.37.10²¹ Hz	1.1.10²² Hz	4.91.10²² Hz
	7360m_e	1840m_e	460m_e	115m_e

For the sake of simplicity we shall assume the closest possible arrangement of particles with less mass in the ones with more mass i.e. - particle is formed by four nucleons forming the disfenoid, a proton (nucleon) is formed by four quarks forming the disfenoid, a quark is formed by four prequarks forming the disfenoid. Table 7 gives the mass, frequency, diameter estimations of force reach according to 3.27, speed estimations of relevant particles existing one in the other, i.e. of prequarks in quarks, quarks in proton (nucleon), nucleons in - particle. More coherent and detailed evaluations and computations will be given in some future article.

The notion of "mass defect" (energetic defect) loses its sense, if we consider that the particles in the nucleus are compressed under high pressure into almost ball-like formations. That is the case of revolvement of subparticles around approximatelly circular path (the edges of the series), and vice versa. Free particles are characterized by low pressure, i.e. by the ellipticallity of the particles paths (ever more of spectral lines including the series heads).

From Table 6 we can find such speeds of circulation of subparticles which enable that 4 subparticles (forming the disfenoid) to be situated in the particle at the same time, i.e. they are smaller than the particles:
4 nucleons in - particle
4 quarks in a proton
4 prequarks in a quark

Naturally, the subparticles must have higher speeds of circulation (i.e. and energy). The energy of a particle is smaller than the sum of energies of the corresponding subparticles:

a) the energy of the - particle is smaller than the sum total of the energies of 4 nucleons forming the - particle

b) the proton energy is smaller than the sum of energies of four quarks forming the proton

c) the quark energy is smaller than the sum of the energies of four prequarks forming the quark.

According to (3.11) and Table 7 for - particle:

for 4 protons:

for 4 x 4 quarks:

for 4 x 4 x 4 prequarks:

see tab.8.

Table 8.

	p	k	pk
v=0.04c	v=0.065c	v=0.11c	v=0.19c
[]_ad=0.0007	< 0.0019	< 0.0053	< 0.014
[]_id=0.0008	< 0.0023	< 0.0071	< 0.024
	< 0.0042	< 0.0124	< 0.038

, ,

It is evident taht the energies of subparticles are bigger than the energy of particle (even through the mass of particle equals the sum of the mass of subparticles). We have thus outlined the way to explain the "mass defect".