Tritium β\beta-decay in chiral effective field theory

We evaluate the Fermi and Gamow-Teller (GT) matrix elements in tritium $\beta$-decay by including in the charge-changing weak current the corrections up to one loop recently derived in nuclear chiral effective field theory ($\chi$ EFT). The trinucleon wave functions are obtained from hyperspherical-harmonics solutions of the Schrodinger equation with two- and three-nucleon potentials corresponding to either $\chi$ EFT (the N3LO/N2LO combination) or meson-exchange phenomenology (the AV18/UIX combination). We find that contributions due to loop corrections in the axial current are, in relative terms, as large as (and in some cases, dominate) those from one-pion exchange, which nominally occur at lower order in the power counting. We also provide values for the low-energy constants multiplying the contact axial current and three-nucleon potential, required to reproduce the experimental GT matrix element and trinucleon binding energies in the N3LO/N2LO and AV18/UIX calculations.Comment: 19 pages,6 figures, corrections to Text as suggested by Referee added; Erratum: 4 pages, 3 figures, corrections to Eq.(20), Tables I, II, III, Figures 4, 5, conclusions unchange

A chiral effective field theory study of hadronic parity violation in few-nucleon systems

We reconsider the derivation of the nucleon-nucleon parity-violating (PV) potential within a chiral effective field theory framework. We construct the potential up to next-to-next-to-leading order by including one-pion-exchange, two-pion-exchange, contact, and 1/M (M being the nucleon mass) terms, and use dimensional regularization to renormalize the pion-loop corrections. A detailed analysis of the number of independent low-energy constants (LEC's) entering the potential is carried out. We find that it depends on six LEC's: the pion-nucleon PV coupling constant $h^1_\pi$ and five parameters multiplying contact interactions. We investigate PV effects induced by this potential on several few-nucleon observables, including the $\vec{p}$-$p$ longitudinal asymmetry, the neutron spin rotation in $\vec{n}$-$p$ and $\vec{n}$-$d$ scattering, and the longitudinal asymmetry in the $^3$He$(\vec{n},p)^3$H charge-exchange reaction. An estimate for the range of values of the various LEC's is provided by using available experimental data.Comment: 31 pages, 7 figures, submitted to Physical Review

Two-spin entanglement distribution near factorized states

We study the two-spin entanglement distribution along the infinite $S=1/2$ chain described by the XY model in a transverse field; closed analytical expressions are derived for the one-tangle and the concurrences $C_r$, $r$ being the distance between the two possibly entangled spins, for values of the Hamiltonian parameters close to those corresponding to factorized ground states. The total amount of entanglement, the fraction of such entanglement which is stored in pairwise entanglement, and the way such fraction distributes along the chain is discussed, with attention focused on the dependence on the anisotropy of the exchange interaction. Near factorization a characteristic length-scale naturally emerges in the system, which is specifically related with entanglement properties and diverges at the critical point of the fully isotropic model. In general, we find that anisotropy rule a complex behavior of the entanglement properties, which results in the fact that more isotropic models, despite being characterized by a larger amount of total entanglement, present a smaller fraction of pairwise entanglement: the latter, in turn, is more evenly distributed along the chain, to the extent that, in the fully isotropic model at the critical field, the concurrences do not depend on $r$.Comment: 14 pages, 6 figures. Final versio

Finite-size effects and collective vibrations in the inner crust of neutron stars

We study the linear response of the inner crust of neutron stars within the Random Phase Approximation, employing a Skyrme-type interaction as effective interaction. We adopt the Wigner-Seitz approximation, and consider a single unit cell of the Coulomb lattice which constitutes the inner crust, with a nucleus at its center, surrounded by a sea of free neutrons. With the use of an appropriate operator, it is possible to analyze in detail the properties of the vibrations of the surface of the nucleus and their interaction with the modes of the sea of free neutrons, and to investigate the role of shell effects and of resonant states

Order-N Density-Matrix Electronic-Structure Method for General Potentials

A new order-N method for calculating the electronic structure of general (non-tight-binding) potentials is presented. The method uses a combination of the ``purification''-based approaches used by Li, Nunes and Vanderbilt, and Daw, and a representation of the density matrix based on ``travelling basis orbitals''. The method is applied to several one-dimensional examples, including the free electron gas, the ``Morse'' bound-state potential, a discontinuous potential that mimics an interface, and an oscillatory potential that mimics a semiconductor. The method is found to contain Friedel oscillations, quantization of charge in bound states, and band gap formation. Quantitatively accurate agreement with exact results is found in most cases. Possible advantages with regard to treating electron-electron interactions and arbitrary boundary conditions are discussed.Comment: 13 pages, REVTEX, 7 postscript figures (not quite perfect

Achieving descriptive accuracy in explanations via argumentation: the case of probabilistic classifiers

The pursuit of trust in and fairness of AI systems in order to enable human-centric goals has been gathering pace of late, often supported by the use of explanations for the outputs of these systems. Several properties of explanations have been highlighted as critical for achieving trustworthy and fair AI systems, but one that has thus far been overlooked is that of descriptive accuracy (DA), i.e., that the explanation contents are in correspondence with the internal working of the explained system. Indeed, the violation of this core property would lead to the paradoxical situation of systems producing explanations which are not suitably related to how the system actually works: clearly this may hinder user trust. Further, if explanations violate DA then they can be deceitful, resulting in an unfair behavior toward the users. Crucial as the DA property appears to be, it has been somehow overlooked in the XAI literature to date. To address this problem, we consider the questions of formalizing DA and of analyzing its satisfaction by explanation methods. We provide formal definitions of naive, structural and dialectical DA, using the family of probabilistic classifiers as the context for our analysis. We evaluate the satisfaction of our given notions of DA by several explanation methods, amounting to two popular feature-attribution methods from the literature, variants thereof and a novel form of explanation that we propose. We conduct experiments with a varied selection of concrete probabilistic classifiers and highlight the importance, with a user study, of our most demanding notion of dialectical DA, which our novel method satisfies by design and others may violate. We thus demonstrate how DA could be a critical component in achieving trustworthy and fair systems, in line with the principles of human-centric AI

Integral quantification of seasonal soil moisture changes in farmland by cosmic-ray neutrons

Soil moisture at the plot or hill-slope scale is an important link between local vadose zone hydrology and catchment hydrology. However, so far only a few methods are on the way to close this gap between point measurements and remote sensing. One new measurement methodology that could determine integral soil moisture at this scale is the aboveground sensing of cosmic-ray neutrons, more precisely of ground albedo neutrons. The present study performed ground albedo neutron sensing (GANS) at an agricultural field in northern Germany. To test the method it was accompanied by other soil moisture measurements for a summer period with corn crops growing on the field and a later autumn-winter period without crops and a longer period of snow cover. Additionally, meteorological data and aboveground crop biomass were included in the evaluation. Hourly values of ground albedo neutron sensing showed a high statistical variability. Six-hourly values corresponded well with classical soil moisture measurements, after calibration based on one reference dry period and three wet periods of a few days each. Crop biomass seemed to influence the measurements only to minor degree, opposed to snow cover which has a more substantial impact on the measurements. The latter could be quantitatively related to a newly introduced field neutron ratio estimated from neutron counting rates of two energy ranges. Overall, our study outlines a procedure to apply the ground albedo neutron sensing method based on devices now commercially available, without the need for accompanying numerical simulations and suited for longer monitoring periods after initial calibration

Quadratic response theory for spin-orbit coupling in semiconductor heterostructures

This paper examines the properties of the self-energy operator in lattice-matched semiconductor heterostructures, focusing on nonanalytic behavior at small values of the crystal momentum, which gives rise to long-range Coulomb potentials. A nonlinear response theory is developed for nonlocal spin-dependent perturbing potentials. The ionic pseudopotential of the heterostructure is treated as a perturbation of a bulk reference crystal, and the self-energy is derived to second order in the perturbation. If spin-orbit coupling is neglected outside the atomic cores, the problem can be analyzed as if the perturbation were a local spin scalar, since the nonlocal spin-dependent part of the pseudopotential merely renormalizes the results obtained from a local perturbation. The spin-dependent terms in the self-energy therefore fall into two classes: short-range potentials that are analytic in momentum space, and long-range nonanalytic terms that arise from the screened Coulomb potential multiplied by a spin-dependent vertex function. For an insulator at zero temperature, it is shown that the electronic charge induced by a given perturbation is exactly linearly proportional to the charge of the perturbing potential. These results are used in a subsequent paper to develop a first-principles effective-mass theory with generalized Rashba spin-orbit coupling.Comment: 20 pages, no figures, RevTeX4; v2: final published versio

Medium polarization isotopic effects on nuclear binding energies

There exist several effective interactions whose parameters are fitted to force mean field predictions to reproduce experimental findings of finite nuclei and calculated properties of infinite nuclear matter. Exploiting this tecnique one can give a good description of nuclear binding energies. We present evidence that further progress can be made by taking into account medium polarization effects associated with surface and pairing vibrations.Comment: 7 pages, 5 figure

Local chiral interactions and magnetic structure of few-nucleon systems

The magnetic form factors of $^2$H, $^3$H, and $^3$He, deuteron photodisintegration cross sections at low energies, and deuteron threshold electrodisintegration cross sections at backward angles in a wide range of momentum transfers, are calculated with the chiral two-nucleon (and three-nucleon) interactions including $\Delta$ intermediate states that have recently been constructed in configuration space. The $A\,$=$\,$3 wave functions are obtained from hyperspherical-harmonics solutions of the Schr\"odinger equation. The electromagnetic current includes one- and two-body terms, the latter induced by one- and two-pion exchange (OPE and TPE, respectively) mechanisms and contact interactions. The contributions associated with $\Delta$ intermediate states are only retained at the OPE level, and are neglected in TPE loop (tree-level) corrections to two-body (three-body) current operators. Expressions for these currents are derived and regularized in configuration space for consistency with the interactions. The low-energy constants that enter the contact few-nucleon systems. The predicted form factors and deuteron electrodisintegration cross section are in excellent agreement with experiment for momentum transfers up to 2--3 fm$^{-1}$. However, the experimental values for the deuteron photodisintegration cross section are consistently underestimated by theory, unless use is made of the Siegert form of the electric dipole transition operator. A complete analysis of the results is provided, including the clarification of the origin of the aforementioned discrepancy.Comment: 24 pages, 13 figure