Particles in classically forbidden area, neutron skin and halo, and pure neutron matter in Ca isotopes

The nucleon density distributions and the thickness of pure neutron matter in Ca isotopes were systematically studied using the Skyrme-Hartree-Fock model (SHF) from the $\beta$-stability line to the neutron drip-line. The pure neutron matter, related with the neutron skin or halo, was shown to depend not only on the Fermi levels of the neutrons but also on the orbital angular momentum of the valence neutrons. New definitions for the thickness of pure neutron matter are proposed.Comment: 6 pages, 5 figure

Pseudospin symmetry and its approximation in real nuclei

The origin of pseudospin symmetry and its broken in real nuclei are discussed in the relativistic mean field theory. In the exact pseudospin symmetry, even the usual intruder orbits have degenerate partners. In real nuclei, pseudospin symmetry is approximate, and the partners of the usual intruder orbits will disappear. The difference is mainly due to the pseudo spin-orbit potential and the transition between them is discussed in details. The contribution of pseudospin-orbit potential for intruder orbits is quite large, compared with that for pseudospin doublets. The disappearance of the pseudospin partner for the intruder orbit can be understood from the properties of its wave function.Comment: 10 pages, 3 figure

The surface diffuseness and the spin-orbital splitting in relativistic continuum Hartree-Bogoliubov theory

The Relativistic Continuum Hartree Bogoliubov theory (RCHB), which is the extension of the Relativistic Mean Field and the Bogoliubov transformation in the coordinate representation, has been used to study tin isotopes. The pairing correlation is taken into account by a density-dependent force of zero range. RCHB is used to describe the even-even tin isotopes all the way from the proton drip line to the neutron drip line. The contribution of the continuum which is important for nuclei near the drip-line has been taken into account. The theoretical $S_{2n}$ as well as the neutron, proton, and matter $rms$ radii are presented and compared with the experimental values where they exist. The change of the potential surface with the neutron number has been investigated. The diffuseness of the potentials in tin isotopes is analyzed through the spin-orbital splitting in order to provide new way to understand the halo phenomena in exotic nuclei. The systematic of the isospin and energy dependence of these results are extracted and analyzed.Comment: 11 figure

Succinct Representations of Dynamic Strings

The rank and select operations over a string of length n from an alphabet of size $\sigma$ have been used widely in the design of succinct data structures. In many applications, the string itself need be maintained dynamically, allowing characters of the string to be inserted and deleted. Under the word RAM model with word size $w=\Omega(\lg n)$, we design a succinct representation of dynamic strings using $nH_0 + o(n)\lg\sigma + O(w)$ bits to support rank, select, insert and delete in $O(\frac{\lg n}{\lg\lg n}(\frac{\lg \sigma}{\lg\lg n}+1))$ time. When the alphabet size is small, i.e. when \sigma = O(\polylog (n)), including the case in which the string is a bit vector, these operations are supported in $O(\frac{\lg n}{\lg\lg n})$ time. Our data structures are more efficient than previous results on the same problem, and we have applied them to improve results on the design and construction of space-efficient text indexes

Relativistic description of magnetic moments in nuclei with doubly closed shells plus or minus one nucleon

Using the relativistic point-coupling model with density functional PC-PK1, the magnetic moments of the nuclei $^{207}$Pb, $^{209}$Pb, $^{207}$Tl and $^{209}$Bi with a $jj$ closed-shell core $^{208}$Pb are studied on the basis of relativistic mean field (RMF) theory. The corresponding time-odd fields, the one-pion exchange currents, and the first- and second-order corrections are taken into account. The present relativistic results reproduce the data well. The relative deviation between theory and experiment for these four nuclei is 6.1% for the relativistic calculations and somewhat smaller than the value of 13.2% found in earlier non-relativistic investigations. It turns out that the $\pi$ meson is important for the description of magnetic moments, first by means of one-pion exchange currents and second by the residual interaction provided by the $\pi$ exchange.Comment: 11 pages, 7 figure

The pseudo-spin symmetry in Zr and Sn isotopes from the proton drip line to the neutron drip line

Based on the Relativistic continuum Hartree-Bogoliubov (RCHB) theory, the pseudo-spin approximation in exotic nuclei is investigated in Zr and Sn isotopes from the proton drip line to the neutron drip line. The quality of the pseudo-spin approximation is shown to be connected with the competition between the centrifugal barrier (CB) and the pseudo-spin orbital potential (PSOP). The PSOP depends on the derivative of the difference between the scalar and vector potentials $dV/dr$. If $dV/dr = 0$, the pseudo-spin symmetry is exact. The pseudo-spin symmetry is found to be a good approximation for normal nuclei and to become much better for exotic nuclei with highly diffuse potential, which have $dV/dr \sim 0$. The energy splitting of the pseudo-spin partners is smaller for orbitals near the Fermi surface (even in the continuum) than the deeply bound orbitals. The lower components of the Dirac wave functions for the pseudo-spin partners are very similar and almost equal in magnitude.Comment: 22 pages, 9figure

The relativistic continuum Hartree-Bogoliubov description of charge-changing cross section for C,N,O and F isotopes

The ground state properties including radii, density distribution and one neutron separation energy for C, N, O and F isotopes up to the neutron drip line are systematically studied by the fully self-consistent microscopic Relativistic Continuum Hartree-Bogoliubov (RCHB) theory. With the proton density distribution thus obtained, the charge-changing cross sections for C, N, O and F isotopes are calculated using the Glauber model. Good agreement with the data has been achieved. The charge changing cross sections change only slightly with the neutron number except for proton-rich nuclei. Similar trends of variations of proton radii and of charge changing cross sections for each isotope chain is observed which implies that the proton density plays important role in determining the charge-changing cross sections.Comment: 10 pages, 4 figure

Sensitivity of neutron radii in the ""sup208Pbnucleusandaneutronstartonucleon−"" sup 208_Pb nucleus and a neutron star to nucleon- sigma_-$ rho_ coupling corrections in relativistic mean field theory

We study the sensitivity of the neutron skin thickness, $S$, in a $^{208}$Pb nucleus to the addition of nucleon-sigma-rho coupling corrections to a selection (PK1, NL3, S271, Z271) of interactions in relativistic mean field model. The PK1 and NL3 effective interactions lead to a minimum value of $S$ = 0.16 fm in comparison with the original value of $S$ = 0.28 fm. The S271 and Z271 effective interactions yield even smaller values of $S$ = 0.11 fm, which are similar to those for nonrelativistic mean field models. A precise measurement of the neutron radius, and therefore $S$, in $^{208}$Pb will place an important constraint on both relativistic and nonrelativistic mean field models. We also study the correlation between the radius of a 1.4 solar-mass neutron star and $S$.Comment: 40 pages 13 figures. to be published in Physical Review