Tunneling Through Rectangular Potential Barrier: Revisiting the Systematics of Alpha-decay

Abstract

The problem of tunneling through a rectangular potential barrier has been reviewed, and the result is applied to study the systematics of alpha-disintegration of even-even alpha-emitters in thorium series. The Coulomb potential barrier outside the nucleus is modeled as a rectangular potential barrier of height equal to the average value over the classically forbidden region. The barrier heights and widths, and hence the decay constants and half-lives, are calculated for the nuclei under study. The calculated half-lives, though deviate by order of magnitudes from the known values, show a systematic variation with $Z/\sqrt E$ (Z is the atomic number of the alpha-emitter and E is the disintegration energy) as consistent with observation and theoretical explanation put forwarded by Gamow, Gurney, and Condon. We study the problem within the scope of the CBCS syllabus at the undergraduate level.