A nucleon occupies an orbital with orbital angular momentum (an orbital) coupled to…

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Nuclear Physics · Nuclear constituents, size and binding

The Nucleus Resolved, Ch Spin, parity and the electromagnetic moments of a nucleus

Problem

A nucleon occupies an orbital with orbital angular momentum

\ell = 3

(an

f

orbital) coupled to its spin

s = \tfrac12

. ((a)) List the allowed values of the total angular momentum

j

. ((b)) Evaluate

\langle\vec\ell\cdot\vec s\rangle

, in units of

\hbar^2

, for each allowed

j

. ((c)) A single proton occupies the

1f_{7/2}

orbital outside a

J^\pi=0^+

core. State the parity of this configuration. ((d)) Calculate the Schmidt value of the magnetic dipole moment of this proton, using

g_\ell = 1

and

g_s = 5.586

for a free proton.