Alpha Decay basics [Sec. 7.1/7.2/8.2/8.3 Dunlap]

Alpha decay Example Parent nucleus Cm-244. The daughter isotope is Pu Cm Pu 240

Why alpha particle instead of other light nuclei Energy Q associated with the emission of various particles from a 235 U nucleus.

There are always two questions that can be asked about any decay in atomic, nuclear or particle physics: (i) How much kinetic energy was released? and (ii) How quickly did it happen? (i.e. Energy? and Time?). Lets look at both of these questions for  decay.

Energy Released Q  Experiments The above diagram (right) shows the experimental energy of release. The above diagram (left) shows the abundance of alpha emitters. Both diagrams are as a function of A. Can you see the relationship?

The Energy of the α-particle, T α Mass of X Mass of Y +  particle QQ And the energy released in the decay is simply given by energy

The Energy of the α-particle, T α Conserving energy and momentum one finds: BEFORE AFTER -p, P 2 /2AM +p, p 2 /8M

Energy Released Q . This can be estimated from the SEMF by realizing that the B(Z,A) curve is rather smooth at large Z, and A and differential calculus can be used to calculate the  B due to a change of 2 in Z and a change of 4 in A. Starting from (8.2) we also have:

There can be multiple alpha energies This diagram shows the alpha decay to the 240 Pu daughter nucleus – and this nucleus is PROLATE and able to ROTATE collectively. Alpha decay can occur to any one of the excited states although not with the same probability. For each decay: where E is the excited state energy

Total angular momentum and parity need be conserved

243 Am 5/2 - 9/2 - 7/2 - 5/2 - 7/2 + 5/ MeV MeV MeV MeV 0 MeV 239 Np 1.1% 10.6% 88% 0.12% 0.16%

How fast did it happen? The mean life (often called just “the lifetime”) is defined simply as 1/ λ. That is the time required to decay to 1/e of the original population. We get:

The first Decay Rate Experiments - The Geiger –Nuttal Law

As early as 1907, Rutherford and coworkers had discovered that the  - particles emitted from short- lived isotopes were more penetrating (i.e. had more energy). By 1912 his coworkers Geiger and Nuttal had established the connection between particle range R  and emitter half- life. It was of the form:

The first Decay Rate Experiments - The Geiger –Nuttal Law

The one-body model of α-decay assumes that the α-particle is preformed in the nucleus, and confined to the nuclear interior by the Coulomb potential barrier. In the classical picture, if the kinetic energy of the -particle is less than the potential energy represented by the barrier height, the α-particle cannot leave the nucleus. In the quantum-mechanical picture, however, there is a finite probability that the -particle will tunnel through the barrier and leave the nucleus. The α-decay constant is then a product of the frequency of collisions with the barrier, or ``knocking frequency'‘ (v α /2R), and the barrier penetration probability P T. vαvα r=b r=R QαQα

How high and wide the barrier? The height of the barrier is: The width of the barrier is w Lets calculate these for taking R 0 =1.2F, we have 30MeV