• Main points of today’s lecture:– Fission. – Formation of actinides– Alpha decay

• Some history• Geiger Nuttall law

– Barrier penetration– WKB approximation– Theory of alpha decay

• Main points of last lecture:– Consequences of nuclear

instablity.• Number of stable isobars• Scarcity of odd-odd nuclei.

– Nuclei with more than one decay mode.

– Long decay chains secular equilibrium

– Evolution of alpha decay q value.

Physic 492 Lecture 12

Formation of the actinides

• The actinides are believed to be formed in supernovae by a rapidneutron capture process (r-process).– long lifetimes are associated with shell effects that low the

masses around Uranium and also lead.

Alpha Decay

• Some history

• Bethe Block Equation:

• Geiger-Nuttal rule

Simpler relationship

• Let’s plot τ vs. Qα

Alpha decay: barrier penetration• Alpha particles can be formed in the surfaces of nuclei:

Simple model for barrier penetration

• Approximate by square barrier.

Solution of S.E.

• reduce to radial eq.

Complete one dimensional analogy

• Calculate transmission coeff. T

Calculation of T• Consider only barrier penetration with wave coming from left onto the

barrier. Also neglect the attractive potential depth at r<R (i.e. V0=0)

• Main points of today’s lecture:– WKB approximation– Theory of alpha decay– Geiger-Nutall relationship– Q value dependence– Angular momentum

dependence.– Structure dependence.

• Main points of last lecture:– Fission. – Formation of actinides– Alpha decay

• Some history• Geiger Nuttall law

– Barrier penetration

Physic 492 Lecture 13

How does on improve the decay rates

• How to improve on T=const⋅exp(-κD)?

Solving the S.E.

• Cleaning up the Eq.

• Trial Solution

Testing the solution

• Calculate the derivatives

• In the limit of slowly varying potentials

• Neglecting the reflection at the outer edge of barrier.

Evaluating the solution

• Assume the barrier is purely Coulomb (l=0)

• Transmission coefficient

• including “knocking rate”

After integrating G

• Following hints in the book, you can show:

• Putting it together to get the mean lifetime.

An example:

• What is the lifetime of 238U

There is a strong dependence on Qα

• Let’s try to describe some data: (Be smart and use a spread sheet or a program to do this.)

5.4x10174.4x10174.08232

1.4x10122.5x10124.77230

2.1x1076x1075.52228

35418546.45226

9.5x10-21.047.31224

1.3x10-42.8x10-38.13222

4.7E-710-58.95220

T1/2 (calc.)

T1/2 (meas.)

Q (MeV)A

What have we neglected

Angular momentum effects

• What are the angular momenta and how are they related?– Taylor expand within the integral.

Let’s make another approximation• Approximate this correction by its value at the maximum of the

barrier.

• Somc specific values when the final states have the same energy.

• Main points of today’s lecture:– Angular momentum

dependence.– Structure dependence. – Nuclear reactions

• Main points of last lecture:– Barrier penetration– WKB approximation– Theory of alpha decay– Geiger-Nutall relationship– Q value dependence

Physic 492 Lecture 14

Let’s make another approximation• Approximate this correction by its value at the maximum of the

barrier.

• Somc specific values when the final states have the same energy.

What if the states are not degenerate?

• We can make a simple estimate.

• Consider the ratio of the decays

Review: what happens in decays of even-even nuclei

• Basic facts

Smoke detector design

What about odd-A nuclear decays

• 241Am is the alpha emitter in many smoke detectors. It decays as follows

In greater detail

Parity?

I=0