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In 1962, Riccardo Giacconi and colleagues flew three Geiger counters to search for lunar X-ray fluorescence. Different mica thicknesses tested penetration; lampblack blocked ultraviolet. Each counter sat in an anticoincidence detector using a scintillation counter to reject cosmic rays. There was no mechanical collimator. Rotation scanned the sky; optical sensors supplied orientation.^[ref]

Counts were sorted by azimuth; a faulty counter and tumbling descent data were excluded. A directional peak lay above a diffuse component. Window, altitude and angular responses tested X-rays against charged particles; the Moon's nondetection checked optical leakage. The authors argued for an origin outside the Solar system, while residual cosmic ray background was not directly measured and source size, position and spectrum remained assumption-dependent.^[ref]

A simple original forward problem makes the distinction precise. Let $\varphi$ be the scan azimuth, let $g(\varphi )$ be a dimensionless directional response with maximum one, let $F$ be a source's band-integrated photon arrival rate per unit area, let $A_0$ be its on-axis X-ray effective area, and let $b$ be a constant accepted background rate. The expected rate isFor a broad illustrative response $g(\varphi )=\max (0,\cos \varphi )$, the full width at half maximum is $120^{\circ }$: $\cos \varphi =1/2$ at $\varphi =\pm 60^{\circ }$. For a one-dimensional ideal collimator model $g(\varphi )=\max (0,1-|\varphi |/{\theta }_c)$, the full width at half maximum is ${\theta }_c$. Choosing ${\theta }_c=20^{\circ }$ narrows the response sixfold without focusing any additional photons. These are teaching response functions, not reconstructions of the rocket's window transmission or geometry. A narrower scan peak can reflect the instrument response even when the source is unresolved.

An absorption edge is an abrupt change in photon absorption as incident photon energy crosses an electronic excitation threshold. For inner-shell photoionization, a new vacancy-production channel opens near the shell's binding energy. This threshold concerns incident energy; a Characteristic X-ray concerns a subsequent difference of atomic energies. They are different observations. Barkla's lecture explicitly treats characteristic emission as requiring a critical excitation condition, while discussing characteristic radiation separately from scattering.^[ref]

In the stipulated X-ray fluorescence model, the K threshold is $10.0\mathrm{keV}$, whereas the K lines are $8.5$ and $9.7\mathrm{keV}$. An absorber made of a different material could have its own absorption edge between those line energies, preferentially removing the upper line. Actual near-edge structure and attenuation values require material data; the following deliberately chosen coefficients are not such data.

X-ray emission spectroscopy studies the frequency spectrum of emitted X-rays. The spectral line positions identify electronic energy differences; their strengths also depend on excitation, photon absorption inside the sample, geometry and detector response. An X-ray tube may excite a sample with Electrons, while X-ray fluorescence uses incident photons. The distinction matters when choosing what the experiment measures: identifying a chemical element from a line position is different from determining its abundance from a line strength.

X-ray fluorescence is Characteristic X-ray emission following excitation by incident photons. In a simple initially unexcited chemical atom, photoionization can eject an inner Electron if the incident photon supplies its binding energy. An outer Electron can then fill the vacancy, releasing an emitted photon with the difference of shell binding energies. Nonradiative relaxation competes with this route, so one absorbed incident photon need not yield one escaping characteristic photon.

Choose a separate stipulated electron shell model with values $B_K=10.0$, $B_L=1.5$ and $B_M=0.3$, all in $\mathrm{keV}$. Ignore subshell splitting, recoil and changes of binding energy during relaxation. The possible shell differences areThese labels denote simplified shell groups, not resolved subshell electronic transitions. With $hc=1.23984\mathrm{keV}\mathrm{nm}$, their calculated wavelengths are respectively $0.145864$, $0.127819$ and $1.03320\mathrm{nm}$. An incident $9.8\mathrm{keV}$ photon exceeds both K-line energies but cannot directly create the K vacancy in this initially unexcited model. A $12.0\mathrm{keV}$ photon can, leaving approximately $2.0\mathrm{keV}$ of photoelectron kinetic energy. This comparison fixes neither the excitation probability nor the radiative branching probability.