Search

We present the MsSpec Atomic Scattering Amplitude Package (MASAP), composed of a computation program and a graphical interface to generate atomic scattering amplitude (ASA) of an atom, either isolated or embedded in an environment, at any chosen energy of the impinging electron up to ≈15 KeV. The ASA is calculated using an effective, complex optical potential which provides damping effects in the scattering process in a fully relativistic framework. Optionally, scalar relativistic and non-relativistic approximations are also available to assess their applicability to a given problem. In order to describe electron propagation in solids we suggest to replace ASA's based on Plane Waves (PW) scattering with effective ASA's based on curved Spherical Waves (SW) using truncated-overlapped potentials of the Muffin-Tin (MT) type constructed according to the Mattheiss prescription. The graphical user interface generates not only ASA data files providing atomic Differential Cross Sections (DCS) but also files of related quantities such as total Cross Section (CS), both elastic and inelastic, atomic t l -matrices and phase shifts. We found in general that the imaginary part of the optical potential enhances the calculated elastic DCSs in the forward direction compared to the same potential without the imaginary part, a feature related to the optical theorem, but gives rise to a lower intensity at all other directions as expected due to the damping effect of the complex part of the potential. We show calculated differential and transport Cross Sections for aluminum and gold atoms both in isolation and in crystals with the Face-Centered-Cubic (FCC) structure. Program Title: MASAP CPC Library link to program files: https://doi.org/10.17632/gtxp3mn5hs.1 Licensing provisions: Apache 2.0 Programming language: FORTRAN 77, Python3 External routines: • SciPy (https://www.scipy.org) • Atomic Simulation Environment (https://wiki.fysik.dtu.dk/ase/) • h5py (https://www.h5py.org) • wxPython (https://www.wxpython.org) Nature of problem: Calculation of atomic scattering amplitudes of scattered electrons by an embedded atom in a solid including damping and relativistic effects. Comparison between ASA's in an isolated atomic system and a solid. Introduction of an effective ASA for electrons propagating in a solid derived from Multiple Scattering Theory. Solution method: Potential scattering theory. Muffin-tin approximation. Superposition of atomic electron densities obtained by self-consistent Dirac-Fock atomic calculations. Hedin-Lundqvist potential as an optical potential. Fully relativistic theory, with scalar-relativistic and non-relativistic approximations for comparison. Additional comments including restrictions and unusual features: Even though the program can perform calculations at impinging electron energies up to ≈15 Kev, DCS calculations are recommended in the range 50 : ≈1500 eV both in the case of isolated atoms and atoms embedded in solids, since this interval is more suitable for studying the details of the atomic potentials in their environment. In the case of solids, at energies lower than ≈50 eV, the details of the electronic structure might be important, whereas in the case of isolated atoms this range might suffer from the neglect of the polarization potential and coupling to available inelastic channels. In this respect an option to add an empirical form of a polarization potential to investigate its effects is available to the interested user. [ABSTRACT FROM AUTHOR]

molscat is a general-purpose program for quantum-mechanical calculations on nonreactive atom–atom, atom–molecule and molecule–molecule collisions. It constructs the coupled-channel equations of atomic and molecular scattering theory, and solves them by propagating the wavefunction or log-derivative matrix outwards from short range to the asymptotic region at long range. It then applies scattering boundary conditions to extract the scattering matrix (S matrix). Built-in coupling cases include atom + rigid linear molecule, atom + vibrating diatom, atom + rigid symmetric top, atom + asymmetric or spherical top, rigid diatom + rigid diatom, rigid diatom + asymmetric top, and diffractive scattering of an atom from a crystal surface. Interaction potentials may be specified either in program input (for simple cases) or with user-supplied routines. For the built-in coupling cases, molscat can loop over total angular momentum (partial wave) and total parity to calculate elastic and inelastic integral cross sections and spectroscopic line-shape cross sections. Post-processors are available to calculate differential cross sections, transport, relaxation and Senftleben–Beenakker cross sections, and to fit the parameters of scattering resonances. molscat also provides an interface for plug-in routines to specify coupling cases (Hamiltonians and basis sets) that are not built in; plug-in routines are supplied to handle collisions of a pair of alkali-metal atoms with hyperfine structure in an applied magnetic field. For low-energy scattering, molscat can calculate scattering lengths and effective ranges and can locate and characterise scattering resonances as a function of an external variable such as the magnetic field. Program Title: molscat Program Files doi: http://dx.doi.org/10.17632/rtzgf5mwpn.1 Licensing provisions: GPLv3 Programming language: Fortran 90 External routines/libraries: LAPACK, BLAS Nature of problem: Quantum-mechanical calculations of scattering properties for non-reactive collisions between atoms and molecules. Solution method: The Schrödinger equation is expressed in terms of coupled equations in the interparticle distance, R. Solutions of the coupled-channel equations are propagated outwards from the classically forbidden region at short range to the asymptotic region. The program calculates scattering S matrices and uses them to calculate scattering properties including elastic, inelastic and line-shape cross sections. Unusual features: 1. molscat contains numerous features to handle quantities important in low-energy collisions. It can propagate very efficiently to very long range, and it can calculate low-energy properties such as the scattering length (complex and energy-dependent if required) and the effective range. 2. molscat can construct and solve sets of coupled equations using basis sets that are not eigenfunctions of the Hamiltonians of the colliding particles at long range. The propagation is carried out in the primitive basis set, and the solutions are transformed to the asymptotic basis set before applying long-range boundary conditions to extract the S matrix. 3. molscat provides an interface that allows users to specify the coupled equations that arise from additional Hamiltonians and basis sets. 4. molscat provides an interface that allows users to include multiple external fields in the Hamiltonian. This same interface also allows users to include a factor which scales the interaction potential, and to investigate how properties vary with this factor. 5. molscat can locate and characterise low-energy Feshbach resonances either as a function of collision energy or as a function of external fields or of the potential scaling factor. [ABSTRACT FROM AUTHOR]

The phase and amplitude (Ph–A) of a wave function vary slowly with distance, in contrast to the wave function that can be highly oscillatory. Hence the Ph–A representation of a wave function requires far fewer computational mesh points than the wave function itself. In 1930 Milne presented an equation for the phase and the amplitude functions (which is different from the one developed by Calogero), and in 1962 Seaton and Peach solved these equations iteratively. The objective of the present study is to implement Seaton and Peach’s iteration procedure with a spectral Chebyshev expansion method, and at the same time present a non-iterative analytic solution to an approximate version of the iterative equations. The iterations converge rapidly for the case of attractive potentials. Two numerical examples are given: (1) for a potential that decreases with distance as 1 / r 3 , and (2) a Coulomb potential ∝ 1 / r . In both cases the whole radial range of [0–2000] requires only between 25 and 100 mesh points and the corresponding accuracy is between 1 0 − 3 and 1 0 − 6 . The 0th iteration (which is the WKB approximation) gives an accuracy of 1 0 − 2 . This spectral method permits one to calculate a wave function out to large distances reliably and economically. [ABSTRACT FROM AUTHOR]

Monte Carlo event generators are a critical tool for the interpretation of data obtained by neutrino experiments. Several modern event generators are available which are well-suited to the GeV energy scale used in studies of accelerator neutrinos. However, theoretical modeling differences make their immediate application to lower energies difficult. In this paper, I present a new event generator, MARLEY, which is designed to better address the simulation needs of the low-energy (tens of MeV and below) neutrino community. The code is written in C++14 with an optional interface to the popular ROOT data analysis framework. The current release of MARLEY (version 1.2.0) emphasizes simulations of the reaction 40Ar (ν e , e −) 40K⁎ but is extensible to other channels with suitable user input. This paper provides detailed documentation of MARLEY's implementation and usage, including guidance on how generated events may be analyzed and how MARLEY may be interfaced with external codes such as Geant4. Further information about MARLEY is available on the official website at http://www.marleygen.org. Program title: MARLEY 1.2.0 CPC Library link to program files: https://doi.org/10.17632/4v7zxnc8j3.1 Developer's respository link: http://github.com/MARLEY-MC/marley Code Ocean capsule: https://codeocean.com/capsule/9868179 Licensing provisions: GNU General Public License 3.0 Programming language: C++14 External routines/libraries used: GNU Scientific Library [1,2] (required), ROOT [3,4] (optional) Nature of problem: Simulation of neutrino-nucleus scattering events at energies of tens-of-MeV and below Solution method: Initial two-to-two scattering kinematics are sampled using the allowed approximation differential cross section and tables of precomputed nuclear matrix elements. Subsequent de-excitations of the remnant nucleus are simulated using a Monte Carlo implementation of the Hauser-Feshbach statistical model and tabulated γ -ray decay schemes for discrete nuclear levels. Additional comments including restrictions and unusual features: Input data are provided with the code that are suitable for producing simulations of the charged-current reaction 40Ar (ν e , e −) 40K⁎, coherent elastic neutrino-nucleus scattering on spin-zero target nuclei, and neutrino-electron elastic scattering on any atomic target. Preparation of new reaction input files (whose format is documented in Appendix B) would enable other reaction channels and nuclear targets to be handled by the existing code framework. Although there is no maximum neutrino energy enforced by the code itself, realistic neutrino-nucleus scattering events may be generated up to roughly 50 MeV. Above this energy, the effects of forbidden nuclear transitions, which are neglected in the current treatment of the cross sections (see section 2.1), become increasingly important. [ABSTRACT FROM AUTHOR]

A FORTRAN implementation of hydrogen-like discrete–discrete atomic form factors is presented. The definition of atomic form factors and their applicability to the calculation of atomic cross sections is briefly discussed. An explicit analytical expression for the discrete–discrete atomic form factors is presented exactly in the way they are implemented in the program. Finally, a description of the program itself and how to use it is given, together with some useful examples and their outputs. [Copyright &y& Elsevier]