Spreading Width for the α Cluster Resonance Evaluated with an Optical Model

We evaluate the spreading width for the $\alpha$ + $^{40}$Ca cluster resonance from the optical potential used in $\alpha$ elastic scattering, which is determined so as to reproduce the differential cross section precisely. The spreading width calculated here represents the decay of the $\alpha$ + $^{40}$Ca resonances into more complicated states. The conversion of the optical potential into the spreading width is achieved by the absorbing boundary condition (ABC) method. The spreading width is derived by comparing the ABC calculation with and without the imaginary potential. We also estimate the upper value of the decay width of the $\alpha$ + $^{40}$Ca resonance into the compound nuclear state. From the results of the widths, the branching ratios decaying into various states are calculated. The effect of the spreading width is also included in the calculation of the isoscalar monopole and dipole transitions from the ground state in $^{44}$Ti to the $\alpha$ + $^{40}$Ca continuum states. We have found that the dissociation strength shifts to the lower-energy region by the effect of the spreading width. The enhancement of the dissociation strength in the low-energy region is discussed in connection with nuclear transmutation.