abstract

We analyze the angular distributions for the (\(\alpha \), \(^{3}\)He) and (\(\alpha \), \(t\)) reactions on \(^{28}\)Si for projectile energies ranging from \(50\) to \(120\) MeV based on the partial-wave representation of the transfer amplitude expressed in terms of the S-matrices for the entrance and exit channels, with an emphasis on identifying Airy minima of various orders. The calculations have been performed using a six-parameter S-matrix model and S-matrix parameters obtained from the analysis of elastic scattering data. The first- and (or) second-order Airy minima are clearly identified in the analyzed transfer reaction angular distributions at intermediate angles. The detected Airy minima are found to be due to the interference between several inner and surface partial waves. The impact parameters of these waves are in the range of \(1\)–\(6\) fm, the upper boundary of which is less than the strong absorption radius.

abstract

We show that time autocorrelation functions exhibiting an asymptotic power law decay \(\sim t^{-\rho }/{\mit \Gamma }(1-\rho )\) take the form of a “stretched” Mittag–Leffler function, \(E_\rho (-(t/\tau )^\rho )\), if the associated memory function attains its asymptotic form on a time scale which is much shorter than the characteristic time scale of the asymptotic regime itself. The range for the exponent is here restricted to if \(0\lt \rho \lt 1\) and we show that the time scale separation can be enforced by downscaling the amplitude of the memory function. Reasoning along the same lines, we demonstrate that the velocity autocorrelation function of an anomalously diffusing particle behaves as \(E_{2-\alpha }(-(t/\tau _{\mathrm {D}})^{2-\alpha })\) if the associated memory function attains its asymptotic form on time scales much shorter than the diffusion time scale, \(\tau _{\mathrm {D}}\). The exponent \(\alpha \) defines here the asymptotic form of its mean square displacement, \(\langle (x(t)-x(0))^2\rangle \sim t^\alpha \), and \(0\lt \alpha \lt 2\).

abstract

Ground-state properties of even–even isotopes of polonium (Po) have been studied. The physical observables of our interest include quadrupole deformation and shape transitions, binding energies, charge radii, and neutron skin thickness. Theoretical results for the differential variation \({\mathrm {d}}S_{2n}(Z,N)\) based on two-neutron separation energy are also presented. Theoretical calculations are carried out by employing covariant density functional theory with density-dependent meson exchange (DD-ME2) and point coupling (DD-PC1) interactions. The presented ground state properties with the RMF (Relativistic Mean Field) model are in good agreement with recently available experimental data. The theoretical estimates calculated by the covariant density functional theory predict shape transition from oblate to spherical and spherical to prolate along the isotopic chain of even–even Po nuclei ranging from mass number of 186 to 218.

abstract

A new approach to quantization of the relativistic Majorana field is presented. It is based on the expansion of the field into eigenfunctions of the axial momentum — a novel observable introduced recently. Relativistic invariance is used as the main guiding principle instead of canonical formalism. The hidden structure of the quantized Majorana field in the form of real Clifford algebra of Hermitian fermionic operators is unveiled. All generators of the Poincaré transformations are found as solutions of certain operator equations, without invoking the principle of correspondence with classical conserved quantities. Also, operators of parity \(\hat {P}\) and time-reversal \(\hat {T}\) are constructed.

abstract

We present a proof of positivity of an invariant kernel, which is of basic importance for the Staruszkiewicz theory of the quantum Coulomb field. Presented proof of positivity is independent of the Staruszkiewicz theory and is based on the classical Schoenberg’s theorem for conditionally negative definite functions, as well as on the generalized Bochner’s theorem.