Solution (source code)

= Solution

For a megavoltage <X-ray> beam, the surface <absorbed dose> is below the subsurface maximum. <Photons> generate energetic secondary <electrons>, mainly through <Compton scattering>; the downstream electron fluence initially builds up until approximate <charged-particle equilibrium> is established. Beyond this buildup region, decreasing primary <photon fluence>, scattering and geometric spreading make the <depth-dose curve> fall gradually. A penetrating photon beam has a substantial exit dose.

A nearly monoenergetic <proton> beam deposits a moderate entrance dose, then a sharp <Bragg peak> near the end of its range. As nonrelativistic <protons> slow, their electronic <stopping power> rises approximately as $1/v^2$ over the relevant part of the track. Once the protons stop, the dose falls steeply. Range straggling and energy spread broaden the peak; nuclear interactions add a smaller nonideal tail, so an exact hard cutoff is an idealization. Superposing appropriate incident energies produces a <spread-out Bragg peak> covering an extended target.<Proton depth-dose proposal (1946)>[pp. 487–489, increasing specific ionization near the end of range]{ref}

The label MV for an <X-ray> treatment beam specifies the nominal accelerating potential of the electron accelerator. Its <bremsstrahlung> beam is a broad <photon energy> spectrum with an endpoint of order $eV$, not a monoenergetic beam whose individual photons all carry the quoted numerical energy. <Proton therapy> beam energies can instead be specified directly in MeV per incident proton.

\Image[/past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2015-s10-depth-dose-and-passive-nozzle.png]
{title=Qualitative photon and proton depth-dose profiles and functions of passive proton beam modifiers}