Natural Units For Nuclear Energy Density Functional Theory

Naive dimensional analysis based on chiral effective theory, when adapted to nuclear energy density functionals, prescribes natural units and a hierarchy of contributions that could be used to constrain fits of generalized functionals. By applying these units, a large sample of Skyrme parametrizations is examined for naturalness, which is signaled by dimensionless coupling constants of order one. The bulk of the parameters are found to be natural, with an underlying scale consistent with other determinations. Significant deviations from unity are associated with deficiencies in the corresponding terms of particular functionals or with an incomplete optimization procedure.Comment: 5 pages, 2 figures, accepted for publication in Phys. Rev.

Thouless-Valatin moment of inertia and removal of the spurious mode in the linear response theory

Symmetry breaking at the mean-field level leads to an appearance of a symmetry restoring Nambu-Goldstone (NG) mode in the linear response theory. These modes represent a special kind of collective motion of the system. However, they can interfere with the calculated intrinsic physical excitations and, hence, they are often called as spurious modes. I discuss translational and rotational NG mode and the inertia parameter associated with these modes, by using the finite amplitude method formalism. I will also discuss how to remove spurious mode from the calculated transition strength function. © Published under licence by IOP Publishing Ltd.Peer reviewe

Combinatorics on words in information security: Unavoidable regularities in the construction of multicollision attacks on iterated hash functions

Classically in combinatorics on words one studies unavoidable regularities that appear in sufficiently long strings of symbols over a fixed size alphabet. In this paper we take another viewpoint and focus on combinatorial properties of long words in which the number of occurrences of any symbol is restritced by a fixed constant. We then demonstrate the connection of these properties to constructing multicollision attacks on so called generalized iterated hash functions.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Neutron skin uncertainties of Skyrme energy density functionals

Background: Neutron-skin thickness is an excellent indicator of isovector properties of atomic nuclei. As such, it correlates strongly with observables in finite nuclei that depend on neutron-to-proton imbalance and the nuclear symmetry energy that characterizes the equation of state of neutron-rich matter. A rich worldwide experimental program involving studies with rare isotopes, parity violating electron scattering, and astronomical observations is devoted to pinning down the isovector sector of nuclear models. Purpose: We assess the theoretical systematic and statistical uncertainties of neutron-skin thickness and relate them to the equation of state of nuclear matter, and in particular to nuclear symmetry energy parameters. Methods: We use the nuclear superfluid Density Functional Theory with several Skyrme energy density functionals and density dependent pairing. To evaluate statistical errors and their budget, we employ the statistical covariance technique. Results: We find that the errors on neutron skin increase with neutron excess. Statistical errors due to uncertain coupling constants of the density functional are found to be larger than systematic errors, the latter not exceeding 0.06 fm in most neutron-rich nuclei across the nuclear landscape. The single major source of uncertainty is the poorly determined slope L of the symmetry energy that parametrizes its density dependence. Conclusions: To provide essential constraints on the symmetry energy of the nuclear energy density functional, next-generation measurements of neutron skins are required to deliver precision better than 0.06 fm.Comment: 5 pages, 4 figure

Uncertainty propagation within the UNEDF models

The parameters of the nuclear energy density have to be adjusted to experimental data. As a result they carry certain uncertainty which then propagates to calculated values of observables. In the present work we quantify the statistical uncertainties of binding energies, proton quadrupole moments and proton matter radius for three UNEDF Skyrme energy density functionals by taking advantage of the knowledge of the model parameter uncertainties. We find that the uncertainty of UNEDF models increases rapidly when going towards proton or neutron rich nuclei. We also investigate the impact of each model parameter on the total error budget.Peer reviewe

Double Beta Decay, Nuclear Structure and Physics beyond the Standard Model

Neutrinoless Double Beta Decay ($0\nu\beta\beta$) is presently the only known experiment to distinguisch between Dirac neutrinos, different from their antiparticles, and Majorana neutrinos, identical with their antiparticles. In addition $0\nu\beta\beta$ allows to determine the absolute scale of the neutrino masses. This is not possible with neutrino oscillations. To determine the neutrino masses one must assume, that the light Majorana neutrino exchange is the leading mechanism for $0\nu\beta\beta$ and that the matrix element of this transition can ba calculated reliably. The experimental $0\nu\beta\beta$ transition amplitude in this mechanism is a product of the light left handed effective Majorana neutrino mass and of this transition matrix element. The different methods, Quasi-particle Random Phase Approximation (QRPA), Shell Model (SM), Projected Hartree-Fock-Bogoliubov (PHFB) and Interacting Boson Model (IBM2) used in the literature and the reliability of the matrix elements in these approaches are reviewed. In the second part it is investigated how one can determine the leading mechanism or mechanisms from the data of the $0\nu\beta\beta$ decay in different nuclei. Explicite expressions are given for the transition matrix elements. is shown, that possible interference terms allow to test CP (Charge and Parity conjugation) violation.Comment: Contribution to the EPS conference in Eilath: "Nuclear Physics in Astrophysics 5." April 3rd to 8th. 201