Preface to the lecture, 1

154

 

calculation of the neutron

 

the field of the  e

-

: E

31

(-) = - E

1

 (r

1

/r

3

), 

the field of the e

+

: E

32

  =     E

2

 (r

2

/r

3

)  =  E

1

 (r

2

/r

3

) 

and in addition the e

+

:       E

3 1

=      E

1

 (r

1

/r

3

). 

 

With the radius relation (eq. 7.4):        r

2

 = 2*r

1

          und          r

3

 = 3* r

1 

The total field is: 

 

(7.12) 

With z

e n

 = 4 elementary vortices 

 

(7.13) 

n

0

 is 12,5% bigger than p± 

 

(7.14) 

n

0

 is 5% heavier than p± 

Fig. 7.11: Calculation of the mass of the neutron 

---

proof

 

155

 

7.11 Calculation of the neutron

 

The calculation of the mass for the structure of the neutron according to fig. 7.10b has still 

remained open.

 

Because in this book for the first time has been shown, how the mass can be calculated, if

 

the particles are understood as potential vortices, we also in this case again want to make 

use of this possibility.

 

We have, like for the

a structure of three shells with the radii r

1

, r

2

 and r

3

. At the outer 

radius r

3

 the fields of the elementary vortices on the inside have an effect on the electron 

On the outside: like is the case for the

 

the field of the e

-: 

E

31

(-)

 =  -E

1

(r

1

/r

3

),

 

the field of the e

+

: E

32

 =   E

2

 (r

2

/r

3

)   =  E

1

 (r

2

/r

3

)

 

and in addition the e

+

: E

31

 =   E

1

 (r

1

/r

3

).

 

The total field is, with the radius relation equation 7.4:

 

 

(7.12)

 

If we compare the neutron, in which now z

e

 = 4  elementary vortices are involved, with 

the proton:

 

 

(7.13)

 

then we infer from the arithmetically determined result that the neutron according to the 

radius is 12,5% bigger than the proton. The mass is calculated to:

 

 

(7.14)

 

The particle therefore has a mass which is 5% larger than for the proton, slightly more as 

has been measured for the neutron. The difference is acceptable. The particle after all is 

structured very asymmetrically, in which the reason is to be seen, why the uncharged 

particle, looked at from close up, nevertheless shows an observable charge distribution.

 

---

156

 

beta-decay

 

 

Fig. 7.12: The electron-neutrino as a ring-like vortex 

---

proof

 

157

 

7.12 

 

In the case of the calculated quasistable particles, the   and the n°, the verification by 

means of the well-known decay processes is still due. Also free neutrons, those which are 

not bound in an atomic nucleus, decay. But with an average life of 918 seconds they are

 

by far the longest living among the quasistable elementary particles. 

Should the neutron decay be triggered by neutrinos, then obviously a distant flying past

 

does not suffice. For that the electron is bound in the proton too tight. There probably has 

to occur a direct "crash", in which a neutrino is used, since the decay equation reads:

 

 (7.15)

 

As could be expected a proton p

+

, an electron e

-

 and the mentioned electron-antineutrino 

  are formed. What here is written down as the emission of an antiparticle, is equivalent 

in the absorption of the particle

, in this case of the neutrino. The reaction equation 7.15 

can be reformulated accordingly

:

 

 

(7.15*)

 

Also for the decay of the myon an electron-neutrino is used. In both cases it provides the 

energy necessary for the decay. But we can really understand the

 only, after we

 

have got to know these particles better.

 

Without charge and without mass neutrinos show hardly any interactions with matter and 

as a consequence they possess the enormous ability of penetration - as is well-known. 

They are said to participate in the ,,weak interaction", which should trigger a conversion of 

the concerned particles, which is their decay. Pauli already has postulated the neutrino 

1930 theoretically, because the transition from a half-integer spin to an integer spin for the 

n

0

 -decay otherwise wouldn't have been explicable.

 

If we imagine an elementary vortex is being born, but the local field strength and energy

 

isn't sufficient for obtaining a quantized state. The result is an incomplete potential vortex,

 

which has an open vortex centre and as a consequence shows no localization at all. In the

 

form of a vortex ring it oscillates around itself, while it continually turns its inside to the

 

outside and then again to the inside.

 

One moment the vortex ring is green, then it is red again, one moment matter, then anti- 

matter, one moment positively charged and the next moment negatively charged. In 

contrast to the photon the number of the involved elementary vortices z

e

 for the neutrino is

 

odd (for the 

= 1). Perpendicular to the direction of propagation the neutrino has a spin

 

  for reason of a rotation, which overlaps the pulsating oscillation. 

This vortex ring is, as said, not a member of stationary matter, because it doesn't form a 

"black hole" in its centre, where the speed of light becomes zero. But it has an absolute 

stability like every elementary vortex, even if it only occurs incomplete and hence not in 

any quantized form,. This concept of the electron-neutrino as an open oscillating 

elementary vortex in the form of a ring-like vortex covers the experimentally determined 

realizations unexpectedly well.

 

:     Kussner, H.G.: Grundlagen einer einheitlichen Theorie der physikalischen 

Teilchen und Felder, Musterschmidt, Gottingen 1976, S.155

 

---