Effects of friction on the chiral symmetry restoration in high energy heavy ion collisions was investigated in detail. It was found that the maximum temperature must be high enough (not lower than 230 MeV) and the friction must be strong enough in order that the chiral symmetry restoration lasts for a long time.

We studied the effects of the expansion of the system and the friction on the parametric amplification of mesonic fields in high energy heavy ion collisions using the linear sigma model. It was found that a strong peak may appear around 267 MeV in the pion transverse momentum distribution in cases with weak friction and high maximum temperature.

Chiral phase transition at finite temperature T and/or finite chemical potential μ was studied using the QCD-like theory with a variational approach. Modified Cornwall-Jackiw-Tomboulis effective potential was derived for generally nonzero current quark mass. We then calculated the effective potential at finite T and/or μ in the chiral limit to investigate the phase structure. We found a tricritical point at T=107MeV and μ =210 MeV. It separates the second order phase transition at higher T and lower μ and the first order transition at higher μ and lower T.

Effects of finite quark mass on the chiral phase transition of QCD was investigated in the improved ladder approximation. We used the Schwinger-Dyson equation to modify the Cornwall-Jackiw-Tomboulis effective potential. The relevant critical exponents and the masses of the scalar and the pseudoscalar mesons at finite temperature were calculated.

An effective action which takes into account the diquark and the meson (quark-antiquark) correlations was constructed in the abelianized QCD by using auxiliary fields. The effective potential was derived in order to investigate the phase structure of QCD.

The quark-diquark picture of the J ^P = (1/2)⁺ octet baryons was used to study the SU(3) structure of the coupling constants between the octet baryons and the J ^P= 0^- octet mesons. The same picture was also used to calculate the magnetic moment of the octet baryons. We found a nonet-like symmetry with F/D=-1 in the meson-baryon coupling scheme.

First order phase transition from quark-gluon plasma into hadron gas via nucleation was studied. We found the possibility that the critical radius of the hadron droplet may be a constant independent of the temperature by considering temperature fluctuation and the energy conservation in the domain of nucleation. This leads to a new scenario which is quite different from the standard Csernai-Kapusta scenario.

The time evolution of the vacuum state in a uniform electric field is studied. We solve the Heisenberg Equation of motion of the Dirac fermion in an external field. Evolution of the creation and annihilation operators are expressed as the time-dependent Bogolioubov transformation. We find that the survival probability of the vacuum state per unit volume obeys the Gaussian decay law instead of the exponential decay law at short time.

We derived analytic expressions of the Coulomb interaction between a spherical and a deformed nuclei which are valid for all separation distance. We then demonstrated their significant deviations from commonly used formulae in the region inside the Coulomb radius, and showed that they remove various shortcomings of the conventional formulae.

We studied the effects of difference of the charge and matter deformation parameters in heavy-ion fusion reactions using the fusion of ^19,37Na isotopes with ²⁰⁸Pb.

We derived analytic formulae for the S-matrix for a two level crossing problem in the presence of potential barriers and pockets by using a three turning point semiclassical theory for a scattering problem and a matrix formalism for the non-adiabatic transition. Our semiclassical S-matrices satisfy the unitarity condition and the elastic and inelasitic S-matrix elements reduce to improved Landau-Zener-St\"uckelberg formulae at high energies where the existence of the potential barriers can be ignored. We discussed qualitative behaviors of the semiclassical S-matrix elements in the weak and strong coupling limits, i.e. in the limits where the one-way Landau-Zener transition probability p → 1 and p → 0, respectively. Also we gave detailed discussions on the interplay between the Landau-Zener transtion and a potential resonance.

We examined the R-matrix theory for the α decay and found that a care should be taken in the preexponential factor in applying the WKB formula to the barrier penetrability.

We performed a systematic study of the structure of superheavy elements claimed to have been discovered in the recent ²⁰⁸Pb(⁸⁶Kr,n) reaction at Berkeley using the Relativistic Mean Field (RMF) approach. We showed that various usually employed RMF forces, which give fair description of normal stable nuclei, give different predictions for superheavy elements. Among the effective forces we tested, TM1 seems to be the good candidate to describe superheavy elements. The binding energies of the ²⁹³118 nucleus and its α -decay daughter nuclei obtained using TM1 agree with those of FRDM within 2 MeV. Similar conclusion that TM1 is the good interaction has been drawn also from the calculated binding energies for Pb isotopes with the Relativistic Continuum Hartree Bogoliubov (RCHB) theory. Using the pairing gaps obtained from the RCHB for protons and filling approximation for neutrons to simplify the blocking effect, we carried out the RMF calculations with deformation for the structure of superheavy elements. We thus discussed the binding energy, shape, single particle levels, and the Q values of the α -decay Q _α and showed that the pairing correlation, blocking effect and deformation are essential to properly understand the structure of superheavy elements. We also calculated the Q _α values for the ground state to ground state transitions and for those respecting the angular momentum selection rule, and compared them with data.

We developed a comuter code to study the phase transition of Na clusters based on the first principle molecular dynamics.

A surface correction term is introduced to a variant of the Gogny force with a stiff incompressibility (K=373 MeV) in order to have a reasonable description of finite nuclei. The antisymmetrized molecular dynamics (AMD) calculations are performed with this stiff Gogny force as well as with the usual Gogny force (K=228 MeV), in order to discuss the effect of the equation of state (EOS). In ⁴⁰Ca+⁴⁰Ca at 35 MeV/u where the reaction is basically binary, larger dissipation is obtained for stiffer EOS. α particles are produced abundantly from the projectile and target components only when the EOS is soft. On the other hand, in more violent collisions (Au + Au at 150 MeV/u), similar effect is found for the degree of the transparency, while the charge distribution of fragments is insensitive to the stiffness.

The isospin dependence of the nuclear collisions is studied with AMD in the above two reaction systems with equal mass and different isospin. Fragments are produced more abundantly in neutron rich ⁵⁸Fe+⁵⁸Fe collisions than in ⁵⁸Ni+⁵⁸Ni collisions in the energy region around 50 MeV/u, which is consistent to the data and may be related to the liquid-gas separation in two-component nuclear matter. In order to get the conclusion about the interesting effects in the flow in these reactions, more simulations should be performed to get better statistical accuracy.

Shibata-Hashitsume's projection operator method was extended in order to calculate the time evolution of the field operators for initial states which are more general than those considered by Shibata et al. A new perturbative expansion formula was derived and is applied to φ ⁴ theory. It does not contain the time convolution integral. The resulting equation of motion indicates the validity of the linear harmonic approximation used in the influence functional method in order to eliminate the time convolution integral. Properties of the time-dependent divergence that occurs at the initial time was investigated in detail in connection with the renormalization of the usual ultraviolet divergence.

We study time evolution of the chiral phase transition in the linear σ model. The equations of motion for the zero momentum modes of the σ and π meson fields are derived by using the projection operator method. The vacuum expectation value and the masses of the σ and π mesons are determined self-consistently. We also discuss about the consistecy of the result with the PCAC relation.

We propose an adiabatic mean-field model for dynamical collective state transitions of a nuclear system. The transition process is described in terms of the nuclear mean-field wave functions which are adiabatically determined in the course of the transition. Solving the eigenvalue equation for the Hamiltonian, we calculate the time evolution of the system. Applying the model to nuclear tunneling processes, we discuss the features of dynamical collective state transitions.

We formulate a full order expression for nuclear collective tunneling in the projection operator method, using an appropriate model Hamiltonian. Collective tunneling transitions are characterized by the slight energy splitting of almost degenerate nuclear states under consideration. The energy splitting yields a time scale of the tunneling. We obtain the expressions, solving the projected Schr\"odinger and Liouville equations.

1. Screening Effect by Bound Electrons on Astrophysical Nuclear Reactions
   Sachie Kimura

2. Fermion Pair Creation and Time Evolution of Vacuum in Homogeneous Electric Field
   Yuji Nakazawa