The Incorporated Institute of Nuclear
Researches (Dubna)
I.M.Motora
Model of Structure Electron and Muon
By the initial precondition of model of structure electron and muon we shall accept universality of known quantum of the magnetic flow which has been found out at research of macroscopic superconductor rings. More precisely, its meaning
|
|
F0 =h*c/(2*e)=2.06785E-7 |
also we shall assume, that
the charge of a particle in regular intervals is distributed on a ring toroidal surface with large radius òîðà
R and small radius of circular section of a ring r0, and r0<<R.
Essential the prospective
presence constant azimuth of speed of a charge equal speed of light "c"
is also.
One of arguments for the
benefit of this assumption is the equality of forces electrostatic repulsion of
a charge and its magnetic tightening directed lengthways perpendicular to a
surface toroid. It is possible also, that following from the Dirac's theory
"vibration" electrons with speed c, actually is this ordered by azimuth movement of its charge. Let's choose cylindrical system of coordinates with the
beginning at the centre of a ring and axis Oz,
its directed on an axis symmetry.
So, according to the first
assumption the magnetic flow F, created above mentioned by azimuth a current,
in electron and muon is expressed as
|
|
F = M*F0 |
( M =...-2,-1,0,1,2,...), |
and the total electrical charge on each
ring is equal "e".
Using known expressions of
vector potential of a ring current Af(r, z),
scalar potential both components of intensity of magnetic and electrical fields
Hr, Hz, Er,
Ez through complete elliptic integrals, for
close to a surface toroid of a vicinity is received the following approached
formulas for Af at r> = r0:
|
|
Af(r) = 2*J*(ln(R/r)+
0.0794)/c H(r) = E(r) =~
2*J/(r*c) |
/2/ /3/ |
where r - distance from a circle
of radius R, located in an equatorial plane of a toroid with the centre in the beginning of coordinates;
J - azimuth
a current in rings.
From electrodynamic
ratio connecting the magnetic moment of a particle "m", a
current J and radius R, we find
|
|
m =~ 2*pi*R*J/c, |
J/c =~ e/(2*pi*R) |
/4/ |
where from
|
|
R =~ 2*m/e, |
J/c =~ e**2/(4*pi*m) |
/5/ |
Then the magnetic flow
penetrating a ring F = 2pi*R*Af(r0),
will be equal
|
|
F =~ 2*e*( ln(R/r)+ 0.0794) = M*F0 |
/6/ |
From last, the expression
for a spectrum of allowable discrete meanings ln(R/r)
follows:
|
|
ln(R/r)=~ M* F0/(2*e) - 0.0794 |
/7/ |
dimensionless quantum which is - F0/(2*e)
=215.2557.
The contribution of an
electromagnetic field to energy of rest W0 makes
|
|
W0 = 1/(8*pi)* ( (H**2+ E**2)dV. |
/8/ |
According to /3/ it shall
present as
|
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W0= e**2 /(2*pi*R)* (ln(Rm/r0)+ ln(Re/r0)) |
/9/ |
As there are such meanings
of size Rm and Re, dimensionality of
length, which substitution in /9/ gives exact meaning W0.
To facilitate understanding
of results of the further consideration, we shall take advantage of that
circumstance, that the overwhelming part of integral /8/ contains in the field
of small r, that gives the basis approximately
to put
|
|
Rm ~ Re ~ R |
|
Then
|
|
W0=e**2/(pi*R)*ln(R/r0)=M*e*h*c/(8*pi*m)-0.0794*e**3/(2*pi*m)=M*e*h*c/(8*pi*m) |
/9'/ |
Nonquantized item in the right part /9 '/ is omitted, as its module at M> 0 makes <
4E-4 from the module of the basic member.
Calculation of the
mechanical moment /of a spin/ in particles, which, obviously, is equal to
multiplication of size of radius R of a ring multiplication, on which
the charge is concentrated, and to a field part of a
pulse of a charge P in the same place, with the regard of /5/ and /7/
gives
|
|
s=R*e*Af(r0)/c= 2*e*( ln(R/r0)+
0.0794)/(pi*c) = M*h/(4*pi) |
/10/ |
From here follows, that all
particles having of spin h/(4pi) should be
characterized by quantum number of a magnetic flow M=1. This caused by
model ratio a spin to size h/(4pi) causes the
certain optimism.
But the particle, having
the mechanical moment, besides energy of a field /9/ or /9 '/ has also
additional energy of rest W0" at the expense of rotation, equal in
view of light speed of a charge
|
|
W0"= P*c =
M*e*h*c/(8*pi*m) |
/11/ |
The complete energy of rest
of a particle, thus, appears equal
|
|
W0"= W0 +
W0" =~ M*e*h*c/(4*pi*m); |
(M =1) |
/12/ |
And by solving /12/ regarding magnetic
moments "m", we have
|
|
m = e*h/(4*pi*me*c)
= e/( me*c)*s, |
/13/ |
Whence we receive correct
quantum-mechanical the relation
|
|
m/s = e/( me *c). |
/14/ |
Is characteristic, that quantums of energy of rest W0 for all four leptons
in /12/:
|
|
W0 = e*h*c/(4*pi*m) |
are amazingly close to experimental
meanings of their energy of rest and make 0.51041MeV for a
electron and 105.533MeV for a muon. The truth, from
behind the above mentioned approximation, allowed by us, in /9
'/ it is impossible to consider concurrence it while exact. The specified
calculation /8/ for an electron (positron) and muon (antimuon) was done on the
computer.
Part of integral on area
contiguous to a surface of the ring r0 < r < R*1E-6,
were calculated analytically, and outside of a toroid r = R*1E-6
is count.
Before initial to result
the table of the parameters, calculated on the basis of offered model, an
electron (positron) and muon (antimuon)
we shall emphasize, that for it the universal physical constants h, c,
e, F0 = h*c/(2*e) and two experimentally
measured meanings of the magnetic moments electron and muon,
equal accordingly 9.28485E-21 and 4.49062E-23. Fitting parameters in model are
absent. The general structural features of particles were
assumed only:
a) toroidal symmetry;
b) homogeneous
distribution of a charge on a surface toroid;
c) equality
of speed of azimuth movement of a charge of speed of light.
The calculation meanings M,
s, W0, R, ln(R/r0),
r0 and J/c - are given in the
table.
The table
|
Particle |
M |
s |
W0 MýB |
R centimeter |
ln(R/r0) |
r0 centimeter |
J/c |
|
electron |
1 |
h/2 |
0.51162 |
3.866E-11 |
215.18 |
1.37E-104 |
1.97 |
|
muon |
1 |
h/2 |
105.782 |
1.870E-13 |
215.18 |
6.64E-107 |
408.8 |
|
tau-lepton |
1 |
h/2 |
1784.0 |
1.1E-14 |
215.18 |
3.9E-108 |
6900.0 |
For tau-lepton, known
experimental energy of which rest W0 = 1784MeV, foretell by model the
magnetic moment "m", is ì=2.65E-24erg/gauss. Besides already marked concurrence calculated the spin with
their experimental meanings the concurrence of mass of rest electron (positron)
and muon (antimuon) not
worse 0.12% is visible also. It can form the basis for the statement, that,
apparently, nature of mass of rest all lepton completely electromagnetic. The
same statement about a nature of lepton muon was made Barut's [1].
The distribution of mass,
charge and magnetic moment has appeared similar partoning
of model hadronics.
All specified
characteristics are concentrated /truth, not in points/ in an extremely small
vicinity of a circle of radius R. Large radius electron Re =
3.87E-11 centimeter, on the first sight, is paradoxical is great. However
unique on size the magnetic moment a
electron could not be created with the help even of light speed of the ordered
movement of a total charge e at the small
characteristic size of a particle. From the ratio vagueness, not connected to
model, also follows that characteristic the size 2R of any particle
should satisfy to expression
|
|
2R > h*c/(p*c) |
/16/ |
/p - characteristic
pulse of internal movement/. Whereas known of the Dirak's
"vibration" even rest an electron has mathematical expectation of the
operator of speed equal "c", for it
|
|
2R > h*c/(m*c**2)
=3.86E-11 centimeter |
Magnetic induction in the
considered rings-particles are so great /at a surface toroids
~ 1E100Gs in the electron and ~ 1E109Gs in the muon,
and at the centre of rings - accordingly 3.2*10E11Gs
and 1.37E16Gs /, that short-range the interaction of such rings of the magnetic
moments is capable to cause strong interaction. In effect it was already shown Barut's and Kraus's [2] shown theoretically c by the help
of introduction of certain effective potentials of interaction of the abnormal
magnetic moment of the lepton with a field motionless the antilepton an
opportunity of occurrence of resonances with the characteristic sizes the hadronic.
Probably, the nuclear
forces also are caused by interaction of the magnetic moments nucleons /though
the considered elementary ring model of structure for a proton has appeared not
quite suitable, electromagnetic mass, designed on its basis, of rest has made
only - 336 MeV/.
Last proves to be true by
the following important feature of structure of nucleuses. In all nucleuses the
even part the nucleons always supposes splitting into pairs: a proton - a
neutron, a proton - a proton and neutron - a neutron, any of which has the
antiparallel magnetic moments. Charge-independent is the mutual orientation in
the specified pairs just of the magnetic moments, whereas the spin in them are
both antiparallel, and parallel /as in deuteron/. It means,
that the interaction of the magnetic moments can be the dynamic factor causing
strong connection.
Besides there is a
concurrence of dependence from distance between particles of nuclear forces and
interaction mutually of antiparallel magnetic moments created by ring currents
with conterminous equatorial planes of rings. It is easy to understand with the
help of known expression of energy of interaction of two magnetic moments, that
at distance between rings r, such, that r>2R, occurs
short-range an attraction | ~ 1/r ** 3 |.
If r=0, the strong pushing away is observed. In the field of 0<r<2R with increase r the
pushing away passes in an attraction.
Thus, it is clear, why just
the antiparallel orientation of the magnetic moments causes their strong
connection. Here outside there is not a barrier of pushing away, as would be in
case of the parallel moments, which would do connection impossible, but zone of
a strong attraction.
In light of these
representations some is natural also non-additivity
of the magnetic moments, which, for example, in the deuteron makes about 2%.
Quantized in the nucleons there are magnetic flows, and the moments because of
the mutual inductance change.
Would be biassed not mention the following feature of the offered
model, which can be interpeted doubly. In well investigated stationary quantum-mechanical systems, for
example, in atom of hydrogen or in superconductor macroscopic rings in the
least a condition / n = 1 for hydrogen and Ì = 1 for a ring /, length of a wave
de Broil's accordingly for the electrons and consisting from two the electrons
quasi-particle, calculated on mathematical expectation of the operators of a
pulse, in accuracy is equal to length of a circle with Bohr's radius and radius
of a ring accordingly. At the same time this length of a wave of a
charge "e" in our model appropriate impulse - Af(r0) from /10/ makes not 2*Pi*R, but
4*Pi*R.
The skeptically adjusted
reader in this connection has the right to regard it as difficulty of model.
The optimist, on the contrary, can think, that in
elementary particles the standing waves de Broil's are carried out.
LITERATURE
1. Barut
A.O. In: Lecture Notes in Physics. Ed. A.Bohm,
Springer6 p.440.
2. Barut
A.O., Kraus J. Phys. Lett., 1975, 59B, No.2, p.175.
February 4, 1981.