Numerical Solutions of the Curium-242 Alpha-Decay Wave Equation

Numerical integration of the previously derived alpha-decay wave equation, including electric quadrupole coupling terms, was carried out for ${\mathrm{Cm}}^{242}$ including $l=0, 2, 4, \mathrm{and} 6$ partial waves. Eight integrations were carried inward in spherical polar coordinates on an IBM-650 computer with different initial conditions, such that a complete set of eight linearly independent solutions to the system of coupled equations was generated. Eight different linear combinations of this base set were found which satisfy the boundary conditions imposed by experimental ${\mathrm{Cm}}^{242}$ alpha-group intensities. Wave amplitudes on a spherical surface near the nucleus are given for all eight cases, and the radial variation throughout the barrier region is given for two cases. The matrix formalism of Fröman is employed in another presentation of the results, and a comparison is made with the analogous Fröman matrix. By using a modified Fröman matrix together with our results, the alpha-wave distributions are calculated for a spheroidal nuclear interaction surface. A discussion is made of conditions for the existence of solutions satisfying boundary conditions imposed by alpha-group intensities, and the quadrupole phase shift problem is considered.