Hartree-Fock wave functions obtained from realistic nucleon-nucleon interaction are employed to calculate cross-sections for the reaction¹²C(π⁺,p)¹¹C(g.s.). These wave functions take into account central correlations between nucleons inside the nucleus. This itself is found to change the cross-section by more than an order of magnitude. The incoming pion is represented by a plane wave while proton-distortion is taken into account in the high-energy or semi-classical approximation, thereby determining the proton optical well parameters. These values agree well with those obtained by more conventional methods. Variation of the cross-section with the oscillator well parameter is also studied. Calculations have been made using the one-nucleon mechanism for the pion-absorption process.

Solutions of the Dirac equation in the presence of a static uniform electric fieldɛ in thez-direction and a linear confining potentialAz, are obtained. Generalized reflection and transmission coefficients are derived for such divergent potentials forɛ >A/e. The eigenspectrum and corresponding localized eigenfunctions forɛ <A/e are obtained from the reflection coefficient and the continuum solutions respectively. The rate for the electric field to decay into pairs is derived from the transmission coefficient. Neglecting nonabelian effects in quantum chromodynamics we identify the fieldɛ with a colour electric field and the produced particles with a quark and an antiquark. By considering a cylindrical geometry, we thus obtain a generalization of Schwinger’s formula, for the fieldɛ in a finite spatial region with the quark (antiquark) being confined in thez direction by the linear potentialAz and in the perpendicular direction by the MIT bag boundary condition. The result is used to qualitatively study Schwinger’s mechanism of quark-gluon plasma (QGP) formation in ultrarelativistic heavy ion collisions. It is found that the critical strength of the field required to create$$q\bar q$$ pairs is enhanced,ɛ_c(A) >ɛ_c(A = 0). The rate of pair creation for constantɛ, decreases for non-zeroA, implying longer QGP formation times. Because ofɛ_c(A) >ɛ_c(0), QGP is predicted to be formed in the early stages of the nuclear collision. The finite size effects and the MIT bag boundary condition effects on QGP formation are also discussed.

The systematics of photon absorption cross sections in nuclei and small metal particles are examined as a function of the number of constituent fermionsA. It is pointed out that the shell-structure-linked oscillations in the full width at half maximum (FWHM) of the photoneutron cross section in nuclei, earlier recognized forA>63, in fact persist down to the lightest nuclei. Averaging over the oscillations or focusing on the lower envelope of the oscillating curve (magic nuclei), the FWHM is seen to generally decrease with increasingA, consistent withA^−1/3, a dependence which was earlier known to hold in metal particle systems. If the FWHMs are scaled by the respective Fermi energies and the inverse radii by the Fermi wave vectors, the two data sets become comparable in magnitude. A schematic theoretical description of the systematics is presented.