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<DIV><FONT color=#000080 size=2 face=Arial>Hi Chip & All,</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>[repeat as my first send doesn't
appear to have arrived - apologies if any duplication]</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Can somebody point me in the
direction of experimental evidence of a single photon being split into two parts
to form an electron-positron pair? I was under the impression that such
pair production takes an opposing pair of photons of requisite
energy.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>It's my understanding that the
history of this discovery goes back to Lev Landau's seminal experiments in 1934
(with his student Evgeny Lifshitz) where he identified the fact that particle
collider experiments producing such pairs always hinged on release of
high-energy photons that then collided to form those pairs - collisions of
photons, in my understanding, always involve more than one photon. In
December of that year - presumably based on this finding - Breit & Wheeler
defined their well-documented process, which again involves collisions between
opposing photons.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>The only practical implementation, to
my knowledge, of a process whereby e-/e+ pairs have been produced from
photons alone was the SLAC experiment in 1997, where a 'Multiphoton
Breit-Wheeler Process' was implemented, successively ramping up the energies of
photons in a laser cavity to the point where, after around four collisions, they
reached the required energies to form e-/e+ pairs on further collision with
bombarding photons.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Clearly it's possible for a photon to
be split - Compton Scattering is a practical illustration in which part of a
photon's energy is absorbed by a (pre-existent) material particle to give it
momentum and the rest of that photon continues on its way with reduced
frequency/energy. However I know of NO situation in which a single photon
has been transformed into a particle-antiparticle pair, as is being suggested
below.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>[As a point of detail, I find it hard
to envisage how linear momentum, angular momentum and energy could all be
conserved by such a happening.]</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Those who are happily discussing
it as if it's 'de facto', I'd be really glad of your references for
same.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial>If no such (reliable) references
exist, I'd suggest that to proceed on the basis that it IS a reality would be
questionable, to say the least.</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>[For avoidance of doubt: Colliding
two opposing photons to thus form two particles is most assuredly NOT "splitting
a photon", in my book - though it IS re-apportioning the energies & momenta
of those two photons to re-cast them as particles.]</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial></FONT> </DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Thanks,</FONT></DIV>
<DIV><FONT color=#000080 size=2 face=Arial>Grahame</FONT></DIV>
<BLOCKQUOTE
style="BORDER-LEFT: #000080 2px solid; PADDING-LEFT: 5px; PADDING-RIGHT: 0px; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="FONT: 10pt arial; BACKGROUND: #e4e4e4; font-color: black"><B>From:</B>
<A title=chipakins@gmail.com href="mailto:chipakins@gmail.com">Chip Akins</A>
</DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A
title=general@lists.natureoflightandparticles.org
href="mailto:general@lists.natureoflightandparticles.org">'Nature of Light and
Particles - General Discussion'</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Tuesday, October 10, 2017 12:22
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [General] A composite
electron?</DIV>
<DIV><BR></DIV>
<DIV class=WordSection1>
<P class=MsoNormal><SPAN style="COLOR: black">Hi Richard<o:p></o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black"><o:p> </o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black">Exactly! The mere act of
splitting a photon (with the requisite energy) causes each “half photon” to
confine itself and the half photons become an electron/positron
pair.<o:p></o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black"><o:p> </o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black">Andrew suggested in the SPIE
conference we attended, that the electron was half a photon (a rectified
photon is what I think he said).<o:p></o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black"><o:p> </o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black">This is part of the concept I
have been trying to convey. The rest of the concept is that space is
composed in a way which makes this possible. A two component tension
medium. This scenario creates quantized electric charge, as we observe.
Creates mass, as we observe. Creates the spin we observe for photon and
electron. Makes more energetic particles smaller particles, as we
observe. And agrees with experiment regarding the velocity of electric
charge, which is much easier to conduct and less ambiguous than the current
LIGO findings. <o:p></o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black"><o:p> </o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black">Regarding LIGO and gravity:
Binary pulsars have been studied for some time. Their orbits simply do
not deteriorate at the rate they would if gravity propagated at light
speed. Many, who firmly believe in the postulate of relativity that
nothing can travel faster than c, have attempted to explain this away.
But I have found none of these explanations to be plausible (in my opinion).
The simplest explanation is the gravity is faster than
light.<o:p></o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black"><o:p> </o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black">That does not mean that it is
impossible for two massive bodies to generate a wave which has a phase
velocity near or at light speed. That is quite possible, and perhaps
even probable.<o:p></o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black"><o:p> </o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black">But back to the photon and
electron. I think you are on the right track with
this.<o:p></o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black"><o:p> </o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black">Chip<o:p></o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black"><o:p> </o:p></SPAN></P>
<DIV>
<DIV
style="BORDER-BOTTOM: medium none; BORDER-LEFT: medium none; PADDING-BOTTOM: 0in; PADDING-LEFT: 0in; PADDING-RIGHT: 0in; BORDER-TOP: #e1e1e1 1pt solid; BORDER-RIGHT: medium none; PADDING-TOP: 3pt">
<P class=MsoNormal><B><SPAN
style="FONT-FAMILY: 'Calibri',sans-serif; FONT-SIZE: 11pt">From:</SPAN></B><SPAN
style="FONT-FAMILY: 'Calibri',sans-serif; FONT-SIZE: 11pt"> General
[mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org]
<B>On Behalf Of </B>Richard Gauthier<BR><B>Sent:</B> Monday, October 09, 2017
11:59 PM<BR><B>To:</B> Andrew Meulenberg
<mules333@gmail.com><BR><B>Cc:</B> Nature of Light and Particles -
General Discussion <general@lists.natureoflightandparticles.org>; Martin
Rivas <martin.rivas@ehu.es>; David Hestenes <Hestenes@asu.edu>;
robert hudgins <hudginswr@msn.com><BR><B>Subject:</B> Re: [General] A
composite electron?<o:p></o:p></SPAN></P></DIV></DIV>
<P class=MsoNormal><o:p> </o:p></P>
<P class=MsoNormal>Hello Andrew and all,<o:p></o:p></P>
<DIV>
<P class=MsoNormal><o:p> </o:p></P>
<DIV>
<P class=MsoNormal> De Broglie proposed his 2 spin-1/2
particle photon idea (not sure if he also had a model for this) in the early
30’s in his book "La Physique Nouvelle et les Quanta” (available free at <A
href="http://archive.org">archive.org</A>) and in English translation as "<A
href="https://www.amazon.com/gp/product/B0007G309U/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1"><SPAN
style="FONT-FAMILY: 'Arial',sans-serif; COLOR: #0066c0; FONT-SIZE: 10pt; TEXT-DECORATION: none">The
revolution in physics: A non-mathematical survey of quanta</SPAN></A>”,
available at <A href="http://Amazon.com">Amazon.com</A>. With the help of
Google Translate (slightly edited) I give below what de Broglle wrote on this
(p. 277-278 in the French edition):<o:p></o:p></P></DIV>
<DIV>
<P class=MsoNormal><o:p> </o:p></P></DIV>
<DIV><PRE><SPAN style="FONT-FAMILY: inherit; COLOR: #212121" lang=EN>From these general remarks, we have concluded that, in order to constitute a theory of the photon, we must first use a relativistic form of wave mechanics comprising elements of symmetry due to polarization and, secondly, introduce something to differentiate the photon from the other particles. The first part of this program is realized immediately by using the theory of the electron of Dirac that we studied previously. We know that Dirac's theory is relativistic and that it contains elements of symmetry with a marked kinship with those of the polarization of light. Nevertheless, it was not sufficient to suppose that the photon is a particle of negligible mass obeying the equations of the Dirac theory, for the model of the photon thus obtained would have, so to speak, only half the symmetry of the real photon; moreover, it would, like the electron, apparently obey Fermi statistics and could not be annihilated in the photoelectric effect. We need something more.</SPAN><o:p></o:p></PRE><PRE><SPAN style="FONT-FAMILY: inherit; COLOR: #212121" lang=EN>This something more, we tried to introduce on the assumption that the photon is constituted not of a Dirac particle, but of two. It can be realized that these two particles or half-photons must be complementary to each other in the same sense as the positive electron is complementary to the negative electron in Dirac</SPAN><SPAN style="FONT-FAMILY: 'Times New Roman',serif; COLOR: #212121">’</SPAN><SPAN style="FONT-FAMILY: inherit; COLOR: #212121" lang=EN>s hole theory. Such a pair of complementary particles is liable to annihilate itself by contact with matter and yielding all its energy, and this perfectly accounts for the chracteristics of the photoelectric effect. Moreover, the photon then being constituted by two elementary particles with spin h/4pi must obey Bose-Einstein statistics, as required by the accuracy of Planck's law for black-body radiation. Finally, this photon model makes it possible to define an electromagnetic field linked to the probability of annihilation of the photon, a field which obeys Maxwell</SPAN><SPAN style="FONT-FAMILY: 'Times New Roman',serif; COLOR: #212121">’</SPAN><SPAN style="FONT-FAMILY: inherit; COLOR: #212121" lang=EN>s equations and possesses all the characteristics of the electromagnetic light wave. Although it is still premature to pronounce definitively on the value of this attempt, it is indisputable that it leads to interesting results and that it heavily draws attention to the properties of symmetry of complementary particles whose existence, suggested by the Dirac theory, was verified by the discovery of the positive electron.</SPAN><o:p></o:p></PRE><PRE><o:p> </o:p></PRE></DIV>
<DIV>
<P class=MsoNormal>So what I have called in the past a spin-1/2 charged photon
I now think should be called a spin-1/2 charged half-photon, since two of them
(one positive and one negative) would move in a double helix to form a spin 1
photon which helps generate electromagnetic waves. This renaming should also
solve the semantic problem of the name of this superluminal charged spin-1/2
particle , which I would no longer consider to be a variety of photon, since
it would take two of them to make a photon. Such a photon model could easily
generate an electron-positron pair when near an atomic nucleus that absorbs
excess momentum (creating two rest masses) and splits a sufficiently energetic
photon into an e-p pair. Comments? <o:p></o:p></P></DIV>
<DIV>
<P class=MsoNormal><o:p> </o:p></P>
<DIV>
<BLOCKQUOTE style="MARGIN-TOP: 5pt; MARGIN-BOTTOM: 5pt">
<DIV>
<P class=MsoNormal>On Oct 2, 2017, at 5:20 AM, Andrew Meulenberg <<A
href="mailto:mules333@gmail.com">mules333@gmail.com</A>>
wrote:<o:p></o:p></P></DIV>
<P class=MsoNormal><o:p> </o:p></P>
<DIV>
<DIV>
<DIV>
<DIV>
<P class=MsoNormal><o:p> </o:p></P></DIV>
<P style="MARGIN-BOTTOM: 12pt" class=MsoNormal>Dear
Folks,<o:p></o:p></P></DIV>
<P class=MsoNormal>The composite electron model has a history of which I was
not aware. From mid-right column of page 4 of (free access):<o:p></o:p></P>
<DIV>
<DIV>
<P style="MARGIN-BOTTOM: 12pt" class=MsoNormal><A
href="https://www.omicsonline.org/open-access/">https://www.omicsonline.org/open-access/</A><B>the-last-challenge-of-modern-physics</B>-2090-0902-1000217.php?aid=87682<o:p></o:p></P>
<DIV style="MARGIN-LEFT: 30pt">
<P style="MARGIN-BOTTOM: 12pt" class=MsoNormal><SPAN
class=gmail-fontstyle0>Louis de Broglie elaborated a most promising
hypothesis to help</SPAN><BR><SPAN class=gmail-fontstyle0>explain these
special characteristics of the photon [7]. Having analyzed</SPAN><BR><SPAN
class=gmail-fontstyle0>them in light of the verifed aspects of the various
pertaining theories,</SPAN><BR><SPAN class=gmail-fontstyle0>he eventually
concluded that the only way for an electromagnetic</SPAN><BR><SPAN
class=gmail-fontstyle0>photon to satisfy at the same time Bose-Einstein's
statistic and Planck's</SPAN><BR><SPAN class=gmail-fontstyle0>law, and to
perfectly explain the photoelectric e</SPAN><SPAN
class=gmail-fontstyle0><SPAN
style="FONT-FAMILY: 'Cambria Math',serif">ff</SPAN></SPAN><SPAN
class=gmail-fontstyle0>ect while obeying</SPAN><BR><SPAN
class=gmail-fontstyle0>Maxwell's equations and conforming to the symmetry
property of</SPAN><BR><SPAN class=gmail-fontstyle0>complementary corpuscles
in Dirac's Hole Theory, would be for it to</SPAN><BR><SPAN
class=gmail-fontstyle0>be made not of one corpuscle, but of two corpuscles,
or half-photons,</SPAN><BR><SPAN class=gmail-fontstyle0>that would be
complementary, like the electron is complementary to</SPAN><BR><SPAN
class=gmail-fontstyle0>the positron in Dirac's Hole Theory
[15].</SPAN><BR><BR><SPAN class=gmail-fontstyle0>This conclusion mandates
the association of charges (possibly</SPAN><BR><SPAN
class=gmail-fontstyle0>unsigned) to each half-photon, and consequently to
the photon itself, ...</SPAN> <BR> <o:p></o:p></P></DIV>
<DIV style="MARGIN-LEFT: 30pt">
<DIV style="MARGIN-LEFT: 30pt">
<P class=MsoNormal><SPAN class=gmail-fontstyle0>7. Michaud A (2016) On
De Broglie’s Double-particle Photon Hypothesis. J Phys</SPAN><BR><SPAN
class=gmail-fontstyle0>Math 7: 153.</SPAN> <BR><BR><SPAN
class=gmail-fontstyle0>15. De Broglie L (1937) New physics and quanta,
Flammarion, 2</SPAN><SPAN class=gmail-fontstyle0><SPAN
style="FONT-SIZE: 4pt">nd </SPAN></SPAN><SPAN class=gmail-fontstyle0>1993
new</SPAN><BR><SPAN
class=gmail-fontstyle0>Preface.</SPAN><o:p></o:p></P></DIV></DIV>
<P class=MsoNormal><o:p> </o:p></P></DIV>
<DIV>
<P style="MARGIN-BOTTOM: 12pt" class=MsoNormal>This would imply that,
historically, the Nature of Light is even more curious than most of us
thought.<o:p></o:p></P></DIV>
<DIV>
<P class=MsoNormal>Andrew M.<o:p></o:p></P></DIV>
<DIV>
<P class=MsoNormal> <o:p></o:p></P></DIV></DIV></DIV>
<DIV>
<P class=MsoNormal><o:p> </o:p></P>
<DIV>
<P class=MsoNormal>On Mon, Sep 25, 2017 at 5:24 PM, Richard Gauthier <<A
href="mailto:richgauthier@gmail.com"
target=_blank>richgauthier@gmail.com</A>> wrote:<o:p></o:p></P>
<BLOCKQUOTE
style="BORDER-BOTTOM: medium none; BORDER-LEFT: #cccccc 1pt solid; PADDING-BOTTOM: 0in; PADDING-LEFT: 6pt; PADDING-RIGHT: 0in; MARGIN-LEFT: 4.8pt; BORDER-TOP: medium none; MARGIN-RIGHT: 0in; BORDER-RIGHT: medium none; PADDING-TOP: 0in">
<DIV>
<DIV>
<P style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto"
class=MsoNormal>Hello Martin (and all),<o:p></o:p></P>
<P style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto"
class=MsoNormal> Thank you for this summary of your CC-CM
approach to a moving particle such as an electron. My approach to modeling
an electron is quite similar to yours, except that in my approach the CC
(center of charge) is the position of a light-speed spin-1/2 charged
quantum particle that I call a choton. It is in circular motion in a
resting electron and moves helically in a moving electron. The linear
momentum of the choton in a resting electron is Po=mc=2.73x10^-22 kg m/s =
0.511 MeV/c (and its energy is mc^2= 0.511 MeV) and this momentum mc
circles with radius Ro= L-compton/4pi = hbar/2mc = 1.93x10^-13m at the
zitterbewegung frequency f-zitt=2mc^2/h. The choton’s average position as
the choton circles around is what you call the CM (center of mass). In a
resting electron the choton (at the position CC) and the CM are separated
by the distance Ro, with the choton circling around its CM at the zitter
frequency. Due to its circular motion with its changing momentum
direction, the choton appears to be acted on by a centripetal force
Fc=dp/dt = w Po = w-zitt Po = 0.424 N , where w-zitt (omega-zitt) =
2 mc^2/hbar = 1.55 x 10^21 rad/sec. The choton’s centripetal acceleration
A-cent in this circular motion in a resting electron is A-cent = r w^2
= Ro (w-zitt)^2 = 4.66x10^29 m/s^2. My article “Derivation of the
inertial mass m=Eo/c^2 of an electron composed of a circling spin-1/2
charge photon” at <A
href="https://richardgauthier.academia.edu/research%23papers"
target=_blank>https://richardgauthier.academia.edu/research#papers</A> (4<SUP>th</SUP> article)
also shows that the above circling choton (spin-1/2 charged photon) has an
inertial mass m = Eo/c^2 = 0.511MeV/c^2 derived from its circling momentum
mc=Eo/c.<o:p></o:p></P>
<P style="mso-margin-top-alt: auto; mso-margin-bottom-alt: auto"
class=MsoNormal> When no external force (besides the apparent
0.424 N central force) acts on the choton, the moving electron model moves
longitudinally with velocity <B>v</B> and with momentum <B>p</B>=gamma
m<B>v</B>. The choton circulates with its longitudinal momentum component
P-long = gamma mv, which is the electron’s linear momentum, and with a
transverse momentum component P-trans = Po = mc. Using the Pythagorean
equation, this gives the choton’s total momentum directed along its
helical trajectory as P-total^2 = P-long^2 + P-trans^2 = (gamma
mv)^2 + (mc)^2 = (gamma mc)^2, or P-total = gamma mc. The choton’s
corresponding total energy is E-total = P-total c = gamma mc^2, which is
the same as a relativistic electron’s total energy. <o:p></o:p></P>
<H4
style="MARGIN-BOTTOM: 9pt; MARGIN-LEFT: 0in; MARGIN-RIGHT: 0in; mso-margin-top-alt: 0in"><SPAN
style="FONT-WEIGHT: normal"> When an external electric field
</SPAN>E<SPAN style="FONT-WEIGHT: normal"> acts on the circulating choton,
the choton (with its inertial mass m=0.511 MeV/c^2) is accelerated by a
net force </SPAN>Fnet<SPAN style="FONT-WEIGHT: normal"> equal to the
rapidly rotating centripetal force </SPAN>Fc<SPAN
style="FONT-WEIGHT: normal">= 0.424 N plus the external force
</SPAN>F<SPAN style="FONT-WEIGHT: normal">=-e</SPAN>E. <SPAN
style="FONT-WEIGHT: normal">The total force on the choton is
</SPAN>Fnet<SPAN style="FONT-WEIGHT: normal"> = </SPAN>Fc<SPAN
style="FONT-WEIGHT: normal"> + e</SPAN>E <SPAN
style="FONT-WEIGHT: normal">= m </SPAN>a-total <SPAN
style="FONT-WEIGHT: normal">in the non-relativistic case or
</SPAN>Fnet<SPAN style="FONT-WEIGHT: normal"> = d</SPAN>p-total<SPAN
style="FONT-WEIGHT: normal">/dt in the relativistic case. The choton’s
helical motion (the motion of the CC) will be changed by the external
electric field </SPAN>E <SPAN style="FONT-WEIGHT: normal">acting on the
choton, and the choton’s CM (average position) will be affected
accordingly, and move in the direction of the applied external force
</SPAN>E<SPAN style="FONT-WEIGHT: normal">.</SPAN><o:p></o:p></H4>
<H4
style="MARGIN-BOTTOM: 9pt; MARGIN-LEFT: 0in; MARGIN-RIGHT: 0in; mso-margin-top-alt: 0in"><SPAN
style="FONT-WEIGHT: normal"> There are also quantum mechanical
features of the above motion. As the choton changes its helical trajectory
due to the applied electric field </SPAN>E<SPAN
style="FONT-WEIGHT: normal">, the choton’s transverse momentum component
P-trans = mc adjusts its orientation so that P-trans continues to be
transverse to the choton’s new longitudinal motion with its new
longitudinal component velocity </SPAN>v’ <SPAN
style="FONT-WEIGHT: normal">(the new electron velocity). In this way the
calculated spin of the choton electron model continues to be Ro x Po =
hbar/2 and the Pythogorean momentum relation continues to be
P-total^2 = P-long^2 + P-trans^2 (which is mathematically equivalent
to the relativistic energy-momentum equation E^2 = p^2 c^2 +m^2 c4).
Further information on the spin-1/2 charged photon model is at “Electron’s
are spin 1/2 charged photons generating the de Broglie wavelength” at <A
href="https://richardgauthier.academia.edu/research#papers"
target=_blank>https://richardgauthier.academia.edu/research#papers</A>
(19<SUP>th</SUP> article).</SPAN><o:p></o:p></H4>
<H4
style="MARGIN-BOTTOM: 9pt; MARGIN-LEFT: 0in; MARGIN-RIGHT: 0in; mso-margin-top-alt: 0in"><SPAN
style="FONT-WEIGHT: normal"> In summary, the choton electron
model does not need to be a rigid body to maintain the relation between CC
and CM. All forces (including the apparent centripetal force F-cent) act
on the choton (at the CC), which has its own inertial mass, producing the
choton’s acceleration and average center of mass position
CM. </SPAN><o:p></o:p></H4>
<DIV>
<P class=MsoNormal>with warm regards,<o:p></o:p></P></DIV>
<DIV>
<P class=MsoNormal>
Richard<o:p></o:p></P></DIV></DIV>
<DIV>
<P
class=MsoNormal> </P></DIV></DIV></BLOCKQUOTE></DIV></DIV></DIV></BLOCKQUOTE></DIV></DIV></DIV></DIV></BLOCKQUOTE></BODY></HTML>