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Physics 135c
H. W. Assignment 8
1.)
(a.) Use the procedure from HW#7 to calculate the mean lifetime of tritium for
β
decay:
3
H
→
3
He +
e

+ ¯
ν
e
(i.e. assume massless neutrinos and ignore nuclear recoil
and Coulomb distortion). The energy released in the decay is Δ =
m
e
+0
.
0185MeV. Note
that
3
H and
3
He both have a ground state spin of
1
2
and in a simple shell model the decay
is simply a neutron decaying to a proton with both particles in the 1
s
level. Compare your
result with the measured lifetime of
τ
(
3
H) = 17
.
8 yrs. Comment on possible causes of any
discrepancy between the calculated and measured values.
(b.) In the nonrelativistic approximation (see Bertulani), the Coulomb correction
factor to the beta decay spectrum
F
(
E
e
, Z
) =
a

ψ
Coulomb
(
r
)

2

ψ
planewave
(
r
)

2
A
assuming that the wave function is evaluated at the origin (
r
= 0). Estimate the magnitude
of this eFect for tritium
β
decay by including this factor into the phase space integral used
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 Spring '11
 Smith
 Physics, Energy, Mass

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