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PHY431 Homework Set 5
Reading:
Lecture Notes
Homework:
See below:
Due date:
Wednesday March 1
Hints and Solutions
Problem V.1
Show that the Angular Momentum Barrier "potential"
L
²
/
2
I
=
l
(
l
+1)
h
²
/
2
mr
²
for the radioactive
decay:
209
83
Bi(J
P
=
9
/
2

)
→
205
81
Tl(J
P
=
1
/
2
+
) +
4
2
He(J
P
=0
+
)
is small compared to the Coulomb potential for the region
r
>
R
, where
R
is the sum of the
radii of the daughter nucleus and the alpha particle.
Hints:
First, show that angular momentum and parity conservation dictates that
l
=5
Solution:
orbital angular momentum
l
= 
9
/
2
±
1
/
2
 = 4 or 5. Parity changes from ve to +ve, so
the angular momentum in the final state must be odd: 1 = ()
l
; thus
l
= 5.
V
L
=
l
(
l
+1)/(2
mR
²) = 5×6×(197 MeV·fm)²/(2×3730 MeV ×(9.0 fm)²) = 1.9 MeV; we took
R
= 1.2 fm × (205
1/3
+4
1/3
) = 9.0 fm.
V
C
= [
e
²/4
πε
0
]
zZ
/
R
= 197 MeV/137 × 2×81/9.0 fm = 26 MeV; i.e. 13× larger than
V
L
.
Problem V.2
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 Spring '01
 Rijssenbeek
 Physics, Angular Momentum, Momentum, Work

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