QUANTUM EVIDENCE / NUCLEAR RESONANCE

Mössbauer Doppler Observatory

Move a gamma source toward an absorber. Build a transmission spectrum, separate a quadrupole doublet and infer its source-relative energy shift from raw counts.

PREPARE / ACQUIRE / QUESTION

Move by millimetres. Resolve nuclear energy.

Predict the change before scanning. Keep the raw counts after.

Absorber shift relative to source

\delta/(\mathrm{mm\,s^{-1}})

0.25

Quadrupole separation

\Delta v/(\mathrm{mm\,s^{-1}})

1

Recoilless source fraction

f_{\mathrm s}

0.8

Resonant optical depth

\eta

0.16

Extra Lorentz FWHM

w_{\mathrm{extra}}/(\mathrm{mm\,s^{-1}})

0

Exposure per reading

\tau/\mathrm{s}

2

Source velocity

v/(\mathrm{mm\,s^{-1}})

0

Moving the probe keeps records. Changing the source or instrument starts a new run. Saved runs survive until reset.

An ideal single-line source and randomly oriented doublet absorber in the thin-absorber limit. Source and absorber linewidths are convolved. No magnetic sextet, thick-absorber saturation, phonon spectrum, thermal shift or velocity calibration error is simulated.

Schematic geometry · enlarged gaps and components · colors and moving markers do not represent visible light or measured trajectories. Drag to orbit.

EXPOSURE / TWO INDEPENDENT COUNTS

Give the spectrum a record.

Each coordinate has a signal exposure and a separate reference: absorber removed. Exposure time controls Poisson noise; scan playback is accelerated.

Ready. Predict, then acquire.

Recorded points

0

Probe energy change · model

0

Convolved FWHM · model

0

ACQUIRED SPECTRUM / COUNTS PER SECOND

Which structure survives measurement?

$v/(\mathrm{mm\,s^{-1}})$ · $N_i/\tau_i\;(\mathrm{s^{-1}})$

Teal: source expectation. Gold: acquired rates with fitted Poisson standard deviations, once a fit exists. Purple dashes: inference from records. Gray dots: saved run. Background is included.

Click or drag to move the probe; its slider supports keyboard input. The vertical scale follows the data.

INFERENCE / JOINT POISSON LIKELIHOOD

Estimate from both exposures.

Inferred absorber shift

\text{—}

Inferred source rate

\text{—}

Deviance per degree

\text{—}

Flat alternative

\text{—}

$r_i=(N_i-\widehat\mu_i)/\sqrt{\widehat\mu_i}$

Gold: signal residuals. Blue: reference residuals. Known response, splitting/width controls and background; unknown source rate and spectral parameter. At least sixteen distinct probe positions are required. Descriptive residuals and deviance do not establish identifiability, confidence intervals or discovery significance.

Keep the original counts.

Save a full or partial run with settings and seed in this page session.

#	$v/(\mathrm{mm\,s^{-1}})$	Signal	Absorber removed	$\tau/\mathrm{s}$

Latest six points shown. CSV includes all raw counts, exposures, settings, units and seed. Changing the probe never changes acquired records.

Scientific scope, geometry & primary sources

A moving single-line gamma source illuminates the absorber and then the upstream face of the transmission counter. Positive velocity means the source moves toward the absorber and raises photon energy. The absorber shift is defined relative to this source, with the same sign.

Rounded 14.4 keV photons and a 141 ns mean nuclear lifetime set the natural linewidth. Equal Lorentzian source and absorber widths add under convolution. The absorber is an isotropic equal-strength quadrupole doublet. Additional Lorentz velocity broadening adds width and reduces peak depth while preserving the integrated absorption area.

Transmission is first order in a resonant optical depth no larger than 0.2. Before convolution the omitted exponential term is bounded by two percentage points. The source recoilless fraction is adjustable; absorber recoilless weight is included in optical depth. Nonresonant source photons form a flat background. No six-line magnetic pattern, full lattice dynamics, temperature shift or dead time is included. The reference exposure removes the absorber.

Independent Poisson exposures, fixed calibrated background and stable source. No drift, dead time or calibration uncertainty. The source follows the displayed model; successful recovery validates the simulator, not the historical discovery.

MIT · Mössbauer laboratory UCSB · recoilless resonance Maryland · experimental scope

Start with the essentials

Focus question: Move by millimetres. Resolve nuclear energy.
One-sentence intuition: Keep the signal and reference counts. Fit their joint Poisson likelihood while estimating the source rate from the same records.

Core mathematical model

Velocity is an energy axis

\Delta E=E_\gamma\frac{v}{c},\qquad \Gamma_E=\frac{\hbar}{\tau},\qquad \Gamma_v=\frac{c\Gamma_E}{E_\gamma}

Positive source velocity points toward the absorber. Lifetime here is mean lifetime; it is not the half-life.

Convolve both linewidths

W=2\Gamma_v+w_{\mathrm{extra}},\qquad g(v)=1-\frac{f_{\mathrm s}\eta\Gamma_v}{2W}\sum_{q=\pm1}\frac{1}{1+4(v-\delta-q\Delta v/2)^2/W^2}

This thin-absorber result includes equal source and absorber widths. Extra Lorentz broadening conserves absorption area and reduces depth.

Recoil still conserves momentum

E_R\simeq\frac{E_\gamma^2}{2Mc^2}

A free nucleus recoils. In the recoilless channel the lattice takes momentum with negligible recoil energy; phonon creation is a different channel.

Two independent exposures

N_i\sim\operatorname{Poisson}\!\left[\tau_i(Sg_i+b)\right],\qquad M_i\sim\operatorname{Poisson}\!\left[\tau_i(S+b)\right]

Background is independently known. Source rate and the spectral parameter are jointly inferred; reference uncertainty is included. Counts are never Gaussian-rounded.

Common difficulties

Recovery is not discovery

Typical misconceptionA good fit independently confirms the law used by the simulator.

Better mental modelThe source response is supplied. Parameter recovery validates this synthetic measurement loop. Descriptive deviance and residuals are not confidence intervals, significance tests or external scientific certification.

Run the experiment

01
Scan both sides
Scan the doublet and save it. Compare the fitted center with the input absorber shift.
What to observe: The center refers to the selected source. The counted events are transmitted gamma rays; a resonance therefore lowers the count.
02
Separate width from depth
Choose the broadened-drive preset. Scan and compare with the saved doublet.
What to observe: An extra normalized Lorentz convolution widens and shallows the dips. Keeping peak depth fixed would violate the area constraint.
03
Remove the resonant channel
Set the source recoilless fraction to zero and scan. Then restore the saved run.
What to observe: The spectrum becomes flat and no shift is inferred. This does not mean a lattice absorbs momentum without conservation.