= Solution
The dominant $z^2/\beta^2$ factor raises the <energy loss> as a charged projectile slows, while the logarithm moderates that rise. This produces a <Bragg peak> close to the end of its <particle range>. At still lower <velocity>, changing effective charge, shell effects and <nuclear stopping> invalidate extrapolation of the elementary <Bethe stopping formula> to zero <energy>. A finite initial <energy> gives a finite <continuous-slowing-down range>,
$$
\boxed{R_{\rm CSDA}=\int_0^{T_0}\frac{dT}{S(T)}.}
$$
A higher initial <energy> increases the <particle range>; greater electron <density> increases <stopping power> per unit length. Absorber $Z/A$ and $I$ also affect the depth. <Multiple Coulomb scattering>, <energy-loss straggling>, nuclear reactions and the incident energy spread broaden the measured peak and distal fall-off; nuclear secondaries can produce a small tail. Superposing many incident energies makes a <spread-out Bragg peak> for an extended target. The schematic curve below illustrates shapes only and is not patient <radiation dosimetry>.
\Image[/past-exam-of-the-short-options-paper-shared-by-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2019-response-curves.png]
{title=Qualitative depth-dose curves and a two-timescale climate response; depth is in arbitrary units}
Back to article page
