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Abstract. Phase transitions of first and second order can easily be distinguished in small systems in the microcanonical ensemble. Configurations of phase coexistence, which are suppressed in the conventional canonical formulation, carry important information about the main characteristics of first order phase transitions like the transition temperature, the latent heat, and the interphase surface tension. The characteristic backbending of the microcanonical caloric equation of state T ( E ) (not to be confused with the well known Van der Waals loops in ordinary thermodynamics or mean field approximations) leading to a negative specific heat is intimately linked to the interphase surface entropy.Keywords: Microcanonical thermodynamics; Phase transitions; Surface tension.Microcanonical thermodynamics describes the dependence of the volume RN of the N-body phase-space of an interacting many-body system on the globally conserved quantities like the total energy, momentum, angular momentum, mass, charge etc. This is the fundamental starting point of any statistical definition of thermodynamics. By Laplace transform of &(E) from the extensive quantities like the energy to intensive ones like inverse temperature Cp = l / T ) one obtains the more familiar Gibb's canonical partition function Z @ ) . For systems interacting by short range two-body forces (with hard cores) both formulations are identical in the thermodynamic limit of infinitely many particles at the same particle density [l]. However, the two formulations are different for finite systems and more essentially are different even in their physical content for systems with long range forces like gravity [2] or Coulomb dominated systems see for example [3]. This will be discussed in a forthcoming paper.One of the most interesting phenomena in thermodynamics are phase transitions. Computer simulations of simple models give a deep insight into the mechanism. Naturally these calculations can only be performed for small systems. The main characteristics like the transition temperature TI,, the specific latent heat qIar, and the interphase surface tension aSwrf are extrapolated to the infinite system. In the thermodynamic limit it should not matter whether the calculations for the finite systems are performed canonically or microcanonically. However, we will show for the two-dimensional, q = 10 states, Potts model, which has a clear phase transition of first order from ordered to disordered spins, the extrapolations converge faster when started from the microcanonical-ensemble. Moreover, our investigation will clarify

We performed self-consistent Hartree-Fock plus random-phase approximation (HF+RPA) calculations for charge-exchange 1 + states in 90 Zr and 208 Pb by using Skyrme interactions with tensor terms. We employed a parameter set in which the tensor terms are added to the SGII interaction. It is pointed out that Gamow-Teller (GT) states can couple strongly with the spin-quadrupole (SQ) 1 + states in the high-energy region above E x = 30 MeV due to the tensor interactions. As a result of this coupling, more than 10% of the GT strength is shifted to the energy region above 30 MeV, and the main GT peak is moved 2 MeV downward. At the same time, the main SQ 1 + peak is moved upward by more than 10 MeV due to the tensor correlations. Schematic separable interactions are proposed to elucidate the quenching mechanism induced by the tensor interaction on the GT state.

The Gamow-Teller (GT) strength distributions and isobaric analog resonance (IAR) states of several N = Z + 2 nuclei with mass number A = 42-58 are studied by using a self-consistent Skyrme Hartree-Fock-Bogoliubov method plus quasiparticle random phase approximation (HFB+QRPA) formalism. The isoscalar spin-triplet pairing interaction is included in QRPA on top of the isovector spin-singlet one in the HFB method. It is found that the isoscalar pairing correlations mix largely the (νj > → πj < ) configurations into the low-energy states, and this mixing plays an important role in the formation and in the collectivity of these low-energy states. Furthermore, the observed excitation energy of the low-energy GT state with respect to the IAR can be well reproduced when the strength of isoscalar pairing is about 1.0-1.05 times that of the isovector pairing, irrespective of the adopted Skyrme interactions. In N = Z + 2 nuclei in the middle of the pf -shell, a mutual cooperative effect of isoscalar pairing and tensor interaction is found; namely, the tensor force reduces the spin-orbit splittings and enhances the effect of the isoscalar pairing.