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It is planned to use the Bethe-Heitler process (e+p → e+p+γ) to measure the luminosity.  It is proposed to use this process because the cross section is large and it is a calculable process in QED (see reference [https://arxiv.org/pdf/1009.2451.pdf paper] and references within).  The analytical expression for the photon energy distribution and the approximate angular distribution from [https://arxiv.org/pdf/1009.2451.pdf paper] are implemented in a Monte Carlo event generator.  The event generator [https://wiki.bnl.gov/eic/index.php/DJANGOH DJANGOH] was used was also used to simulate this process.  The results for the expected scattering angle distribution of the photons is shown below.
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It is planned to use the Bethe-Heitler process (e+p → e+p+γ) to measure the luminosity.  It is proposed to use this process because the cross section is large and it is a calculable process in QED (see reference [https://arxiv.org/pdf/1009.2451.pdf paper] and references within).  The rate of photons measured from this process can then be related to the luminosity as L=N/Aσ, where L is the luminosity, N is the number of measured photons, A is the combined acceptance and efficiency corrections for detecting the photons, and σ is the cross section calculated from QED.  The analytical expression for the photon energy distribution and the approximate angular distribution from [https://arxiv.org/pdf/1009.2451.pdf paper] are implemented in a Monte Carlo event generator.  The event generator [https://wiki.bnl.gov/eic/index.php/DJANGOH DJANGOH] was used was also used to simulate this process.  The results for the expected scattering angle distribution of the photons is shown below for 20x250 GeV e+p collisions.  The red line displays the analytical expression from [https://arxiv.org/pdf/1009.2451.pdf paper] and the blue line the results from the DJANGOH simulation.  The results are qualitatively consistent.  As seen in the figure, the BH process produces photons within a very narrow cone around the electron beam direction.  This means that the luminosity monitoring system needs to be placed downstream from bending magnets so that the electron beam can be bent away from the BH photon cone.  The cone is expected to be roughly +/- 20 μrad in size.
 
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|[[image:BH_thetaDist.png|thumb|500px|]]
 
|[[image:BH_thetaDist.png|thumb|500px|]]
 
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The BH photon cone size will be smeared by the angular divergence of the beams at the IP and its magnitude will depend on the design of the beam optics.  This has also been studied.  Though the parameters on the machine are still being optimized, a study was carried out using the parameters found in , assuming an (normalized) emittance, &epsilon; = 23x10<sup>-6</sup> m (58x10<sup>-6</sup> m) for e+p (e+Au) and a &beta;<sup>*</sup> = 5 cm.  The dependence of the angular beam divergence on the e beam energy assuming the above parameters is shown in the figure below.
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|[[image:DivergenceBeamDependence.png|thumb|500px|]]
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Details specific to the implementation of the luminosity monitoring system with the eRHIC IR in the EicRoot simulation can be found [here].
    
== Lepton polarimetry ==
 
== Lepton polarimetry ==
    
requirements need still to be worked out
 
requirements need still to be worked out
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