<div dir="ltr"><div>Dear Richard,</div><div><br></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 style="color:rgb(17,17,17);font-family:Roboto,Arial,sans-serif;font-size:14px;text-align:left;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial;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><br></div><div>My memory of photon energy threshold >2 MeV for pair creation from a collision with an electron is consistent with
<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);text-decoration-style:initial;text-decoration-color:initial;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.<br></div><div><br></div><div>Andrew<br></div><div><br></div><div><br></div><div><br></div><div><div class="gmail_extra"><br><div class="gmail_quote">On Thu, Jul 26, 2018 at 10:04 AM, <span dir="ltr"><<a href="mailto:richgauthier@gmail.com" target="_blank">richgauthier@gmail.com</a>></span> wrote:<br><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">Hi Andrew and all,<div> 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.<wbr>researchgate.net/publication/<wbr>235335367_The_Miracle_of_the_<wbr>Electron-Positron_Pair_<wbr>Production_Threshold</a> 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><span class="HOEnZb"><font color="#888888"><div> Richard</div><div></div></font></span></div><br><div style="word-wrap:break-word;line-break:after-white-space"><div></div><div><br><div><br><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><br class="m_-1799926813271640078Apple-interchange-newline"><div><div dir="ltr"><div><br></div><div>Note that the threshold energy for pair production "... given by
<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);text-decoration-style:initial;text-decoration-color:initial;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.<br></div><div><br></div><div>Andrew<br></div></div><div class="gmail_extra"><br><div class="gmail_quote">On Tue, Jul 24, 2018 at 1:35 PM, Richard Gauthier <span dir="ltr"><<a href="mailto:richgauthier@gmail.com" target="_blank">richgauthier@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Hi Chip and all,<div> Here's a little background on experimental pair production from the abstract to an article on <a href="http://Researchgate.net" target="_blank">Researchgate.net</a> at <a href="https://www.researchgate.net/publication/235335367_The_Miracle_of_the_Electron-Positron_Pair_Production_Threshold" target="_blank">https://www.researchgate.ne<wbr>t/publication/235335367_The_Mi<wbr>racle_of_the_Electron-Positron<wbr>_Pair_Production_Threshold</a> </div><div> Richard</div><div><br></div><div><br></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);text-decoration-style:initial;text-decoration-color:initial;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>
<br></div></div>
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