Related papers: Complex Geometry of Nuclei and Atoms
We present in this article a family of new combinatorial identities via purely differential/complex geometry methods, which include as a speical case a unified and explicit formula for Chern numbers of all complex flag manifolds. Our…
The algebraic approach to the phase problem for the case of X-ray scattering from an ideal crystal is extended to the case of the neutron scattering, overcoming the difficulty related to the non-positivity of the scattering density. In this…
Explicit formulas determining the dimension and the degree of the singular subscheme of hypersurfaces in ${\mathbb P}^n$ are given in terms of the graded Betti numbers of the minimal free resolution of the corresponding Jacobian algebra.…
Using vertex algebra techniques, we determine a set of generators for the cohomology ring of the Hilbert schemes of points on an arbitrary smooth projective surface over the field of complex numbers.
The nuclear interactions of atomic and low energy antiprotons are studied. Measurements of level shifts and widths in the lightest elements are analyzed and compared with new results obtained in heavy nuclei. Simple geometric properties of…
Neutron star matter is investigated in a hadronic chiral model approach using the lowest flavor-SU(3) multiplets for baryons and mesons. The parameters are determined to yield consistent results for saturated nuclear matter as well as for…
Understanding the properties of the crust and the core as well as its interface is essential for accurate astrophysical modeling of phenomena such as glitches, X-ray bursts or oscillations in neutron stars. To study the crust-core…
We propose a novel neutron interferometry setup to explore the potential existence of mirror neutrons, a candidate for dark matter. Our work demonstrates that if mirror neutrons exist, neutrons will acquire an observable geometric phase due…
I present a proof-of-concept study of nuclear radii and binding energies within NUCLEI-PACK, a novel semi-classical framework based on optimized sphere packing of nucleons and clusters. In this approach, proton and neutron positions are…
A fundamental goal of algebraic geometry is to do for singular varieties whatever we can do for smooth ones. Intersection homology, for example, directly produces groups associated to any variety which have almost all the properties of the…
The shape of crystalline nanoparticles (NP) can often be described by polyhedra with flat facet surfaces. Thus, structural studies of polyhedral bodies can help to describe geometric details of NPs. Here we consider compact polyhedra of…
Neutron stars provide a natural laboratory for studying the properties of dense nuclear matter under extreme conditions. In this proceeding, we review our current understanding of dense isospin symmetric and asymmetric matter and neutron…
The Standard Model does not explain the hierarchy problem. Before the discovery of nonzero lepton mixing angle {\theta}13 high hopes in explanation of the shape of the lepton mixing matrix were combined with non abelian symmetries.…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to…
Atomic experiments bring meaningful and valuable information on fundamental symmetries. The hypothesis of a large ($\sim 100$ eV) P-odd weak matrix element between single-particle states in heavy nuclei is inconsistent with the results of…
Previously defined spin-dependent quark densities that are matrix elements of specific density operators in proton states of definite spin-polarization generally have an infinite variety of non-spherical shapes. The present application is…
We investigate the properties of isospin-symmetric nuclear matter and neutron stars in a chiral model approach adopting the SU(2) parity doublet formulation. This ansatz explicitly incorporates chiral symmetry restoration with the limit of…
The structure of the crust of a neutron star is completely determined by the experimentally measured nuclear masses up to a density of the order of 10^11 g.cm^{-3}. At higher densities, the composition of the crust still remains uncertain,…
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…