Potential description of the positive- and negative-energy properties of the α+40Ca system andα-cluster structure ofTi44

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Abstract
The α-cluster structure of the Ti44 nucleus is investigated within a local potential model description, starting from the unique optical potential which describes elastic Ca40(α,α) scattering on broad angular and energy ranges, and which has recently been shown to describe the broad oscillations seen in the low energy fusion excitation function as well. It is found that the various α-cluster states group into quasirotational bands whose properties are not dissimilar to those of the well-understood Ne20 nucleus. The lowest lying band is composed of states of even parity with moderate cluster character at low spin; it agrees within a few MeV’s in absolute energy with the Ti44 experimental ground state band, and the experimental intraband quadrupole transition probabilities are reproduced with good accuracy. The potential supports an excited positive parity band with strong cluster character, starting a few MeV’s above the α+40Ca threshold; the states of this band with spins ranging from 6 to 12 are responsible for the oscillations observed in the fusion excitation function. It supports, in addition, a negative parity band starting just above the threshold and composed of narrow states with intermediate cluster character; the latter has up to now no experimentally known counterpart. The states of higher lying bands are very broad and overlapping but they play an important role in enhancing the Ca40(α,α) backward angle cross section. Our results are discussed in terms of the available experimental evidence and of the various, often conflicting theoretical interpretations which have been put forward to describe the Ti44 α-cluster spectroscopy.