The Deuterium Nucleus Spin Question

[TriTertButoxy]

Ok, I have a question that's really irritating me.

I am trying to explain why deuterium's nucleus has a spin of 1.

By the addition of angular mometum of the individual nucleons (1 proton and 1 neutron) that make up the deuterium nucleus, there are three possible choices (from the triangle inequality theorem): 0, 1/2, and 1.

I can rule out 1/2 because that would imply that the z-component is either -1/2 or +1/2... something I can't do by adding the z-components of the angular momentum of the individual nucleons (you can only get 0 or 1).

But I can't seem to rule out the possibility of spin-0 deuterium nucleus.

Any thoughts?

 

[Meir Achuz]

It de[emds on the properties of the nuclear force. The n-p attraction is slightly stronger in the spin 1 state than in the spin zero state. The theoretical reason for this has to do with the exchange of pions between the n and the p.

 

[denian]

There are several factors that contribute to the spin of a nucleus, including the individual spins of the protons and neutrons, their relative orientations, and the overall shape and structure of the nucleus. In the case of deuterium, the addition of the individual spins of the proton and neutron does indeed result in three possible choices, as you have correctly identified. However, we must also consider the overall shape and structure of the nucleus, which can affect the spin. In the case of deuterium, the two nucleons are bound together in a specific way, resulting in a non-zero spin of 1. This is supported by experimental evidence and theoretical models.

Furthermore, ruling out the possibility of a spin-0 deuterium nucleus also requires considering the conservation of angular momentum. If the individual nucleons have non-zero spins and the overall nucleus has a spin of 0, this would violate the principle of conservation of angular momentum. Therefore, we can confidently say that the deuterium nucleus does indeed have a spin of 1, as supported by both theoretical models and experimental evidence.

In summary, the spin of a nucleus is a complex concept that is influenced by multiple factors, including the individual spins of the nucleons and the overall structure of the nucleus. In the case of deuterium, the combination of these factors results in a spin of 1, which is consistent with experimental data and theoretical models.