Sketch the potential for a-decay, assuming can be modelled as a pre-formed particle inside the daughter nucleus. On this sketch, illustrate a typical tunnelling wave-function, which has an energy Qwhich is less than the potential for R for a-decays approximately obeys Z In λx const. + √Q Relate the answer you obtain to that in part (a). 1 ㅠ (You may use the approximation V [²√ ² - 1 dr ~ √b for b> R.) r 2
Sketch the potential for a-decay, assuming can be modelled as a pre-formed particle inside the daughter nucleus. On this sketch, illustrate a typical tunnelling wave-function, which has an energy Qwhich is less than the potential for R for a-decays approximately obeys Z In λx const. + √Q Relate the answer you obtain to that in part (a). 1 ㅠ (You may use the approximation V [²√ ² - 1 dr ~ √b for b> R.) r 2
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Transcribed Image Text:Sketch the potential for a-decay, assuming it can be modelled as a pre-formed particle
inside the daughter nucleus. On this sketch, illustrate a typical tunnelling wave-function,
which has an energy Q which is less than the potential for R<r<b, where r is the radius
from the centre of the daughter nucleus, and r = R and r = b are the radii where the
potential has the value Q.
The transmission probability is P = e-2G where the Gamow factor is
G =
2m
ħ² R
S -
√V (r) – Q dr,
where m = ma is the mass of the a-particle. The potential for a-decay in terms of a
daughter nucleus with Z protons and mass number A is
V(r) =
R
From this, show that the Gamow factor is x Z/√Q. Hence show that the decay constant
for a-decays approximately obeys
In λ x const. +
2e²Z
4π€or
Relate the answer you obtain to that in part (a).
ob 1
(You may use the approximation
r
1
- dr ~
Z
√Q
π
VO
√b for b> R.)
2
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