What are Z+, Z-, N+, and N- in the Axial Charge Definition?

[angweieng]

TL;DR

Understand N+, N-, Z+, and Z- and how to calculate them with spin consideration.

Hi all,

I was trying to understand an equation where:
axial charge, $G_A=g^P_A(Z_+-Z_-)+ g^N_A(N_+-N_-)$

What is the meaning of $Z_+$ , $Z_-$, $N_+$ and $N_-$? From the article I read, axial charge will be zero when the nuclei has zero spin. What if I have Germanium 73 which has (9/2+) spin? How do I calculate for $Z_+$ , $Z_-$, $N_+$ and $N_-$?

$g^P_A$ and $g^N_A$ here have constant values.

I don't have background of high energy physics but need the equation for my work, I really appreciate any help for this! Thank you so much!

 

[Astronuc]

Summary:: Understand N+, N-, Z+, and Z- and how to calculate them with spin consideration.

From the article I read, axial charge will be zero when the nuclei has zero spin.

What article was one reading?

Summary:: Understand N+, N-, Z+, and Z- and how to calculate them with spin consideration.

What if I have Germanium 73 which has (9/2+) spin?

Wouldn't the Z₊,Z_-;N₊,N_- be the number of spin states (+,-) respectively, where Z and N represent the number of protons and neutrons, respectively, in those spin states? To have a spin +9/2, means the 9 nucleons are unpaired.

Is one asking how to predict ⁷³Ge will have +9/2 spin?

Is one particularly interested in ⁷³Ge? ⁹³Nb and ¹¹³In are also stable odd(Z)-even(N) nuclides with +9/2.

 

[angweieng]

What article was one reading?Wouldn't the Z₊,Z_-;N₊,N_- be the number of spin states (+,-) respectively, where Z and N represent the number of protons and neutrons, respectively, in those spin states? To have a spin +9/2, means the 9 nucleons are unpaired.

Is one asking how to predict ⁷³Ge will have +9/2 spin?

Is one particularly interested in ⁷³Ge? ⁹³Nb and ¹¹³In are also stable odd(Z)-even(N) nuclides with +9/2.

Hi, thank you so much, the reason I ask to identify the $Z_+$ and $Z_-$ or $N_+$ and $N_-$ because I wish to calculate $G_A$ value. Assuming that I know the constant values of $g^p_A$ and $g^N_A$, what is the $Z_+$ and $Z_-$ or $N_+$ and $N_-$?

Now I understand that $Z_+$ and $Z_-$ mean the number of proton with spin up and spin down (same goes to neutron). In my case, my interested isotope is Ge73. In this case can I assumed that:
$Z_+$ = 16, $Z_-$ = 16
$N_+$ = 21, $N_-$ =20

Is it correct? Thank you so much again.