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NAD+ is the oxidized form of nicotinamide adenine dinucleotide; NADH is its reduced form.

A magnetic horn uses a pulsed magnetic field around a high-current conductor to focus charged secondary pions and kaons of a selected sign. Their decays then create a directed neutrino beam. The field acts on the charged parents, not on the neutral neutrinos.

A decay tunnel provides a low-density flight region where selected unstable particles decay before remaining charged particles are removed or absorbed. For a pion-produced neutrino beam, its length balances pion decay probability against backgrounds from longer-lived daughters.

Neptunium-239 is a radioactive isotope with ninety-three protons and one hundred forty-six neutrons. It beta-decays to plutonium-239.

It occurs in the sequence following neutron capture by uranium-238 and beta decay of uranium-239. This is an example of transmutation changing the chemical element through a nuclear process, unlike an ordinary chemical reaction that rearranges electrons and bonds.

Outside a Schwarzschild metric horizon $r_s$, write $r-r_s={\rho }^2/(4r_s)$. To leading order the radial metric isIt has Rindler coordinates with $\alpha =c/(2r_s)$. The proper-distance-like coordinate $\rho$ has null paths exponential in $\pm ct/(2r_s)$; the Schwarzschild coordinate difference $r-r_s\propto {\rho }^2$ is exponential in $\pm ct/r_s$.

Inside, writing $r_s-r={\rho }^2/(4r_s)$ instead gives $d{s}^2\simeq d{\rho }^2-[c\rho /(2r_s){]}^{2}d{t}^2$, where the radial coordinate is timelike. The negative-$x$ Rindler wedge is therefore not the black-hole interior: its time coordinate retains the same causal type as in the positive-$x$ wedge. The flat radial limit does not remove the genuine curvature of the full Schwarzschild spacetime.

The physics course entries follow the Cavendish Laboratory's 2025–26 teaching list.^[ref]

Past examination papers: Physics Teaching Information System past-paper search (University sign-in required). Specific paper years and their solution availability must be checked inside the system.

A public release includes physics papers for 2017–2019 and 2021–2022, with examiner reports and some answers. ^[ref]

Can two readout values locate a hit between wires? Only with a specified response model. Place two readout wires at $0$ and $p$, put $u=x/p\in [0,1]$, and stipulate calibrated, noiseless electric chargesThese are assumptions for a toy sensor response, not the natural response law of adjacent anode wires. Under these assumptions the centroidrecovers position exactly. The apparent gain in precision comes from adding calibrated analogue information. Taking the mean of two fired wire addresses without their electric charges would instead give the fixed midpoint $p/2$.

For a chosen noise model, replace the two electric charges by $q_L+n_L$ and $q_R+n_R$, with independent random variables $n_L,n_R$ of zero expected value and common standard deviation $s$. Assume $s/Q\ll 1$ and no threshold censoring. First-order expansion of the ratio givesFor stipulated $p=2\mathrm{mm}$ and $s/Q=0.02$, this approximation gives $0.0283\mathrm{mm}$ at the midpoint and $0.0400\mathrm{mm}$ at either endpoint. The endpoint values describe uncensored signed channel readouts, including small negative values after baseline subtraction. They do not assume that both channels would pass a positive threshold. A ratio with a fluctuating denominator also need not have exactly zero bias; this is a local small-noise approximation.

Three original counterexamples show why calibration and selection matter:

Likewise, two equal hits at $u=1/4$ and $u=3/4$ have exactly the same total two-channel response as one hit at $u=1/2$ with twice the electric charge. A centroid can hide multiplicity even when each charge measurement is exact.

Diffusion enabled the lecture's Orsay interpolation, without establishing this model's linear response.^[ref]

Consider an original idealized track reconstruction model. Let equally spaced wires have positions $x_k=kp$ and assign each event to the nearest wire, reporting $\hat{x}=x_k$. Assume exactly one correct wire address, perfect detection efficiency, exact wire positions and a uniform distribution of true positions within each cell. These assumptions explicitly exclude missed pulses, false addresses and several unresolved tracks.

Writing $u=x-x_k$, the measurement error is $e=\hat{x}-x=-u$, with $u$ uniform on $[-p/2,p/2]$. Symmetry gives zero expected value. Its variance and standard deviation follow by integration:For chosen wire pitches $p=2\mathrm{mm}$ and $1\mathrm{mm}$ this gives $0.577\mathrm{mm}$ and $0.289\mathrm{mm}$ respectively. These are model standard deviations, not measured chamber spatial resolutions. The largest possible absolute error in this model is $p/2$, which is a different quantity.

A useful subtlety is that the formula depends on the illumination. For an unresolved pencil beam fixed at $x=x_k+0.4p$, every reconstructed position is $x_k$. The repeated estimates have zero variance, but every error is $-0.4p$. Small repeat-to-repeat spread can coexist with a biased position. The uniform-cell result therefore cannot be transferred to an arbitrary beam profile or detector selection.

The wire address supplies one transverse coordinate in this model. Combining several separated measurements supports track reconstruction; a single address does not specify a complete trajectory. If two charged particles enter the same cell during one accepted interval, an address-only record can be identical to that from one particle. No reconstruction of that record can recover the lost multiplicity without additional information.

The centre-to-centre spacing $p$ of adjacent wires. A wire address alone specifies a cell, rather than a continuous position.

The original apparatus used $40\mu \mathrm{m}$ stainless-steel wires between meshes $7.5\mathrm{mm}$ away, flowing argon with organic vapor, negative mesh voltage and individual electronic amplifiers. A $5.9\mathrm{keV}$ X-ray source calibrated pulse height while voltage was varied.^[ref]

A coincidence circuit defined a narrow proton or pion beam. Scanning it across wires tested localization; the response edge matched the beam width, limiting the inference. Distant counts were attributed to accidental coincidences. Separate electron scans measured pulse delay versus position, comparing gas mixtures and pulse-height-dependent electronics.^[ref]

Thresholds rejected small pulses, reducing detection efficiency. Wire-independence tests did not establish unlimited separation of overlapping tracks.^[ref]

Multiple Coulomb scattering is the accumulated deflection of a charged particle passing through matter, mainly through repeated Rutherford scattering by atomic nuclei. Many small deflections broaden a beam or make a reconstructed particle track wander. A roughly Gaussian distribution describes the central angular core in a useful regime, while rarer large-angle encounters produce tails.^[ref]

The angular width increases with traversed material and decreases as particle momentum increases. It is commonly parameterized using material thickness relative to the radiation length. In a particle detector, adding measurement layers can improve position sampling while also increasing Multiple Coulomb scattering; track precision therefore depends on material as well as sensor accuracy. A width projected onto one measurement plane must be distinguished from the full spatial deflection angle.