The critical density of neutral pion condensation is reinvestigated based on the relativistic framework and compared with nonrelativistic results. The particle-hole and delta-hole polarizations of the pion selfenergy are calculated in the relativistic way by using a new set of Landau–Migdal parameters derived from recent experimental data. It is concluded that the use of relativistic particle-hole and delta-hole excitations for the pion selfenergy increases the critical density, but still leads to condensation for densities from two to three times the normal nuclear matter density within the random phase approximation.

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Including the vacuum effects, the compressional properties of nuclear matter are studied in the cutoff field theory. Under the Hartree approximation, the low-energy effective Lagrangian is derived in the framework of the renormalization group methods. The coefficients are determined in a way where the physical results hardly depend on the value of the cutoff which is conveniently introduced into the theory. It is shown that, to reproduce the empirical data of the nucleus incompressibility, the compressibility of the nuclear matter is favorable to be 250∼350MeV.

At zero-density, meson-nucleon vertex corrections to vacuum polarization are studied in the σ-ω model with the cutoff. It is shown that the properties of the vertex corrections to vacuum polarization are somewhat different from those described by the ordinary renormalization procedures when the cutoff is small ( < 5GeV). The low-energy effective Lagrangian is constructed in the framework of the renormalization group method. The weak tensor and derivative couplings of meson-nucleon interactions may be needed in the lowenergy effective theory of mesons and nucleons.

This paper describes an analysis of the close to carrier phase noise characteristics of the Colpitts and Butler oscillator circuits.It is shown that the quality factor can be improved by introducing two or more crystal resonators in the oscillation circuits. Based on the Leeson's model, the near carrier phase noise is estimated using the calculated quality-factor obtained by the analysis of the frequency slope in the output impedance. As a result, it was shown by using plural crystal resonators in the phase noise close to carrier frequencies are improved.