Related papers: Complex Geometry of Nuclei and Atoms
A previous paper (M.F.Atiyah and N.S.Manton, Complex geometry of nuclei and atoms, arXiv:1609.02816) modelled atoms and their isotopes by complex algebraic surfaces, with the projective plane modelling Hydrogen. In this paper, models of the…
While the parameters of atomic nuclei, Z and A, indicate a general structural pattern for the nuclei, their exact masses in their fine differences seem not to exhibit the orderly kind of logical system that systematic and orderly nature…
The complex nature of the nuclear forces generates a broad range and diversity of observational phenomena. Heavy nuclei, though orders of magnitude less massive than neutron stars, are governed by the same underlying physics, which is…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
The role of discrete (or point-group) symmetries in alpha-cluster nuclei is discussed in the framework of the algebraic cluster model which describes the relative motion of the alpha-particles. Particular attention is paid to the discrete…
The recent and older level shifts and widths in pbar atoms are analyzed. The results are fitted by an antiproton-nucleus optical potential with two basic complex strength parameters. These parameters are related to average S and P wave…
We determine all Chern numbers of smooth complex projective varieties of dimension at least four which are determined up to finite ambiguity by the underlying smooth manifold. We also give an upper bound on the dimension of the space of…
A geometric interpretation is given of matrix elements of a short-range interaction between states that are written in terms of aligned neutron-proton pairs.
Several topics concerning nuclear structure and electromagnetic interactions of heavy nuclei are reviewed. These comprehend the deformed single-particle shell model, nuclear collective motion, symmetry breaking and approximate symmetry…
We discuss some of the challenges that future nuclear modeling may face in order to improve the description of the nuclear structure. One challenge is related to the need for A-body nuclear interactions justified by various contemporary…
The neutron is largely spherical and incompressible in atomic nuclei. These two properties are however challenged in the extreme pressure environment of a neutron star. Our variational computation within the Cornell model of Coulomb gauge…
The algebraic cluster model is is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the…
In this paper geometry is studied with a novel approach. Every geometrical object is defined as a symbol which satisfies some properties. These symbols are then coded into a class of numbers which are named here as many dots numbers (MDN).…
Real algebraic geometry is the study of semi-algebraic sets, subsets of $\R^k$ defined by Boolean combinations of polynomial equalities and inequalities. The focus of this thesis is to study quantitative results in real algebraic geometry,…
The purpose of these lectures is to illustrate how symmetry and pattern recognition play essential roles in the progression from experimental observation to an understanding of nuclear phenomena in terms of interacting neutrons and protons.…
The properties of inhomogeneous neutron matter are crucial to the physics of neutron-rich nuclei and the crust of neutron stars. Advances in computational techniques now allow us to accurately determine the binding energies and densities of…
Ever since the discovery of neutron stars it has been realized that they serve as probes of a physical regime that cannot be accessed in laboratories: strongly degenerate matter at several times nuclear saturation density. Existing nuclear…
A systematics of the atomic nuclei in the frame of the nucleon number $A = Z + N$ and the proton-neutron difference $F = Z - N$ is considered. The classification scheme is provided by means of the non-compact algebra $sp(4,R)$. In this…
We study properties of the proton component of neutron star matter for a number of realistic nuclear models. Protons which form a few percent admixture tend to be localized in potential wells corresponding to neutron matter inhomogeneities…
There have been many empirical evindences which show that the single-particle picture holds to a good approximation in atomic nuclei. In this picture, protons and neutrons move independently inside a mean-field potential generated by an…