Nuclear shell evolution and in-medium NN interaction

We report on a quantitative study of the evolution of the nuclear shell structure, in particular, effective single-particle energies (ESPEs), based on the spin-tensor decomposition of an effective two-body shell-model interaction. While the global trend of the ESPEs is mainly due to the central term of the effective interaction, variations of shell gaps invoke various components of the in-medium NN force. From a detailed analysis of a well-fitted realistic interaction in the sdpf shell-model space, two most important contributions for the evolution of the N = 20 and N = 28 shell gaps are confirmed to be the central term and the tensor term. The role of the latter is dominant to explain the energy shift of spin-orbit partners. Spin-tensor analysis of microscopic effective interactions in sd, pf, and gds shell-model spaces, contrasted with that of the phenomenologically adjusted ones, shows no evidence of amplification of the tensor component contribution; however, it points toward the neglect of three-body forces in the present microscopic interactions

Proton-neutron quadrupole interactions: an effective contribution to the pairing field

We point out that the proton-neutron energy contribution, for low multipoles (in particular for the quadrupole component), effectively renormalizes the strength of the pairing interaction acting amongst identical nucleons filling up a single-j or a set of degenerate many-j shells. We carry out the calculation in lowest-order perturbation theory. We perform a study of this correction in various mass regions. These results may have implications for the use of pairing theory in medium-heavy nuclei and for the study of pairing energy corrections to the liquid drop model when studying nuclear masses.Comment: 19 pages, TeX, 3 tables, 2 figures. Accepted in PR

The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing

A connection is made between the exact eigen states of the BCS Hamiltonian and the predictions made by the Tamm-Dancoff Approximation. This connection is made by means of a parametrised algebra, which gives the exact quasi-spin algebra in one limit of the parameter and the Heisenberg-Weyl algebra in the other. Using this algebra to construct the Bethe Ansatz solution of the BCS Hamiltonian, we obtain parametrised Richardson-Gaudin equations, leading to the secular equation of the Tamm-Dancoff Approximation in the bosonic limit. An example is discussed in depth.Comment: Submitted to the proceedings of the Group28 conference (Newcastle-upon-Tyne, UK). Journal of Physics: Conference Serie

N_pN_n dependence of empirical formula for the lowest excitation energy of the 2^+ states in even-even nuclei

We examine the effects of the additional term of the type $\sim e^{- \lambda' N_pN_n}$ on the recently proposed empirical formula for the lowest excitation energy of the $2^+$ states in even-even nuclei. This study is motivated by the fact that this term carries the favorable dependence of the valence nucleon numbers dictated by the $N_pN_n$ scheme. We show explicitly that there is not any improvement in reproducing $E_x(2_1^+)$ by including the extra $N_pN_n$ term. However, our study also reveals that the excitation energies $E_x(2_1^+)$, when calculated by the $N_pN_n$ term alone (with the mass number $A$ dependent term), are quite comparable to those calculated by the original empirical formula.Comment: 14 pages, 5 figure

Coframe teleparallel models of gravity. Exact solutions

The superstring and superbrane theories which include gravity as a necessary and fundamental part renew an interest to alternative representations of general relativity as well as the alternative models of gravity. We study the coframe teleparallel theory of gravity with a most general quadratic Lagrangian. The coframe field on a differentiable manifold is a basic dynamical variable. A metric tensor as well as a metric compatible connection is generated by a coframe in a unique manner. The Lagrangian is a general linear combination of Weitzenb\"{o}ck's quadratic invariants with free dimensionless parameters \r_1,\r_2,\r_3. Every independent term of the Lagrangian is a global SO(1,3)-invariant 4-form. For a special choice of parameters which confirms with the local SO(1,3) invariance this theory gives an alternative description of Einsteinian gravity - teleparallel equivalent of GR. We prove that the sign of the scalar curvature of a metric generated by a static spherical-symmetric solution depends only on a relation between the free parameters. The scalar curvature vanishes only for a subclass of models with \r_1=0. This subclass includes the teleparallel equivalent of GR. We obtain the explicit form of all spherically symmetric static solutions of the ``diagonal'' type to the field equations for an arbitrary choice of free parameters. We prove that the unique asymptotic-flat solution with Newtonian limit is the Schwarzschild solution that holds for a subclass of teleparallel models with \r_1=0. Thus the Yang-Mills-type term of the general quadratic coframe Lagrangian should be rejected.Comment: 28 pages, Latex error is fixe

Optimal Monte Carlo Updating

Based on Peskun's theorem it is shown that optimal transition matrices in Markov chain Monte Carlo should have zero diagonal elements except for the diagonal element corresponding to the largest weight. We will compare the statistical efficiency of this sampler to existing algorithms, such as heat-bath updating and the Metropolis algorithm. We provide numerical results for the Potts model as an application in classical physics. As an application in quantum physics we consider the spin 3/2 XY model and the Bose-Hubbard model which have been simulated by the directed loop algorithm in the stochastic series expansion framework.Comment: 6 pages, 5 figures, replaced with published versio

Intruder bands and configuration mixing in the lead isotopes

A three-configuration mixing calculation is performed in the context of the interacting boson model with the aim to describe recently observed collective bands built on low-lying $0^+$ states in neutron-deficient lead isotopes. The configurations that are included correspond to the regular, spherical states as well as two-particle two-hole and four-particle four-hole excitations across the Z=82 shell gap.Comment: 20 pages, 4 figures, accepted by PRC, reference added for section 1 in this revised versio

Identifying structure-selectivity correlations in the electrochemical reduction of CO₂: a comparison of well-ordered atomically-clean and chemically-etched Cu single crystal surfaces

Despite significant theoretical efforts, the identification of the active sites for the electrochemical reduction of CO2 (CO2RR) to specific chemical products has remained elusive. This is partially due to insufficient experimental data gathered on clean and atomically well-ordered electrode surfaces. Here, ultrahigh vacuum based preparation methods and surface science characterization techniques are used together with gas chromatography to demonstrate that subtle changes in the preparation of well-oriented Cu(100) and Cu(111) single crystal surfaces drastically affect their CO2RR selectivity. Copper single crystals with clean, flat, and atomically ordered surfaces are theoretically predicted to yield hydrocarbons. However, these were found experimentally to favour the production of H2. Only when roughness and defects are introduced, for example through an electrochemical etchingor a plasmatreatment, significant amounts of hydrocarbons are generated. These results clearly indicate that structural and morphological effects are the key factors determining the catalytic selectivity of CO2RR

Identifying structure-selectivity correlations in the electrochemical reduction of CO₂: a comparison of well-ordered atomically-clean and chemically-etched Cu single crystal surfaces

Despite significant theoretical efforts, the identification of the active sites for the electrochemical reduction of CO2(CO2RR) to specific chemical products has remained elusive. This is partially due to insufficient experimental data gathered on clean and atomically well-ordered electrode surfaces. Here, ultrahigh vacuum based preparation methods and surface science characterization techniques are used together with gas chromatography to demonstrate that subtle changes in the preparation of well-oriented Cu(100) and Cu(111) single crystal surfaces drastically affect their CO2RR selectivity. Copper single crystals with clean, flat, and atomically ordered surfaces are theoretically predicted to yield hydrocarbons. However, these were found experimentally to favour the production of H2. Only when roughness and defects are introduced, for example through an electrochemical etching or a plasma treatment, significant amounts of hydrocarbons are generated. These results clearly indicate that structural and morphological effects are the key factors determining the catalytic selectivity of CO2RR