Physics 135c
Homework 5
1.)
Determine the nonrelativistic elastic scattering form factor
F
(

q

) =
integraldisplay
d
3
rρ
(
r
)
e
i
q
·
r
for the following two densities:
a)
ρ
(
r
) =
ρ
0
=constant for
r
≤
R
and
ρ
= 0 for
r > R
,
b)
ρ
(
r
) =
ρ
0
e

r/R
2.)
Beginning with the nonrelativistic elastic scattering form factor
F
(

q

) =
integraldisplay
d
3
rρ
(
r
)
e
i
q
·
r
show that the mean square radius of the charge distribution is related to the
derivative of the form factor, i.e.:
< r
2
>
= lim
q
→
0
6
vextendsingle
vextendsingle
vextendsingle
dF
(

q

)
d

q

2
vextendsingle
vextendsingle
vextendsingle
3.)
What are the nuclei, spins, parities, isospins, and “3” component of isospin
for the diagrams [a)  h)], shown on the next page, representing states of the
three nucleon system.
Note that these diagrams are shorthand for the full
states but are sufficient to identify the nuclei. Use the shell model as a guide,
and assume the state of lowest excitation energy in each case. If some of the
total spins are not unique, list the range of possible values.
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 Spring '11
 Smith
 Physics, Particle Physics, Work, Neutron, Fundamental physics concepts, nonrelativistic elastic scattering

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