Solving Dirac equations on a 3D lattice with inverse Hamiltonian and spectral methods

A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in momentum space with the help of the discrete Fourier transform, i.e., the spectral method. This method is demonstrated in solving the Dirac equation for a given spherical potential in 3D lattice space. In comparison with the results obtained by the shooting method, the differences in single particle energy are smaller than $10^{-4}$~MeV, and the densities are almost identical, which demonstrates the high accuracy of the present method. The results obtained by applying this method without any modification to solve the Dirac equations for an axial deformed, non-axial deformed, and octupole deformed potential are provided and discussed.Comment: 18 pages, 6 figure

Modified equation of state, scalar field, and bulk viscosity in Friedmann universe

A generalized dynamical equation for the scale factor of the universe is proposed to describe the cosmological evolution, of which the $\Lambda$CDM model is a special case. It also provides a general example to show the equivalence of the modified equation of state (EOS) and a scalar field model. In the mathematical aspect, the EOS, the scalar field potential $V(\phi)$, and the scale factor $a(t)$ all have possessed analytical solutions. Such features are due to a simple form invariance of the equation inherited which determines the Hubble parameter. From the physical point of view, this dynamical equation can be regarded as the $\Lambda$CDM model with bulk viscosity, an existence content in the universe. We employ the SNe Ia data with the parameter $\mathcal{A}$ measured from the SDSS data and the shift parameter $\mathcal{R}$ measured from WMAP data to constrain the parameters in our model. The result is that the contribution of the bulk viscosity, accumulated as an effective dark energy responsible for the current cosmic accelerating expansion, is made approximately ten percent to that of the cosmological constant.Comment: 4 figs, pl

Octet baryon masses in next-to-next-to-next-to-leading order covariant baryon chiral perturbation theory

We study the ground-state octet baryon masses and sigma terms using the covariant baryon chiral perturbation theory (ChPT) with the extended-on-mass-shell (EOMS) renormalization scheme up to next-to-next-to-next-to-leading order (N$^3$LO). By adjusting the available 19 low-energy constants (LECs), a reasonable fit of the $n_f=2+1$ lattice quantum chromodynamics (LQCD) results from the PACS-CS, LHPC, HSC, QCDSF-UKQCD and NPLQCD collaborations is achieved. Finite-volume corrections to the lattice data are calculated self-consistently. Our study shows that N$^3$LO BChPT describes better the light quark mass evolution of the lattice data than the NNLO BChPT does and the various lattice simulations seem to be consistent with each other. We also predict the pion and strangeness sigma terms of the octet baryons using the LECs determined in the fit of their masses. The predicted pion- and strangeness-nucleon sigma terms are $\sigma_{\pi N}=43(1)(6)$ MeV and $\sigma_{s N}=126(24)(54)$ MeV, respectively.Comment: 28 pages, 6 figures, minor revisions, typos corrected, version to appear in JHE

Dynamical synthesis of 4He in the scission phase of nuclear fission

In the exothermic process of fission decay, an atomic nucleus splits into two or more independent fragments. Several aspects of nuclear fission are not properly understood, in particular the formation of the neck between the nascent fragments, and the subsequent mechanism of scission into two or more independent fragments. Using an implementation of time-dependent density functional theory, based on a relativistic energy density functional and including pairing correlations, we analyze the final phase of the process of induced fission of $^{240}$Pu, and show that the time-scale of neck formation coincides with the assembly of two $\alpha$-like clusters (less than 1 zs = 10$^{-21}$ s). Because of its much larger binding energy, the dynamical synthesis of 4He in the neck predominates over other light clusters, e.g., $^3$H and $^6$He. At the instant of scission the neck ruptures exactly between the two $\alpha$-like clusters, which separate because of the Coulomb repulsion and are eventually absorbed by the two emerging fragments. The newly proposed mechanism of light charged clusters formation at scission provides a natural explanation of ternary fission.Comment: 5 pages, 4 figures, Final version for publicatio