A nucleon occupies an orbital with (a orbital) coupled to its spin .

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

\ell = 2

d

orbital) coupled to its spin

s = \tfrac12

. ((a)) List the allowed values of

j

. ((b)) Evaluate

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

, in units of

\hbar^2

, for each allowed

j

. ((c)) A single neutron occupies the

1d_{3/2}

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 neutron, using

g_\ell = 0

and

g_s = -3.826

for a free neutron.