cross section of charge loop model of electron
Bob Morrison
A long time ago in a galaxy far away, I put together the charge
loop idea, which is basically a permutation of the old Bohr magneton
(bound photon state that has the correct (quantum mechanical) angular
momentum). I found several derivations that match physical reality
that I haven't seen anyone do--the two best ones are the geometrical
basis for the Lorentz transform equations and the equivalance of the
Lorentz force equations (the electrostatic equation to the magnetic
force equation).
However, the big guys in this business never bought it, the
primary reason being the scattering results of the electron/positron
collisions, showing that the electron size is at least three
orders of magnitude smaller than what the charge loop predicts.
So, at the time I said that the charge loop model could appear to be
much smaller than it is because its cross section interaction would
be a function of the ring thickness, not its diameter (this is a
simplification, but not an unreasonable one, of the actual diffuse
field of the charge loop). At that time, Matthew Nobes tactfully
said something like I doubt it, a ring cross section will likely be
substantially different that the infinitessimally smal point cross
section--thus plopping the charge loop firmly in the pig-sty of
dumb physics ideas.
Nevertheless, I took some time to study cross section interactions,
and believe I have found him to be correct in general--with one
exception. If the rings are parallel to each other, the rings'
collision behavior will exactly match the behavior of a particle
of the same mass whose diameter is equal to the thickness of the ring.
How could we possibly expect random collisions of loops to line up
like that? Every particle with a magnetic moment approaching another
such particle will see the moments line up parallel to each other.
So, I'm sure it is to Matthew's regret that I still think there's
a possibility that electrons aren't as small as we all think they are.
Of course, it is likely that there are other means for determining the
electron's size that back up the collision results, I'd be interested
in references.
Any thoughts welcome.
Bob Morrison
xxr...@zzboiyy.xxhp.zzcomzz
remove x, y, z
FrediFizzx
news:snbmb.22$SK5....@news.uswest.net...
I have been thinking along the same lines as you and of course the
interaction size thing just doesn't make sense with the charge loop size.
One thing I was thinking about and considering is that we are down at the
level of where spacetime might be actually be being defined. So maybe there
is some kind of gross error in interaction cross section calculations? IOW,
does 10^-20 meters actually mean 10^-20 meters once you are down at the
level where spacetime is being defined?
FrediFizzx
Bob Morrison
> "Bob Morrison" <rd...@bxxoi.hyyp.comzz> wrote in message
> news:snbmb.22$SK5....@news.uswest.net...
> | Hi s.p.p folks,
> | A long time ago in a galaxy far away, I put together the charge
> | loop idea, which is basically a permutation of the old Bohr magneton
[part deleted]
> | So, I'm sure it is to Matthew's regret that I still think there's
> | a possibility that electrons aren't as small as we all think they are.
> | Of course, it is likely that there are other means for determining the
> | electron's size that back up the collision results, I'd be interested
> | in references.
> | Any thoughts welcome.
>
> I have been thinking along the same lines as you and of course the
> interaction size thing just doesn't make sense with the charge loop size.
> One thing I was thinking about and considering is that we are down at the
> level of where spacetime might be actually be being defined. So maybe there
> is some kind of gross error in interaction cross section calculations? IOW,
> does 10^-20 meters actually mean 10^-20 meters once you are down at the
> level where spacetime is being defined?
>
> FrediFizzx
>
That's an interesting way to put the question, which begs the question,
"defined by who?". But anyway, I think I know what you mean, and I
think the scattering evidence would actually be my answer to that--
there is "something" that has compositional details with that type of
scale. If I understand you right, I think you are proposing some
variation of a (possibly diffuse) lattice with 10^-20 meter spacing
and asking if there could be errors in electron size derivation due
to artifacts resulting from the lattice at that scale.
I have two comments to this, first is that this is a very different
proposal than the charge loop model. The second comment I would make
is this is getting dangerously close to Occam's razor--it doesn't buy
us anything to propose that artifacts of some construct happen to
create particles at that scale. Yes, it's possible, but it doesn't
answer the question of why little cows aren't also created at that
scale--I'm attempting to be humorous of course, but I think you will
see my point..?
Bob
FrediFizzx
Defined by nature. It is a Machian kind of thing. If we consider the
Universe to be a closed system, then spacetime necessarily should be
defined by *all* the quantum objects in it. Including the "fleeting"
vacuum "particles". So what happens to space and time down at a level of
where it is being defined by the very objects you are trying to measure?
Well, I would think for sure that time is getting very "goofy" on us down
there. To me, this is probably one source of uncertainty.
| But anyway, I think I know what you mean, and I
| think the scattering evidence would actually be my answer to that--
| there is "something" that has compositional details with that type of
| scale. If I understand you right, I think you are proposing some
| variation of a (possibly diffuse) lattice with 10^-20 meter spacing
| and asking if there could be errors in electron size derivation due
| to artifacts resulting from the lattice at that scale.
Actually the lattice I am thinking of is much bigger. 10^-13 meter scale.
I highly suspect space and time below this scale are not exactly what we
think they are. You are definitely into quantum fuzziness below this
scale.
| I have two comments to this, first is that this is a very different
| proposal than the charge loop model. The second comment I would make
| is this is getting dangerously close to Occam's razor--it doesn't buy
| us anything to propose that artifacts of some construct happen to
| create particles at that scale. Yes, it's possible, but it doesn't
| answer the question of why little cows aren't also created at that
| scale--I'm attempting to be humorous of course, but I think you will
| see my point..?
No, I wasn't trying to be different than what you are proposing. I am
only trying to come up with an explanation of why we see these point-like
interaction cross sections when a lot of things point to quantum objects
being bigger. An electron definitely has a "local" sphere of influence
out to about a radius of the compton wavelength divided by 2pi. Why so
big?
FrediFizzx
Bob Morrison
> Hi s.p.p folks,
> A long time ago in a galaxy far away, I put together the charge
> loop idea, which is basically a permutation of the old Bohr magneton
> (bound photon state that has the correct (quantum mechanical) angular
> momentum). I found several derivations that match physical reality
> that I haven't seen anyone do--the two best ones are the geometrical
> basis for the Lorentz transform equations and the equivalance of the
> Lorentz force equations (the electrostatic equation to the magnetic
> force equation).
>
One more thing I've found about charge loops--it provides a
reasonable explanation for inertial mass, and thus I am guessing
that the Higgs particle will not be found. In this model, mass
is a property that emerges when you take the momentum of an
massless (exchange) particle such as a photon and confine it to a
finite volume.
The properties of inertial mass result from how a
particle responds to absorbing an exchange particle. If a
photon absorbs an exchange particle (another photon)
perpendicular to its path, it deflects the photon (adds a
transverse momentum component to its forward momentum). If
it absorbs the exchange particle in the parallel direction, it
changes the energy of the photon.
However, if massive particles are charge loops, the momentum is
confined to a loop. You cannot apply a net force (have the
particle absorb an exchange photon, eg) in the tangental
direction of this momentum because it is both "coming and going",
thus the exchange particle cannot change the energy of the loop
(the massive particle). It can only apply a net force in the
transverse direction--and the change in direction is proportionate
to the ratio of the exchange particle's momentum and the charge
loop particle's intrinsic momentum (rest mass). You can see
how the F=ma inertial behavior of a massive particle emerges from
the charge loop model--and in the process, a nice connection
emerges between exchange particles and massive particles.
Of course, if you guys find the Higgs particle, I am back to
looking stupid...!
Bob
Michael Moroney
>being bigger. An electron definitely has a "local" sphere of influence
>out to about a radius of the compton wavelength divided by 2pi. Why so
>big?
When does an electron behave differently on a smaller-than-Compton scale
than a larger-than-Compton scale?
--
-Mike
FrediFizzx
news:bnedai$bc5$1...@pcls4.std.com...
Hi Mike, how have you been?
When you give it more energy than its "natural" energy range I would
suppose. IOW, to get two electrons in a space smaller than the Compton
scale, you have to apply more energy to them. Two electrons at relative
rest with respect to each other, will stay apart from each other on the
order of hbar/m_e*c. The probability to find two electrons closer than
hbar/m_e*c in this situation is very low. However, you can increase the
probability by applying much more energy to them. So we are forcing them
to behave differently. What happens to an electron when you give it more
energy? You have reduced the scale at which two electrons can be closer
together. IOW, you are changing the "normal" definitions of length and
time or spacetime quite possibly if spacetime is being defined at this
level. See what I am trying to get at? So the more energy we throw at
particles to try to get them closer together, will just result in their
interaction cross sections being smaller and smaller and more point-like
as we go higher and higher energy-wise. Higher energy possibly means a
"re-definition" of spacetime scales.
FrediFizzx
Gordon D. Pusch
> When does an electron behave differently on a smaller-than-Compton scale
> than a larger-than-Compton scale?
An electron localized to less than its compton wavelength has a
relativistically large uncertainty to its momentum, such that the
uncertainty in its kinetic energy exceeds its own rest mass.
Localize the electron in a sufficiently small volume, and one can
no longer say with any degree of certainty that one has only _one_
electron localized; instead, there is a significant probability that
that electron will be accompanied by some number of particle/anti-particle
pairs, of any species whose compton wavelengths exceed the transverse
dimensions of the volume the electron is localized in.
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
Y.Porat
first forget about massless particles.
2 have you ever heared about the basic particle
that moves naturally in a close circle?
if not you can do a google search.
all the best
Y.porat
---------------------------
FrediFizzx
message news:gin0bov...@pusch.xnet.com...
| mor...@world.std.spaamtrap.com (Michael Moroney) writes:
|
| > When does an electron behave differently on a smaller-than-Compton
scale
| > than a larger-than-Compton scale?
|
| An electron localized to less than its compton wavelength has a
| relativistically large uncertainty to its momentum, such that the
| uncertainty in its kinetic energy exceeds its own rest mass.
|
| Localize the electron in a sufficiently small volume, and one can
| no longer say with any degree of certainty that one has only _one_
| electron localized; instead, there is a significant probability that
| that electron will be accompanied by some number of
particle/anti-particle
| pairs, of any species whose compton wavelengths exceed the
transverse
| dimensions of the volume the electron is localized in.
Yes, that is a very good description relating to current established
theory. What do you mean by "tranverse dimensions" of the volume?
FrediFizzx
Gordon D. Pusch
> "Gordon D. Pusch" <g_d_pusch_remo...@xnet.com> wrote in
> message news:gin0bov...@pusch.xnet.com...
>> mor...@world.std.spaamtrap.com (Michael Moroney) writes:
>>
>>> When does an electron behave differently on a smaller-than-Compton
>>> scale than a larger-than-Compton scale?
>>
>> An electron localized to less than its compton wavelength has a
>> relativistically large uncertainty to its momentum, such that the
>> uncertainty in its kinetic energy exceeds its own rest mass.
>>
>> Localize the electron in a sufficiently small volume, and one can
>> no longer say with any degree of certainty that one has only _one_
>> electron localized; instead, there is a significant probability that
>> that electron will be accompanied by some number of particle/anti-
>> particle pairs, of any species whose compton wavelengths exceed the
>> transverse dimensions of the volume the electron is localized in.
>
> Yes, that is a very good description relating to current established
> theory. What do you mean by "tranverse dimensions" of the volume?
How wide, tall, etc. the volume is.
FrediFizzx
Thanks. That is what I thought it meant. Just wanted to make sure it
didn't mean something special.
FrediFizzx
Michael Moroney
>mor...@world.std.spaamtrap.com (Michael Moroney) writes:
>> When does an electron behave differently on a smaller-than-Compton scale
>> than a larger-than-Compton scale?
>An electron localized to less than its compton wavelength has a
>relativistically large uncertainty to its momentum, such that the
>uncertainty in its kinetic energy exceeds its own rest mass.
But this is just the Heisenberg Uncertainty Principle at work, and applies
to any massive particle, not just the electron. What happens that if the
distance is small, the uncertainty in distance must be small, therefore
Heisenberg says the uncertainty in momentum must be large, therefore
the momentum, and thus energy is large.
--
-Mike
FrediFizzx
Yes, but I think the "massive" particle has to be elementary. Maybe
the important concept here is that an electron does seem to have a
"local" domain of influence on the order of hbar/m_e*c for "normal"
energies. Why? Well, I can somewhat explain it by invoking a "spin
matrix" concept for the vacuum. However, it makes the quantum vacuum
organized and I am having a little trouble reconciling it with SR.
But I am close to maybe getting it to work out.
FrediFizzx
Gordon D. Pusch
Yes. And your point is what, exactly ???
You did not ask about electrons versus other particles --- you asked why
an electron behaves differently on a sub-compton scale than it does on a
supra-compton scale. And of course, this same conclusion _does_ hold for
other particles as well, unless they are composite objects larger than
their own compton wavelengths (in which case it is not possible to confined
them in a region smaller than their compton wavelength without destroying
them).
Gordon D. Pusch
> "Michael Moroney" <mor...@world.std.spaamtrap.com> wrote in message
> news:bnh7rs$tu5$2...@pcls4.std.com...
>> g_d_pusch_remo...@xnet.com (Gordon D. Pusch) writes:
>>
>>> mor...@world.std.spaamtrap.com (Michael Moroney) writes:
>>>
>>>> When does an electron behave differently on a smaller-than-Compton
>>>> scale than a larger-than-Compton scale?
>>
>>> An electron localized to less than its compton wavelength has a
>>> relativistically large uncertainty to its momentum, such that the
>>> uncertainty in its kinetic energy exceeds its own rest mass.
>>
>> But this is just the Heisenberg Uncertainty Principle at work,
>> and applies to any massive particle, not just the electron.
>> What happens that if the distance is small, the uncertainty
>> in distance must be small, therefore Heisenberg says the uncertainty
>> in momentum must be large, therefore the momentum, and thus energy is
>> large.
>
> Yes, but I think the "massive" particle has to be elementary.
Not true --- it can also be composite, as long as its size is smaller
than its compton wavelength. (A composite object larger than its own
compton wavelength obvious cannot be confined in a region smaller
than its compton wavelength without destroying it.)
There is, of course, the minor detail that there _aren't_ any known
composite particles smaller than their own compton wavelengths
(the pion comes close, but even it is still too large) ---
but that is a separate issue.
> Maybe the important concept here is that an electron does seem to have a
> "local" domain of influence on the order of hbar/m_e*c for "normal"
> energies. Why? Well, I can somewhat explain it by invoking a "spin
> matrix" concept for the vacuum. However, it makes the quantum vacuum
> organized and I am having a little trouble reconciling it with SR. But I
> am close to maybe getting it to work out.
I'm sorry, but that is where I must part company with you. Your so-called
"quantum vacuum" is still an aether by another name, and as many have
pointed out to you, your notions do not make sense even from the standpoint
of not ven having the correct physical _units_, let alone the correct physics.
Michael Moroney
>mor...@world.std.spaamtrap.com (Michael Moroney) writes:
>> But this is just the Heisenberg Uncertainty Principle at work, and applies
>> to any massive particle, not just the electron. What happens that if the
>> distance is small, the uncertainty in distance must be small, therefore
>> Heisenberg says the uncertainty in momentum must be large, therefore
>> the momentum, and thus energy is large.
>Yes. And your point is what, exactly ???
>You did not ask about electrons versus other particles --- you asked why
>an electron behaves differently on a sub-compton scale than it does on a
>supra-compton scale. And of course, this same conclusion _does_ hold for
>other particles as well, unless they are composite objects larger than
>their own compton wavelengths (in which case it is not possible to confined
>them in a region smaller than their compton wavelength without destroying
>them).
I was responding to Fredi's post about his current loops, where he said
something funny happens at a wavelength smaller than the Compton length,
implying that there is something to these current loops of his. My point
was that things do get funny but only due to Heisenberg.
--
-Mike
FrediFizzx
| "FrediFizzx" <fredi...@hotmail.com> writes:
|
| > "Michael Moroney" <mor...@world.std.spaamtrap.com> wrote in
message
| > news:bnh7rs$tu5$2...@pcls4.std.com...
| >> g_d_pusch_remo...@xnet.com (Gordon D. Pusch) writes:
| >>
| >>> mor...@world.std.spaamtrap.com (Michael Moroney) writes:
| >>>
| >>>> When does an electron behave differently on a
smaller-than-Compton
| >>>> scale than a larger-than-Compton scale?
| >>
| >>> An electron localized to less than its compton wavelength has a
| >>> relativistically large uncertainty to its momentum, such that
the
| >>> uncertainty in its kinetic energy exceeds its own rest mass.
| >>
| >> But this is just the Heisenberg Uncertainty Principle at work,
| >> and applies to any massive particle, not just the electron.
| >> What happens that if the distance is small, the uncertainty
| >> in distance must be small, therefore Heisenberg says the
uncertainty
| >> in momentum must be large, therefore the momentum, and thus
energy is
| >> large.
|
| > Maybe the important concept here is that an electron does seem to
have a
| > "local" domain of influence on the order of hbar/m_e*c for
"normal"
| > energies. Why? Well, I can somewhat explain it by invoking a
"spin
| > matrix" concept for the vacuum. However, it makes the quantum
vacuum
| > organized and I am having a little trouble reconciling it with SR.
But I
| > am close to maybe getting it to work out.
|
| I'm sorry, but that is where I must part company with you. Your
so-called
| "quantum vacuum" is still an aether by another name, and as many
have
| pointed out to you, your notions do not make sense even from the
standpoint
| of not ven having the correct physical _units_, let alone the
correct physics.
Huh? Vacuum charge = +,- sqrt(hbar*c) in cgs does absolutely have the
correct units for charge (I think you must have missed some threads
discussing this). It is easy to see this from the fine structure
constant relationship,
sqrt(alpha) = e/sqrt(hbar*c).
The sqrt(alpha) is simply the ratio of observed electronic charge to
vacuum charge and the sqrt(alpha) is also the "basic" probability that
an electron and photon will interact. Please tell me what the
sqrt(hbar*c) could be other than vacuum charge?
FrediFizzx
Y.Porat
> "Gordon D. Pusch" <g_d_pusch_remo...@xnet.com> wrote in
> message news:giptgjt...@pusch.xnet.com...
> | "FrediFizzx" <fredi...@hotmail.com> writes:
> |
> | > "Michael Moroney" <mor...@world.std.spaamtrap.com> wrote in
> message
> | > news:bnh7rs$tu5$2...@pcls4.std.com...
> | >> g_d_pusch_remo...@xnet.com (Gordon D. Pusch) writes:
> | >>
> | >>> mor...@world.std.spaamtrap.com (Michael Moroney) writes:
> | >>>
> | >>>> When does an electron behave differently on a
> smaller-than-Compton
> | >>>> scale than a larger-than-Compton scale?
>
> | >>> An electron localized to less than its compton wavelength has a
> | >>> relativistically large uncertainty to its momentum, such that
> the
> | >>> uncertainty in its kinetic energy exceeds its own rest mass.
> | >>
> | >> But this is just the Heisenberg Uncertainty Principle at work,
> | >> and applies to any massive particle, not just the electron.
> | >> What happens that if the distance is small, the uncertainty
> | >> in distance must be small, therefore Heisenberg says the
> uncertainty
> | >> in momentum must be large, therefore the momentum, and thus
> energy is
> | >> large.
> [snip]
>
> But I
> | > am close to maybe getting it to work out.
> |
> | I'm sorry, but that is where I must part company with you. Your
> so-called
> | "quantum vacuum" is still an aether by another name, and as many
> have
> | pointed out to you, your notions do not make sense even from the
> standpoint
> | of not ven having the correct physical _units_, let alone the
> correct physics.
>
> Huh? Vacuum charge = +,- sqrt(hbar*c) in cgs does absolutely have the
> correct units for charge (I think you must have missed some threads
> discussing this). It is easy to see this from the fine structure
> constant relationship,
>
> sqrt(alpha) = e/sqrt(hbar*c).
>
> The sqrt(alpha) is simply the ratio of observed electronic charge to
> vacuum charge and the sqrt(alpha) is also the "basic" probability that
> an electron and photon will interact. Please tell me what the
> sqrt(hbar*c) could be other than vacuum charge?
>
> FrediFizzx
imho you think too abstract
and you know that 'abstract is safe' but cannot lead you
too far away:
as far as i get the electron, it is not a basic ' particle'
ie it is a conglomeration of subparticles- suborbitals
not just one
have you heared about my 'chain of orbitsls'?
it is orbitals connected in a linear chain (it must be perpendicular
to each other or else they will destroy each other)
my only unsolved question is :
what defines the number of suborbitals, to what it is
what gives it its final stability.
----------------
all the best
Y.Porat
--------------
FrediFizzx
So I guess part of it is what is the fundamental cause of the HUP. Is it
because we are at the level of where spacetime is actually being defined?
That was simply my whole point and question. It just seems odd that you
*can* somewhat model an electron as if it were an extended object in a
volume of space on the order of hbar/m_e*c but if we try to get closer to
it, it "shrinks" for the lack of a better word.
FrediFizzx
Y.Porat
> "
> | I was responding to Fredi's post about his current loops, where he said
> | something funny happens at a wavelength smaller than the Compton length,
> | implying that there is something to these current loops of his. My point
> | was that things do get funny but only due to Heisenberg.
>
> So I guess part of it is what is the fundamental cause of the HUP. Is it
> because we are at the level of where spacetime is actually being defined?
> That was simply my whole point and question. It just seems odd that you
> *can* somewhat model an electron as if it were an extended object in a
> volume of space on the order of hbar/m_e*c but if we try to get closer to
> it, it "shrinks" for the lack of a better word.
>
> FrediFizzx
interesting
i as well independantly was thinking about the possibility that
the electron orbital can have different sizes
sort of shrinking and extending
we find electrons in a big extention ouside the nucleus
and inside (or part of the nuc. as well) so there
inside the nuc, it must have much smaller dimentions.
but how do you get it to do it ?
(forget imho about curvature of spacetime)
----------
all the best
Y.porat
------------------
FrediFizzx
news:1f9c772b.03102...@posting.google.com...
What is abstract about sqrt(hbar*c)? It is right in the fine
structure "constant" relationship for everyone to see. Everyone is
afraid to call it for what it is because it has to result in an
organized quantum vacuum. Vacuum charge is the only thing it can be.
The "particles" that make virtual e+e- pairs are the source of vacuum
charge. It is really quite simple. Vacuum charge is responible for
EM fields. Photons do not have intrinsic EM fields. But they sure
can excite vacuum charge to produce EM fields that we can measure.
Yes, I have heard of your obitals. You sent me your book, remember?
You are sort of mixing quantum objects in with the spin matrix of the
quantum vacuum. In a way, I suppose you can think of a quantum
particle as extending into the vacuum spin matrix. All quantum
particles are linked up (coupled) with the matrix. The way I see it,
particles are more like "holes" in the matrix.
FrediFizzx
Dave Thomson
> You are sort of mixing quantum objects in with the spin matrix of the
> quantum vacuum. In a way, I suppose you can think of a quantum
> particle as extending into the vacuum spin matrix. All quantum
> particles are linked up (coupled) with the matrix. The way I see it,
> particles are more like "holes" in the matrix.
Yes, I agree with this paradigm. A particle can be seen as a hole in the
vacuum spin matrix just as much as we think of space as being a hole in a
physical object.
Dave
Y.Porat
my point it first of all to get some phicical idea about it
*before * the mathematical definition.
thats exactly what the qm is running away from
but running away cannot lead far.away.
----------
Everyone is
> afraid to call it for what it is because it has to result in an
> organized quantum vacuum. Vacuum charge is the only thing it can be.
> The "particles" that make virtual e+e- pairs are the source of vacuum
> charge. It is really quite simple. Vacuum charge is responible for
> EM fields. Photons do not have intrinsic EM fields. But they sure
> can excite vacuum charge to produce EM fields that we can measure.
>
> Yes, I have heard of your obitals. You sent me your book, remember?
> You are sort of mixing quantum objects in with the spin matrix of the
> quantum vacuum. In a way, I suppose you can think of a quantum
> particle as extending into the vacuum spin matrix. All quantum
> particles are linked up (coupled) with the matrix. The way I see it,
> particles are more like "holes" in the matrix.
> ----------------
again
1 the chain of orbitals is not too essential in my book
anyway the idea that subparticles connect linearily
is very dominant there.
whatever is that unit that is connected linearily
and whatever are the detailes about how that can be done.
2
the main reason people get stuck in the mudd is to explain
how is it that something basic can be formed as a circular enetity.
the main obstacle here is the firt Newton law of movement.
so i think
the particle that moves naturally in a closed circle
is unevitable on the long run.
if you call it wholes in a matrix (not at all clear to me
what that matrix is
whatever
once you geting closer to something that moves *naturally*
in a closed circle,- you are getting closer to my idea.
but please dont forget the necessity of subparticles
connecting linearily
you see the outcome of it in my book very substanciated
by many cross verifications.
even orbitals of different order.(ie not necessarily
only orbitals of the same kind !)
all the best
Y.porat
--------------------
all the best
Y.porat
---------------------