Gamma-ray spectroscopy

Smooth a spectrum and count gross, background, and net peak counts.

Gamma-ray pulse-height spectra arrive as counts per channel. Answering “how many counts sit under this peak” needs a small pipeline: smooth the spectrum, delimit the peak window $[c_1, c_2)$, and subtract the background. The demo below runs the verified crate passes over caller-supplied counts:

• E1 — rectangular smoothing with window width $m$ (odd, $m \ge 3$):

smooth[i] = (1/m) * sum(counts[i-ext..=i+ext]) for ext <= i < N - ext, with ext = (m - 1) / 2; edge channels are copied unchanged.

• E2 — five-point smoothing:

smooth[i] = (c[i-2] + c[i+2] + 2*c[i+1] + 2*c[i-1] + 3*c[i]) / 9 for 2 <= i < N - 2; the first and last two channels are copied.

• E3 — background under the peak (m == 1 only):

low = sum(counts[c1-2..c1]), high = sum(counts[c2..c2+2]), and bg = (low + high) * (c2 - c1 + 1) / 6.

• E4 — gross counts: gc = sum(counts[c1..c2]), half-open (channel c2 is excluded).
• E5 — net counts: nc = gc - bg.

Smoothing and counting

Pick a smoother, set the peak window, then press Smooth spectrum. The Oracle counts default replays fixtures/spectroscopy/smooth_oracle.json ([2, 5, 1, 6, 3, 8, 4], $c_1 = 2$, $c_2 = 5$ — the worked example in the theory page), and Synthetic peak loads hand-picked small numbers with one bump. Channels are labelled positionally (0..N-1); counts must be finite and non-negative.

TSV, calibration, and SPE readers

The same demo also hosts the scalar bundle: the runtime decay-line TSV interchange (parseLinesTsv), E6 energy bins plus E7 efficiency (energyBins, detectorEfficiency), and the dollar/plain .spe readers (parseDollarSpe, parsePlainSpe capped summaries).

See also

• Tutorial: Run spectroscopy
• Theory: Gamma-ray spectroscopy
• Crate docs: crates/spectroscopy/src/lib.rs