Basic invariants of geometric mappings

This study is motivated by the researches in the field of invariants of geodesic and conformal mappings presented in (T. Y. Thomas, [22]) and (H. Weyl, [25]). The Thomas projective parameter and the Weyl projective tensor are generalized in this article. Generators for vector spaces of invariants of geometric mappings are obtained in here

Final Project Report: Plan for a Model PIMS

Development of the performance information and management systems (PIMS) to monitor labor market outcomes of program participants, and guide program management of active labor market programs (ALMPs)

Novel invariants for almost geodesic mappings of the third type

Two kinds of invariance for geometrical objects under transformations are involved in this paper. With respect to these kinds, we obtained novel invariants for almost geodesic mappings of the third type of a non-symmetric affine connection space in this paper. Our results are presented in two sections. In the Section 3, we obtained the invariants for the equitorsion almost geodesic mappings which do not have the property of reciprocity. In the Section 4, we obtained the invariants for almost geodesic mappings of the third type which have the property of reciprocity.Comment: 18 pages, 0 figure

A unified analytical solution for elastic–plastic stress analysis of a cylindrical cavity in Mohr–Coulomb materials under biaxial in situ stresses

This paper presents a unified analytical solution for elastoplastic stress analysis around a cylindrical cavity under biaxial in-situ stresses during both loading and unloading. The two-dimensional solution is obtained by assuming that the connected plastic zone is statically determinate and using the complex variable theory in the elastic analysis. It is shown that the biaxial state of initial stresses applies significant influences on the stress distribution around the inner cavity. Under biaxial far-field stresses, the asymptotic conformal mapping function predicts that the outer boundary of the statically determinate plastic zone is in oval-shape in Mohr-Coulomb materials. The major axis of the elastic-plastic interface lies in the direction of the greatest far-field compression pressure during loading whereas it is along the perpendicular direction during unloading. The loading and unloading solutions are validated by comparing with numerical simulation results and other analytical solutions. In the assumed states, the new solution provides an accurate analytical method to capture the biaxial in-situ stress effect in the prediction of the plastic failure zone and calculations of the static stress field and the elastic displacement field around a cylindrical cavity within an infinite medium

Quasi-free (p,2p) reactions in inverse kinematics for studying the fission yield dependence on temperature

Despite the recent experimental and theoretical progress in the investigation of the nuclear fission process, a complete description still represents a challenge in nuclear physics because it is a very complex dynamical process, whose description involves the coupling between intrinsic and collective degrees of freedom, as well as different quantum-mechanical phenomena. To improve on the existing data on nuclear fission,we produce fission reactions of heavy nuclei in inverse kinematics by using quasi-free (p,2p) scattering, which induce fission through particle-hole excitations that can range from few to ten\u27s of MeV. The measurement of the four-momenta of the two outgoing protons allows to reconstruct the excitation energy of the fissioning nucleus and therefore to study the evolution of the fission yields with temperature. The realization of this kind of experiment requires a complex experimental setup, providing full isotopic identification of both fission fragments and an accurate measurement of the momenta of the two outgoing protons. This was realized recently at the GSI/FAIR facility and here some preliminary results are presented

Comprehensive investigation of fission yields by using spallation- and (p,2p)-induced fission reactions in inverse kinematics

In the last decades, measurements of spallation, fragmentation and Coulex induced fission reactions in inverse kinematics have provided valuable data to accurately investigate the fission dynamics and nuclear structure at large deformations of a large variety of stable and non-stable heavy nuclei. To go a step further, we propose now to induce fission by the use of quasi-free (p,2p) scattering reactions in inverse kinematics, which allows us to reconstruct the excitation energy of the compound fissioning system by using the four-momenta of the two outgoing protons. Therefore, this new approach might permit to correlate the excitation energy with the charge and mass distributions of the fission fragments and with the fission probabilities, given for the first time direct access to the simultaneous measurement of the fission yield dependence on temperature and fission barrier heights of exotic heavy nuclei, respectively. The first experiment based on this methodology was realized recently at the GSI/FAIR facility and a detailed description of the experimental setup is given here.Comment: 4 pages, 15th International Conference on Nuclear Data for Science and Technology (ND2022

Collectivity at the prolate-oblate transition:the 2₁⁺ lifetime of ¹⁹⁰W

The neutron-rich rare isotope 190W is discussed as a candidate for a prolate-oblate transitional nucleus with maximum γ-softness. The collectivity of this isotope is assessed for the first time by the measurement of the reduced E2 transition probability of its first 2+ state to the ground state. The experiment employed the FAst TIming Array (FATIMA), comprised of 36 LaBr3(Ce) scintillators, which was part of the DESPEC setup at GSI, Darmstadt. The 41+ and 21+ states of 190W were populated subsequently to the decay of its 127(12) μs isomeric Jπ  = 10- state. The mean lifetime of the 21+ state was determined to be τ = 274(28) ps, which corresponds to a B(E2; 21+ → 01+) value of 95(10) W.u. The results motivated a revision of previous calculations within an energy-density functional-based interacting boson model-2 approach, yielding E2 transition properties and spectroscopic quadrupole moments for tungsten isotopes. From comparison to theory, the new data suggest that 190W is at the transition from prolate to oblate structure along the W isotopic chain, which had previously been discussed as a nuclear shape-phase transition

The shape of the <i>T</i>_z = +1 nucleus ⁹⁴Pd and the role of proton-neutron interactions on the structure of its excited states

Reduced transition probabilities have been extracted between excited, yrast states in the N = Z + 2 nucleus 94Pd. The transitions of interest were observed following decays of the Iπ = 14+ , Ex = 2129-keV isomeric state, which was populated following the projectile fragmentation of a 124Xe primary beam at the GSI Helmholtzzentrum für Schwerionenforschung accelerator facility as part of FAIR Phase-0. Experimental information regarding the reduced E2 transition strengths for the decays of the yrast 8+ and 6+ states was determined following isomer-delayed Eγ1 − Eγ2 − △T2,1 coincidence method, using the LaBr3(Ce)-based FATIMA fast-timing coincidence gamma-ray array, which allowed direct determination of lifetimes of states in 94Pd using the Generalized Centroid Difference (GCD) method. The experimental value for the half-life of the yrast 8+ state of 755(106) ps results in a reduced transition probability of B(E2:8+ →6+ ) = 205+34 −25 e2fm4 , which enables a precise verification of shell-model calculations for this unique system, lying directly between the N = Z line and the N = 50 neutron shell closure. The determined B(E2) value provides an insight into the purity of (g9/2)n configurations in competition with admixtures from excitations between the (lower) N = 3 pf and (higher) N = 4 gds orbitals for the first time. The results indicate weak collectivity expected for near-zero quadrupole deformation and an increasing importance of the T = 0 proton-neutron interaction at N = 48

Fast-timing measurements in ⁹⁶Pd:improved accuracy for the lifetime of the 4⁺₁ state

Direct lifetime measurements via γ–γ coincidences using the FATIMA fast-timing LaBr3(Ce) array were performed for the excited states below previously reported isomers. In the N = 50 semi-magic 96Pd nucleus, lifetimes below the I π = 8+ seniority isomer were addressed as a benchmark for further analysis. The results for the I π = 2+ and 4 + states confirm the published values. Increased accuracy for the lifetime value was achieved for the 4 + state.peerReviewe