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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://www.researchgate.net/deref/http%3A%2F%2Fwww.slac.stanford.edu%2Fexp%2Fe144%2F" 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>
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<span>On Sun, 29 Jul 2018 06:08:32 -0400, Andrew Meulenberg <mules333@gmail.com> wrote:</mules333@gmail.com></span><br>
<div dir="ltr">
<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="http://adsabs.harvard.edu/abs/2006RaPC...75..614H" target="_blank">http://adsabs.harvard.edu/abs/<wbr>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="http://adsabs.harvard.edu/cgi-bin/author_form?author=Hubbell,+J&fullauthor=Hubbell,%20J.%20H.&charset=UTF-8&db_key=PHY" 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="http://www.elsevier.com/" 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://doi.org/10.1016/j.radphyschem.2005.10.008" style="color:rgb(64,0,160)" target="_blank">10.1016/j.radphyschem.2005.10.<wbr>008</a></td>
</tr>
<tr>
<td valign="top" align="left"><b>Bibliographic Code:</b></td>
<td> </td>
<td valign="top" align="left"><a href="http://adsabs.harvard.edu/abs/2006RaPC...75..614H" 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="h5">
<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_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_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_32599331786726808Apple-converted-space"> </span><span class="m_32599331786726808Apple-converted-space"> </span><span dir="ltr"><<a href="mailto:richgauthier@gmail.com" target="_blank">richgauthier@gmail.com</a>></span><span class="m_32599331786726808Apple-converted-space"> </span><wbr>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_32599331786726808Apple-converted-space"> </span>Below is a pdf copy of the article <a href="https://www.researchgate.net/publication/235335367_The_Miracle_of_the_Electron-Positron_Pair_Production_Threshold" target="_blank">https://www.researchga<wbr>te.net/publication/235335367_<wbr>The_Miracle_of_the_Electron-<wbr>Positron_Pair_Production_<wbr>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><span class="m_32599331786726808HOEnZb"><font color="#888888"> <span class="m_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_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_32599331786726808Apple-converted-space"> </span><span dir="ltr"><<a href="mailto:richgauthier@gmail.com" target="_blank">richgauthier@gmail.<wbr>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">Hi Chip and all,
<div> <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="http://researchgate.net/" target="_blank">Researchgate.net</a><span class="m_32599331786726808Apple-converted-space"> </span>at <a href="https://www.researchgate.net/publication/235335367_The_Miracle_of_the_Electron-Positron_Pair_Production_Threshold" target="_blank">https:/<wbr>/www.researchgate.net/<wbr>publication/235335367_The_Mira<wbr>cle_of_the_Electron-Positron_<wbr>Pair_Production_Threshold</a> </div>
<div> <span class="m_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_32599331786726808Apple-converted-space"> </span></div>
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