Investigations of fluctuations on phase transitions in light nuclei

Recently a renewed interest in the study of phase transition has emerged as an exciting topic. It is really a fascinating and still open question whether phase transitions do exist in finite systems of nuclei at finite temperature and signature of these transitions remains regardless of fluctuations. Phase transition from superfluid to normal fluid has been investigated based on finite temperature mean field theories such as Bardeen-Cooper-Schrieffer (BCS), Hartree-Fock (HF) and Hartree-Fock-Bogliubov (HFB) formalisms. However the empirical analysis of experimental data does not predict a sudden phase transition, the reason being the neglect of fluctuations in the mean field approximations. Especially in light nuclei, quantal and statistical fluctuations are inevitable in identifying phase transitions [1]. A system at zero temperature has quantal number and spin fluctuations and at finite temperature there are statistical fluctuations in the pair gap, deformation and energy. Very recently a self consistent quasiparticle RPA shows that pairing phase transitions are indeed smoothed out with a long exponential tail that extends up to higher temperature. In the present study, we have extended our investigation of nuclear phase transitions [2] in light nuclei with the inclusion of quantal and statistical fluctuations. Calculations are executed for the fluctuations of selected observables that convey the signals for the phase transition like particle number, spin, pair gap, deformation, and energy using the finite temperature statistical theory. This theory has been used in our earlier calculations pertaining to the evaluation of single particle level density parameter, neutron separation energy and emission probability at high spins. To our knowledge, so far efforts have not yet been made to explain the effects of all these fluctuations in light nuclei hence the present work discusses them in detail. Formalism