How to determine half life by Theoretical Computational method?

Half life determination: Part 5

Determination of t_1/2 ~ultra short or ultra high by Theoretical computation method

Theoretical computation of half life

There are several theoretical laws for the determination of half life of a radioisotopes. Geiger-Nuttall law is oldest among them, which is an empirical law for the determination of half lives of alpha particle emitters. [Geiger, H., (1911) et al] using the following equation

where λ is the decay constant (λ = ln2/half-life), Z the atomic number, E the total kinetic energy (of the alpha particle and the daughter nucleus), and a1 and a2 are constants. 

    Apart from this half life can be computed by using Universal decay law (UDL) from R-matrix theory [Akrawy, D. T., (2019) et al.], Semifission formula [Poenaru, D. N., (2006) et al] etc. Theoretical estimation have profound application is super heavy radionuclides, where experimental half life measurements are yet to be carried out as well as for the radioisotopes with very very long half lives e.g. 124Xe (1.8 x 10^22y), 128Te (2.41×10^24 yr), 209Bi (4.6 x 10^19). It is often claimed that the calculated half-life values are is in agreement with the experimental data. Theoretically calculated half lives often in good agreement with measured results e.g. theoretical prediction of 209Bi’s half life was 4.6 x 10^19 y which is in good agreement with obtained result 1.9 (± 0.2)  x 10^19y [Dumé, B. (2007)]. 

Advantage

Minimum or no experiment

Very useful for extreme cases e.g. very low or very high half lives

Disadvantage 

Predictive in nature

Reference

Akrawy, D. T., Hassanabadi, H., Hosseini, S. S., & Santhosh, K. P. (2019). Systematic study of alpha decay half-lives using new universal decay law. International Journal of Modern Physics E, 28(09), 1950075.

 

Dumé, B. (2007). Bismuth breaks half-life record for alpha decay. Physics World. Retrieved, 12-21.

 

Geiger, H., & Nuttall, J. M. (1911). LVII. The ranges of the α particles from various radioactive substances and a relation between range and period of transformation. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 22(130), 613-621.

 

Poenaru, Dorin N., Ileana-Hania Plonski, and Walter Greiner. "α-decay half-lives of superheavy nuclei." Physical Review C 74, no. 1 (2006): 014312.