Active scatterer / Coincidence

Compton Coincidence Energy Analyzer

Do the scattered photon and the recoiling electron together carry all of the incoming photon's energy? Yes. In every scattering event the photon's energy plus the electron's recoil energy equals the incoming photon's energy, whatever the angle. Pulses from one event arrive within nanoseconds of each other. Unrelated pulses can land that close by chance, so count pairs with long delays, which are all accidental, scale that count to the narrow window and subtract it before averaging the sums.

An active scattering target records the pulse heights of the recoil electron and the scattered photon, and the time between them. Move the coincidence window, subtract the time sidebands, and estimate the incoming energy from the pairs that remain.

Scatter photons, then infer from the detector records

Do the scattered photon and the recoiling electron together carry all of the incoming photon's energy?

Source incident energy · excluded from inference

E_0/\mathrm{keV}

662

Calibrated channel standard deviation

\sigma_E/\mathrm{keV}

12

Calibrated angular slit half-width

a/\mathrm{deg}

2

Source correlated-pair fraction · excluded from inference

p

0.65

Source true-pair timing spread

\sigma_t/\mathrm{ns}

6

Retained candidate pairs

N

1024

Analysis prompt half-width · retains records

w/\mathrm{ns}

15

Acquisition detector angle

\theta/\mathrm{deg}

90

Changing the time gate reanalyzes the same pairs. Acquisition changes clear current records; the saved run remains.

The recoil energy and the scattered photon's energy are both fully absorbed, and the two channels are calibrated, independent and Gaussian. Time differences of true pairs follow a Gaussian. Accidental pairs have a flat time distribution, and their pulse heights do not depend on time. Real source rates, trigger efficiency, electron binding, escape and the detector continuum are not modeled. The sideband subtraction holds only under these assumptions.

Incoming photons travel rightward. The detector faces the target at the selected angle. Paths and sizes are schematic; energy data appear below.

Calibrated pulse heights of the kept events

Keep both energies and their time difference.

Collimated photonActive recoil targetTwo energy channels + timing

Every candidate pair retains two calibrated pulse heights and a delay. The analysis window can move after acquisition. The simulated candidate mixture does not model source activity or trigger rates.

Ready. Predict, then acquire.

Raw detector records

A shared event leaves complementary energies.

$E_\gamma/\mathrm{keV},\quad K_e/\mathrm{keV}$

Inside time gateOutside time gateInferred energy sum

Color depends only on the time gate. The analysis never sees which pairs are true. The recoil energy is deposited inside the active target; there is no separate electron collector.

All candidate delays and non-overlapping sidebands

Select a prompt window and measure the background.

$\Delta t/\mathrm{ns},\quad N_{\rm bin}$

Rebinned from the same raw pairs

The energy sum after sideband subtraction.

$(E_\gamma+K_e)/\mathrm{keV},\quad N_P-\alpha N_B$

Teal: prompt counts. Gold: width-scaled sideband counts. Purple: their difference with approximate counting errors. Negative bins are preserved. Source energy never enters this histogram.

Inference from the records alone

What the retained observations support

Retained events

\text{—}

Sideband-corrected incoming energy

\text{—}

Approximate standard error

\text{—}

Net prompt excess

\text{—}

Sideband correction assumes time-independent accidental energy distributions. A weak net prompt excess withholds the energy estimate. Gaussian true-pair tails can leak into sidebands at extreme timing spread; this is not an automatic background classifier.

Saved comparison, kept in memory

Save a run to compare or restore its settings and raw events.

Measure the angular spectrum Read the historical evidence ORTEC apparatus reference Compton 1923 paper

Start with the essentials

Focus question: Do the scattered photon and the recoiling electron together carry all of the incoming photon's energy?
One-sentence intuition: Keep what the simulation assumes about the source apart from what you estimate from the recorded events.

Core mathematical model

Energy shared by the photon and the electron

E_0=E_\gamma+K_e

The recoil electron stops inside the target, and the scattered photon is absorbed in the distant detector. Each measured pulse height carries its own independent resolution noise.

Subtracting accidentals with timing sidebands

\begin{aligned}N_{\rm net}&=N_P-\alpha N_B\\[2pt]\alpha&=\frac{2w}{2(160-80)\,\mathrm{ns}}\end{aligned}

A pair is prompt when the size of its delay is within the chosen half-width. The two sidebands take pairs whose delay size lies between eighty and one hundred sixty nanoseconds. The subtraction requires a background that is flat in time.

Incident energy from the subtracted energy sum

\widehat E_0=\frac{\sum_{i\in P}(E_{\gamma i}+K_{ei})-\alpha\sum_{i\in B}(E_{\gamma i}+K_{ei})}{N_P-\alpha N_B}

The estimate uses no hidden event labels and no source energies. Bins that go negative after subtraction stay on the plot. If the net excess is too weak, no energy estimate is reported. The standard error shown is approximate and is not a confidence interval.

Common difficulties

The simulation already contains the law

Typical misconceptionGetting the source parameter back independently confirms the law.

Better mental modelThe events were generated from that law, so getting the parameter back tests the measurement and estimation steps. The data are not historical observations, they do not give a confidence interval for the parameter, and they are not external scientific certification.

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