Why isn’t an atom’s nucleus round?

Since the atomic nucleus was first proposed in 1911, physicists simply assumed it was round. ​

But are the nuclei of atoms really round? Intuitively this shape makes sense and physicists believed it aptly explained early measurements of nuclear properties. It wasn't until years later that the first evidence of a more complex picture started to emerge.

First, let's explore the atom's architecture. Formed from a cluster of protons and neutrons at the center of an atom, a nucleus is 10,000 times smaller than the atom as a whole, "like a fly in a cathedral," said David Jenkins, a nuclear physicist at the University of York in the U.K. Despite containing the overwhelming majority of an atom's mass, the nucleus itself has very little impact on the atom's properties at first glance. An atom's chemistry is determined by the electron configuration, while any physical characteristics arise from how it interacts with other atoms.

Paralleling the idea of electron shells in atomic physics, in 1949 scientists proposed the nuclear shell model: protons and neutrons sit in distinct nuclear shells, and additional energy input can excite these particles to jump up and down between fixed energy levels.

"But later, it became obvious that most of the behavior in nuclei was described by what you call collective behavior — it acts as one coherent object," Jenkins told Live Science. The result is that the nucleus as a whole can then manifest two types of properties: It can rotate, or it can vibrate.

Related: Where do electrons get energy to spin around an atom's nucleus?

Spectroscopic methods can detect this rotation in most molecules, measuring a fingerprint of different rotational energy levels. But spherical objects look the same whichever direction they are turned, so symmetrical systems — like atoms — don't generate a spectrum.

"The only way that you can see evidence of rotation in nuclei is if the nucleus is deformed," Jenkins explained. "And people saw the nucleus has patterns of excitation known as rotational bands, so that pointed to the nucleus being deformed."

Since this astonishing discovery in the 1950s, targeted experiments have revealed a raft of nuclear shapes, from pears to M&Ms — and round is very much the exception and not the rule. About 90% of nuclei are shaped like an American football — technically termed "prolate deformed" — in their lowest energy state, with surprisingly few taking the opposite squashed-sphere, M&M-like shape, called oblate deformed.

"We don't know why this prolate shape seems more favorable than the oblate shape," Jenkins said. "Some nuclei also have multiple shapes so they can exhibit one in the ground state, and then you put some energy into them and they deform into another shape."

The more exotic pear-shaped nucleus is restricted to certain areas of the nuclear chart, particularly around radium, while spherical nuclei are generally confined to atoms with "magic" numbers (or full shells) of nuclear particles. But what causes the deformation?

"It feels intuitive that the basic shape of an object not being excited or wobbled or stretched should be spherical," said Paul Stevenson, a nuclear physicist at the University of Surrey in the U.K. "But actually, in the case of nuclei, it's surprising that any of them are spherical because they obey the laws of quantum mechanics."

The Schrödinger equation — one of the most fundamental principles in quantum mechanics — mathematically predicts how an object's wave function will change over time, essentially providing a means to estimate the possible movement and position of that object. Solving this for an atomic nucleus therefore provides a cloud of probability for all of the possible places it could be, which, taken together, give the nuclear shape.

"The basic solutions of Schrödinger's equation don't look spherical — you get these shapes that sort of go in a circle, but then they start waving," Stevenson explained. "So because these quantum wave-function solutions have asymmetry themselves, it makes the particles in the nucleus more likely to point in one direction."

For rare spherical nuclei, this waviness just happens to cancel out. But scientists don't yet understand the reason — or if there even is one — why some of these deformed shapes are much more common than others.

"This is overturning a legacy," Jenkins said. "It's a complete reversal from how people originally perceived nuclei, and there are still a lot of open questions."