Measuring lead nucleus tells of neutron stars

Physicists have just collected the most accurate measurement of the thickness of the neutron ‘skin’ of a lead (Pb) nucleus, and it could help them figure out the structure and size of neutron stars.

Atoms have a nucleus filled with protons and neutrons. The number and distribution of these subatomic particles, plus how they interact with each other, determine the identity and properties of the atom.

A team of physicists at the Thomas Jefferson National Accelerator Facility, US, measured the size of the sphere of neutrons that surrounded the protons in lead; it had a thickness of 0.28 millionths of a nanometre, they report in a paper, published in Physical Review Letters.

Lighter nuclei usually have a similar number of protons and neutrons, but bigger nuclei with lots of protons need extra neutrons to balance them out. For example, one isotope of lead has 82 protons and 126 neutrons.

“The question is about where the neutrons are in lead,” says Kent Paschke from the University of Virginia, US. “Lead is a heavy nucleus – there’s extra neutrons, but as far as the nuclear force is concerned, an equal mix of protons and neutrons works better.

“The protons in a lead nucleus are in a sphere, and we have found that the neutrons are in a larger sphere around them, and we call that the neutron skin.”

Neutrons are tricky to measure, so the team used a technique that measured weak nuclear force instead of electric charge.

“Protons have an electric charge and can be mapped using the electromagnetic force,” explains Paschke. “Neutrons have no electric charge, but compared to protons they have a large weak charge, and so if you use the weak interaction, you can figure out where the neutrons are.”

The team collected the measurement by shooting a beam of electrons into a sheet of cryogenically cooled lead and measuring the direction of the electrons as they rebounded off the sheet.

“On average over the entire run, we knew where the right- and left-hand beams were, relative to each other, within a width of 10 atoms,” says Krishna Kumar, of the University of Massachusetts Amherst.

“The charge radius is about 5.5 femtometres [1 nanometre = 1 million femtometres],” says Paschke. “And the neutron distribution is a little larger than that – around 5.8 femtometres, so the neutron skin is 0.28 femtometres, or about 0.28 millionths of a nanometre.”

The thickness of the skin was larger than previous measurements, which could have implications for the size of neutron stars: stars which were so big they collapsed and crushed their protons and electrons into neutrons.

“We need to know the content of the neutron star and the equation of state, and then we can predict the properties of these neutron stars,” says Kumar. “So, what we are contributing to the field with this measurement of the lead nucleus allows you to better extrapolate to the properties of neutron stars.”

As neutron stars spiral around each other, they emit gravitational waves that are detected by the Laser Interferometer Gravitational-wave Observatory (LIGO).

“As [the neutron stars] get close in the last fraction of a second, the gravitational pull of one neutron star makes the other neutron star into a teardrop – it actually becomes oblong, like an American football,” says Kumar.

“If the neutron skin is larger, then it means a certain shape for the football, and if the neutron skin were smaller, it means a different shape for the football. And the shape of the football is measured by LIGO.

“The LIGO experiment and the [current lead] experiment did very different things, but they are connected by this fundamental equation – the equation of state of nuclear matter.”

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