Re: What is nuclear spin?

Alex,

There are two distinct but related concepts in your question: spin angular momentum and magnetic dipole moment. Spin is an essentially quantum mechanical notion that can be explained only loosely by analogy with macroscopic objects with which you are familiar not using the full mathematical machinery of quantum theory. When thinking this way, one must be careful not to stretch the analogy too far.

Spin is a kind of angular momentum. Consider for a minute the Earth in its orbit around the Sun. The Earth has an "orbital" angular momentum because it revolves around the Sun - this is the product of the Earth's mass, its speed, and its orbital radius. The Earth also has a "spin" angular momentum because it rotates on its north-south axis - this is the product of the Earth's moment of inertia and its angular speed. The spin is the angular momentum that is not due to orbital motion. The name "spin" is inspired by an object not orbiting but spinning on its axis like a top.

Now back to the proton. Even if the proton is not orbiting another object, even if you bring the proton to rest, it still possesses an angular momentum - this is the spin angular momentum. Is the proton really rotating on its axis like a tiny Earth? No. That would be stretching the analogy too far. The neutron also has a spin angular momentum. In fact, even pointlike particles like the electron and the quarks, which can not be pictured as little spinning balls because they have zero size, nevertheless have a spin angular momentum. What could be spinning? There is nothing there to spin. That is only one of the many bizarre consequences of quantum mechanics. Spin is an intrinsic angular momentum that particles have even when they are not orbiting anything. The net spin of a nucleus depends on the spins of the individual protons and neutrons that comprise it.

Now, magnetic dipole moment. Your textbook is employing a model of the proton to help you understand why the electrically charged proton has a north and a south magnetic pole like a bar magnet. Unfortunately, this simplistic model breaks down when applied to the electrically neutral neutron. (Another example of stretching the analogy too far.) The resolution to this paradox is that both the proton and the neutron are composed of quarks. The proton is made of two "up" quarks and one "down" quark, while the neutron is made of two "down" quarks and one "up" quark. Each pointlike electrically charged quark has its own spin angular momentum and its own magnetic dipole moment. When quarks combine to form composite particles, the spins and magnetic dipole moments add like vectors.

--Dr. Randall J. Scalise http://www.physics.smu.edu/scalise/