The thick-thin decomposition and the bilipschitz classification of normal surface singularities

We describe a natural decomposition of a normal complex surface singularity $(X,0)$ into its "thick" and "thin" parts. The former is essentially metrically conical, while the latter shrinks rapidly in thickness as it approaches the origin. The thin part is empty if and only if the singularity is metrically conical; the link of the singularity is then Seifert fibered. In general the thin part will not be empty, in which case it always carries essential topology. Our decomposition has some analogy with the Margulis thick-thin decomposition for a negatively curved manifold. However, the geometric behavior is very different; for example, often most of the topology of a normal surface singularity is concentrated in the thin parts. By refining the thick-thin decomposition, we then give a complete description of the intrinsic bilipschitz geometry of $(X,0)$ in terms of its topology and a finite list of numerical bilipschitz invariants.Comment: Minor corrections. To appear in Acta Mathematic

Prescriptions for the scaling variable of the nucleon structure function in nuclei

We tested several choices of the in-medium value of the Bjorken scaling variable assuming the nucleon structure function in nucleus to be the same as that of free nucleon. The results unambiguously show that it is different.Comment: 11 pages, 3 figures, 1 tabl

Theory of doorway states for one-nucleon transfer reactions. II. Model-independent study of nuclear correlation effects

The correlation effects in nuclei owing to which the nuclear wave functions are different from the Slater determinants are studied on the basis of the original theory. The calculated numbers of nucleons out of the nuclear Fermi-surface are in reasonable agreement with the finding from the high-momentum components of the nucleon momentum distributions in nuclei. The problems concerning the nuclear binding energy are also discussed.Comment: 11 pages LaTeX, epsfig.sty + 1 PostScript figure. submitted to Journal of Nuclear Physic

An introduction to Lipschitz geometry of complex singularities

The aim of this paper to introduce the reader to a recent point of view on the Lipschitz classifications of complex singularities. It presents the complete classification of Lipschitz geometry of complex plane curves singularities and in particular, it introduces the so-called bubble trick and bubble trick with jumps which are key tools to study Lipschitz geometry of germs. It describes also the thick-thin decomposition of a normal complex surface singularity and built two geometric decompositions of a normal surface germ into standard pieces which are invariant by respectively inner and outer bilipschitz homeomorphisms. This leads in particular to the complete classification of Lipschitz geometry for the inner metric.Comment: 50 pages, 36 figure

Multiplicity of singularities is not a bi-Lipschitz invariant

It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.Lev Birbrair: Partially supported by CNPq grant 302655/2014-0. Alexandre Fernandes: Partially supported by CNPq grant grant304221/2017-9 and by CAPES-BRASIL Finance Code 001. J. Edson Sampaio: Partially supported by CNPq-Brazil grant 303811/2018-8, by the ERCEA 615655 NMST Consolidator Grant and also by the Basque Government through the BERC 2018-2021 program and Gobierno Vasco Grant IT1094-16, by the Spanish Ministry of Science, Innovation and Universities: BCAM Severo Ochoa accreditation SEV-2017-0718. Misha Verbitsky: Partially supported by the Russian Academic Excellence Project ‘5-100’, FAPERJ E-26/202.912/2018 and CNPq - Process 313608/2017-2

Schiff moment of the Mercury nucleus and the proton dipole moment

We calculated the contribution of internal nucleon electric dipole moments to the Schiff moment of $^{199}$Hg. The contribution of the proton electric dipole moment was obtained via core polarization effects that were treated in the framework of random phase approximation with effective residual forces. We derived a new upper bound $|d_p|< 5.4\times 10^{-24} e\cdot$cm of the proton electric dipole moment.Comment: 4 pages, 2 figures, RevTex

The nonrelativistic limit of the relativistic point coupling model

We relate the relativistic finite range mean-field model (RMF-FR) to the point-coupling variant and compare the nonlinear density dependence. From this, the effective Hamiltonian of the nonlinear point-coupling model in the nonrelativistic limit is derived. Different from the nonrelativistic models, the nonlinearity in the relativistic models automatically yields contributions in the form of a weak density dependence not only in the central potential but also in the spin-orbit potential. The central potential affects the bulk and surface properties while the spin-orbit potential is crucial for the shell structure of finite nuclei. A modification in the Skyrme-Hartree-Fock model with a density-dependent spin-orbit potential inspired by the point-coupling model is suggested.Comment: 21 pages, latex, 1 eps figure. accepted for publication in annals of physic

Nuclear Magnetic Quadrupole Moments in Single Particle Approximation

A static magnetic quadrupole moment of a nucleus, induced by T- and P-odd nucleon-nucleon interaction, is investigated in the single-particle approximation. Models are considered allowing for analytical solution. The problem is also treated numerically in a Woods-Saxon potential with spin-orbit interaction. The stability of results is discussed.Comment: LATEX, 9 pages, 1 postscript figure available upon request from "[email protected]". BINP 94-4

P- and T-violating Schiff moment of the Mercury nucleus

The Schiff moment of the $^{199}$Hg nucleus was calculated using finite range P- and T-violating weak nucleon-nucleon interaction. Effects of the core polarization were considered in the framework of RPA with effective residual forces.Comment: 10 pages and 2 figures,to appear in Yad. Fi

The Nuclear Sigma Term in the Skyrme Model: Pion-Nucleus Interaction

The nuclear sigma term is calculated including the nuclear matrix element of the derivative of the NN interaction with respect to the quark mass, $m_q\frac{\partial V_{NN}}{\partial m_q}$. The NN potential is evaluated in the skyrmion-skyrmion picture within the quantized product ansatz. The contribution of the NN potential to the nuclear sigma term provides repulsion to the pion-nucleus interaction. The strength of the s-wave pion-nucleus optical potential is estimated including such contribution. The results are consistent with the analysis of the experimental data.Comment: 16 pages (latex), 3 figures (eps), e-mail: [email protected] and [email protected]