Nuclear Instruments and Methods in Physics Research B79 (1993) 286-289 North-Holland NINMI zyxwvutsrqp B Beam Interactions with Materials&Atoms Structural changes in high spin nuclei M. Rajasekaran, T.R. Rajasekaran, P. Ratna Prasad, and V. Devanathan R. Premanand, D. Caleb Chanthi Raj zyxwvutsrq Depatiment of Nuclear Physics, University of Madras, Guindy campus, Madras 600 025, India The interplay of various degrees of freedom and their influence on the behaviour of nuclei formed as fused compounds in heavy-ion reactions is investigated. A statistical theory which incorporates deformation, collective and noncollective rotational degrees of freedom and shell effects is developed to study highly excited fused compounds which deexcite by particle emission and yrastlike cascades. We find that the nucleonic separation energies, which are functions of spin and temperature, decrease rather sharply for particular angular momentum states of the nuclei due to shape transitions. We predict an enhancement of nucleonic emission at these spins, and evidence for this is already present in the experiment of Henss et al. Results for heavy systems like Er, Yb and Hg which emit neutrons while rotating fast, and for light nuclei like **Si, etc. which have greater probability for emitting protons and light charged particles, are presented. Bohr’s [l] prediction of collective rotations from liquid drop model considerations and the subsequent observation in Coulomb excitation of tantalum (Ta) by McClelland and Huus et al. [2], have given rise to a new area of interesting theoretical and experimental nuclear physics. The advent of heavy ion accelerators introduced a new dimension to this area by producing highly excited fused compounds with very high angular momentum. Fused compounds formed in heavy ion reactions may be described as a thermodynamical system of fermions with several degrees of freedom like deforma- tion, collective and noncollective rotations, particle number fluctuations etc. The quantum aspects of the system are incorporated in single particle level schemes of the Nilsson type or Woods-Saxon potentials which involve deformation and shell structures. The grand partition function Q contains all the information about the statistical average of energy, particle number, angu- lar momentum and the entropy, which determines the phase space or the probability of finding the system with a particular set of observables. The development of the statistical theory by Bethe [3], Ericson [4], Ig- natyuk [5], Morreto [6] and by us [7] has resulted in the successful application to high spin nuclei. The loga- rithm of the grand canonical partition function for a system of N neutrons in the BCS formalism [6] is where ’ EkN= [(E; - A,)’ + AN] I/‘. Eq. (1) yields the following conservation equations in terms of the single particle eigenvalues ck and spins mk, at a temperature T( = l/P). N= x(1’-($-AN) itanh[@/z)(&” - rmf)l/2%), E= &;(l-((~r - zyxwvutsrqponmlkjihgfedcbaZYXWVUT hN) tanh[ (P/2) k (2) X (E,i” - rd)] /2Et} - &% (3) and J,=~ {my/[l+expp(E:-ymp)]}. (4) A similar set of equations exist for 2 protons. The Lagrangian multipliers A, p, y are fixed by the above equations. If one uses the Cranked-Nilsson Hamilto- nian, y may be dropped. The temperature may be fixed by the excitation energy of the fused compound. The separation energy of the neutron (S,) or proton (S,) may be obtained [8] from the thermodynamical potential 0 and eqs. (l)-(4): ON= -T In Qhr, (5) S,=TN x(1-#)r$ -l. zyxwvutsrqponmlkjihgfedcbaZY [ 1 (6) i It is obvious from eq. (6), that S, depends on the single particle level density near the fermi energy. So it is reasonable to use any level scheme which yields the shell corrections fairly accurately like the one em- ployed by Seeger [9] over a wide range of nuclei. This 0168-583X/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved