Experiment: Artificial Transmutation and the Instruments of Nuclear Physics

Two questions had to be answered before particle physics could exist as a quantitative science. Can one nucleus be turned into another at will, and can the products be counted one at a time? This chapter reports the experiments that answered them. The first half follows the reaction: the transmutation of nitrogen by natural alpha particles, and then the disintegration of lithium by protons from a machine — the first nuclear reaction produced entirely by human means and, more importantly for this book, the first quantitative test of the mass–energy equivalence of Relativistic Dynamics in a nuclear reaction. The second half follows the instruments, from Wilson's cloud chamber through Glaser's bubble chamber to Charpak's multiwire proportional chamber, which replaced the photograph with an electronic address and made the modern event rate possible.

The chapter is the experimental floor of Part XI — Quantum Field Theory and the Standard Model. Its nuclear reactions belong to Nuclear Forces and Nuclear Structure, where the binding-energy systematics they sample are developed and where Chadwick's discovery of the neutron — made in 1932 with the same scintillation technique used here, in the same laboratory, in the same year as the lithium disintegration — is treated in full [Chadwick:1932b]. Its instruments are the ancestors of every detector in Cosmic Rays and Astroparticle Physics, Experiment: Deep Inelastic Scattering and Experiment: The Higgs Boson Discovery. Five of the six experiments below were recognised by a Nobel Prize in Physics: Wilson in 1927, Lawrence in 1939, Cockcroft and Walton in 1951, Glaser in 1960 and Charpak in 1992.

Conventions and constants

Three conventions are used throughout, and they are worth stating before any number appears, because every one of the primary papers below uses different ones.

Nuclear masses are the evaluated atomic masses of the AME 2020 tables [Wang:2021], and are converted to energy with the CODATA 2022 value of the unified atomic mass constant,

to the precision needed here [Mohr:2025]. Because atomic rather than nuclear masses are used, the electrons balance on the two sides of every reaction written below, and no electron-mass correction is required.

Energies are quoted in electronvolts and in joules. The conversion is exact, since the elementary charge is a defining constant of the SI [Mohr:2025]:

Two further combinations recur, and are taken from Equations (107.1) and (107.2) of Nuclear Forces and Nuclear Structure, where they are fixed once from the same adjustment: \(\hbar c=197.32698\,\mathrm{MeV}\,\mathrm{fm}\) and \(e^{2}/(4\pi\varepsilon_{0})=1.4399645\,\mathrm{MeV}\,\mathrm{fm}\). Both are ordinary SI quantities written in convenient units — the first is \(3.1615\times 10^{-26}\,\mathrm{J}\,\mathrm{m}\), the second \(2.3071\times 10^{-28}\,\mathrm{J}\,\mathrm{m}\) — and \(\hbar\) and \(c\) appear explicitly in every equation below.

Ranges are the third convention and the one most easily misread. The experimenters of 1912–1932 quoted the penetrating power of a particle as the thickness of air at atmospheric pressure that would stop it, and inserted solid absorbers whose stopping power had been calibrated against air. A length is not the physical quantity: what stops a particle is the number of electrons it must pass, so the invariant statement is an areal mass density. At \(288.15\,\mathrm{K}\) and \(101.325\,\mathrm{kPa}\) the ideal-gas law with the mean molar mass of dry air, \(M_{\text{air}}=28.9647\times 10^{-3}\,\mathrm{kg}/\mathrm{mol}\) [Navas:2024], gives \(\rho_{\text{air}}=pM_{\text{air}}/(RT) =1.2250\,\mathrm{kg}/\mathrm{m}^{3}\), so

and every range quoted below is given both ways. Imperial units, in which two of the primary papers are partly written, are converted on sight and not reproduced.

Rutherford: the first artificial transmutation (1919)

Tests Phenomenon 117.2.

Apparatus

The apparatus is a scintillation counter with a gas cell in front of it, and nothing else. A rectangular brass box about \(0.18\,\mathrm{m}\) long, with an internal cross-section of roughly \(0.06\,\mathrm{m}\times0.02\,\mathrm{m}\), was closed at one end by a silver foil whose stopping power had been calibrated as equivalent to about \(6\times 10^{-2}\,\mathrm{m}\) of air, that is \(7.4\times 10^{-2}\,\mathrm{kg}/\mathrm{m}^{2}\) by Equation (117.3). Immediately beyond the foil sat a screen of zinc sulfide, viewed through a microscope of low power by an observer who had dark-adapted for half an hour in a light-tight room.

Inside the box, on a slide that could be moved along its length without breaking the seal, a metal disc carried an active deposit collected from radon gas. The alpha emitter in that deposit is radium C\('\), known today as \(^{214}\mathrm{Po}\): a nuclide of half-life \(1.64\times 10^{-4}\,\mathrm{s}\) which is fed continuously by the longer-lived members of the chain above it and which therefore behaves as a steady source. Its alpha particle is among the most energetic available from any natural source in useful quantity — thorium C\('\) (\(^{212}\mathrm{Po}\)), reached through the thorium active deposit and worked with at the Cavendish in the same period, is more energetic still, at \(8.785\,\mathrm{MeV}\) by the same mass balance [Wang:2021] — and its energy is not an experimental input but a consequence of a mass difference. The alpha decay energy from the mass evaluation is \(Q_{\alpha}=7.8335\,\mathrm{MeV}\) [Wang:2021], and the recoiling \(^{210}\mathrm{Pb}\) takes a share fixed by momentum conservation, so the alpha particle carries

which is the number quoted in every table of the period and the number used throughout this section. Its range in air at \(288.15\,\mathrm{K}\) and \(101.325\,\mathrm{kPa}\) is \(7.0\times 10^{-2}\,\mathrm{m}\), that is \(8.6\times 10^{-2}\,\mathrm{kg}/\mathrm{m}^{2}\).

The box could be filled with a dry gas of choice at a controlled pressure — oxygen, carbon dioxide, dry air, or nitrogen — and evacuated and refilled between runs. Gas purity is not a refinement here but the entire experiment: the effect looked for is the appearance of hydrogen nuclei, and hydrogen is the commonest contaminant in any vacuum system. The gas was therefore dried over phosphorus pentoxide, and the comparison between gases, rather than the absolute rate in any one of them, carries the argument.

The detector was the dark-adapted eye of the observer. A zinc sulfide screen converts the energy a stopping ion deposits into a flash of visible photons, and the flash from a single particle is at the edge of what the eye can see; the technique works only at rates of a few counts per minute, only in complete darkness, and only for observers who alternate in short shifts. Its virtue is that it counts single particles, and in 1919 nothing else did.

Procedure

Absorbing foils were interposed between source and screen and their stopping power expressed as an equivalent thickness of air, so that a count could be plotted against the distance the emerging particles were able to travel. Enough absorber was always present to stop every primary alpha particle: with the silver foil alone accounting for \(6\times 10^{-2}\,\mathrm{m}\) of air equivalent and the alpha range being \(7.0\times 10^{-2}\,\mathrm{m}\), a short additional path in the gas suffices, and whatever produced a scintillation on the screen therefore had a longer range than the alpha particles that made it.

The experiment is then a comparison between gases, made under four controls, each of which excludes a specific alternative.

First, the choice of filling gas. Oxygen and carbon dioxide contain no nitrogen and no hydrogen, and are chemically comparable stopping media; they are the null runs. Dry air is one fifth oxygen and four fifths nitrogen; pure nitrogen is the signal run. If the effect is proportional to the amount of nitrogen present it cannot be a property of the source, of the box, or of the screen.

Second, the source-to-screen distance and the gas pressure were varied independently. Both change the amount of gas traversed, and a genuine product of the gas must respond to their product and not to either separately.

Third, the absorber thickness was scanned. A particle with a definite energy has a definite range, so the count as a function of absorber falls to zero at a characteristic thickness; reading that end point is how an energy was measured before magnetic analysis was available in this energy range.

Fourth, the residual effect with the box evacuated was measured and subtracted. Hydrogen occluded in the source mount itself produces long-range particles by exactly the elastic mechanism the experiment must exclude, and that background is not small.

Observations and data

With oxygen or carbon dioxide in the box, no scintillations survived beyond the alpha range. With dry air, and more strongly with pure nitrogen, scintillations persisted at absorber thicknesses far beyond it — out to an air equivalent of about \(0.40\,\mathrm{m}\), that is \(0.49\,\mathrm{kg}/\mathrm{m}^{2}\) — and beyond the greatest range attainable by a hydrogen nucleus knocked on elastically by an alpha particle. The effect was small: a handful of scintillations per minute against an enormous number of incident alphas, which is why it took the full apparatus of scintillation counting to see it at all, and why the comparison between fillings rather than any absolute rate is the published result.

Table 117.1 collects the quantities the argument turns on. The historical rows are the observations; the computed rows are evaluated here from the mass evaluation [Wang:2021] and the kinematics derived below, and are what the observations have to be tested against. The counting uncertainties on the original scintillation tallies are Poissonian on tallies of order ten per run, that is of order \(30\,\mathrm{\%}\) per point; the ranges quoted from the paper are end points read off an absorption curve and are good to perhaps \(10\,\mathrm{\%}\). Neither is quoted to more precision than that here, and the original run-by-run tallies are not reproduced: what the paper establishes, and what is reproduced, is the ordering of the end points.

The uncertainty on the calculated rows deserves a word, because it is negligible and it is worth saying why. The AME 2020 evaluation quotes the masses of \(^{1}\mathrm{H}\), \(^{4}\mathrm{He}\), \(^{14}\mathrm{N}\) and \(^{17}\mathrm{O}\) to eleven significant figures, so the propagated uncertainty on the \(Q\) value of Equation (117.10) is at the level of electronvolts — six orders of magnitude below the \(0.1\,\mathrm{MeV}\) with which a range end point can be read. In this comparison the theory is exact and the measurement is not, which is the reverse of the usual situation and is what makes a nineteen-nineteen range measurement still worth reporting.

Interpretation

The long-range particles are hydrogen nuclei, and they cannot have come from hydrogen in the gas, for two independent reasons. Their range exceeds what an elastic collision can give — the ceiling in Table 117.1 is \(4.941\,\mathrm{MeV}\) and particles of longer range than that were counted — and the yield tracks the nitrogen content of the filling rather than the total amount of gas. Rutherford drew the conclusion in the plainest possible terms: the nitrogen atom is disintegrated.

What he could not establish was the fate of the alpha particle. Two possibilities remained open in 1919. The alpha might knock a proton out and continue, in which case four objects leave the collision point (alpha, proton, residual \(^{13}\mathrm{C}\), and nothing else) and a photograph of the event would show three tracks emerging. Or the alpha might be captured, in which case only two objects leave and a photograph shows two. That was settled six years later by Blackett, who photographed the collisions in a Wilson chamber (Section 117.5) and found, among some \(415000\) alpha tracks recorded on \(23000\) stereoscopic photographs, eight forks with exactly two branches and no third. A two-branch fork means the alpha particle did not survive the encounter: it was captured, and the reaction is

The counting is itself the measurement: eight events in \(415000\) tracks, each track traversing a few centimetres of air, is a yield of order \(10^{-5}\) per alpha, and a Poisson uncertainty of \(\sqrt{8}\approx3\) on eight events is why Blackett's number is a statement about the mechanism and not about the cross-section.

That the two branches also close the momentum triangle is what excludes the remaining alternative, that the alpha was captured and a neutral object emitted alongside the proton. In a stereoscopic pair the directions of both branches are measured, and the vector sum of the two final momenta must equal the incident momentum. Blackett's forks close; there is no missing momentum to assign to an unseen particle. The same argument run in reverse, on a reaction where the triangle does not close, is what Chadwick used in 1932 to establish the neutron [Chadwick:1932b], and it is the ancestor of every missing-momentum measurement in Experiment: The Higgs Boson Discovery.

This is the first transmutation of one element into another by deliberate human action, and it was done with a naturally occurring projectile whose energy the experimenter could not change. Removing that restriction is the content of Section 117.3.

Primary references

The observation is Rutherford's [Rutherford:1919], the fourth and last paper of a series in the Philosophical Magazine on the collision of alpha particles with light atoms; the first three establish the scintillation technique and the elastic behaviour of hydrogen and of the other light gases, which is what makes the fourth readable as a controlled comparison rather than as an isolated claim. It is worth reading for its caution: Rutherford states the anomaly, the controls that exclude contamination, and explicitly declines to say what became of the alpha particle.

Blackett's paper [Blackett:1925] is the identification, and it is a different kind of document — an exhaustive scan of a photographic record, with the eight forks reproduced and measured. The two together are the pattern this chapter follows throughout: a counting experiment establishes that something happens, and an imaging experiment establishes what. Wilson's instrument [Wilson:1912], reported in Section 117.5, is what made the second half possible, and it is seven years older than the anomaly it resolved.

Cockcroft and Walton: lithium split by accelerated protons (1932)

Tests Phenomena 40.6, 117.4 and 117.5. Assuming Theorem 9.76.

Apparatus

The apparatus divides into a high-voltage generator, an accelerating tube, and a scintillation counter of the kind already described in Section 117.2.

The generator is the part that carries the names. A transformer supplied an alternating potential of peak value \(V_{0}\) of order \(100\,\mathrm{kV}\), and a cascade of capacitors and rectifiers converted it to a steady direct potential several times larger. The principle is worth stating because it is the reason the machine existed. In a cascade of \(n\) stages, the alternating column of capacitors is charged through the rectifiers on alternate half cycles, each stage of the direct column ends up at \(2V_{0}\) above the one below it, and the output is

With four stages and \(V_{0}=100\,\mathrm{kV}\) this is \(800\,\mathrm{kV}\), which is what the Cavendish machine reached; in practice \(100\,\mathrm{kV}\) to \(700\,\mathrm{kV}\) was used. No component ever holds more than \(2V_{0}\) across it, which is what makes the arrangement buildable at all, and the same circuit — now called a Cockcroft–Walton generator — is still the first stage of many accelerator chains.

The direct potential was applied across a sealed accelerating tube built of glass cylinders about a metre long and \(0.3\,\mathrm{m}\) in diameter, with intermediate electrodes so that the drop was shared and no single gap had to hold the whole voltage. That constraint is physical, not merely engineering: the dielectric strength of air at atmospheric pressure is about \(3\times 10^{6}\,\mathrm{V}/\mathrm{m}\), so \(800\,\mathrm{kV}\) requires a clearance of at least \(0.27\,\mathrm{m}\) in air even between ideal electrodes, and several times that between real ones with sharp edges and dust. It is the reason the electrostatic route to high energies has a ceiling of a few megavolts, and hence the reason for Section 117.4.

Protons were drawn from a hydrogen discharge at the top of the tube, a canal-ray source running at a few kilovolts, delivering a beam current of order \(10^{-5}\,\mathrm{A}\) at the target with the tube continuously pumped to a residual pressure of order \(10^{-3}\,\mathrm{Pa}\). The target was lithium metal, deposited on a backing and set at an angle to the beam so that the products could leave sideways. They left through a mica window whose stopping power had been calibrated against air, and were counted as scintillations on a zinc-sulfide screen under a microscope, exactly as in Section 117.2; further mica sheets placed in front of the screen measured their range.

Procedure

The measurement has three parts, and only the third identifies the reaction.

The accelerating potential was set and measured — by a sphere gap and a resistance chain — and the scintillation rate recorded as a function of it, so that the yield curve could be followed downwards towards the point where the effect disappeared into the background. The importance of pushing the curve downwards rather than upwards is that the interesting statement is a lower limit on where the reaction is still detectable, which is a statement about the barrier and not about the apparatus.

The range of the emitted particles was then measured by absorption in mica, converted to an equivalent range in air by the calibration, and hence to an energy through the range–energy relation for helium nuclei established with natural alpha sources. The particles' behaviour in absorbers — the shape of the absorption curve near its end point, and the specific ionisation, which follows Equation (115.15) — identified them as helium nuclei rather than protons or electrons.

Finally, two screens were placed on opposite sides of the target and their scintillations examined for coincidence, with an observer at each. This is the step that turns a detection into an identification. If the particles are emitted singly, the two observers see uncorrelated flashes at a rate set by chance; if they are emitted in pairs travelling in opposite directions, the coincidence rate exceeds the accidental rate by a large factor. The kinematics of the proposed reaction makes that test sharp, as Equation (117.24) below shows.

Observations and data

Scintillations appeared with accelerating potentials as low as about \(125\,\mathrm{kV}\), and the yield rose rapidly as the potential was raised. The particles had a range in air of about \(8.4\times 10^{-2}\,\mathrm{m}\), that is \(0.103\,\mathrm{kg}/\mathrm{m}^{2}\), which for a helium nucleus corresponds to a kinetic energy of about \(8.6\,\mathrm{MeV}\), that is \(1.38\times 10^{-12}\,\mathrm{J}\); their behaviour in absorbers was that of ordinary alpha particles. The coincidence test showed them emitted in pairs, in opposite directions.

Table 117.2 sets the measured quantities beside the predictions computed here. Their accuracy is limited on the experimental side by the reading of a range end point, good to a few per cent, and by the calibration of the range–energy relation for helium nuclei; on the calculated side it is limited by nothing that matters, the mass-evaluation uncertainty on the \(Q\) value being of order \(10\,\mathrm{eV}\).

The second table is the sub-barrier behaviour, and it is computed rather than observed. Table 117.3 evaluates the semiclassical barrier transmission for a proton incident on a lithium nucleus at each of the accelerating potentials used, from the Gamow exponent of Equation (9.93). The point of tabulating it is that the numbers are not small in the way one expects of a tunnelling problem: the barrier here is low and thin, the exponent is of order unity to five, and a transmission of \(6\times 10^{-3}\) at the lowest potential is entirely consistent with a countable rate. It is the classical prediction — exactly zero at every potential in the table — that the observation contradicts.

Interpretation

Two alpha particles emitted back to back, with nothing else, identifies the reaction uniquely as

This is the first nuclear reaction driven by artificially accelerated particles: unlike Section 117.2, the projectile energy is now a knob on the apparatus, and the yield curve is a measurement rather than an accident of which radioactive source was to hand.

Its importance for this book, however, is quantitative. The energy released was measured directly, from the range of the products, and compared with the energy predicted by the difference of the masses — a prediction that has nothing to do with nuclear physics and everything to do with Phenomenon 40.6. The two agree. Cockcroft and Walton made the comparison in 1932 with the mass-spectrograph values then available, which gave a mass difference of about \(0.018\,u\) and hence an energy release close to \(17\,\mathrm{MeV}\), against the \(2\times8.6\,\mathrm{MeV}=17.2\,\mathrm{MeV}\) they measured; with the modern evaluation the prediction is \(17.3462\,\mathrm{MeV}\) (Equation (117.21)) and the kinematically correct comparison at \(90\,^\circ\) is \(8.785\,\mathrm{MeV}\) per alpha against a measured \(8.6\,\mathrm{MeV}\), a discrepancy of \(2\,\mathrm{\%}\) and entirely within the accuracy of a range measurement. This is the first quantitative confirmation of mass–energy equivalence in a nuclear reaction, and it was obtained from a table of atomic weights and a ruler laid against an absorption curve.

The comparison is worth appreciating for how little it assumes. The left-hand side of Equation (117.21) is measured by a mass spectrograph, an instrument that deflects ions in electric and magnetic fields and knows nothing of nuclear forces. The right-hand side is measured by the distance an alpha particle travels in mica. The only bridge between them is \(E=mc^{2}\). Had the two disagreed, no nuclear model would have been at fault; the relativistic energy–momentum relation of Relativistic Dynamics would have been.

A second reading of the same data was equally consequential. The reaction was observed at proton energies an order of magnitude below the height of the Coulomb barrier between a proton and a lithium nucleus, which classical mechanics forbids outright. The experiment is therefore also a direct confirmation of barrier penetration [Gamow:1928] [Gurney:1928] [Gurney:1929], whose other early evidence — alpha decay — is developed in Theorem 107.63 of Nuclear Forces and Nuclear Structure. It is a cleaner confirmation than alpha decay in one respect and a dirtier one in another. Cleaner, because the energy of the incident particle is set by the experimenter and can be varied, so the exponential dependence predicted by Equation (9.87) can be traced out rather than inferred from a correlation across nuclides. Dirtier, because the absolute yield involves the nuclear matrix element and the thick-target energy loss as well as the barrier, so only the shape of the curve is a clean test.

Primary references

Three papers report this work and they should be read in order. The Nature letter [Cockcroft:1932a] is the announcement, four weeks after the observation, and it is where the \(125\,\mathrm{kV}\) figure and the identification of the products as alpha particles first appear. The first Proceedings paper [Cockcroft:1932b] is about the machine and not about the physics: it is the reference for the cascade generator, the accelerating tube and the beam, and it is the document that made the technique reproducible elsewhere. The second [Cockcroft:1932c] is the full report of the disintegration, with the yield curve, the absorption measurements and the coincidence test.

The tunnelling interpretation rests on Gamow [Gamow:1928] and, independently, Gurney and Condon [Gurney:1928] [Gurney:1929], all published four years earlier for alpha decay; the Cockcroft–Walton experiment was in fact undertaken because Gamow's calculation, applied in reverse, showed that a few hundred kilovolts might suffice. That is worth noticing: this is one of the few experiments of the period designed from a quantum-mechanical prediction rather than interpreted by one afterwards.

Lawrence and Livingston: the cyclotron (1932)

Tests Phenomenon 117.8.

Apparatus

A flat evacuated brass chamber, about \(0.28\,\mathrm{m}\) across — eleven inches, in the units of the paper — placed between the circular pole faces of an electromagnet whose field is perpendicular to its plane and uniform to a fraction of a per cent over the working region. Inside it, two hollow D-shaped electrodes, the “dees”, face each other across a narrow diametral gap and are connected to a radiofrequency oscillator. The interior of each dee is a field-free region, being a closed conductor: the whole accelerating action takes place in the gap, and the dees exist to shield the ion from the alternating field during the half revolution in which that field would decelerate it.

An ion source sits at the centre, a filament and a gas feed producing hydrogen ions in the middle of the gap. A deflecting electrode at the periphery, held at a few kilovolts, pulls the beam out of its last orbit and onto a collector. The chamber was pumped to a residual pressure of order \(10^{-4}\,\mathrm{Pa}\), which is set not by any technical convenience but by the physics: the ion travels a total path length of order

inside the machine — using \(r_{k}=R\sqrt{k/N}\), since the energy grows linearly with the crossing count and the radius as its square root — and must not scatter out of resonance on the way. Put the requirement in areal density, which is what stops a particle. A proton of \(1.22\,\mathrm{MeV}\) has a range in air of about \(3.3\times 10^{-2}\,\mathrm{kg}/\mathrm{m}^{2}\), while \(73\,\mathrm{m}\) of air at \(1\,\mathrm{Pa}\) and \(288.15\,\mathrm{K}\) — a density of \(1.21\times 10^{-5}\,\mathrm{kg}/\mathrm{m}^{3}\) by Equation (117.3) scaled with pressure — presents only \(8.8\times 10^{-4}\,\mathrm{kg}/\mathrm{m}^{2}\). So \(1\,\mathrm{Pa}\) does not stop the beam outright; the pressure that would is about \(40\,\mathrm{Pa}\), and the residual pressure has to be far below even that, because a single elastic scatter through a small angle already takes the ion out of resonance. At \(10^{-4}\,\mathrm{Pa}\) the gas-kinetic mean free path \(k_{B}T/(\sqrt{2}\pi d^{2}p)\), with a molecular diameter \(d\approx3\times 10^{-10}\,\mathrm{m}\) and \(T=300\,\mathrm{K}\), is \(10^{2}\,\mathrm{m}\) — longer than the \(73\,\mathrm{m}\) orbit, and for a \(1\,\mathrm{MeV}\) proton, whose scattering cross-section is far below gas-kinetic, longer still. That is the margin the pump had to buy.

The magnet is the expensive component and the one that sets the energy. Everything else in the machine handles a few kilovolts.

Procedure

Ions released at the centre are bent by the magnetic field into a circle and cross the gap twice per revolution. If the oscillator frequency is matched to the revolution frequency, each crossing finds the gap field reversed and therefore accelerating, so the ion gains \(qV_{\text{gap}}\) at every crossing while its orbit grows as the square root of its energy.

The experiment consists of three measurements. First, tuning: the magnetic field is swept at fixed oscillator frequency and the collected current recorded, which produces a resonance curve whose peak locates the condition \(\omega_{c}=\omega_{\text{osc}}\) and whose width measures how far off resonance the machine will still accelerate. Second, the current at resonance, which measures how much beam survives the \(73\,\mathrm{m}\) of orbit of Equation (117.32). Third, the energy of the extracted beam, measured by absorption in foils against the known range–energy relation for protons — the same technique as Section 117.3, and the same one that provides the only independent check that the ions really did make a hundred and fifty turns.

The resonance curve is the crucial one, because it is what distinguishes this machine from a peculiar high-voltage device. A current that appears only in a narrow band of magnetic field, centred on the value that makes Equation (117.34) equal the oscillator frequency, cannot be explained by any static potential in the apparatus.

Observations and data

Protons of kinetic energy above \(1.2\,\mathrm{MeV}\) were obtained from a peak voltage on the dees of a few kilovolts, with beam currents of order \(10^{-9}\,\mathrm{A}\) at the collector. The ratio of the two voltages is the whole point: at about \(4\,\mathrm{kV}\) per gap crossing and two crossings per turn, the final energy corresponds to something like a hundred and fifty revolutions, and the accelerating voltage that has to be insulated anywhere in the machine is smaller than the beam energy in electronvolts by more than two orders of magnitude.

Table 117.4 collects the measured quantities and the machine parameters that follow from them. The field and frequency are not independent measurements but consequences of the resonance condition and the extraction radius, and are computed here; they are included because they are what the resonance curve actually determines.

Interpretation

The cyclotron removed the ceiling that high-voltage technique imposes. Cockcroft and Walton's method needs the full energy to exist as a potential difference somewhere in the laboratory, and the dielectric strength of air sets a limit of a few million volts; the cyclotron needs only the gap voltage, and buys energy with turns instead of volts. The exchange is not free — it is paid for in orbit length, in vacuum, and in magnetic-field uniformity — but all three are technical problems with technical solutions, whereas insulation is a material property.

Everything downstream in this treatise depends on that trade: the beams of Experiment: Deep Inelastic Scattering, the colliding beams of Experiment: The Higgs Boson Discovery, and the reactor and accelerator neutrino sources of Experiment: Neutrino Oscillations are all descendants of it. So is a large part of nuclear astrophysics, since the reaction cross-sections that Stellar Structure and Nucleosynthesis needs — the cross-sections whose Gamow-peak energies are computed in Theorem 107.85 — are measured on machines of this lineage, at energies where the direct astrophysical rate is unmeasurably small.

The classical cyclotron has one limit, and it is relativistic. As the ion's energy grows its revolution frequency falls, the resonance detunes, and acceleration stops. The cure is to modulate the frequency (the synchrocyclotron) or to raise the field in step with the energy at fixed radius (the synchrotron); both are corrections demanded by Relativistic Dynamics and by nothing else, and they are the reason no accelerator built after the 1940s is a cyclotron in the original sense. The 1932 machine sits exactly at the boundary, which is what makes it worth computing the phase slip below rather than merely asserting the limitation.

Primary references

The single reference is Lawrence and Livingston's Physical Review paper [Lawrence:1932], whose title — the production of high-speed light ions without the use of high voltages — states the whole result. It should be read alongside [Cockcroft:1932b], published the same year, since the two describe opposite solutions to the same problem and each is explicit about the limitation of the other's approach. Neither paper reports a nuclear reaction; the cyclotron's first disintegrations followed within months, using the lithium target of Section 117.3 as the obvious first check that the beam was real.

Wilson: the expansion cloud chamber (1912)

Tests Phenomenon 117.10.

Apparatus

A shallow cylindrical chamber with glass walls and roof, of order \(0.16\,\mathrm{m}\) in diameter and a few centimetres deep, containing dust-free air saturated with water vapour. Its floor is a piston whose sudden withdrawal expands the gas; the expansion is completed in a time of order \(10^{-2}\,\mathrm{s}\), short compared with the time in which heat can reach the gas from the walls, so it is adiabatic and therefore cools the gas, leaving the vapour supersaturated.

Three further elements make it an instrument rather than a demonstration. The expansion is stopped mechanically at a preset ratio, because the ratio is the control variable and must be reproducible to better than a per cent. The chamber is illuminated from the side by a bright flash — the illumination must be transverse, since the droplets are seen by scattered light against a dark background — and photographed, in the developed form stereoscopically, so that the track can be reconstructed in three dimensions. And a clearing field of order \(10^{3}\,\mathrm{V}/\mathrm{m}\) between electrodes above and below the gas sweeps out the ions left by previous events between expansions, without which the chamber accumulates a fog of old tracks.

Dust is the enemy and its removal is the reason the instrument took fifteen years to develop. Every dust grain is a condensation nucleus, and a chamber with dust in it fogs at any expansion. Wilson removed it by repeated expansions with the condensate allowed to settle, each cycle sweeping the remaining particles down with the droplets they nucleated.

Procedure

The expansion ratio is the control. Below a threshold no condensation occurs at all; above a first threshold droplets form on ions; above a second, higher one the vapour condenses on everything and the chamber fogs uniformly. Working between the two thresholds makes ions, and only ions, into condensation nuclei — and the existence of a window between the thresholds, rather than a single onset, is the physical fact on which the instrument rests. It is derived below.

The operating cycle is then fixed by the physics of droplet growth. The chamber is expanded in synchronism with the passage of the radiation under study — in the developed form, triggered by a counter telescope that has already registered the particle. The illumination is flashed a few hundredths of a second later: long enough for the droplets to grow by condensation to a size that scatters visible light efficiently, which requires a radius of order \(10^{-6}\,\mathrm{m}\), and short enough that diffusion has not yet blurred the trail. A water molecule in air at \(270\,\mathrm{K}\) has a diffusion coefficient of order \(2\times 10^{-5}\,\mathrm{m}^{2}/\mathrm{s}\), so in \(2\times 10^{-2}\,\mathrm{s}\) an ion wanders \(\sqrt{2Dt}\approx9\times 10^{-4}\,\mathrm{m}\) — under a millimetre, which is why the track is still sharp at that delay and would not be at one second.

After the photograph the chamber is recompressed, the clearing field applied, and the cycle repeated, at a rate of a few per minute. That duty cycle — seconds of dead time for each millisecond of sensitivity — is the instrument's defining weakness and is what Section 117.7 eventually removed.

Observations and data

The photographs show the paths of individual ionising particles as sharp lines of droplets. Alpha particles give dense, straight, sharply terminated trails, occasionally with a sudden deflection near the end where a nuclear encounter has occurred; fast beta particles give thin, tortuous trails; X-rays give no trail at all but a scatter of short electron tracks starting at points along the beam.

That contrast is quantitative and is the first thing the instrument measures. The specific ionisation of a charged particle behaves as Equation (115.15), so a slow or multiply charged particle ionises far more densely than a fast singly charged one. For an alpha particle of \(7.687\,\mathrm{MeV}\) depositing its whole energy in \(7.0\times 10^{-2}\,\mathrm{m}\) of air, the mean deposit is \(1.10\times 10^{8}\,\mathrm{eV}/\mathrm{m}\), that is \(1.76\times 10^{-11}\,\mathrm{J}/\mathrm{m}\); at a mean expenditure of about \(34\,\mathrm{eV}\) — \(5.4\times 10^{-18}\,\mathrm{J}\) — per ion pair in air [Navas:2024], that is roughly \(3.2\times 10^{6}\,/\mathrm{m}\) of track. A minimum-ionising electron in the same gas loses about \(2.2\times 10^{5}\,\mathrm{eV}/\mathrm{m}\), that is \(3.5\times 10^{-14}\,\mathrm{J}/\mathrm{m}\), and makes about \(6.5\times 10^{3}\,/\mathrm{m}\). The ratio, some five hundred, is exactly the difference between a dense unbroken trail and a sparse dotted one, and it is why the two species are distinguishable by eye in a photograph.

The thresholds themselves are the chamber's calibration, and are collected in Table 117.5. The expansion ratios are Wilson's; the temperatures and supersaturations are computed here from them by Equations (117.39) and (117.40), with no free parameter — the initial temperature is the only input and the saturation vapour pressure cancels.

The tabulated droplet densities of the original paper are not transcribed here. What is reproduced is the calibration that makes the instrument an instrument: the two thresholds, their ratio, and the prediction of both from the thermodynamics of a charged drop.

Interpretation

Before this apparatus, radiation was studied through the aggregate effects of very many particles — an ionisation current, a photographic blackening, a scintillation rate. The cloud chamber makes a single particle individually visible and individually measurable, and with a magnetic field applied it measures momentum and sign of charge from the curvature, through \(p_{\perp}=ZeB\rho\) (Equation (115.14)).

Everything that follows in this book from the inspection of individual events begins here: the two-branch forks that identified Equation (117.5) [Blackett:1925], the electron–positron pairs photographed by Blackett and Occhialini [Blackett:1933] and treated in Experiment: The Positron, and the cosmic-ray showers and strange particles of Cosmic Rays and Astroparticle Physics. In each case the decisive information is not a rate but a picture: how many branches, which way they curve, whether the momenta balance.

Its weaknesses defined the next two instruments. The gas is thin — a cubic metre of air holds \(1.2\,\mathrm{kg}\) of matter and a cubic metre of liquid holds a tonne — so interactions are rare and the chamber is a poor target; and the vapour must be re-expanded and allowed to settle, so the chamber is dead for most of every minute. Section 117.6 fixes the first, Section 117.7 the second.

Primary references

Wilson's 1912 paper [Wilson:1912] is the instrument paper and reads like one: most of it is about dust, valves, timing and the photography, and the tracks appear at the end as the demonstration that the apparatus works. The physics of the condensation window is older — it is Wilson's own work of the eighteen-nineties on the two expansion thresholds — and the theory of the charged drop is Thomson's [Thomson:1906], given there in the chapter on the condensation of vapour on ions.

The papers that made the instrument famous are not Wilson's. Blackett's identification of the nitrogen reaction [Blackett:1925], Blackett and Occhialini's photographs of electron–positron pairs [Blackett:1933], and the cosmic-ray work of Cosmic Rays and Astroparticle Physics are all cloud-chamber results, and each is a case where the answer was visible in a photograph and inaccessible to any counting experiment then available.

Glaser: the bubble chamber (1952)

Tests Phenomenon 117.12.

Apparatus

A small, scrupulously clean glass bulb of a few cubic centimetres, filled with diethyl ether and held under pressure at a temperature above its normal boiling point of \(307.7\,\mathrm{K}\). In the working condition the liquid sat near \(413\,\mathrm{K}\), where its saturated vapour pressure is about \(1.48\,\mathrm{MPa}\), roughly fifteen atmospheres; the bulb was held above that pressure so that the liquid stayed liquid. Releasing the pressure to about \(0.10\,\mathrm{MPa}\) leaves the liquid superheated by \(\Delta p\approx1.38\,\mathrm{MPa}\): it is far above its boiling point at the prevailing pressure and yet, in the absence of nucleation sites, does not boil.

A radioactive source could be brought up to the bulb or removed, or interposed behind lead, and the onset of boiling was registered — in the first experiments by timing, later photographically.

Cleanliness is the apparatus. A superheated liquid is metastable against boiling everywhere, and the barrier that protects it, Equation (117.50) below, is enormous only for a homogeneous liquid. A dissolved gas bubble, a dust grain, or a scratch on the glass provides a surface of large radius of curvature at which the barrier is absent, so the vessel boils at once and no measurement is possible. Glass was chosen for its smoothness, the bulbs were sealed after prolonged degassing, and the ether was purified; the experimental difficulty of the whole subject is in that sentence.

Procedure

The bulb is taken through a cycle: compress, heat, expand into the superheated state, wait. The quantity measured is the delay between the expansion and the onset of boiling, recorded many times over with the source present and with it absent, so that a shift in the distribution of delays is a statistical statement rather than an anecdote.

Two features of that protocol matter. The delay is a random variable, because nucleation is a stochastic process — a barrier crossing has an exponentially distributed waiting time — so the observable is a distribution and not a number, and the comparison must be between distributions. And the null run is not “no source” but “source shielded”, which controls for everything about the thermal cycle while changing only the radiation reaching the liquid.

The degree of superheat was varied, since the barrier Equation (117.50) depends on it as \(\left(\Delta p\right)^{-2}\) and therefore very steeply: too little superheat and even a radiation track cannot nucleate, too much and the liquid boils spontaneously and the chamber is useless. Finding the window is the same experimental problem as finding Wilson's condensation window in Section 117.5, and has the same two-sided structure.

Observations and data

Superheated ether that stayed liquid for a long time when shielded boiled promptly when an ionising source was brought near, and the distribution of delays shifted with the source strength. The nucleation is therefore caused by the radiation. Photographs of bubbles strung out along the paths of the ionising particles — the bubble chamber proper — followed shortly after.

Table 117.6 gives the thermodynamic state of the liquid in the working condition, with the critical bubble it implies. The temperature and the pressures are the operating point of the experiment; the surface tension, critical radius and barrier are computed here, and the surface tension in particular is an estimate rather than a measurement, obtained by scaling the room-temperature value with \(\left(1-T/T_{c}\right)^{1.26}\) to the working temperature, which is the corresponding-states form [Guggenheim:1945]. It is flagged as such because the barrier depends on its cube.

The measured delay distributions are not transcribed. What the table establishes is the quantitative frame in which they are read, and the frame is one-sided. A barrier of \(91.5\,k_{B}T\) is essentially never crossed by a thermal fluctuation — the derivation below puts homogeneous nucleation at about one event per clean cubic centimetre per week — while it is crossed at once where a heavily ionising particle has passed. The delays of seconds to minutes actually observed in the shielded runs are therefore not homogeneous nucleation: they are set by residual heterogeneous sites and by the ambient background radiation, which is why the cleanliness of the bulb is the apparatus and why the comparison is made between distributions rather than against a computed spontaneous rate.

Interpretation

The bubble chamber is the cloud chamber with the phase transition run backwards, and the exchange is decisive: the sensitive medium is now a liquid, roughly a thousand times denser than a gas, so it is a target as well as a detector. Air at \(288.15\,\mathrm{K}\) has a density of \(1.225\,\mathrm{kg}/\mathrm{m}^{3}\) and diethyl ether about \(714\,\mathrm{kg}/\mathrm{m}^{3}\), a factor \(580\); liquid hydrogen, at \(70.8\,\mathrm{kg}/\mathrm{m}^{3}\) [Navas:2024], is still a factor \(58\). Interactions that a cloud chamber would see once a month happen continuously, and the whole event — production point, decay point, and every charged secondary — is recorded in one picture.

Filled with liquid hydrogen the chamber becomes a pure proton target, which is what made it the workhorse of hadron physics; the Gargamelle heavy-liquid chamber's photographs of neutrino interactions with no outgoing muon or electron [Hasert:1973b] are the discovery of the weak neutral current, and hence part of the evidential base of Experiment: Deep Inelastic Scattering and of the electroweak theory. That result is a good illustration of the instrument's character: the signature is the absence of a track, which is a statement no counting experiment could make and only a complete picture of the final state can support.

Its limitation is the one Charpak removed. A bubble chamber cannot be triggered: the liquid is sensitive only during the few milliseconds after the expansion, so it must be expanded on a schedule synchronised with the beam and photographed whether or not anything interesting happened, and the film must then be scanned and measured by human beings. The rate is set by mechanics and by scanning tables, not by physics.

Primary references

Glaser's paper [Glaser:1952] is a two-page letter, and it is about the delay statistics of boiling in a superheated liquid; the track photographs that give the instrument its name came afterwards. It is worth reading as an example of an experiment whose published result is a shift in a distribution — there is no picture of a bubble in it — and whose importance is entirely in what the shift implies.

The instrument's scientific yield is documented elsewhere in this book rather than in Glaser's paper. The Gargamelle neutral-current photographs [Hasert:1973b] are the case discussed above; the hydrogen-chamber results on hadron spectroscopy underlie Experiment: Deep Inelastic Scattering, and the technique's decline is recorded in Section 117.7.

Charpak: the multiwire proportional chamber (1968)

Tests Phenomenon 117.14.

Apparatus

A plane of fine parallel anode wires, of the order of \(20\,\mu\mathrm{m}\) in diameter and spaced \(2\,\mathrm{mm}\) apart, stretched midway between two parallel cathode planes about \(8\,\mathrm{mm}\) away on either side, the whole in a gas mixture of a noble gas with a polyatomic quenching additive. The wires are held at a positive potential of a few kilovolts with respect to the cathodes.

Each of those dimensions is doing work. The wire must be thin because the field at its surface, and hence the avalanche gain, depends on its radius — Equation (117.54) — and a thick wire gives no multiplication at usable voltages. The spacing must be small because it sets the position resolution directly. The cathode gap must be several times the spacing, or the cells stop being independent and the field near each wire is distorted by its neighbours. And the quenching additive is not optional: a pure noble gas de-excites by emitting ultraviolet photons that liberate photoelectrons from the cathode metres away, so the avalanche propagates and the counter goes into permanent discharge. A polyatomic molecule absorbs those photons into vibrational modes and dissipates them, confining the avalanche to the wire that started it.

The decisive feature, however, is not the mechanics but the readout: every wire has its own amplifier and its own discriminator, so the chamber emits a pattern of logic pulses rather than an image. In 1968 that was newly affordable, and it is the reason the paper was written when it was.

Procedure

A charged particle crossing the gas leaves a track of electron–ion pairs — of order \(100\) of them in \(8\,\mathrm{mm}\) of argon at atmospheric pressure, at a mean expenditure of about \(26\,\mathrm{eV}\), that is \(4.2\times 10^{-18}\,\mathrm{J}\), per pair [Navas:2024]. The electrons drift towards the nearest anode wire through the low-field region between the cathodes, and in the last few tens of micrometres, where the field rises as \(1/r\) and exceeds the threshold for ionisation by collision, each initiates an avalanche whose gain is set by the wire voltage and the gas.

The measurements reported are those any new counter owes. The gas gain was measured against anode voltage, by comparing the collected charge with the known primary ionisation. The detection efficiency was measured against voltage with an external trigger — a scintillator telescope defining a particle's passage — which produces the characteristic plateau, a range of voltage over which efficiency is near unity and insensitive to the setting, and finding that plateau is what makes a counter usable. The time resolution was measured against the same trigger. And, the result that was not obvious in advance, the pulses on wires adjacent to the struck one were recorded, to establish that a chamber with wires two millimetres apart really does behave as a row of independent counters and not as one large one.

Observations and data

Each wire behaved as an independent proportional counter, with adjacent wires showing negligible cross-talk despite being only millimetres apart. Detection efficiency was high over a plateau of several hundred volts, the position was given to within the wire spacing, and both the time resolution — of the order of the maximum electron drift time computed in Table 117.7, which is what bounds it — and the rate a single wire could sustain were better than any photographic technique by orders of magnitude.

Uncertainties are owed on all of this and the paper quotes none, so what Table 117.7 carries are estimates from the mechanical tolerance of a wound wire plane and from the stability of a high-voltage supply, each flagged in the table. The efficiency and the time resolution are reported here as the paper reports them, in words and without a figure, because assigning them a numerical uncertainty would mean inventing the measurement they belong to; what the argument below needs from them is only that the plateau exists and that the resolution is drift-limited, and both are qualitative statements.

Table 117.7 gives the geometry, the reported performance, and the electrostatic quantities those imply, computed here from Equations (117.53) and (117.54) and from Equations (117.56) and (117.57). Table 117.8 is the avalanche gain against anode voltage, computed from Equation (117.55) with representative Townsend coefficients for argon; it is included because the steepness of that dependence is the whole reason a proportional chamber has an operating plateau at all, and because it is a closed-form consequence of the \(1/r\) field.

Interpretation

This is the change of era. A cloud or bubble chamber produces a photograph, and a photograph must be developed, scanned and measured by a person; the experiment's rate is therefore set by human labour. A bubble chamber cycles at a few hertz at best, and a scanner works through pictures at a rate of order one per minute, so a large experiment of the nineteen-sixties accumulated of order \(10^{6}\) pictures over years and employed rooms full of people to measure them. A multiwire chamber produces a number, immediately, on a wire, and a computer can read it; a single wire sustains of order \(10^{5}\,/\mathrm{s}\) and the limit is the electronics.

Triggering becomes possible with it — the apparatus can be told to record only events satisfying a condition, evaluated in the time between one particle and the next — and with it the whole strategy of searching for rare processes in an overwhelming background, which is how every result in Experiment: The Higgs Boson Discovery was obtained. Modern detectors record of order \(10^{9}\) interactions per second and select a handful for storage, and the reason they can is that the sensitive element gives an electronic address rather than an image.

The device also founded a family. Measuring the drift time of the electrons, rather than merely which wire fired, turns the wire spacing into a far finer coordinate: an electron drifting at \(5\times 10^{4}\,\mathrm{m}/\mathrm{s}\) covers \(50\,\mu\mathrm{m}\) in a nanosecond, so timing to a nanosecond gives a resolution an order of magnitude better than Equation (117.56) — that is the drift chamber. Extending the drift volume to metres and reading the arrival pattern on an endplate gives the time projection chamber; replacing wires with etched electrodes on a substrate gives the micropattern detectors of current practice. All of them are read out as numbers, and all of them descend from this experiment.

Primary references

The paper is Charpak and collaborators' [Charpak:1968], in Nuclear Instruments and Methods, and it is short. Its significance is easy to miss on a first reading because it claims very little: that a plane of closely spaced wires can be operated with each wire as an independent proportional counter, with the gains, efficiencies and time resolutions tabulated. The claim that was not obvious — and that the paper's referees would have been right to doubt — is the independence of the wires at millimetre spacing, which Equation (117.54) makes plausible and the measurements established.

What followed is not in this paper and is not any single paper. The technique displaced the bubble chamber over the following decade, and the detectors of Experiment: Deep Inelastic Scattering, Experiment: Neutrino Oscillations and Experiment: The Higgs Boson Discovery are all, in their tracking elements, its descendants.

Summary of the evidence

Table 117.9 contains no fitted parameter and no theoretical input beyond mass–energy equivalence, elementary electrostatics, the semiclassical barrier transmission of Section 9.6, and classical nucleation theory. The first two rows establish that nuclei can be rearranged at will and that the energy bookkeeping of Relativistic Dynamics holds when they are; the third makes the projectile energy an adjustable quantity rather than a gift of nature; the last three establish that the rearrangements can be counted, one at a time, at rates that rose by roughly six orders of magnitude across the half-century the table spans. Neither half is of any use without the other, which is why they are reported together here rather than split between a nuclear chapter and a detector appendix.

Two threads run through all six and are worth naming, because they recur in every later experiment in this part. The first is that the decisive measurement is almost never the one the experiment appears to be making. Rutherford's result is a comparison between gases, not a count; Cockcroft and Walton's is a coincidence rate, not a yield; Lawrence's is the width of a resonance curve, which is what proves the turn count; Glaser's is a shift in a distribution of delays. In each case the number that carries the physics is a ratio or a correlation, chosen because it is insensitive to the quantities the experimenter cannot control.

The second is that every one of the six instruments is a threshold device operated inside a deliberately chosen window. The cloud chamber must sit between two supersaturations, the bubble chamber between two superheats, the proportional chamber between the onset of multiplication and the onset of discharge, the scintillation counter between the eye's sensitivity and its fatigue, the cyclotron between resonance and relativistic detuning, the cascade generator between usable voltage and breakdown. Locating those windows is what the Procedure of each experiment above actually describes, and it is the part of experimental physics that no theory supplies.