bei48482_FM

468 Appendix to Chapter 12

Appendix to Chapter 12

Theory of Alpha Decay

I

n the discussion of the tunnel effect in Sec. 5.10 a beam of particles of kinetic

energy Ewas considered which was incident on a rectangular potential barrier

whose height Uwas greater than E. An approximate value of the transmission

probability—the ratio between the number of particles that pass through the barrier

and the number that arrive—was found to be

Te^2 k^2 L (5.60)

where Lis the width of the barrier and

k 2  (5.61)

Equation (5.60) was derived for a rectangular potential barrier, whereas an alpha particle

inside a nucleus is faced with a barrier of varying height, as in Figs. 12.8 and 12.31.

It is now our task to adapt Eq. (5.60) to the case of a nuclear alpha particle.

The first step is to rewrite Eq. (5.60) in the form

ln T 2 k 2 L (12.33)

2 m(UE)





Wave number

inside barrier

Approximate

transmission

probability

R r

0

0

Energy

E

U =^2 Ze

2

4 π 

0 r

R =^2 Ze

2

4 π 

0 E

ψ

Figure 12.31Alpha decay from the point of view of the quantum mechanics. The kinetic energy of

alpha particle is E.

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