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Alpha Decay basics

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Alpha Decaybasics

[Sec. 7.1/7.2/8.2/8.3 Dunlap]

Alpha decay Example

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

96Cm244

94Pu240

Why alpha particle instead of other light nuclei

Energy Q associated with the emission of various particles from a 235U 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.

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?

Mass of X

Q

Mass of Y

+ particle

And the energy released in the decay is simply given by energy

Conserving energy and momentum one finds:

BEFORE

AFTER

+p, p2/8M

-p, P2/2AM

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:

This diagram shows the alpha decay to the 240Pu 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

243Am

5/2-

1.1%%

10.6%%

88%%

9/2-

0.172 MeV

0.12%%

0.16%%

7/2-

0.118 MeV

5/2-

0.075 MeV

7/2+

0.031 MeV

5/2+

0 MeV

239Np

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:

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 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.

vα

Qα

r=R

r=b

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'‘ (vα/2R), and the barrier penetration probability PT.

How high and wide the barrier?

The height of the barrier is:

The width of the barrier is

w

30MeV

Lets calculate these for taking R0=1.2F, we have