<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><font face="Times New Roman" class=""><span style="font-size: 14px;" class="">Hello Andrew and all,</span></font><br class=""><div class=""><br class=""></div><div class=""><span class="js-non-expanded-comment" style="box-sizing: border-box; color: rgb(73, 72, 72); font-family: Georgia, serif; font-size: 14px; white-space: pre-wrap;"> A physics colleague who reviewed my earlier electron and photon work on his blog Renaissance Universal asked for information to help compare my older work to the double-helix photon model and the quantum vortex electron model. I'm sharing what I replied below.
Richard
Thanks for your detailed look into the new photon and electron models. Your earlier article “A guide to Richard Gauthier’s electron models” at </span><span class="js-non-expanded-comment"><span style="font-size:
10.5pt;font-family:Georgia;mso-fareast-font-family:"Times New Roman";
color:#494848" class=""><a href="https://sureshemre.wordpress.com/2016/11/15/a-guide-to-richard-gauthiers-electron-models/" class="">https://sureshemre.wordpress.com/2016/11/15/a-guide-to-richard-</a></span></span><span class="js-expanded-comment"><span style="font-size:10.5pt;font-family:Georgia;
mso-fareast-font-family:"Times New Roman";color:#494848" class=""><a href="https://sureshemre.wordpress.com/2016/11/15/a-guide-to-richard-gauthiers-electron-models/" class="">gauthiers-electron-models/</a> </span></span><span style="color: rgb(73, 72, 72); font-family: Georgia, serif; font-size: 14px; white-space: pre-wrap;" class=""> was written before either my double-helix photon model article or my quantum-vortex electron model article (which followed rather quickly after). Both models are significant improvements with significant differences over my one-superluminal-energy-quantum photon model and my previous (spindle torus) transluminal-energy-quantum (TEQ) electron model. Here I summarize some of the properties of the double-helix photon and quantum vortex electron models, in comparison to the earlier models. (I actually first developed the double-helix photon model in 2002 and published it, before going on to the single-helix photon model because of lack of experimental evidence for a composite photon.)</span></div><div class=""><span class="js-expanded-comment" style="box-sizing: border-box; color: rgb(73, 72, 72); font-family: Georgia, serif; font-size: 14px; white-space: pre-wrap;">
1) The charged-dipole double-helix photon model has stability (due to Coulomb attraction) that the uncharged single-helix photon model could not demonstrate.
2) The 2 TEQ’s in the double-helix photon are oppositely charged (+and - e sqrt(2/alpha) = 16.6e) while the single-helix photon model was uncharged. The possible QED connection to alpha in the double-helix photon model is intriguing.
3) The double-helix photon conserves total momentum and is held together by the Coulomb attractive force as the two oppositely-charged superluminal energy quanta circle helically due to this attractive force.
4) The double-helix photon’s two half-photons (each composed of one superluminal quantum) are proposed to be quantum mechanically entangled (share quantum wave functions) so that the double-helix photon acts like a single spin-1 particle.
5) The quantum vortex electron model for a resting electron has a closed helix trajectory of wavelength 1/2 Compton wavelength rather than a double-looping 1 Compton wavelength trajectory.
6) The quantum vortex electron is stable because the quantum waves of the circulating half-photon interfere constructively after each closed helical loop. And the quantum vortex electron model is also stable because it (like the actual electron) would have to violate conservation laws such as conservation of charge or other conservation laws in order to spontaneously transform to one or more other known particles.
7) The frequency of a 1/2 Compton wavelength (1/2 h/mc) photon is the zitterbewegung frequency f=2mc^2/h which is the same frequency as the photon of minimum energy E=2mc^2 from which an electron/positron pair is produced in pair production.
8) The wavelength Lambda and helical radius Lambda/2pi of the quantum vortex electron are also the same as that of each of the spin-1/2 charged half-photons from the double-helix photon model from which the quantum-vortex e-p pair is derived. This is also true for higher energy photons E=2 gamma m c^2 which produce an electron and positron of energy E=gamma mc^2 for a relativistic electron/positron pair.
9) The wavelength Lambda and helical radius Lambda/2pi of the circulating double-helix photon that produces an e-p pair, and of the the relativistic quantum vortex electron and positron produced, both decrease as 1/gamma in relation their values required for a rest electron-positron. Both the double-helix photon frequency and quantum vortex frequency increase proportional to gamma: f=2 gamma mc^2/h for the photon producing an e-p pair and f=2 gamma mc^2/h for the relativistic quantum vortex electron.
10) The radius of the helical axis of the circling quantum helix in the resting quantum vortex electron decreases as 1/gamma^2 as the quantum vortex model moves relativistically. This relationship was predicted in my "spin 1/2 charged photon model of the electron” (Figure 4 in the quantum vortex electron article). The proposed “spin-1/2 charged photonl" of the previously proposed electron model has been renamed the "spin-1/2 charged half-photon" of the quantum vortex electron model.
11) In a moving or relativistic quantum vortex electron, the helical vortex motion of the superluminal quantum’s helical trajectory is not completely closed due to the linear velocity of the model as its internal superluminal quantum circulates. It is more and more open as the speed of the quantum vortex electron increases relativistically.
12) The superluminal quantum in the quantum vortex electron moves along the surface of a mathematical horn torus. The mathematical torus moves (and contracts) along with the relativistic electron model on its surface. Any closed helix lies on the surface of a mathematical torus, but the quantum vortex electron’s torus is a horn torus.
13) The speed of the superluminal quantum in a resting quantum vortex electron varies from c sqrt(5) to c.
14) Generation of an e-p quantum vortex model pair from a double-helix photon model seems like it could be a continuous process, with the double helix opening separating and the two charged half-photons separately forming into an e-p pair (charge drops from 16.6 e to e in the process.
15) The drop of electric charge from -16.6e and +16.6 e from the double-helix photon model to -1e and +e on the electron/positron models could help the helically moving TEQ’s to separate when forming e-p pair due to the decreased Coulomb attractive force between the rapidly rotating energy quanta compared to when they form the double-helix photon.
16) The quantum vortex electron is like a stable “ground state” particle (similar to the stable ground state energy level of the electron in an atom), as compared to a less stable quantum-vortex muon or quantum-vortex tau in the electron family, which would also have some stability due to their constructive self-interference of their own 1/2 Compton wavelength (h/mc calculated for their muon or tau mass) but are unstable due to having decay pathways in to other particles, that don’t violate conservation laws.</span><br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Jul 30, 2018, at 7:16 AM, André Michaud <<a href="mailto:srp2@srpinc.org" class="">srp2@srpinc.org</a>> wrote:</div><br class="Apple-interchange-newline"><div class="">
<title class=""></title>
<div class="">
<div class="userStyles" style="font-family: Arial; font-size: 12pt;"><div style="margin: 0in 0in 0.0001pt;" class=""><span style="font-size:12pt" class=""><span style="font-family:"Times New Roman","serif"" class="">Dear Chandra,</span></span></div><p style="margin:0in 0in 0.0001pt" class=""> </p><div style="margin: 0in 0in 0.0001pt;" class=""><span style="font-size:12pt" class=""><span style="font-family:"Times New Roman","serif"" class="">I have no personal interpretation of these experiments carried out at SLAC.</span></span></div><p style="margin:0in 0in 0.0001pt" class=""> </p><div style="margin: 0in 0in 0.0001pt;" class=""><span style="font-size:12pt" class=""><span style="font-family:"Times New Roman","serif"" class="">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 class="">
<br class="">
The process appears to have been successfully recorded a sufficient number of times to be accepted as significant to the peer-reviewers.</span></span></div><p style="margin:0in 0in 0.0001pt" class=""> </p><div style="margin: 0in 0in 0.0001pt;" class=""><span style="font-size:12pt" class=""><span style="font-family:"Times New Roman","serif"" class="">The description in the related documentation is there for anyone to do his own study and interpretation. </span></span></div><p style="margin:0in 0in 0.0001pt" class=""> </p><div style="margin: 0in 0in 0.0001pt;" class=""><span style="font-size:12pt" class=""><span style="font-family:"Times New Roman","serif"" class="">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></div><p style="margin:0in 0in 0.0001pt" class=""> </p><div style="margin: 0in 0in 0.0001pt;" class=""><span style="font-size:12pt" class=""><span style="font-family:"Times New Roman","serif"" class="">I am satisfied with the interpretation made by the McDonald team.</span></span></div><p style="margin:0in 0in 0.0001pt" class=""> </p><div style="margin: 0in 0in 0.0001pt;" class=""><span style="font-size:12pt" class=""><span style="font-family:"Times New Roman","serif"" class="">Best Regards</span></span></div><p style="margin:0in 0in 0.0001pt" class=""> </p><div style="margin: 0in 0in 0.0001pt;" class=""><span style="font-size:12pt" class=""><span style="font-family:"Times New Roman","serif"" class="">André</span></span></div>
<footer class="signatureDivContainer">
<footer class="signatureContainer" style="display:inline;">---<br class="">
André Michaud<br class="">
"GSJournal admin" <<a href="mailto:ntham@gsjournal.net" class="">ntham@gsjournal.net</a>><br class="">
<a href="http://www.gsjournal.net/" class="">http://www.gsjournal.net/</a><br class="">
<a href="https://orcid.org/0000-0003-2740-5684" class="">https://orcid.org/0000-0003-2740-5684</a><br class="">
<a href="http://www.srpinc.org/" class="">http://www.srpinc.org/</a></footer>
</footer>
<footer class="replyforwardcontainer"><br class="">
<br class="">
<span class="">On Mon, 30 Jul 2018 01:53:39 +0000, "Roychoudhuri, Chandra" <chandra.roychoudhuri@uconn.edu class=""> wrote:</chandra.roychoudhuri@uconn.edu></span><br class="">
<br class="">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" class=""> Andre:
<div class="">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 class="">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 class=""> How come there is no photon-Photon interaction to generate particles?</div>
<div class="">If my observation is backdated, kindly send me a recent reference. </div>
<div class="">Chandra.<br class="">
<div class="">Sent from my iPhone</div>
<div class=""><br class="">
On Jul 29, 2018, at 2:58 PM, André Michaud <<a href="mailto:srp2@srpinc.org" class="">srp2@srpinc.org</a>> wrote:<br class="">
</div>
<blockquote type="cite" class="">
<div class=""> </div>
</blockquote>
</div>
</div>
</footer>
</div>
<title class=""></title>
<div class="userStyles" style="font-family: Arial; font-size: 12pt;"><p style="margin:0in 0in 10pt" class=""><span style="font-size:11pt" class=""><span style="line-height:115%" class=""><span style="font-family:"Calibri","sans-serif"" class=""><span style="font-size:12.0pt" lang="EN-US" class=""><span style="line-height:115%" class="">Dear Andrew,</span></span></span></span></span></p><p style="margin:0in 0in 10pt" class=""><span style="font-size:11pt" class=""><span style="line-height:115%" class=""><span style="font-family:"Calibri","sans-serif"" class=""><span style="font-size:12.0pt" lang="EN-US" class=""><span style="line-height:115%" class="">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" class=""><span style="font-size:11pt" class=""><span style="line-height:115%" class=""><span style="font-family:"Calibri","sans-serif"" class=""><span style="font-size:12.0pt" class=""><span style="line-height:115%" class=""><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" originalsrc="https://www.researchgate.net/deref/http%3A%2F%2Fwww.slac.stanford.edu%2Fexp%2Fe144%2F" shash="Hqs2MqD8pE/E2KxGBFQ8G9XWh8cQgv5gS+DfpSopZTpXO7BMEdr5r2247/HZzKiLaJ6NMH1cad34qI2JWcnSS0r5wC7GsBuca+FA/RtPGJBa81XxoswM4aAINlbWaIM/WwNfo6D8ei8OtN3m5nDCaJUIFkqsM1d24TlZItsbqtg=" style="color:blue; text-decoration:underline" target="_blank" class="">http://www.slac.stanford.edu/exp/e144/</a></span></span></span></span></span></p><p style="margin:0in 0in 10pt" class=""><span style="font-size:11pt" class=""><span style="line-height:115%" class=""><span style="font-family:"Calibri","sans-serif"" class=""><span style="font-size:12.0pt" lang="EN-US" class=""><span style="line-height:115%" class="">Best Regards</span></span></span></span></span></p><p style="margin:0in 0in 10pt" class=""><span style="font-size:11pt" class=""><span style="line-height:115%" class=""><span style="font-family:"Calibri","sans-serif"" class=""><span style="font-size:12.0pt" class=""><span style="line-height:115%" class="">André</span></span></span></span></span><br class="">
---</p>
<br class="">
André Michaud<br class="">
"GSJournal admin" <<a href="mailto:ntham@gsjournal.net" class="">ntham@gsjournal.net</a>><br class="">
<a href="http://www.gsjournal.net/" class="">http://www.gsjournal.net/</a><br class="">
<a href="https://orcid.org/0000-0003-2740-5684" class="">https://orcid.org/0000-0003-2740-5684</a><br class="">
<a href="http://www.srpinc.org/" class="">http://www.srpinc.org/</a><br class="">
<br class="">
<span class="">On Sun, 29 Jul 2018 06:08:32 -0400, Andrew Meulenberg <mules333@gmail.com class="">wrote:</mules333@gmail.com></span><br class="">
<div dir="ltr" class="">
<div class="">Dear Richard,</div>
<div class=""> </div>
<div class="">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 class=""> </div>
<div class="">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 class=""> </div>
<div class="">Andrew</div>
</div>
<div class="gmail_extra">
<div class="gmail_quote">On Sun, Jul 29, 2018 at 2:28 AM, <span dir="ltr" class=""><<a href="mailto:richgauthier@gmail.com" target="_blank" class="">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" class="">Hello Andrew (and all),
<div class=""> 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" originalsrc="http://adsabs.harvard.edu/abs/2006RaPC...75..614H" shash="S6F388unRntXoIaoktycmZdS6x9+qiy4DjkNIWkR+U1euNdGev3hCsEJcbjTbt9oNKtSZ4cJhLIbUi7xwFuOWYneVYgFR6Jh8A3Xxb4S+FDABIRqxzOOIfIA7R1HD8xDVYTudUPyIqWxh4gU+cLOUW4WHwhG5aQhlBcyvhxcVd8=" target="_blank" class=""> http://adsabs.harvard.edu/abs/<wbr class="">2006RaPC...75..614H</a> supports your comment about pair production in photon-electron interactions.</div>
<div class=""> Richard</div>
<div class=""> </div>
<div class="">
<table style="font-family:-webkit-standard;background-color:rgb(255,255,255)" class="">
<tbody class="">
<tr class="">
<td valign="top" align="left" class=""><b class="">Title:</b></td>
<td class=""> </td>
<td valign="top" align="left" class="">Electron positron pair production by photons: A historical overview</td>
</tr>
<tr class="">
<td valign="top" align="left" class=""><b class="">Authors:</b></td>
<td class=""> </td>
<td valign="top" align="left" class=""><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" originalsrc="http://adsabs.harvard.edu/cgi-bin/author_form?author=Hubbell,+J&fullauthor=Hubbell,%20J.%20H.&charset=UTF-8&db_key=PHY" shash="x8SDr6wsVOyuItI42+wLDXtCeIJRtVczYjztAurgLDrdYr15S1qvPCUmhM1va+nfcOTOp0DpMQoIu1l3Rq8y38vJllnZZr3xPibfkSzvgW1VDL7dzdxBC6YPsHn0TtYnxEcPa+Ua0PssvkWbZXss427SMZl49d6IeDMoY30uwzk=" style="color:rgb(64,0,160)" target="_blank" class="">Hubbell, J. H.</a></td>
</tr>
<tr class="">
<td valign="top" align="left" class=""><b class="">Affiliation:</b></td>
<td class=""> </td>
<td valign="top" align="left" class="">AA(National Institute of Standards and Technology, Mail Stop 8463, Gaithersburg, MD 20899-8463, USA.)</td>
</tr>
<tr class="">
<td valign="top" align="left" class=""><b class="">Publication:</b></td>
<td class=""> </td>
<td valign="top" align="left" class="">Radiation Physics and Chemistry, Volume 75, Issue 6, p. 614-623.</td>
</tr>
<tr class="">
<td valign="top" align="left" class=""><b class="">Publication Date:</b></td>
<td class=""> </td>
<td valign="top" align="left" class="">06/2006</td>
</tr>
<tr class="">
<td valign="top" align="left" class=""><b class="">Origin:</b></td>
<td class=""> </td>
<td valign="top" align="left" class=""><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" originalsrc="http://www.elsevier.com/" shash="vHKRdX8i7Y93a/F+Mz/Bqn72MRiDDTALH08FbuOtxzWYPnvf6iAsPnAHv/JGRVyxabZcV7arMIpVUWFsGrtYsqzAtxgvqgwRn7dTSYh1u28QvsACq8X1iBbpj2kySMlFgSlLOLVdI3ExAJpsgySq16Iyg042pEzESsxPqAgeYS4=" style="color:rgb(64,0,160)" target="_blank" class="">ELSEVIER</a></td>
</tr>
<tr class="">
<td valign="top" align="left" class=""><b class="">Abstract Copyright:</b></td>
<td class=""> </td>
<td valign="top" align="left" class="">(c) 2006 Elsevier Science B.V. All rights reserved.</td>
</tr>
<tr class="">
<td valign="top" align="left" class=""><b class="">DOI:</b></td>
<td class=""> </td>
<td valign="top" align="left" class=""><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" originalsrc="https://doi.org/10.1016/j.radphyschem.2005.10.008" shash="t+Y/4oa01GICxjW1Hk3zbHqdeJgsDKilyOwNYQH4b+j2fCIAsw5lyy5Ach39RR3WegZGlFQY2XFkZDfxuwhZM67MJhZxa9jUkfUOOqJFedfo+KxHfJFqxe72C6CSSN6bzYXrk6731t/AUhkJ4cLscYwFo81xGrTLnFeGHrbU5DQ=" style="color:rgb(64,0,160)" target="_blank" class="">10.1016/j.radphyschem.2005.10.<wbr class="">008</a></td>
</tr>
<tr class="">
<td valign="top" align="left" class=""><b class="">Bibliographic Code:</b></td>
<td class=""> </td>
<td valign="top" align="left" class=""><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" originalsrc="http://adsabs.harvard.edu/abs/2006RaPC...75..614H" shash="utLdQK8b1oGKTaUwa903CpwBUIOKuw000/Hcl8FNsmJLcFY+evAYmqDPOQEc/IFYmwKtDDb9av2el/jt8gRxMWMQdvUELfx0eVZ9Q2tIdbbDJoF3i14S1uVEvTBJGT+/uthH5pfYw5k1MAai0otX7YWz3xzPIw0g5fPgaTGhEaU=" style="color:rgb(64,0,160)" target="_blank" class="">2006RaPC...75..614H</a></td>
</tr>
</tbody>
</table>
<h3 style="font-family:-webkit-standard;background-color:rgb(255,255,255)" align="center" class="">Abstract</h3>
<span style="font-family: -webkit-standard; font-size: 12px; background-color: rgb(255, 255, 255);" class="">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)" class="">e</sub><span style="font-family: -webkit-standard; font-size: 12px; background-color: rgb(255, 255, 255);" class="">c</span><sup style="font-family:-webkit-standard;background-color:rgb(255,255,255)" class="">2</sup><span style="font-family: -webkit-standard; font-size: 12px; background-color: rgb(255, 255, 255);" class=""> (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 class="">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 class=""><sub style="font-family:-webkit-standard;background-color:rgb(255,255,255)" class="">e</sub><span style="font-family: -webkit-standard; font-size: 12px; background-color: rgb(255, 255, 255);" class="">c</span><sup style="font-family:-webkit-standard;background-color:rgb(255,255,255)" class="">2</sup></b><span style="font-family: -webkit-standard; font-size: 12px; background-color: rgb(255, 255, 255);" class=""><b class=""> (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 class="">
<div class="h5">
<div class="">
<blockquote type="cite" class="">
<div class="">On Jul 27, 2018, at 3:28 AM, Andrew Meulenberg <<a href="mailto:mules333@gmail.com" target="_blank" class="">mules333@gmail.com</a>> wrote:</div>
<div class="">
<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" class="">
<div class="">Dear Richard,</div>
<div class=""> </div>
<div class="">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_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" class="">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 class=""> </div>
<div class="">My memory of photon energy threshold >2 MeV for pair creation from a collision with an electron is consistent with<span class="m_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" class="">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 class=""> </div>
<div class="">Andrew</div>
<div class=""> </div>
<div class=""> </div>
<div class=""> </div>
<div class="">
<div class="gmail_extra">
<div class="gmail_quote">On Thu, Jul 26, 2018 at 10:04 AM,<span class="m_32599331786726808Apple-converted-space"> </span><span class="m_32599331786726808Apple-converted-space"> </span><span dir="ltr" class=""><<a href="mailto:richgauthier@gmail.com" target="_blank" class="">richgauthier@gmail.com</a>></span><span class="m_32599331786726808Apple-converted-space"> </span><wbr class="">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" class="">Hi Andrew and all,
<div class=""> <span class="m_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" originalsrc="https://www.researchgate.net/publication/235335367_The_Miracle_of_the_Electron-Positron_Pair_Production_Threshold" shash="RSixIXxqfnIcGmu/8mowxGjmB08DKF78I/ejkqilBhqooM5MXqQEylh3gaE147fJmR7RX08Jj9RUxAek6ch51BW5Ov+QfRAe5zcLCUUdJJrZvEoz3v/BB6aOD7nWcrMUg0uTQ4iZuojFjfacbYMsGg1O5HdcRPvumr7+YKj7uQE=" target="_blank" class="">https://www.researchga<wbr class="">te.net/publication/235335367_<wbr class="">The_Miracle_of_the_Electron-<wbr class="">Positron_Pair_Production_<wbr class="">Threshold</a> <span class="m_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 class=""><span class="m_32599331786726808HOEnZb"><font color="#888888" class=""> <span class="m_32599331786726808Apple-converted-space"> </span>Richard</font></span></div>
<div class=""> </div>
</div>
<div style="word-wrap:break-word;line-break:after-white-space" class="">
<div class=""> </div>
<div class="">
<div class="">
<blockquote type="cite" class="">
<div class="">On Jul 25, 2018, at 9:36 PM, Andrew Meulenberg <<a href="mailto:mules333@gmail.com" target="_blank" class="">mules333@gmail.com</a>> wrote:</div>
<div class="">
<div dir="ltr" class="">
<div class=""> </div>
<div class="">Note that the threshold energy for pair production "... given by<span class="m_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" class="">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 class=""> </div>
<div class="">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_32599331786726808Apple-converted-space"> </span><span dir="ltr" class=""><<a href="mailto:richgauthier@gmail.com" target="_blank" class="">richgauthier@gmail.<wbr class="">com</a>></span><span class="m_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" class="">Hi Chip and all,
<div class=""> <span class="m_32599331786726808Apple-converted-space"> </span>Here's a little background on experimental pair production from the abstract to an article on<span class="m_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" originalsrc="http://researchgate.net/" shash="fzpBzY8TW0EZRsBBBf/BlM9WD4jSbdjf9r4ves9filAIDZCyGzJU0AeNHetA5zVz5Otfgwvoky3BZS2v1j6Jw0qqbxY9Va1+YZSAYGVE68Z9CFDq+IoznpEEW8itKV7u/EE5ZjKEwerMp6a5Ht0oJFCTABkUKEv1RAEQ97AP0so=" target="_blank" class="">Researchgate.net</a><span class="m_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" originalsrc="https://www.researchgate.net/publication/235335367_The_Miracle_of_the_Electron-Positron_Pair_Production_Threshold" shash="eGIt0AdOKsUVVn+RCvbgoUshbVks06XJ88cTag1cfLAEwefy+IpHlVkhsy7ivHrmM65NUwtDOwJbCc69CtfMhdL0P/tXocvixMGADt1DOGOG0bcj9EmWz7AX90/e/Asf8ix8PSk9r7OY1+VzGSbI2VjcwkZgHWXmATS8bmZb5sA=" target="_blank" class="">https:/<wbr class="">/www.researchgate.net/<wbr class="">publication/235335367_The_Mira<wbr class="">cle_of_the_Electron-Positron_<wbr class="">Pair_Production_Threshold</a> </div>
<div class=""> <span class="m_32599331786726808Apple-converted-space"> </span>Richard</div>
<div class=""> </div>
<div class=""> </div>
<div class=""><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" class="">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_32599331786726808Apple-converted-space"> </span></div>
</div>
<br class="">
______________________________<wbr class="">_________________<br class="">
If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at<span class="m_32599331786726808Apple-converted-space"> </span><a href="mailto:mules333@gmail.com" target="_blank" class="">mules333@gmail.com</a><br class="">
<a href="<a href="https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flists.natureoflightandparticles.org%2Foptions.cgi%2Fgeneral-natureoflightandparticles.org%2Fmules333%2540gmail.com%3Funsub%3D1%26unsubconfirm%3D1&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368824072&sdata=9Gw9kLki%2BWyK7RdCMGDPBDjSqV%2FZh7nFCh6%2BuE2X1OM%3D&reserved=0" originalsrc="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/mules333%40gmail.com?unsub=1&unsubconfirm=1" rel="noreferrer" shash="p13WZ38Gc0Yk8B0lcKh2wgKZBGMzNKbCk41/YOwTPJUi+y8tp7E7e+LnrcRREp5B3g/Y0HgtLq5CyU8TxFSk6vuQKIr5wjFaxZsx1d3i33zelez7wJooyb5sgOzY/aFQqRthLQH0FYPd/fiFFmraFIOadDRcjCQ253fskIPDptU=" target="_blank" class="">http://lists.natureoflig<wbr class="">htandparticles.org/options.cgi<wbr class="">/general-natureoflightandparti<wbr class="">cles.org/mules333%40gmail.com?<wbr class="">unsub=1&unsubconfirm=1</a>"><br class="">
Click here to unsubscribe<br class="">
</a><br class="">
</blockquote>
</div>
</div>
______________________________<wbr class="">_________________<br class="">
If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at<span class="m_32599331786726808Apple-converted-space"> </span><a href="mailto:richgauthier@gmail.com" target="_blank" class="">richgauthier@gmail.com</a><br class="">
<a href="<a href="https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flists.natureoflightandparticles.org%2Foptions.cgi%2Fgeneral-natureoflightandparticles.org%2Frichgauthier%2540gmail.com%3Funsub%3D1%26unsubconfirm%3D1&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368834080&sdata=QBif0kfHeq4d4aRUkFi6eOXWWTnkiMo%2Fg0oYtGi4E%2BQ%3D&reserved=0" originalsrc="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/richgauthier%40gmail.com?unsub=1&unsubconfirm=1" shash="xXYMWIWcz9YCvvTCm9jKk7O0xAe/0hSE3u1zTo7nbCgHzY1bGZ6SaqYF4SqrCy/0Mi9oLyIxFG/qhoUCFiNoPsTPT+H7vxVPZvz8LUVFrN/ejlvSY2D11qGz95AnZxzcnZFueD+hAVtx2fjHRzdGnVwLyVc/Hlue2YLcCZwhvOE=" target="_blank" class="">http://lists.natureoflig<wbr class="">htandparticles.org/options.<wbr class="">cgi/general-natureoflightandpa<wbr class="">rticles.org/richgauthier%<wbr class="">40gmail.com?unsub=1&<wbr class="">unsubconfirm=1</a>"><br class="">
Click here to unsubscribe<br class="">
</a></div>
</blockquote>
</div>
</div>
</div>
<br class="">
______________________________<wbr class="">_________________<br class="">
If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at<span class="m_32599331786726808Apple-converted-space"> </span><a href="mailto:mules333@gmail.com" target="_blank" class="">mules333@gmail.com</a><br class="">
<a href="<a href="https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flists.natureoflightandparticles.org%2Foptions.cgi%2Fgeneral-natureoflightandparticles.org%2Fmules333%2540gmail.com%3Funsub%3D1%26unsubconfirm%3D1&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368834080&sdata=t8A1ebBZQhelH%2B0md8cEafEy7qIDSzusW59405Z6OcI%3D&reserved=0" originalsrc="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/mules333%40gmail.com?unsub=1&unsubconfirm=1" rel="noreferrer" shash="fCp4xF7sR+dMWFJIjCL56hJjZQgSrQHS9ZKM01DvKtWhY31RpiitbjbZebU8mOg88rT6kGddWbNq1NdZXXki3J7wyASMMknd0944KBLhytFKwwIgw37qATUnZKyeHu0GjG0FqpNu2c/A2HVhnkxNX4B8gqjCJrJMDIJ9tSnyM40=" target="_blank" class="">http://lists.natureoflig<wbr class="">htandparticles.org/options.<wbr class="">cgi/general-natureoflightandpa<wbr class="">rticles.org/mules333%40gmail.<wbr class="">com?unsub=1&unsubconfirm=1</a>"><br class="">
Click here to unsubscribe<br class="">
</a><br class="">
</blockquote>
</div>
</div>
</div>
</div>
<span 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;float:none;display:inline!important" class="">______________________________<wbr class="">_________________</span><br 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" class="">
<span 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;float:none;display:inline!important" class="">If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at<span class="m_32599331786726808Apple-converted-space"> </span></span><a href="mailto:richgauthier@gmail.com" 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" target="_blank" class="">richgauthier@gmail.com</a><br 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" class="">
<span 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;float:none;display:inline!important" class=""><a href="</span><a href="https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flists.natureoflightandparticles.org%2Foptions.cgi%2Fgeneral-natureoflightandparticles.org%2Frichgauthier%2540gmail.com%3Funsub%3D1%26unsubconfirm%3D1&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368844093&sdata=iFd3mObCwTMqImLNY3OjMGJqYg9lFdu5XWaTiWgOqU0%3D&reserved=0" originalsrc="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/richgauthier%40gmail.com?unsub=1&unsubconfirm=1" shash="ZDvAoGbBG79M77rjqTFtiUgdZHB7agyvBOLXGxcRNcBskbpd0d9IPHToKIJLC+dvzS+p3OURkz3lRH0FbNZQA0qObFEfcGbCd0Z5gM9iV1mCPVzAF3RVJWxlb3sSmh6QL+eNs+oYuJcSiGuGmEjooD/uJ3CM6Pv/XRdtDYzCaEc=" 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" target="_blank" class="">http://lists.<wbr class="">natureoflightandparticles.org/<wbr class="">options.cgi/general-<wbr class="">natureoflightandparticles.org/<wbr class="">richgauthier%40gmail.com?<wbr class="">unsub=1&unsubconfirm=1</a><span 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;float:none;display:inline!important" class="">"></span><br 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" class="">
<span 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;float:none;display:inline!important" class="">Click here to unsubscribe</span><br 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" class="">
<span 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;float:none;display:inline!important" class=""></a></span></div>
</blockquote>
</div>
</div>
</div>
</div>
</div>
<br class="">
______________________________<wbr class="">_________________<br class="">
If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at <a href="mailto:mules333@gmail.com" class="">mules333@gmail.com</a><br class="">
<a href="<a href="https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flists.natureoflightandparticles.org%2Foptions.cgi%2Fgeneral-natureoflightandparticles.org%2Fmules333%2540gmail.com%3Funsub%3D1%26unsubconfirm%3D1&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368844093&sdata=cP8EWdpbh1XUAYPkVKOEn%2FQAJt6CZ8Vyo8FXSis6LOA%3D&reserved=0" originalsrc="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/mules333%40gmail.com?unsub=1&unsubconfirm=1" rel="noreferrer" shash="pVHIElXqUdAZJ9emMW1HfbL0VeCCAshKKp+SMEgI//GbG2ueTJmcTlisgMYyUNkZJbH28ZiX/E7kKQffjXRVkwOxuzfclz/aQkZWZdnrepVp5bgUsO++1abgXAAQg47T1kj8UjafVs20En83Q/b5U4uy5S31jM0E2+WvbGWLg+k=" target="_blank" class="">http://lists.<wbr class="">natureoflightandparticles.org/<wbr class="">options.cgi/general-<wbr class="">natureoflightandparticles.org/<wbr class="">mules333%40gmail.com?unsub=1&<wbr class="">unsubconfirm=1</a>"><br class="">
Click here to unsubscribe<br class="">
</a><br class="">
</blockquote>
</div>
</div>
_______________________________________________<br class="">
If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at <a href="mailto:srp2@srpinc.org" class="">srp2@srpinc.org</a><br class="">
<br class="">
<a href="https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flists.natureoflightandparticles.org%2Foptions.cgi%2Fgeneral-natureoflightandparticles.org%2Fsrp2%2540srpinc.org%3Funsub%3D1%26unsubconfirm%3D1&data=02%7C01%7Cchandra.roychoudhuri%40uconn.edu%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368854101&sdata=4bQgrrcKVub8ZrAyOZ2gIDE%2BnvseMXnEtCl5170x87o%3D&reserved=0" originalsrc="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/srp2%40srpinc.org?unsub=1&unsubconfirm=1" shash="pk9+P50yNkRJssGl5dzuRpgXzIZ3YvBtprzhKiIjdmqrFHA0HN0dXhu8NlKWL6Nx9zlWXCUxKrJy29BI4ol3vLHRKMcamc/AVSL6CzqcMD9FJ0Q+/l2ZIE/wzZHEvGURi71MlK2mS34NudObcyWeuRfz9xoqqR8Xn10YoYGB+3o=" class="">Click here to unsubscribe</a><br class="">
</div>
<blockquote type="cite" class="">
<div class=""><span class="">_______________________________________________</span><br class="">
<span class="">If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at <a href="mailto:chandra.roychoudhuri@uconn.edu" class="">chandra.roychoudhuri@uconn.edu</a></span><br class="">
<span class=""><a href="<a href="https://na01.safelinks.protection.outlook.com/" class="">https://na01.safelinks.protection.outlook.com</a>/?url=http%3A%2F%<a href="http://2flists.natureoflightandparticles.org/" class="">2Flists.natureoflightandparticles.org</a>%2Foptions.cgi%<a href="http://2fgeneral-natureoflightandparticles.org/" class="">2Fgeneral-natureoflightandparticles.org</a>%2Fchandra.roychoudhuri%<a href="http://2540uconn.edu/" class="">2540uconn.edu</a>%3Funsub%3D1%26unsubconfirm%3D1&data=02%7C01%7Cchandra.roychoudhuri%<a href="http://40uconn.edu/" class="">40uconn.edu</a>%7C969044c478e64c58fa8908d5f585541e%7C17f1a87e2a254eaab9df9d439034b080%7C0%7C0%7C636684875368874113&sdata=SNFZV2D73pRETL5S4ir7CF68DtbmHeRRcrvDc6mhdq8%3D&reserved=0"></span><br class="">
<span class="">Click here to unsubscribe</span><br class="">
<span class=""></a></span></div>
</blockquote>
</div>_______________________________________________<br class="">If you no longer wish to receive communication from the Nature of Light and Particles General Discussion List at <a href="mailto:richgauthier@gmail.com" class="">richgauthier@gmail.com</a><br class=""><a href="<a href="http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/richgauthier%40gmail.com?unsub=1&unsubconfirm=1" class="">http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/richgauthier%40gmail.com?unsub=1&unsubconfirm=1</a>"><br class="">Click here to unsubscribe<br class=""></a><br class=""></div></blockquote></div><br class=""></div></body></html>