NEUTRON MAGNETIC MOMENT CALCULATION - Chapter 26 Physics of the
Universe Copyright (c) 1998 by Gerald Grushow
Let us look at the magnetic moment from an ordinary physics point
of view and then from a Quantum mechanics point of view. According to
Elementary Modern Physics by Weidner & Sells 1965, the electron in the
Bohr Orbit has a magnetic moment of one Bohr Magnetron. This means that
an electron traveling at C/137 in a spherical pattern around the proton
at a radius of 0.528E-10 meters produces a spherical DC electrical field,
which is actually an alternating pattern of plus and minus DC charges,
of 0.9273E-23 coulomb (meters^2)per second for the MCS system of units
or Kilogram (meters^3)/ sec^2 for the GG modified MKS system of units.Th
Bohr Magnetron= Qh/4 pi Me = 0.9273E-23 (26-1)
The measurement of the proton magnetic moment according to the Bohr
Theory was supposed to be:
Nuclear magneton = Q h/ 4 pi Mp = 5.051E-27 (26-2)
The ratio of these two value is:
Ratio = 1835.87 (26-3)
It was assumed in equation 26-3 that the ratio of the magnetic
moments of the proton and the electron should have been the ratio
of the proton mass to the electron mass.In addition, it was assumed
that the proton magnetic moment and the electron magnetic moment
should balance out and that the neutron's magnetic moment should
equal zero. When the neutron was discovered, the following measurements
were discovered as well.
Proton Mag Moment = 2.7928 Nuclear Magneton (26-4)
Neutron Mag Moment = -1.9128 Nuclear Magneton (26-5)
This presents a problem which people have been working on a long
time. It took the author only one night to solve the problem. Let us
now understand the solution.
The equation for the ratio of the mass of the proton to the
mass of the electron was shown in a previous chapter as:
Mp/Me = 4 pi 137 Rn /Rp = 136.2 (26-6)
Where Rn = 1.409E15 which is the root mean square value of the
electron motion in the neutron shell and Rp is is 1.321E-15 where
the protons has a perfect standing wave pattern and the wavelength
of the proton is identical with the radius of the proton.
When we look at magnetic moments for the electron in the Bohr
orbit, the root mean square (RMS) of the electron orbit is identical
with the Bohr orbit of 0.528E-10. Thus no correction is necessary for
the electron's magnetic moment. It is simple.
When we enter the proton we find a perfect sphere. The RMS
value of the location of the excess positive charge Q within the complex
plus and minus charges of the proton occurs at the inertial radius.Thus:
RMS Rp = 0.7071 Rp (26-7)
We see in equation 26-7 that the location of the charge Q within the
proton is at the radius of the proton divided by the square root of two.
Since in magnetic moment we are dealing with a spherical wave, the
magnetic moment of the proton will not be 1.414 times as much as that
of the electron in the Bohr orbit but the cube of this number. Thus:
Magnetic Moment of Proton =MMP = 2^(3/2) MME (26-8)
MMP = 2.828 MME (26-9)
Thus the magnetic moment of the proton is 2.828 of the magnetic
moment of the electron in the Bohr Orbit. Since the experimental
measurement was:
MMP = 2.7928 MME (26-10)
The results have an error of 1.2%. The error of 1.2 percent can be
attributed to the disturbance of the protons magnetic moment by the
measuring field.
Let us now calculate the neutron magnetic moment. As shown
in Chapter 23, The Bohr Orbit, the value of the electron energy in
the Bohr orbit is:
Ve = 0.91318C (26-11)
Meg = 2.4537 Me (26-12)
Mei= 4.076 Me (26-13)
When we deal with gravitational attraction we use the inertial mass,
Meg. When we deal with electrical field and light momentum we use the
inertial mass of 4.076 Me. Since the neutron operates to exact
mathematical relationships, let us use Mei = 4 Me.
Mei = 4 Me (26-14)
In equation 26-14 we quantize the mass of the electron in the first
neutron shell at four times the mass of the electron in the Bohr Orbit.
The corresponding magnetic moment of the electron in the neutron shell
at 0.14087E-15 is:
MM (electron in neutrons orbit) = 4 MME (26-15)
Now it is only necessary to calculate the magnetic moment of the
neutron. The magnetic moment of the neutron depends upon your measuring
system. The measurement by an electron field places the measurement in
the electrons domain. This is unfortunate since we really live in a
proton world and proton universe. The electron exists at a phase angle
with respect to the proton.Even though they are spherical waves, they
have phase relationships. Thus we get two answers. One for the electron
world and one for the proton world.
For the electron world we get:
MM (Neutron)= MM(Proton) Cosine (Z) + MMN(Electron) (26-16)
The angle (Z) can be found from qunatum theory:
The angle of the spin angular momentum along the Z axis is:
Cos (z)= Ms / [(S(S+1)]^0.5 (26-17)
In general S=1/2 for normal quantum mechanics. However the extention
into the neutron orbit is obvious. Thus S=1 and Ms =1.
Cos(Z) = 1 / [1.(2)]^0.5 (26-18)
Cos (z) = 1/2^0.5 - 0.7071 (26-19)
Thus :
Angle Z = 45 degrees (26-20)
Since angle Z is 45 degrees, the electron proton phase angle appears
like an 8 phase electrical AC generator.The author started his career
in AC power distribution and likes to refer things to this field.We
can now return to equation 26-16 and calculate MM (Neutron)
MM(Neutron) = 2.818 MME cosine (45)- 4 MME = -2.000MME (26-21)
The measured value is -1.9128 MME for an error of 4.36 percent.
Although the error is a little over four percent, this is reasonable
since the magnetic field damages the results. Besides it was very
difficult to actually measure the neutron magnetic moment.
Let us now look at the magnetic moment from the point of view
of the proton. The whole structure of the universe depends upon the
proton.When we look at the electron we act as an outsider to the process.
The magnetic moment of the neutron referred to the proton is:
MM(neutron) = MMN(electron)Cosine (Z)+ MMN(proton) (26-21)
MM(neutron) = -4.0 MME Cosine(Z) + 2.828 MMN (proton) (26-22)
MM (Neutron) = 0 (26-23)
Thus the magnetic moment of the neutron when referred to a
proton universe is zero. The measurements were done with conventional
electron circuits and thus we measured 2.828 MME.
The author thought that this Chapter would take a long time,
however the 2.828 value for the proton was a clear indication of a
forty five degree phase shift.gg