bei48482_FM

Tunnel Theory of Alpha Decay

While a heavy nucleus can, in principle, spontaneously reduce its bulk by alpha decay,

there remains the problem of howan alpha particle can actually escape the nucleus.

Figure 12.8 is a plot of the potential energy Uof an alpha particle as a function of its

distance rfrom the center of a certain heavy nucleus. The height of the potential barrier

is about 25 MeV, which is equal to the work that must be done against the repulsive

electric force to bring an alpha particle from infinity to a position adjacent to the nucleus

but just outside the range of its attractive forces. We may therefore regard an alpha

particle in such a nucleus as being inside a box whose walls require an energy of 25 MeV

to be surmounted. However, decay alpha particles have energies that range from 4 to

9 MeV, depending on the particular nuclide involved—16 to 21 MeV short of the energy

needed for escape.

Although alpha decay is inexplicable classically, quantum mechanics provides a

straightforward explanation. In fact, the theory of alpha decay, developed independently

in 1928 by Gamow and by Gurney and Condon, was greeted as an especially striking

confirmation of quantum mechanics.

In the Appendix to this chapter we shall find that even a simplified treatment of

the problem of the escape of an alpha particle from a nucleus gives results in agree-

ment with experiment. Gurney and Condon made these observations in their paper:

“It has hitherto been necessary to postulate some special arbitrary ‘instability’ of the

nucleus; but in the following note it is pointed out that disintegration is a natural con-

squence of the laws of quantum mechanics without any special hypothesis.... Much

has been written about the explosive violence with which the -particle is hurled from

its place in the nucleus. But from the process pictured above, one would rather say

that the particle slips away almost unnoticed.”

434 Chapter Twelve

(a) (b)

Alpha particle

cannot escape

(classically)

Potential energy of

alpha particle

Alpha particle cannot

enter (classically)

Kinetic energy of

alpha particle

r

R 0

0

Energy

Wave function of

alpha particle

r

R 0

0

Energy

Figure 12.8(a) In classical physics, an alpha particle whose kinetic energy is less than the height of the potential barrier around a nucleus

cannot enter or leave the nucleus, whose radius is R 0. (b) In quantum physics, such an alpha particle can tunnel through the potential

barrier with a probability that decreases with the height and thickness of the barrier.

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