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<p style="margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="line-height:115%">Dear Andrew,</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">As a complement of info for interpreting the pair production in the trispatial geometry, it must be emphasized that the trispatial mechanics is not grounded on the traditional energy conservation principle that mandates that momentum must be accounted in all circumstances for as you and Chandra describe, but on the fact that energy is adiabatically induced in charged particles strictly as a function of the distance separating charges. I now will explain further.</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">From this perspective, the energy conservation principle holds only for charges stabilized into least action electromagnetic equilibrium states, such as rest orbitals in atoms, for example, or even masses lying on the ground. Electromagnetic photons and free moving electrons are not in this state. They are not stabilized into least action states, which means that their instantaneous momentum energy constantly varies adiabatically as a function of the Coulomb law stemming from Maxwell's first equation, which is Gauss's equation for the electric field, when charges are assumed present at any distance from the test charge.</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">I realize that adiabatic energy induction cannot be directly related to the Hamiltonian currently used as a founding principle, which is grounded on the classical Principle of energy conservation established from past experiments carried out with macroscopic masses at our macroscopic level. Here is why:</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">The adiabatic variations of energy in such macroscopic masses that are made to interact at ground level are so infinitesimal by nature as to be impossible to measure. For example, a 1 kg mass falling 1 meter to the ground releases the familiar 9.78 joules of kinetic energy in sync with the principle of conservation as it stabilizes in this relative rest state, but an easy to carry out calculation also shows that it is also adiabatically induced with a mass increment 13 orders of magnitude smaller than 1 gram.</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">Too small to be measured, and never considered as even existing.</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">These effects can be, and have been measured when sufficient axial distances are involved, for example, such as taking atomic clocks in altitude, but this adiabatic effect resulting from atomic and nucleonic orbitals contraction due to the weakening effect of the Coulomb interaction due to increased distance between the charged elementary particles of which the small mass of the bodies are made, that move to higher altitudes and those making up the mass of the Earth, have been mistakenly confused with so-called relativistic time-dilation effects due to beliefs in the misconceptions perpetuated by SRT and GRT. </span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">They also have been assumed by popular belief to underlie the operation of the GPS system even if it is well known in the specialized community that the GPS and other localization systems do not use this effect, but rather multilateration to calculate locations and live positioning, unrelated to time.</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">In 2003, Paul Marmet demonstrated from a derivation from the Biot-Savart equation that the magnetic field of an accelerating electron increases in synchronicity with its velocity related relativistic mass increment, and that his magnetic energy actually was what provided this "classical mass" increment.</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">Further analysis of Marmet's discovery and of the Kaufman experimental data demonstrates that the same Lorentz gamma factor related energy and mass growth with velocity of massive bodies leading to a theoretical infinite mass at the asymptotic speed of light limit, also applies to an identical energy and mass growth with proximity between elementary charged particles leading to a theoretical infinite mass at asymptotic zero distance proximity. </span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">This second "Lorentz" gamma factor related energy and mass growth curve always was and still is undetectable from all experiments carried out with masses manageable at ground level level because they happen to all occur at the infinitesimal end of the proximity mass growth curve between the charged elementary particles making up macroscopic masses nearing each other, just like velocities experimentally manageable in Newton's time all were at the infinitesimal end of the relativistic velocities growth curve.</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">We know now that even the fastest meteorites falling on the Earth reach at best about 60 km/s, which is way below the approximate 2000 km/s required to measurably be in the low relativistic range, which is why non-relativistic Newton remains fine for all velocities that we are likely to deal with at our macroscopic level.</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">This always prevented becoming aware of the adiabatic nature of the mass increases with proximity between elementary charged particles making up macroscopic massive bodies moving away from or towards to each other.</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">But now that the relation is established, the traditional Principle of conservation of energy can be located where it belongs, that is, at the infinitesimal limit of the adiabatic energy/mass growth curve with proximity between elementary charged particles, just like Newton's mechanics was at the infinitesimal limit of the relativistic energy/mass growth curve with velocity of massive bodies.</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">Since all material bodies are made exclusively of charged elementary particles, it is to this second adiabatic growth curve that I have been trying to draw attention to with my papers, because it puts in perspective that the concepts of Lagrangian and Hamiltonian as currently formulated grounded on the principle of kinetic-energy/potential-energy total conservation prevents completely exploring the submicroscopic level, where adiabatic energy/mass induction with proximity is well into the detectable range of the magnetic-energy/mass-increase growth curve.</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">I found that this growth curve with proximity of elementary particles is due to the adiabatic nature of kinetic-energy/electromagnetic-energy induction by the Coulomb interaction, that can be calculated with the natural variations of the well established Maxwell first equation, that is, Gauss's equation for the electric field. </span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">I analyzed adiabatic energy variation in elementary charges in this paper:</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif""><a href="https://www.omicsonline.org/open-access/on-adiabatic-processes-at-the-elementary-particle-level-2090-0902-1000177.pdf" style="color:blue; text-decoration:underline">https://www.omicsonline.org/open-access/on-adiabatic-processes-at-the-elementary-particle-level-2090-0902-1000177.pdf</a></span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">Best Regards</span></span></span></span></span></p>
<p style="margin-bottom:.0001pt; margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:normal"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="font-family:"Times New Roman","serif"">André</span></span></span></span></span></p>
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<span>On Mon, 20 Aug 2018 18:38:12 -0400, André Michaud <srp2@srpinc.org> wrote:</srp2@srpinc.org></span></footer>
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<p style="margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="line-height:115%">Hi Andrew,</span></span></span></span></span></p>
<p style="margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="line-height:115%"><span style="text-transform:uppercase">A</span></span></span><span style="font-size:12.0pt" lang="EN-US"><span style="line-height:115%">s I mentioned to Chandra from the get to, I make no personal interpretation of the McDonald et al. experiment<span style="text-transform:uppercase">.</span></span></span></span></span></span></p>
<p style="margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="line-height:115%">From the data collected, it seems that the interaction between the electron and the beam resulted in a high energy gamma to be emitted, which further along the beam decoupled into an electron-positron pair from what can apparently be nothing else but some interaction between this high energy gamma and one or more other photons in the tightly collimated beam<span style="text-transform:uppercase">.</span></span></span></span></span></span></p>
<p style="margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="line-height:115%">Since this is consistent with the manner in which the de Broglie double-particle photon can be destabilized when grazing a massive particle in the trispatial geometry, it also is consistent with the possibility that such a high energy gamma could be destabilized in the same manner when chancing to graze sufficiently closely another photon, in the very narrow window provided by the fact that both move at the speed if light and can only fleetingly be close enough for such interaction to result in destabilization. This is where the high concentration of the highly collimated laser beam can insure sufficient density of ambient photons moving in the same direction as the high energy gamma previously produced by the electron-beam interaction for this destabilizing interaction to occur.</span></span></span></span></span></p>
<p style="margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="line-height:115%">If interested in how such decoupling of an electromagnetic photon can result in the materialization of an electron-positron pair in the trispatial geometry, here is a link to the paper that describes this decoupling mechanics:</span></span></span></span></span></p>
<p style="margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="line-height:115%"><a href="http://ijerd.com/paper/vol6-issue10/f06103649.pdf" style="color:blue; text-decoration:underline">http://ijerd.com/paper/vol6-issue10/f06103649.pdf</a></span></span></span></span></span></p>
<p style="margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="line-height:115%">Best regards</span></span></span></span></span></p>
<p style="margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt"><span style="line-height:115%">André</span></span></span></span></span></p>
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<span>On Mon, 20 Aug 2018 17:12:32 -0400, Andrew Meulenberg <mules333@gmail.com> wrote:</mules333@gmail.com></span><br>
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<div>Dear <span class="gmail-im"><span style="font-size:12pt"><span style="font-family:"Times New Roman","serif"">André</span></span></span>,</div>
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<div>I might have to agree with Chandra in this case. Nevertheless, it is an interesting experiment and result.</div>
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<div>I have not read the paper; so, I can't hear the arguments the authors would make. While the some model(s) predicts gamma emission from collision of the electron with the laser beam, the gamma would need to be phased and energetic enough to interact with the coherent laser beam<b> E</b>-field at the proper angle to divide and transfer the proper momentum to the beam. The beam would probably need to have enough "cohesiveness" to provide an effective mass adequate to absorb the necessary momentum. On the one hand, if the beam could generate the very energetic gamma, then it would require a large number of laser photons (or a sufficient portion of the coherent wave energy). Thus, the beam energy (photons) might be able to interact sufficiently to act as a massive momentum absorbing body. On the other hand, to have two major events (gamma creation and lepton-pair formation) within the same small volume of time and space and with the proper phase and energy relationships, a major statistical miracle would be needed.</div>
<div> </div>
<div>With this background, I would agree with Chandra that it is more likely that a sufficient portion (energetically and spatially) of the laser beam interacts only once with the electron to produce the lepton pair. The gamma, if one actually exists in this scenario, might be a virtual "creature" (in my view an evanescent wave) with properties still needing definition. To claim that the experiment confirms photon-photon interaction (which I believe does exist in other contexts) is the same as using the model of charge being a result of photon exchange to claim that all lepton creation (and all light interaction with charged particles) is a photon-photon interaction. I believe that this would be the view (claim?) of QED where any <b>E</b>- or <b>B</b>-field is considered to be a photon.</div>
<div> </div>
<div>Andrew</div>
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<div dir="ltr">On Mon, Jul 30, 2018 at 1:16 AM "André Michaud" <<a href="mailto:srp2@srpinc.org">srp2@srpinc.org</a>> wrote:</div>
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<p style="margin:0in 0in 0.0001pt"><span style="font-size:12pt"><span style="font-family:"Times New Roman","serif"">Dear Chandra,</span></span></p>
<p style="margin:0in 0in 0.0001pt"> <span style="font-size:12pt"><span style="font-family:"Times New Roman","serif"">I have no personal interpretation of these experiments carried out at SLAC.</span></span></p>
<p style="margin:0in 0in 0.0001pt"> </p>
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<p style="margin:0in 0in 0.0001pt"><span style="font-size:12pt"><span style="font-family:"Times New Roman","serif"">Apparently, the electron collision with the beam generated a gamma photon in excess of 1.022 MeV that then decoupled into an electron positron pair further away in the beam apparently due to interaction between this photon and other less energetic photons in the beam, after the initial electron had been deflected at an angle coherent with the recoil due to the process of emission of the high energy gamma photon.<br>
<br>
The process appears to have been successfully recorded a sufficient number of times to be accepted as significant to the peer-reviewers.</span></span></p>
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<p style="margin:0in 0in 0.0001pt"><span style="font-size:12pt"><span style="font-family:"Times New Roman","serif"">The description in the related documentation is there for anyone to do his own study and interpretation. </span></span></p>
<p style="margin:0in 0in 0.0001pt"> </p>
<p style="margin:0in 0in 0.0001pt"><span style="font-size:12pt"><span style="font-family:"Times New Roman","serif"">Given that all EM photons move at c, it seems mandatory that least one photon in excess of 1.022 MeV be present in the same highly focused volume of space with a sufficient concentration of other less energetic photons for the process to be possible. This seems to be what allows the process. </span></span></p>
<p style="margin:0in 0in 0.0001pt"> </p>
<p style="margin:0in 0in 0.0001pt"><span style="font-size:12pt"><span style="font-family:"Times New Roman","serif"">I am satisfied with the interpretation made by the McDonald team.</span></span></p>
<p style="margin:0in 0in 0.0001pt"> </p>
<p style="margin:0in 0in 0.0001pt"><span style="font-size:12pt"><span style="font-family:"Times New Roman","serif"">Best Regards</span></span></p>
<p style="margin:0in 0in 0.0001pt"> </p>
<p style="margin:0in 0in 0.0001pt"><span style="font-size:12pt"><span style="font-family:"Times New Roman","serif"">André</span></span></p>
---<br>
André Michaud<br>
"GSJournal admin" <<a href="mailto:ntham@gsjournal.net" target="_blank">ntham@gsjournal.net</a>><br>
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<span>On Mon, 30 Jul 2018 01:53:39 +0000, "Roychoudhuri, Chandra" wrote:</span><br>
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Andre:
<div>The experiment you have cited starts with an electron. The intermediate Gamma is a conjecture of current particle theory. To me, this is not pure light beam-light beam scattering in pure vacuum.</div>
<div>The world has several laser fusion labs. Enormous amount of laser energy is focussed into about 100 micron size D2/D3 pellet. Only time the labs record real particles output when the laser beams successfully hit the pellet. Whenever the focussed laser beams miss the pellet, no particles are generated.
<div> How come there is no photon-Photon interaction to generate particles?</div>
<div>If my observation is backdated, kindly send me a recent reference. </div>
<div>Chandra.<br>
<div id="m_-4007217526553906849AppleMailSignature">Sent from my iPhone</div>
<div><br>
On Jul 29, 2018, at 2:58 PM, André Michaud <<a href="mailto:srp2@srpinc.org" target="_blank">srp2@srpinc.org</a>> wrote:<br>
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<p style="margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="line-height:115%">Dear Andrew,</span></span></span></span></span></p>
<p style="margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="line-height:115%">Just to mention that what seems not to have been covered in the pair production historical overview is pair production from photon-photon interaction in experiments carried out by McDonald et al. in 1997:</span></span></span></span></span></p>
<p style="margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt"><span style="line-height:115%"><a href="https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.researchgate.net%2Fderef%2Fhttp%253A%252F%252Fwww.slac.stanford.edu%252Fexp%252Fe144%252F&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368774034&sdata=FlWkFZa7z2%2FSaBoHykstrQ8cBHP4WSjcmFK6b19LGDU%3D&reserved=0" style="color:blue;text-decoration:underline" target="_blank">http://www.slac.stanford.edu/exp/e144/</a></span></span></span></span></span></p>
<p style="margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt" lang="EN-US"><span style="line-height:115%">Best Regards</span></span></span></span></span></p>
<p style="margin:0in 0in 10pt"><span style="font-size:11pt"><span style="line-height:115%"><span style="font-family:"Calibri","sans-serif""><span style="font-size:12.0pt"><span style="line-height:115%">André</span></span></span></span></span><br>
---</p>
<br>
André Michaud<br>
"GSJournal admin" <<a href="mailto:ntham@gsjournal.net" target="_blank">ntham@gsjournal.net</a>><br>
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<span>On Sun, 29 Jul 2018 06:08:32 -0400, Andrew Meulenberg wrote:</span><br>
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<div>Dear Richard,</div>
<div> </div>
<div>Thank you for looking that up. The words you highlighted in the abstract are almost exactly like what I remember. I suspect that I read them in "The Atomic Nucleus" by Evans (1982), which was often a "Bible" for me in my work; but, I may have encountered the info earlier.</div>
<div> </div>
<div>The main point is that the curvature of the photon path during its "division" in passing by a charge can be quite different for the electron interaction compared with that from a nucleus. This puts some light (and limits) on the models for conversion of light to matter.</div>
<div> </div>
<div>Andrew</div>
</div>
<div class="gmail_extra">
<div class="gmail_quote">On Sun, Jul 29, 2018 at 2:28 AM, <span dir="ltr"><<a href="mailto:richgauthier@gmail.com" target="_blank">richgauthier@gmail.com</a>></span> wrote:
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div style="word-wrap:break-word;line-break:after-white-space">Hello Andrew (and all),
<div> The below abstract from <a href="https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2006RaPC...75..614H&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368784038&sdata=ZhaaCuAlBx%2BD0QAVLexyQ8kO41MR%2FGmvb7QrpHQOsTQ%3D&reserved=0" target="_blank"> http://adsabs.harvard.edu/abs/2006RaPC...75..614H</a> supports your comment about pair production in photon-electron interactions.</div>
<div> Richard</div>
<div> </div>
<div>
<table style="font-family:-webkit-standard;background-color:rgb(255,255,255)">
<tbody>
<tr>
<td valign="top" align="left"><b>Title:</b></td>
<td> </td>
<td valign="top" align="left">Electron positron pair production by photons: A historical overview</td>
</tr>
<tr>
<td valign="top" align="left"><b>Authors:</b></td>
<td> </td>
<td valign="top" align="left"><a href="https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fadsabs.harvard.edu%2Fcgi-bin%2Fauthor_form%3Fauthor%3DHubbell%2C%2BJ%26fullauthor%3DHubbell%2C%2520J.%2520H.%26charset%3DUTF-8%26db_key%3DPHY&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368784038&sdata=Ic9NsCEom2NNJBBy9Ysg7XQVAO45oVG%2F4jCB%2FKrysrA%3D&reserved=0" style="color:rgb(64,0,160)" target="_blank">Hubbell, J. H.</a></td>
</tr>
<tr>
<td valign="top" align="left"><b>Affiliation:</b></td>
<td> </td>
<td valign="top" align="left">AA(National Institute of Standards and Technology, Mail Stop 8463, Gaithersburg, MD 20899-8463, USA.)</td>
</tr>
<tr>
<td valign="top" align="left"><b>Publication:</b></td>
<td> </td>
<td valign="top" align="left">Radiation Physics and Chemistry, Volume 75, Issue 6, p. 614-623.</td>
</tr>
<tr>
<td valign="top" align="left"><b>Publication Date:</b></td>
<td> </td>
<td valign="top" align="left">06/2006</td>
</tr>
<tr>
<td valign="top" align="left"><b>Origin:</b></td>
<td> </td>
<td valign="top" align="left"><a href="https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.elsevier.com%2F&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368794051&sdata=M98OE92Qya3E7RJECgcpIhUT7oNjmf6FbSbgrfr%2ByM0%3D&reserved=0" style="color:rgb(64,0,160)" target="_blank">ELSEVIER</a></td>
</tr>
<tr>
<td valign="top" align="left"><b>Abstract Copyright:</b></td>
<td> </td>
<td valign="top" align="left">(c) 2006 Elsevier Science B.V. All rights reserved.</td>
</tr>
<tr>
<td valign="top" align="left"><b>DOI:</b></td>
<td> </td>
<td valign="top" align="left"><a href="https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdoi.org%2F10.1016%2Fj.radphyschem.2005.10.008&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368794051&sdata=EMRxjvup2k1mzhFgHx6NW8VY%2BJCIyGtsehs%2BGjmFaG4%3D&reserved=0" style="color:rgb(64,0,160)" target="_blank">10.1016/j.radphyschem.2005.10.008</a></td>
</tr>
<tr>
<td valign="top" align="left"><b>Bibliographic Code:</b></td>
<td> </td>
<td valign="top" align="left"><a href="https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fadsabs.harvard.edu%2Fabs%2F2006RaPC...75..614H&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368804059&sdata=20rE2Qa4XJnvMhyV4jzHv6ncDFnQ7fqsZYcAlihVjzU%3D&reserved=0" style="color:rgb(64,0,160)" target="_blank">2006RaPC...75..614H</a></td>
</tr>
</tbody>
</table>
<h3 style="font-family:-webkit-standard;background-color:rgb(255,255,255)" align="center">Abstract</h3>
<span style="font-family:-webkit-standard;font-size:medium;background-color:rgb(255,255,255)">This account briefly traces the growth of our theoretical and experimental knowledge of electron-positron pair production by photons, from the prediction of the positron by Dirac [1928a. The quantum theory of the electron. Proc. R. Soc. (London) A 117, 610-624; 1928b. The quantum theory of the electron. Part II. Proc. R. Soc. (London) A 118, 1928b, 351-361] and subsequent cloud-chamber observations by Anderson [Energies of cosmic-ray particles. Phys. Rev. 43, 491-494], up to the present time. Photons of energies above 2 m</span><sub style="font-family:-webkit-standard;background-color:rgb(255,255,255)">e</sub><span style="font-family:-webkit-standard;font-size:medium;background-color:rgb(255,255,255)">c</span><sup style="font-family:-webkit-standard;background-color:rgb(255,255,255)">2</sup><span style="font-family:-webkit-standard;font-size:medium;background-color:rgb(255,255,255)"> (1.022 MeV) can interact with the Coulomb field of an atomic nucleus to be transformed into an electron-positron pair, the probability increasing with increasing photon energy, up to a plateau at high energies, and increasing with increasing atomic number approximately as the square of the nuclear charge (proton number). <b>This interaction can also take place in the field of an atomic electron, for photons of energy in excess of 4 m</b></span><b><sub style="font-family:-webkit-standard;background-color:rgb(255,255,255)">e</sub><span style="font-family:-webkit-standard;font-size:medium;background-color:rgb(255,255,255)">c</span><sup style="font-family:-webkit-standard;background-color:rgb(255,255,255)">2</sup></b><span style="font-family:-webkit-standard;font-size:medium;background-color:rgb(255,255,255)"><b> (2.044 MeV), in which case the process is called triplet production due to the track of the recoiling atomic electron adding to the tracks of the created electron-positron pair.</b> The last systematic computations and tabulations of pair and triplet cross sections, which are the predominant contributions to the photon mass attenuation coefficient for photon energies 10 MeV and higher, were those of Hubbell et al. [Pair, triplet, and total atomic cross sections (and mass attenuation coefficients) for 1 MeV-100 GeV photons in elements Z=1-100. J. Phys. Chem. Ref. Data 9, 1023-1147], from threshold (1.022 MeV) up to 100 GeV, for all elements Z=1-100. These computations required some ad hoc bridging functions between the available low-energy and high-energy theoretical models. Recently (1979-2001), Sud and collaborators have developed some new approaches including using distorted wave Born approximation (DWBA) theory to compute pair production cross sections in the intermediate energy region (5.0-10.0 MeV) on a firmer theoretical basis. These and other recent developments, and their possible implications for improved computations of pair and triplet cross sections, are discussed.</span>
<div>
<div class="m_-4007217526553906849h5">
<div>
<blockquote type="cite">
<div>On Jul 27, 2018, at 3:28 AM, Andrew Meulenberg <<a href="mailto:mules333@gmail.com" target="_blank">mules333@gmail.com</a>> wrote:</div>
<div>
<div dir="ltr" style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:normal;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px">
<div>Dear Richard,</div>
<div> </div>
<div>I realize that I might not have been clear enough in my statement about the scattering charge being a lepton rather than a proton or nucleus. And, my mistake in using the expression for<span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span><span style="color:rgb(17,17,17);font-family:Roboto,Arial,sans-serif;font-size:14px;text-align:left;background-color:rgb(255,255,255);float:none;display:inline">Eγ</span> certainly did not help the situation. You (and the reference) were focusing on the minimum energy threshold for pair production and the difficulties associated with the low production rates near the threshold. I was looking at the other end of the question where a light scattering center (e.g., an electron) makes energy and momentum conservation have a much greater effect.</div>
<div> </div>
<div>My memory of photon energy threshold >2 MeV for pair creation from a collision with an electron is consistent with<span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span><span style="color:rgb(17,17,17);font-family:Roboto,Arial,sans-serif;font-size:14px;text-align:left;background-color:rgb(255,255,255);float:none;display:inline">Eγ ≥ 2 mec (1 + me/mr)</span> = 4 mec = 2.044 MeV. This may only have been based on theoretical calculation. I'm not sure that there was any definitive experimental work to support it. However, the recoiling electron from this interaction would be energetic enough to give good confirming information. I'm not sure that Compton scattering would not interfere with the experiment.</div>
<div> </div>
<div>Andrew</div>
<div> </div>
<div> </div>
<div> </div>
<div>
<div class="gmail_extra">
<div class="gmail_quote">On Thu, Jul 26, 2018 at 10:04 AM,<span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span><span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span><span dir="ltr"><<a href="mailto:richgauthier@gmail.com" target="_blank">richgauthier@gmail.com</a>></span><span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span>wrote:
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
<div style="word-wrap:break-word;line-break:after-white-space">Hi Andrew and all,
<div> <span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span>Below is a pdf copy of the article <a href="https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F235335367_The_Miracle_of_the_Electron-Positron_Pair_Production_Threshold&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368804059&sdata=iVz71uH04xB8So0UO7004Le3X9To%2BXATlwlRkOVoggw%3D&reserved=0" target="_blank">https://www.researchgate.net/publication/235335367_The_Miracle_of_the_Electron-Positron_Pair_Production_Threshold</a> <span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span>with the abstract (below) you are quoting from. Definitely the minimum incoming photon energy is much less than 2 MeV and much nearer to the quoted value. It turns out that it’s very hard (as explained in the article) to experimentally confirm the minimum photon energy value for a particular recoil nuclear mass, given by the formula, so there’s surprisingly much experimental (and perhaps theoretical also) work still needed on this relatively straightforward conversion process of a photon to an electron-positron pair.</div>
<div><span class="m_-4007217526553906849m_32599331786726808HOEnZb"><font color="#888888"> <span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span>Richard</font></span></div>
<div> </div>
</div>
<div style="word-wrap:break-word;line-break:after-white-space">
<div> </div>
<div>
<div>
<blockquote type="cite">
<div>On Jul 25, 2018, at 9:36 PM, Andrew Meulenberg <<a href="mailto:mules333@gmail.com" target="_blank">mules333@gmail.com</a>> wrote:</div>
<div>
<div dir="ltr">
<div> </div>
<div>Note that the threshold energy for pair production "... given by<span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span><span style="color:rgb(17,17,17);font-family:Roboto,Arial,sans-serif;font-size:14px;text-align:left;background-color:rgb(255,255,255);float:none;display:inline">the relation Eγ ≥ 2 mec (1 + me/mr), where mr is the mass of the recoiling particle</span>," gives > 1 MeV for an electron or positron. My memory said that a >2 MeV photon was required. It may be related to the angle of recoiI. I don't have time to look it up.</div>
<div> </div>
<div>Andrew</div>
</div>
<div class="gmail_extra">
<div class="gmail_quote">On Tue, Jul 24, 2018 at 1:35 PM, Richard Gauthier<span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span><span dir="ltr"><<a href="mailto:richgauthier@gmail.com" target="_blank">richgauthier@gmail.com</a>></span><span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span>wrote:
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
<div dir="ltr">Hi Chip and all,
<div> <span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span>Here's a little background on experimental pair production from the abstract to an article on<span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span><a href="https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fresearchgate.net%2F&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368814063&sdata=j19qTH1qlbtqEx2KUXM1W728mOTtyEZgDNcaFLCLuGk%3D&reserved=0" target="_blank">Researchgate.net</a><span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span>at <a href="https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F235335367_The_Miracle_of_the_Electron-Positron_Pair_Production_Threshold&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368824072&sdata=qj81KsSgsqtZbO3uWGwxjncHFKSQmBobqxxhiEbPWvA%3D&reserved=0" target="_blank">https://www.researchgate.net/publication/235335367_The_Miracle_of_the_Electron-Positron_Pair_Production_Threshold</a> </div>
<div> <span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span>Richard</div>
<div> </div>
<div> </div>
<div><span style="color:rgb(17,17,17);font-family:Roboto,Arial,sans-serif;font-size:14px;text-align:left;background-color:rgb(255,255,255);float:none;display:inline">Pair production was first observed in 1932, which led to two early Nobel prizes in physics, to Carl Anderson for the discovery of positrons (1936) and to Paul Dirac for the theory of anti particles (1933). Science textbooks state that the production of electron-positron pairs is possible at photon energies above 1.022 MeV, which is the sum of the rest masses of the particles involved. Measurements at the threshold require a selectable photon energy in the range above 1 MeV, high-energy resolution to scan the onset, and high intensities. Due to the need of simultaneous energy and momentum conservation, pair production needs a recoiling particle, and thus it can be observed most easily in solid matter. More exactly, the minimum energy required for pair production is given by the relation Eγ ≥ 2 mec (1 + me/mr), where mr is the mass of the recoiling particle [1]. With the particle rest energy of me = 511 keV/c , in heavy atoms we get mr >> me, and thus in a good approximation photon energies Eγ ≥ 2·mec = 1.022 keV allow the creation of electron-positron pairs. However, for a proton as recoil particle the calculated threshold energy is increased by 557 eV, for a copper target by 9 eV, and even for the very heavy element 111Roentgenium by about 2.1 eV. Thus pair production cannot take place at exactly 2ámec.</span><span class="m_-4007217526553906849m_32599331786726808Apple-converted-space"> </span></div>
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