ACTIVE SCATTERER / COINCIDENCE

Compton Coincidence Energy Analyzer

Use an active scattering target to retain recoil and photon pulse heights with their time difference. Move the coincidence window, subtract time sidebands, and infer the incoming energy from the retained pairs.

Ideal full containment of recoil energy and scattered-photon energy, calibrated independent Gaussian channels. True-pair timing is Gaussian; accidental pulse heights are independent of a flat time distribution. No real source rate, trigger efficiency, binding, escape or detector continuum. Sideband subtraction is conditional on 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 / RETAINED 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 uses the time gate only. The analyzer never receives a true-pair label. Recoil energy is deposited inside the active target, not at a separate electron collector.

ALL CANDIDATE DELAYS / DISJOINT SIDEBANDS

Select a prompt window. 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 / RECORDS ONLY

What the retained observations support

Retained events

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Sideband-corrected incoming energy

\text{—}

Approximate standard error

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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.

IN-MEMORY COMPARISON

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: Two pulses. One energy account.
One-sentence intuition: Keep source assumptions separate from estimates made from records.

Core mathematical model

Two deposited energies

E_0=E_\gamma+K_e

The target contains the recoil electron; the distant detector contains the scattered photon. Both measured pulse heights carry independent resolution noise.

Use time to subtract accidentals

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

Prompt means absolute delay within the selected half-width. Two sidebands run from eighty to one hundred sixty nanoseconds in absolute delay. A flat time background is required.

An estimate from weighted records

\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}

No latent labels or source energies enter. Negative subtracted bins remain visible. Weak net excess withholds the energy estimate; the displayed standard error is approximate, not a confidence interval.

Common difficulties

A simulation supplies its law

Typical misconceptionRecovering a source parameter independently confirms the law.

Better mental modelThese synthetic records test a measurement and inference workflow. They are not historical observations, a parameter confidence interval, or external scientific certification.

Run the experiment

01
Acquire the candidate stream
Keep photon energy, target energy and delay for every candidate pair.
What to observe: Prompt points cluster along a constant energy sum. Gray points are outside the time gate, not known background labels.
02
Move the window after acquisition
Change the analysis half-width without reacquiring.
What to observe: All raw pairs remain. Both timing counts and the subtracted energy-sum histogram are recomputed from the same stream.
03
Remove true pairs
Select no correlated pairs and acquire a new stream.
What to observe: A gate can select accidental pairs too. Sidebands and weak-information diagnostics prevent a fabricated conservation estimate.