A consistent description of the nuclear α-decay process
The essential features of a new theory of α decay and the need for such a theory are reviewed. An approximate relationship between half life and α-particle energy is deduced and checked for the decay of even polonium isotopes. Detailed calculations of one-body widths and spectroscopic factors for the polonium decays are presented and the implications of the results are discussed. It is also shown that the result for the α decay of 212Po is consistent with the reverse α-transfer reaction.
Coupled-channel, alpha decay rate theory applied to 212mPo
Abstract A new application of the coupled channel formalism is made for the case of the alpha decay of the high spin, J = 18+ state of 212Po to the ground state and various excited states of 208Pb. In the first part of this paper (sect. 2), we apply the microscopic or “shell-model” rate theory neglecting coupling. It is found that the theory underestimates both the experimental 1% alpha branch to the 3−, first excited state of 208Pb and the 2% branch to the second, 5− state, for connection radius R = 9.5 fm. Choice of a small R of 7.5 fm results in a satisfactory agreement for the branching to the 5− state but leaves a discrepancy of over an order of magnitude for the branch to the 3− state. In the second part of this paper (sects. 3–5), we solved the radial Schrodinger equations for L = 18 and L = 15 waves coupled to the collective octupole vibrational field. We show that the channel coupling has a substantial effect on over-all barrier penetrability, but that coupling does not help much in removing the underestimate of the 3− intensity for R ≧ 7.5 fm for the parameters we used. It is suggested that neglected octupole core polarization in parent nuclear wave functions may be responsible for the remaining discrepancy.
Contributions to the theory of alpha-decay
The theory of α-decay is reformulated in order to point out the necessary approximations in a rigorous way. The connection between the formulas given byThomas and byMang is easily established.Mang's explicit expressions of reduced widths, valid for shell model wave functions, are brought into a general form.The theory is applied to BCS wave functions and the decay constants of several Po-isotopes are calculated as an example. Furthermore results are presented which favour a spin assignmentI=18 and a predominating (h9/2)82 (i11/2)102 configuration for the Po212 isomeric state. The penetrabilities are calculated numerically, since the WKB-method is found to be unsatisfactory.