Modern Physics Letters A

We study (2+1)-dimensional Dirac equation with complex scalar and Lorentz scalar potentials. It is shown that the Dirac equation admits exact analytical solutions with real eigenvalues for certain complex potentials while for another class of potentials zero energy solutions can be obtained analytically. For the scalar potential cases, it has also been shown that the effective Schrödinger-like equations resulting from decoupling the spinor components can be interpreted as exactly solvable energy-dependent Schrödinger equations.

We propose the mimetic F(R) theory and investigate the early-time and late-time acceleration in such theory. It is demonstrated that inflation consistent with observable data may be realized in such theory. The reconstruction of realistic ΛCDM era is also possible as well as the unification of early-time inflation with late-time acceleration or bounce universe. It is stressed that specific universe evolution is governed by mimetic F(R) theory which is different from convenient F(R) gravity. The corresponding examples are presented. Mimetic F(R) gravity is generalized by the addition of the scalar potential in the formulation of convenient F(R) gravity with specific Lagrange multiplier constraint. It is demonstrated that such theory may admit the arbitrary universe evolution via the corresponding choice of the scalar potential and/or function F(R).

An extension of the Standard Model (SM) is studied in which two right-handed (RH) neutrinos per generation are incorporated, but considering the hypothesis of the symmetry of lepton and quark contents in order to deprive the number of RH neutrinos of freedom, generate Dirac neutrinos and accommodate naturally tiny values for their masses. The high scale type-I seesaw regime is applied to the first, ordinary RH neutrino, whereas a low scale pseudo-Dirac scenario is used for the second, adulterant RH neutrino, implying that the first RH neutrino decouples at the high scale, while the second RH neutrino survives down to the low scale to pair off in a Dirac-like form with the corresponding left-handed (LH) neutrino. The small mass and couplings of this extra RH neutrino are explained by means of the statement of the symmetry of fermionic content, only regarded as a guideline to the natural choice of parameters since it is not a proper symmetry in the Lagrangian.

A search for rare decay η′ → 4 π⁰ has been performed with GAMS-4π setup. The new upper limit is BR(η′ → 4 π⁰) < 3.2 ⋅10^-4 at 90% confidence level. The π^- p charge-exchange reaction at 32.5 GeV/c was used as a source of 1.3⋅10⁶η′ mesons. Experiment was carried out at the IHEP U-70 accelerator.

By using semiclassical method and considering Woods–Saxon and Coulomb potentials, the level density parameter a was calculated for three superheavy nuclei ²⁷⁰110, ²⁷⁸112 and ²⁹⁰116. Obtained results showed that the value of level density parameter of these nuclei is near to the simple relation a ≈ A/10. In framework of the dinuclear system model, the effects of level density parameter on the probability of the formation of a compound nucleus, the ratio of neutron emission width and fission width, and evaporation residue cross-section of three cold fusion reactions ⁶²Ni+²⁰⁸Pb, ⁷⁰Zn+²⁰⁸Pb and ⁸²Se+²⁰⁸Pb, leading to superheavy elements were investigated. The findings indicate that the level density parameter play a significant role in calculations of heavy-ion fusion–fission reactions. The obtained results in the case of a = A/12 have larger values in comparison with calculated level density parameter with Woods–Saxon potential (a_WS) and a = A/10. The theoretical results of the evaporation residue cross-section are very sensitive to the choice of level density parameter. The calculated values with a_WS are in good agreement with experimental values.

We revisit the free-fall energy density of scalar fields semiclassically by employing the trace anomaly on a two-dimensional Schwarzschild black hole with respect to various black hole states in order to clarify whether something special at the horizon happens or not. For the Boulware state, the energy density at the horizon is always negative divergent, which is independent of initial free-fall positions. However, in the Unruh state the initial free-fall position is responsible for the energy density at the horizon and there is a critical point to determine the sign of the energy density at the horizon. In particular, a huge negative energy density appears when the freely falling observer is dropped just near the horizon. For the Hartle–Hawking state, it may also be positive or negative depending on the initial free-fall position, but it is always finite. Finally, we discuss physical consequences of these calculations.