Alpha Decayi
Parameter values are taken from Betheii
An alpha particle of energy E has a wave function inside the nucleus given by

  D exp i 2mE  V x

Outside the barrier to the right

  A exp i 2mE x

Within the barrier approximated by a single value V
  B exp



2m V  E  x  C exp  2m V  E  x

There is “independent” evidence that the speed is 109 cm/sec. After a bit of algebra matching
derivatives
T
A
D
2
2
This is the transmission probability each time the alpha particle hits the barrier. The speed of the
particle is used to estimate how many times his is and the decay time is estimated from this.
i
ii
David Bohm ,, Quantum Theory, Printice Hall (1961) pp 241-242
H, Bethe, Elementaary Nuclear Physics, p. 110