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Those who read my diaries regularly know that neutrinos are one of my obsessions, and so I will tend to zero in on any progress on understanding them. For a brief review of what neutrinos are, I will quote myself:
Neutrinos are ghostly particle that have no charge, at most very little mass, and travel at speed close to that of light. They only interact with other particles through the weak nuclear force, which can change a neutron to a proton, ejecting an electron, or (for an antineutron) change a proton into a neutron, ejecting a positron (antielectron). Because the weak force is so weak, such events happen rarely, so observing these particles is quite difficult. Trillions of neutrinos are passing through your body every second, but you’d never know it because so few actually interact with the nuclei in your body.
Some of my neutrino diaries have focused on neutrino mass, a subject of active research as it is known that these particles have a tiny rest mass, though no one yet has managed to measure it. Tonight, however, I want to focus on the size of a neutrino, that is, the extent of space taken up by a neutrino. There is a new experimental result in a recently published article that gives a lower limit for the size of an electron neutrino.
Now you might think that a fundamental particle with a tiny mass must itself be very tiny, but we’re in the land of quantum theory, where you have to get used to counterintuitive ideas. When we consider the spacial aspects of a quantum particle, we always have to keep the Heisenberg uncertainty principle in mind. The common way nonscientists think of the uncertainty principle is that if you know where are particle is, you don’t know where it’s going, and vice versa. However, there is a more precise statement that relates the uncertainties in particle location and momentum in a quantitative fashion, to be precise:
The Heisenberg uncertainty relation for position and momentum of a particle.
Here, Δx represents the particle’s uncertainty in position, Δp represents the particle’s uncertainty in momentum, and the product of these two quantities is always greater than or equal to a universal constant (Planck’s constant divided by 2). In the absence of any other information, the uncertainty of the position of the particle can simply be taken as an estimate for the size of the particle. If it’s not possible to measure Δx directly, it may be possible to obtain a measurement of Δp, whereby one can use the above equation to calculate Δx, and hence have an estimate on the size of the particle. This is the principle on which the new measurement is based.
Now consider this equation in the context of the very-low-mass neutrino. Momentum is mass times velocity, and because the neutrino mass is so tiny, we can expect Δp to be a very small number. In order for ΔxΔp to still equal to Planck’s constant, Δx (i. e. the size of the neutrino) would have to be quite large. Estimates for the size of a neutrino, previous to the new study, have ranged from smaller than an atomic nucleus to a couple of meters (say, 6 or 7 feet), which is a gargantuan range. The new experiment places a lower limit to this range.
In this experiment, the researchers measured the recoil energy of an atom undergoing a nuclear decay in which a neutrino is released. In this case, the atom in question is beryllium-7 (7Be), and the nuclear decay it undergoes is called electron capture (EC), where an electron within the atom is captured by a neutron in the nucleus, converting the atom to lithium-7 and releasing a neutrino. The 7Be atoms are placed on a superconducting tunnel junction, which is capable of measuring the recoil energy of the lithium atom. These measurements are repeated many times to obtain a distribution of recoil energies. The width of the distribution is taken to be the uncertainty of the recoil energy. From the uncertainty in the recoil energy, it is possible to calculate the uncertainty in the recoil momentum. From Newton’s third law of motion, it’s apparent that the uncertainty in the recoil momentum of the lithium atom is equal to the uncertainty in the momentum of the ejected neutrino, so this quantity is the Δp that gets plugged into the above equation. What comes out as Δx, the estimated lower limit of the size of the neutrino, is 6.2 picometers (6.2x10-12 meters). This is smaller than an atom (50-300 pm) but much larger than an atomic nucleus (~0.001 pm). Hence, when the electron capture takes place in the tiny volume of the beryllium nucleus, a honkin’ huge neutrino comes flying out. Plus, keep in mind that this measurement is just a lower limit; the neutrino could still be as large as a couple meters in diameter.
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