Alpha Decay Energy relations

1. Alpha Decay Energy relations experimental binding energy of 4He Qa recoil term effect a binding energy (-Qa)

2. Alpha Decay Theory of Alpha decay 1928 Gamow U(r) Coulomb potential Attractive nuclear potential Time-dependent approach At t=0, alpha particle is localized inside the nucleus. It can be represented by a wave packet. At large times, the wave function is an outgoing wave. In the first step, one solves the stationary problem for the auxiliary potential U(r) Summation or integration

3. Alpha Decay Theory of Alpha decay Continuity equation Since a current of alpha-particles is leaving the nucleus, the density rhas to be a decreasing function of time. If we want to approximate the initial wave function through a stationary state, we have to assume complex E: Line width

4. Alpha Decay Theory of Alpha decay Approximations Realistic potential Square well Transmission problem

5. Alpha Decay Theory of Alpha decay • square-well potential • spherical symmetry • l=0 Radial Schroedinger equation Region I: Region II: Region III: In almost all cases |cIII| is much larger than |cI|. We are now interested in those situations where |cIII| is as small as possible.

6. Alpha Decay Theory of Alpha decay …In almost all cases |cIII| is much larger than |cI|. We are now interested in those situations where |cIII| is as small as possible. defines “virtual” levels in region I: alpha particle is well localized; very small penetrability through the barrier

7. Alpha Decay Theory of Alpha decay When c+=0, the penetrability becomes proportional to exp(-G), i.e., This is the semi-classical WKB result: In the case of the Coulomb barrier, the above integral can be evaluated exactly. The decay constant can be obtained by multiplying the probability of barrier penetration by a frequency of impacts on the barrier (v/R). Geiger-Nutall law of alpha decay 1911

8. Alpha Decay Theory of Alpha decay Data… • One still has to consider: • preformation process • angular momentum of alpha particle (centrifugal barrier effects)

9. Alpha Decay Theory of Alpha decay Fine structure in alpha decay 238Pu centrifugal barrier effect

10. Alpha Decay Parity violation in strong (alpha) decay Experimental limit (1991) for parity breaking in this case is 10-13 (strong interactions conserve parity!)