Give the expected shell-model spin and parity assignments for the ground states
ID: 494773 • Letter: G
Question
Give the expected shell-model spin and parity assignments for the ground states of^7Li;^11B;^15C:^17F;^31P;^141 Pr. the low-lying levels of^3C are ground state, 3.09 MeV, 1/2 +; 3.68 MeV, 1/2; 3.85 MeV. 5/2^+. the next states are about 7 MeV and above. Interpret these four states according to the shell model. in the single-particle shell model, the ground state of a nucleus with an odd proton and an odd neutron is determined from the coupling of the proton and neutron shell-model states: I = j_p + j_n. Consider the following nuclei:^16N - 2^-;^12B - 1+;^34P - 1+;^28Al - 3+. Draw simple vector diagrams illustrating these couplings, then replace j_p and respectively, by l_p + s_p and + s_n. Examine your four diagrams and deduce an empirical rule for the relative orientation of J_p and s_n in the ground state. Finally, use your empirical rule to predict the I^pi assignments of^26Na and^28Na. Compute the expected shell-model quadrupole moment of^209Bi (9/2) and compare with the experimental value, -0.37 b.Explanation / Answer
if we had a lithium-7 (Z=3) nucleus, say where the a proton from 1 s 1 / 2 was excited (by some means) to the 2s1/2 state. Now we have 2 unpaired protons, one in the 1p3/2 state and the 2s1/2 what would the spin and the parity of this nucleus be?
Do we still look at the unpaired nucleon in teh outermost shell only? In this case, then the spin would be
(1/2)+, since the j value of the outermost nucleon in 1/2 and l=0.
(Spin and parity is given by i
where i=j and
=(1)l
a) 3 Li7 (lithium) (p) 3/2-
b) 4Be9 (beryllium) (n) 3/2-
c) 20Ca40 (calcium) 0+
d) 5B11 (boron) (p) 3/2-
e) 6C15 (carbon) (n) 5/2+
f) 15P31 (Phosphorus) (p) 1/2+
g) 59Pr141 (Praseodymium) (p) 5/2+
h) 11Na23 (sodium) (p) 5/2+
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