Influence of pairing correlations on the radius of neutron-rich nuclei

The influence of pairing correlations on the neutron root mean square (rms) radius of nuclei is investigated in the framework of self-consistent Skyrme Hartree-Fock-Bogoliubov calculations. The continuum is treated appropriately by the Green's function techniques. As an example the nucleus $^{124}$Zr is treated for a varying strength of pairing correlations. We find that, as the pairing strength increases, the neutron rms radius first shrinks, reaches a minimum and beyond this point it expands again. The shrinkage is due to the the so-called `pairing anti-halo effect', i. e. due to the decreasing of the asymptotic density distribution with increasing pairing. However, in some cases, increasing pairing correlations can also lead to an expansion of the nucleus due to a growing occupation of so-called `halo' orbits, i.e. weakly bound states and resonances in the continuum with low-$\ell$ values. In this case, the neutron radii are extended just by the influence of pairing correlations, since these `halo' orbits cannot be occupied without pairing. The term `anti-halo effect' is not justified in such cases. For a full understanding of this complicated interplay self-consistent calculations are necessary.Comment: 18 pages, 5 figure

Optimization of bus stop locations for on-demand public bus service

This paper proposes an optimization model formulation for the design of bus stop spacing of on-demand public bus (ODPB) service. The objective of this model is to minimize the total travel time of all the passengers. To capture the unique characteristics of ODPB service, model constraints such as the length of segment, the configuration of shed line, minimum stop spacing, vehicle capacity limitation, are explicitly considered. Numerical results show that the optimal bus stop spacing for ODPB is very different from a conventional bus. Factors like passenger density, travel time perception weight ratio, access/egress walking speed, and the time loss near/at the stop would affect the ODPB stop spacing significantly

Effects of tensor forces in nuclear spin-orbit splittings from ab initio calculations

A systematic and specific pattern due to the effects of the tensor forces is found in the evolution of spin-orbit splittings in neutron drops. This result is obtained from relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. It forms an important guide for future microscopic derivations of relativistic and nonrelativistic nuclear energy density functionals.Comment: 14 pages, 3 figure

Fully self-consistent relativistic Brueckner-Hartree-Fock theory for finite nuclei

Starting from the relativistic form of the Bonn potential as a bare nucleon-nucleon interaction, the full Relativistic Brueckner-Hartree-Fock (RBHF) equations are solved for finite nuclei in a fully self-consistent basis. This provides a relativistic ab initio calculation of the ground state properties of finite nuclei without any free parameters and without three-body forces. The convergence properties for the solutions of these coupled equations are discussed in detail at the example of the nucleus $^{16}$O. The binding energies, radii, and spin-orbit splittings of the doubly magic nuclei $^{4}$He, $^{16}$O, and $^{40}$Ca are calculated and compared with the earlier RBHF calculated results in a fixed Dirac Woods-Saxon basis and other non-relativistic ab initio calculated results based on pure two-body forces.Comment: 22 pages, 13 figure

Relativistic Brueckner-Hartree-Fock theory for neutron drops

Neutron drops confined in an external field are studied in the framework of relativistic Brueckner-Hartree-Fock theory using the bare nucleon-nucleon interaction. The ground state energies and radii of neutron drops with even numbers from $N = 4$ to $N=50$ are calculated and compared with results obtained from other nonrelativistic \textit{ab initio} calculations and from relativistic density functional theory. Special attention has been paid to the magic numbers and to the sub-shell closures. The single-particle energies are investigated and the monopole effect of the tensor force on the evolutions of the spin-orbit and the pseudospin-orbit splittings is discussed. The results provide interesting insight of neutron rich systems and can form an important guide for future density functionals.Comment: 31 pages, 12 figure

Dark viscous fluid described by a unified equation of state in cosmology

We generalize the $\Lambda$CDM model by introducing a unified EOS to describe the Universe contents modeled as dark viscous fluid, motivated by the fact that a single constant equation of state (EOS) $p=-p_0$ ($p_0>0$) reproduces the $\Lambda$CDM model exactly. This EOS describes the perfect fluid term, the dissipative effect, and the cosmological constant in a unique framework and the Friedmann equations can be analytically solved. Especially, we find a relation between the EOS parameter and the renormalizable condition of a scalar field. We develop a completely numerical method to perform a $\chi^2$ minimization to constrain the parameters in a cosmological model directly from the Friedmann equations, and employ the SNe data with the parameter $\mathcal{A}$ measured from the SDSS data to constrain our model. The result indicates that the dissipative effect is rather small in the late-time Universe.Comment: 4 pages, 2 figures. v2: new materials added. v3: matches the version to appear in IJMP