Neutrons Knock at the Cosmic Door

Figure 1 (Left) Neutron mirror apparatus. An ultracold neutron (UCN) enters a space between two mirrors that act as potential wells, giving rise to a discrete energy spectrum. A detector measures neutrons exiting the cavity formed by the mirrors. The bottom mirror sits upon a nanopositioning table that induces a vertical oscillation that produces dips in the neutron transmission at the resonances. (Right) Energy-level diagram for the neutrons in a gravitational field caught between the walls, which oscillate owing to the mirror motion (horizontal direction here is vertical in the apparatus). This, in turn, causes the neutrons to move up and down energy levels. A measurement of the energy-level spacing yields constraints on parameters of scenarios describing dark energy and dark matter, which would slightly shift the levels as indicated by the dashed lines.

Figure 1 (Left) Neutron mirror apparatus. An ultracold neutron (UCN) enters a space between two mirrors that act as potential wells, giving rise to a discrete energy spectrum. A detector measures neutrons exiting the cavity formed by the mirrors. The bottom mirror sits upon a nanopositioning table that induces a vertical oscillation that produces dips in the neutron transmission at the resonances. (Right) Energy-level diagram for the neutrons in a gravitational field caught between the walls, which oscillate owing to the mirror motion (horizontal direction here is vertical in the apparatus). This, in turn, causes the neutrons to move up and down energy levels. A measurement of the energy-level spacing yields constraints on parameters of scenarios describing dark energy and dark matter, which would slightly shift the levels as indicated by the dashed lines.

Wolfgang P. Schleich, Ernst Raselhttp://physics.aps.org/articles/v7/39

The quantum behavior of a neutron bouncing in the gravitational field of the Earth can improve what we know about dark energy and dark matter.

Spectroscopy has always set the pace of physics. Indeed, the observation of the Balmer series of the hydrogen atom led to the Bohr-Sommerfeld model about 100 years ago. A little later the discreteness of the spectrum moved Werner Heisenberg to develop matrix mechanics and Erwin Schrödinger to formulate wave mechanics. In 1947, the observation of a level shift in hydrogen by Willis E. Lamb ushered in quantum electrodynamics.

Now, a group led by Hartmut Abele of the Technical University of Vienna, Austria, reports, in Physical Review Letters [1] [http://arxiv-web3.library.cornell.edu/abs/1404.4099], experiments that once more take advantage of the unique features of spectroscopy to put constraints on dark energy and dark matter scenarios. However, this time it is not a “real atom” (consisting of an electron bound to a proton) that provides the insight. Instead, the research team observes an “artificial atom”—a neutron bouncing up and down in the attractive gravitational field of the Earth (Fig. 1). This motion is quantized, and the measurement of the separation of the corresponding energy levels allows these authors to make conclusions about Newton’s inverse square law of gravity at short distances.

Setup and results for the employed gravity resonance spectroscopy: Left: The lowest eigenstates and eigenenergies with conning mirrors at bottom and top separated by 30.1 µm. The observed transitions are marked by arrows. Center: The transmission curve determined from the neutron count rate behind the mirrors as a function of oscillation frequency shows dips corresponding to the transitions shown on the left. Right: Upon resonance at 280 Hz the transmission decreases with the oscillation amplitude in contrast to the detuned 160 Hz. Because of the damping no revival occurs. All plotted errors correspond to a standard deviation around the statistical mean. [http://arxiv-web3.library.cornell.edu/abs/1404.4099]

Setup and results for the employed gravity resonance spectroscopy: Left: The lowest eigenstates and eigenenergies with conning mirrors at bottom and top separated by 30.1 µm. The observed transitions are marked by arrows. Center: The transmission curve determined from the neutron count rate behind the mirrors as a function of oscillation frequency shows dips corresponding to the transitions shown on the left. Right: Upon resonance at 280 Hz the transmission decreases with the oscillation amplitude in contrast to the detuned 160 Hz. Because of the damping no revival occurs. [arxiv]

The energy wave function of a quantum particle in a linear potential [2], corresponding, for example, to the gravitational field close to the surface of the Earth, has a continuous energy spectrum [3]. However, when a quantum particle such as a neutron is also restricted in its motion by two potential walls, the resulting spectrum is discrete.

Read also: “With neutrons, scientists can now look for dark energy in the lab

This elementary problem of nonrelativistic quantum mechanics is a slight generalization of the familiar “particle in a box” where the bottom of the box, which usually corresponds to a constant potential, is replaced by a linear one representing the gravitational field. Continue reading Neutrons Knock at the Cosmic Door

Neutrons Become Cubes Inside Neutron Stars

Intense pressure can force neutrons into cubes rather than spheres, say physicists

Trial wavefunction that interpolates between sphere (for N = 2), and cube (as N → ∞) for N = 2, 4, 8, 12.

Inside atomic nuclei, protons and neutrons fill space with a packing density of 0.74, meaning that only 26 percent of the volume of the nucleus in is empty.

That’s pretty efficient packing. Neutrons achieve a similar density inside neutron stars, where the force holding neutrons together is the only thing that prevents gravity from crushing the star into a black hole.

Today, Felipe Llanes-Estrada at the Technical University of Munich in Germany and Gaspar Moreno Navarro at Complutense University in Madrid, Spain, say neutrons can do even better.
These guys have calculated that under intense pressure, neutrons can switch from a spherical symmetry to a cubic one. And when that happens, neutrons pack like cubes into crystals with a packing density that approaches 100%.
Anyone wondering where such a form of matter might exist would naturally think if the centre of neutron stars. But there’s a problem.
On the one hand, most neutron stars have a mass about 1.4 times that of the Sun, which is too small to generate the required pressures for cubic neutrons. On the other, stars much bigger than two solar masses collapse to form black holes.
That doesn’t leave much of a mass range in which cubic neutrons can form.
As luck would have it, however, last year astronomers discovered in the constellation of Scorpius the most massive neutron star ever seen. This object, called PSR J1614-2230, has a mass 1.97 times that of the Sun.
That’s about as large as theory allows (in fact its mere existence rules out various theories about the behaviour of mass at high densities). But PSR J1614-2230 is massive enough to allow the existence of cubic neutrons.
Astrophysicists will be rubbing their hands at the prospect. The change from spherical to cubic neutrons should have a big influence on the behaviour a neutron star. It would change the star’s density, it’s stiffness and its rate of rotation, among other things.
So astronomers will be getting their lens cloths out and polishing furiously in the hope of observing this entirely new form of matter in the distant reaches of the galaxy.
Ref: arxiv.org/abs/1108.1859: Cubic Neutrons

My favourite particle: the neutron

A guest post by Jim Grozier on particles you can store in a beryllium bottle without a lid on
I’m not really one for favourites, but I do have a soft spot for the neutron; and after all, it would be a shame to leave it out, wouldn’t it?

There are two things I really like about neutrons, and these in turn will lead me on to talking about two of my favourite experiments. The first thing I like is that you can bottle them: you can put them in a container and they just stay there, until either you let them out or they decay (which they do in about 15 minutes). Well, OK, you can also bottle protons and electrons, but your bottle has to be made of magnetic fields, and these have to be shaped very carefully to stop the particles escaping. With neutrons, you need just two things: a container lined with a suitable material (beryllium will do) and a way of slowing your neutrons down a bit.

A beam of neutrons at room temperature.

The speeds of particles can be expressed in various ways. In particle accelerators it is common to quote the kinetic energy of the particle (usually in giga-electron-volts or GeV); this is related to the speed, although the actual relationship is quite complicated because particles in accelerators travel at near-light speeds, where special relativity has to be taken into account. But you can also describe them in terms of temperature. The temperature of a gas, for instance, is related to the average speed of its molecules (or, to be more precise, it’s actually the squares of the speeds that are averaged) and since a collection of particles behaves something like a gas, the temperature analogy can be useful here too. For instance, we speak of “thermal” neutrons as free neutrons that have acquired, by collision, the same kinetic energy as the atoms of the medium they are travelling in, when that medium is the moderator in a nuclear reactor – so, rather hot, by human standards. (They have a temperature of the order of 1000 K, and speeds of a few km/s). But you can slow them down so that they become cold, then very cold , and finally ultra-cold neutrons (UCN). Ultra-cold neutrons are travelling at just a few metres per second – you could keep abreast of them at a run. (Unfortunately, as visitors to Sellafield are told by their guide, you couldn’t keep abreast of the neutrons from an explosion in a nuclear fuel reprocessing plant, but that is another story).

Something strange happens when neutrons reach this ultra-cold region: they have so little energy that they are unable to escape from our special beryllium-lined bottle. As they approach the wall of the vessel, they feel a repulsive force caused by something called the Fermi potential, which is a characteristic of the material. They can’t get through, so they just bounce off. (Strictly speaking, the “bottle” doesn’t even need a lid if it is more than about 2 metres high, as any UCN reaching that height will have lost all its energy in climbing through the earth’s gravitational field. Yes, they are that slow.)

Storing neutrons in this way is a tremendous advantage if you are doing an experiment into the nature of the neutron, especially if your experiment takes a long time. When the bottling of neutrons was first achieved, in the 1970s, it provided a huge boost to an experiment that had already been running, off and on, for 20 years by then, and is still running, in a later incarnation, today. It is the experiment to measure theelectric dipole moment (EDM) of the neutron, and it first came about as a result of a bet between Richard Feynman and fellow-US physicist Norman Ramsey, over the question of parity conservation. Parity conservation is another story entirely; suffice it to say that in 1950 it was thought that the violation of parity conservation would be accompanied by an asymmetry in the charge inside the neutron. Now the neutron is an electrically neutral particle, hence its name, but it is thought to have charged constituents (see Lily’s blog on quarks), and therefore it is possible that the charge is not distributed uniformly, which would produce a non-zero EDM. And in fact a non-zero EDM would help us to understand one of the great mysteries of the universe, which is why all the matter and antimatter that came into being at the Big Bang didn’t just annihilate each other, but in fact left a small residue of matter, enough to make all the stars, planets, and us. So in other words it’s quite important. (See Mark’s blog on the muon for more details). The EDM experiment requires us to observe our neutrons over as long a time as possible, so bottling them is obviously beneficial.

The neutron EDM experiment is still going on today. No-one has yet found a non-zero value for this quantity; what the experiment has done, over the years, is to drive down the uncertainties by several orders of magnitude. In other words, what the experiments have been able to show is that there is a high probability that the EDM lies somewhere between two limiting values, and those limiting values have been getting closer and closer to each other all the time. The results of all quantitative experiments are expressed in this way: a central value is given, together with a measure of how far away from that value the true value is likely to be. This measure is sometimes called the error, but I think that gives the wrong impression – it makes it look like we are saying we have made a mistake, when we haven’t. It is better to call it the uncertainty. And one of the things you learn when you study science is that there is always an uncertainty – you can’t eliminate it entirely. (This is nothing to do with Heisenberg’s Uncertainty Principle, by the way, which links together uncertainties in various pairs of quantities).

This brings me on to the second experiment I want to tell you about. Unlike the EDM experiment, it’s not one I have been involved in, or even know very much about. It’s the very existence of the experiment that appeals to me. It’s an experiment to measure the electric charge of the neutron.

Hang on a minute, I hear you say. Didn’t you just tell us, a couple of paragraphs back, that the neutron is electrically neutral, in other words its charge is zero? So why is someone trying to measure it?

Well, OK, we “know” that the neutron is neutral because our current best theory of the neutron – the Standard Model of particle physics – predicts that its charge will be zero. But like all predictions of theory, that one has to be tested in the laboratory; so far, the results of experiment are consistent with the prediction, but no-one will ever be able to confirm that it is indeed precisely zero – only that it is zero plus or minus the uncertainty, which, last time I looked, was roughly 0.000000000000000000001 times the charge on the electron. Now that’s small, but it is not zero, and however much we refine the experiment, it will never be zero.

So it looks like the knowledge we have of the universe falls into two categories: theoretical knowledge, which offers precise, clean-cut answers which are, in a sense, “at one remove” from reality; and experimental knowledge, which gives us first-hand answers that tend to be messy and probabilistic. Quite often, when scientists say they know something, it is the former kind of knowledge they are talking about. So, the next time you hear a scientist saying that we “know” that, say, dark matter exists, it will probably just mean that a theory in which dark matter exists is consistent with the results of experiment, not that someone has actually detected any.

http://www.guardian.co.uk/science/life-and-physics/2011/jul/14/1