# Angular momentum of an Odd-Odd nucleus (in its ground state)

• I
• JD_PM
In summary: The table must give one of the states as the ground state, and that is the one which is the ground state.
JD_PM
TL;DR Summary
Issue explaining why sometimes the table just gives one of the possible values for the total AM of an O/O nucleus.
What I know is the following:

The total angular momentum of the nucleus is just the total sum of the angular momentum of each nucleon.

If the nucleons are even the total angular momentum in the ground state will simply be ##0+##.

If the odd number of nucleons is close to one of the magic numbers then the shell model can explain what total angular momentum we'll get.

There are 3 cases to consider:

1) E/E nucleus (40-Ca for instance): Both proton and neutron numbers are even so the total angular momentum of the nucleus (I have read in other sources they call it Isospin) in the ground state will be ##0+##.

2) E/O nucleus (41-Ca for instance): The proton number is even. Thus the contribution by protons to the final angular momentum is none because ##j_p = 0##. What about neutrons? The unpaired neutron will be located in the 1f7/2 shell, then ##j_n = 7/2-##. Then the final angular momentum of 41-Ca in its GS will be ##I = 7/2-##.

Here comes my issue:

3) O/O nucleus (14-N for instance): here both proton and neutron numbers are odd so we expect that both contribute to the final angular momentum of 14-N.

Proton contribution: The unpaired proton will be located in the 1p1/2 shell, then ##j_p = 1/2-##.

Neutron contribution: The unpaired neutron will be located in the 1p1/2 shell, then ##j_n = 1/2-##.

$$I = 1+, 0+$$

But in the table just 1+ is given. Why?

JD_PM said:
Summary: Issue explaining why sometimes the table just gives one of the possible values for the total AM of an O/O nucleus.

$$I = 1+, 0+$$

But in the table just 1+ is given. Why?
Because the states of different angular momenta are not, in general, of equal energy.
Therefore only one of the different states is the ground state. The others must be excited states.
If the table must be that of ground states then it has to give just one, and namely the one which is the ground state.
Though this sometimes causes problems of relevance. Notoriously so with Ta-180.

vanhees71 and JD_PM
snorkack said:
Therefore only one of the different states is the ground state.

I see, but how can we predict theoretically which of the states is the GS?

In my example how can we know which is the GS? (I = 1+, 0+; the table says 1+ but I guess that is an experimental result).

## 1. What is the definition of angular momentum in the context of an Odd-Odd nucleus in its ground state?

Angular momentum refers to the measure of the rotational motion of a nucleus around its center of mass. In the case of an Odd-Odd nucleus, it is the sum of the individual angular momenta of the odd number of protons and neutrons in the nucleus.

## 2. How is the angular momentum of an Odd-Odd nucleus calculated?

The angular momentum of an Odd-Odd nucleus is calculated by multiplying the spin of the nucleus by its rotational frequency. The spin is determined by the number of unpaired protons and neutrons, while the rotational frequency is determined by the energy levels of the nucleus.

## 3. What is the significance of the angular momentum of an Odd-Odd nucleus?

The angular momentum of an Odd-Odd nucleus is an important property that affects the stability and behavior of the nucleus. It can also provide information about the nuclear structure and the interactions between protons and neutrons within the nucleus.

## 4. How does the angular momentum of an Odd-Odd nucleus change as it transitions to different energy levels?

The angular momentum of an Odd-Odd nucleus remains constant as it transitions to different energy levels. However, the orientation of the angular momentum vector may change, resulting in different nuclear states with different spin and parity values.

## 5. Can the angular momentum of an Odd-Odd nucleus be altered or manipulated?

Yes, the angular momentum of an Odd-Odd nucleus can be altered or manipulated through external factors such as an external magnetic field or collisions with other particles. This can result in changes to the nuclear structure and properties of the nucleus.

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