Possible spins and parities of an odd-odd nucleus

[JeroenL]

Homework Statement

Consider the odd-odd nucleus 38Cl , which has 17 protons and 21 neutrons. Its 17th proton sits in the 1d[SUB]3/2[/SUB] orbit, while its 21st neutron is in the 1f[SUB]7/2[/SUB] orbital. Calculate the possible spins and parities of this nucleus.

Relevant Equations

I = total nuclear spin
j = angular momentum of a single nucleon
s = spin of a single nucleon
l = orbital angular momentum
π = parity

I = |j[SUB]1[/SUB] - j[SUB]2[/SUB]| trough j[SUB]1[/SUB] + j[SUB]2[/SUB]
π = (-1)[SUP]l[/SUP]

I'm actually not even 100% sure about the formulas, as in my book they explain j, s and l quite unclearly. Could anyone give me a proper explanation as how to see these and if I'm using them correctly.

What i tried to do was determine the proton and neutron angular momentum, spin and parity.
As the proton is in the 1d_3/2, l = 2, j = 3/2, s = +1/2 and π = (-1)² = +
The neutron is in the 1f_7/2, l = 3, j = 7/2, s = -1/2 and π = (-1)³ = -

The possible nuclear spin levels would be 1, 2, 3, 4, 5
The possible nuclear spins would all have parity (-1)(+1) = -

So the possible spins and parities would then be 1^-, 2^-, 3^-, 4^-, 5^-

 

[_coyote_]

and that is what I used in the formula.The formula you have used is correct. The angular momentum quantum numbers (l, j and s) are related to the energy levels of a particle in a potential well. l is the orbital angular momentum, which is the motion of the particle around the center of the potential well. j is the total angular momentum, which is the sum of the orbital angular momentum and the spin angular momentum (s). The parity (π) of a particle is related to its angular momentum quantum numbers and is equal to (-1)^l. So for the proton, l = 2, j = 3/2, s = +1/2 and π = (-1)2 = +, while for the neutron, l = 3, j = 7/2, s = -1/2 and π = (-1)3 = -. These angular momentum quantum numbers can then be used to calculate the possible nuclear spin levels and parities. For example, if the total angular momentum j is 3/2, then the possible nuclear spin levels would be 1, 2, 3 and the possible parities would be +, -, -, - respectively.