Modeling Polonium212 Alpha Halflife
The shape of the barrier must obviously be taken into account since it drops rapidly. But it is instructive to calculate the halflife for a rectangular barrier of that height and width. Using the barrier penetration calculation gives a halflife of 1.5 x 10^{7} seconds, about 13 orders of magnitude longer than the observed halflife. This gives some insight into the large range of alpha halflives; the tunneling probability depends very strongly on the nature of the barrier. The probability depends exponentially on the height and width, and in this case the height is dropping like 1/r with distance from the nucleus.
When this tunneling probability is used to calculate the halflife, a value of 0.25 microseconds is obtained. This is surprisingly close to the measured value of 0.3 microseconds, considering that an incorrect barrier can take you off many orders of magnitude. It should be admitted that the same calculation for other nuclei does not yield such close agreement, but this example shows that the observed halflives are within the range which can be calculated from quantum mechanical tunneling.

Index Alpha Decay Concepts References Rohlf Sec 74 Eisberg & Resnick Sec 162  

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What could you do to change the polonium halflife?For the modeling of the alpha decay halflife of polonium212 with the tunneling probability, a value of 0.25 microseconds was obtained. This is surprisingly close to the measured value of 0.3 microseconds, considering that an incorrect barrier can take you off many orders of magnitude. It suggests that the major factors affecting such alpha decay have been accounted for in a reasonable manner. What could you do to change the polonium halflife? The answer is that there is no way to experimentally change that parameter because it ultimately depends upon the values of fundamental physical constants. The illustration below points out that the characteristics which affect the barrier and the tunneling probability are:

Index Alpha Decay Concepts References Rohlf Sec 74 Eisberg & Resnick Sec 162  

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