The ground state of ( ) has and is described as a single proton in the orbital ( , )…

PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · Nuclear constituents, size and binding · The nuclear force and nuclear models

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

Problem

The ground state of

^{121}\mathrm{Sb}

(

Z=51

) has

J^\pi=\tfrac52^+

and is described as a single proton in the

1d_{5/2}

orbital (

\ell=2

j=\tfrac52

) outside a core with

J^\pi=0^+

. Its measured spectroscopic quadrupole moment is

Q_{\rm sp}=-0.36\,e\,\mathrm{b}

. ((a)) Using

R=r_0A^{1/3}

with

r_0=1.2\,\mathrm{fm}

and

\langle r^2\rangle=\tfrac35R^2

, calculate the single-proton value of

Q_{\rm sp}

for a

1d_{5/2}

proton. ((b)) Compare the single-proton value with the measured moment: give the ratio of magnitudes and state whether the signs agree, then say what the comparison implies about the nuclear charge distribution.

Related theory

Nuclear Physics

Browse the problem library