Settings A B C D Beam energy (GeV) 2.302 4.482 1.1 3.3 Central angle 5.0 ◦ 5.5 ◦ 5.0 ◦ 5.0 ◦ Effective angles (4.5,5.5) (5.25,6.0) (4.5,5.5) (4.5,5.5) Target T/X$_{0}$ (ratio $^{a}$) 4.25% (1:1) 10% (1:1) 0.58% (1:3) 10% (1:1) Beam current ( µA ) 80 80 80 80 Central momentum (GeV) 1.145 2.230 0.545 1.634 Singles (negative polarity) e − (MHz) 4.5 0.7 6. 2.9 π − (kHz) 640. 2200 36. 2500. Singles (positive polarity) π $^{+}$+ p (kHz) 640. 2200 36. 2500. e + (kHz) 31. 3.6 24. 23. Trigger/DAQ: Trigger b (kHz) 4. 0.4 3.2 3.4 Signal to background: Trident (Hz) 610 70 350 530 Two-step (Hz) 35 15 5 75 Background c (Hz) 70 1.3 70 35 a The listed total target thickness is split between two sets of wire mesh planes, located at different z to produce the two indicated effective angles. The numbers in parentheses denote the ratio of target thickness at the larger effective angle to that at the smaller effective angle. b Trigger: Coincidence with 20 ns time window between S0-N (assuming pions are rejected by a factor of 100) and S0-P signals. c Dominated by e $^{+}$e − accidental rate. We assume pion rejection by a factor of 10 4 in offline cuts, a 2 ns time window and additional factor of 4 rejection of accidentals from the target vertex. Further rejection using kinematics is expected, but not included in the table. VII. MEASUREMENTS AND REACH IN APEX TABLE II: Expected counting rates for the proposed experiment. trigger timing windows. These accidental coincidences are a dominant part of the recorded events in APEX, and determine the maximum rate at which potential sig- nal trident events can be recorded. A typical composi- tion of the single rate in the spectrometers is expected to be e − /π − ≈ 80/20 in the negative polarity arm and π $^{+}$/p/e+ ≈ 80/19/1 in the positive polarity arm. The fraction of the true coincidence events could be up to 50% for the e − π + rate within a 2 ns time window, and could be significant for the e − p events in certain regions of momenta. We consider a twelve-day run in the configuration “B” of Table II and six-day runs in each of the remaining configurations, to search for new resonances in e $^{+}$e − tri- dent spectra from 65 to 550 MeV. For settings “A” and “C”, the target thickness and beam current have been optimized to accumulate the largest possible sample of trident events without saturating the data acquisition system. Settings “B” and “D” are far from data acqui- sition limits, but we do not use T/X$_{0}$ > 10% to avoid limits on the total radiation produced (this can possibly be side-stepped at other facilities). Besides the trident events discussed in § V, an addi- tional source of true coincidence events is the “two-step” (incoherent) trident process, in which an electron radi- ates a real, hard photon in the target that subsequently converts to a high-mass e $^{+}$e − pair. For thin targets, this process is suppressed compared to the trident rate, and so it is sub-dominant for all the settings we consider. The mass range from 65 to 550 MeV is chosen to take advantage of the Hall A HRS spectrometers, as well as for its theoretical interest. Lower masses are more ef- fectively probed by using lower beam energies, improved forward acceptance, and/or vertexing (see also [12]). Set- tings at higher masses are possible but have significantly reduced sensitivity and are better suited to exploration with higher-acceptance equipment and an experiment op- timized to accept muon and pion pairs as well as elec- trons. The consideration of these rates determine trigger rates and upper bounds on offline accidental rates shown in Table II. 13