Potential description of the positive- and negative-energy properties of the alpha + 40Ca system and alpha -cluster structure of 44Ti.

Abstract

The \ensuremath{\alpha}-cluster structure of the $^{44}\mathrm{Ti}$ nucleus is investigated within a local potential model description, starting from the unique optical potential which describes elastic $^{40}\mathrm{Ca}$(\ensuremath{\alpha},\ensuremath{\alpha}) 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 \ensuremath{\alpha}-cluster states group into quasirotational bands whose properties are not dissimilar to those of the well-understood $^{20}\mathrm{Ne}$ 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 $^{44}\mathrm{Ti}$ 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 \ensuremath{\alpha}${+\mathrm{}}^{40}$Ca 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 $^{40}\mathrm{Ca}$(\ensuremath{\alpha},\ensuremath{\alpha}) 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 $^{44}\mathrm{Ti}$ \ensuremath{\alpha}-cluster spectroscopy.