Spin-parity for excited O-15 states

In summary, the shell model can be used to determine the configurations and spin-parity of the first 5 excited states of O-15, with the ground state having a spin-parity of (1/2)-. The first excited state has a spin-parity of (1/2)+, with the possibility of promoting a neutron from the 1p_{1/2} subshell to the 1d_{5/2} subshell to create a spin-parity of (5/2)+. Other valid excitations include promoting a neutron from the 1s_{1/2} or 1p_{3/2} subshell to the 1p_{1/2} subshell, resulting in
  • #1
Warr
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Homework Statement



Use the shell model to find reasonable configurations for the first 5 excited states of O-15.

Homework Equations



The spin-parity and energy above the ground state for the first five excited states are:

ground state: (1/2)-

excited states:
5.18 MeV, (1/2)+
5.24 MeV, (5/2)+
6.18 MeV, (3/2)-
6.79 MeV, (3/2)+
6.86 MeV, (5/2)+

Parity of an unpaired nucleon is given by (-1)^l, with l_s = 0, l_p=1, etc.

The order of shells is: [tex]1s_{1/2}, 1p_{3/2}, 1p_{1/2}, 1d_{5/2}, 2s_{1/2}, 1d_{3/2}, 1f_{7/2}[/tex]

The Attempt at a Solution



First off, O-15 has 8 protons and 7 neutrons, so the ground state config is given by

protons: [tex](1s_\frac{1}{2})^2(1p_\frac{3}{2})^4(1p_\frac{1}{2})^2[/tex]
neutrons: [tex](1s_\frac{1}{2})^2(1p_\frac{3}{2})^4(1p_\frac{1}{2})^1[/tex]

so for the neutrons we have [tex](1p_\frac{1}{2})^{-1}[/tex]. This has a spin of 1/2 and l_p = 1, so the parity is -1, hence the state (1/2)-, confirming the ground state.

For the first excited state, we need the parity to be (1/2)+. Here is where my first confusion is. Can the [tex]1p_{1/2}[/tex] in the protons be promoted? If so, how high can it be promoted. For example, let's say it is promoted to the next subshell, [tex]1d_{5/2}[/tex]

protons: [tex](1s_\frac{1}{2})^2(1p_\frac{3}{2})^4(1p_\frac{1}{2})^2[/tex]
neutrons: [tex](1s_\frac{1}{2})^2(1p_\frac{3}{2})^4(1d_\frac{5}{2})^1[/tex]

Does this make the spin-parity (5/2)+? Or do we have to take something into account for the fact that there is now no neutrons in the [tex]1p_{1/2}[/tex] subshell (thus a gap between the protons in the [tex]1p_{3/2}[/tex] and the proton in the excited subshell [tex]1d_{5/2}[/tex]), yet there are 2 in the [tex]1p_{1/2}[/tex] for the neutrons.

are other valid 'excitations' to have a neutron in the [tex]1s_{1/2}[/tex] or [tex]1p_{3/2}[/tex] be promoted to the [tex]1p_{1/2}[/tex] shell, thus creating a spin parity of (1/2)+ and (3/2)- respectively? If these are right, I think I have the first 3 states.
 
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  • #2
"Does this make the spin-parity (5/2)+? "

Yes, so you only look where you have particles and "holes", and then couple them. In this case you have only one particle outside closed shells and paired nucleons, so its quantum numbers decides the total spin and parity of the nucleus.

And yes, you my break a pair and move that nucleon to higher shell and couple the angular momenta and parities. But remember that it requires energy to break pairs (approx 1MeV).
 

1. What is spin-parity for excited O-15 states?

Spin-parity is a quantum number that describes the intrinsic angular momentum and parity of a particle or system. In the case of excited O-15 states, it refers to the spin and parity of the nucleus when it is in an excited energy state.

2. How is spin-parity determined for excited O-15 states?

Spin-parity is typically determined through experimental methods such as nuclear reactions or gamma-ray spectroscopy. These methods involve bombarding the nucleus with particles or photons and analyzing the resulting energy levels and emitted radiation.

3. What is the significance of spin-parity for excited O-15 states?

Spin-parity provides important information about the structure and behavior of atomic nuclei. In the case of O-15, it can help us understand the nuclear forces and interactions that govern its behavior.

4. Can spin-parity change for excited O-15 states?

Yes, spin-parity can change for excited states as the nucleus absorbs or releases energy. This can result in different spin and parity values for different energy levels of O-15.

5. How does spin-parity affect the stability of excited O-15 states?

The spin-parity of a nucleus can affect its stability by influencing its decay modes and lifetime. For example, nuclei with certain spin-parity values may be more likely to decay through specific pathways, while others may have longer or shorter lifetimes based on their spin-parity values.

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