A simple and efficient numerical scheme to integrate non-local potentials

As nuclear wave functions have to obey the Pauli principle, potentials issued from reaction theory or Hartree-Fock formalism using finite-range interactions contain a non-local part. Written in coordinate space representation, the Schrodinger equation becomes integro-differential, which is difficult to solve, contrary to the case of local potentials, where it is an ordinary differential equation. A simple and powerful method has been proposed several years ago, with the trivially equivalent potential method, where non-local potential is replaced by an equivalent local potential, which is state-dependent and has to be determined iteratively. Its main disadvantage, however, is the appearance of divergences in potentials if the wave functions have nodes, which is generally the case. We will show that divergences can be removed by a slight modification of the trivially equivalent potential method, leading to a very simple, stable and precise numerical technique to deal with non-local potentials. Examples will be provided with the calculation of the Hartree-Fock potential and associated wave functions of 16O using the finite-range N3LO realistic interaction.Comment: 8 pages, 2 figures, submitted to Eur. Phys. J.

The TESS-Keck Survey. II. An Ultra-Short-Period Rocky Planet And Its Siblings Transiting The Galactic Thick-Disk Star TOI-561

We report the discovery of TOI-561, a multiplanet system in the galactic thick disk that contains a rocky, ultra-short-period planet. This bright (V = 10.2) star hosts three small transiting planets identified in photometry from the NASA TESS mission: TOI-561 b (TOI-561.02, P = 0.44 days, Rp = 1.45 ± 0.11 R⊕), c (TOI-561.01, P = 10.8 days, Rp = 2.90 ± 0.13 R⊕), and d (TOI-561.03, P = 16.3 days, Rp = 2.32 ± 0.16 R⊕). The star is chemically ([Fe/H] = −0.41 ± 0.05, [α/Fe] = +0.23 ± 0.05) and kinematically consistent with the galactic thick-disk population, making TOI-561 one of the oldest (10 ± 3 Gyr) and most metal-poor planetary systems discovered yet. We dynamically confirm planets b and c with radial velocities from the W. M. Keck Observatory High Resolution Echelle Spectrometer. Planet b has a mass and density of 3.2 ± 0.8 M⊕ and ${5.5}_{-1.6}^{+2.0}$g cm−3, consistent with a rocky composition. Its lower-than-average density is consistent with an iron-poor composition, although an Earth-like iron-to-silicates ratio is not ruled out. Planet c is 7.0 ± 2.3 M⊕ and 1.6 ± 0.6 g cm−3, consistent with an interior rocky core overlaid with a low-mass volatile envelope. Several attributes of the photometry for planet d (which we did not detect dynamically) complicate the analysis, but we vet the planet with high-contrast imaging, ground-based photometric follow-up, and radial velocities. TOI-561 b is the first rocky world around a galactic thick-disk star confirmed with radial velocities and one of the best rocky planets for thermal emission studies

The L 98-59 System: Three Transiting, Terrestrial-Size Planets Orbiting A Nearby M Dwarf

We report the Transiting Exoplanet Survey Satellite (TESS) discovery of three terrestrial-size planets transiting L 98-59 (TOI-175, TIC 307210830)—a bright M dwarf at a distance of 10.6 pc. Using the Gaia-measured distance and broadband photometry, we find that the host star is an M3 dwarf. Combined with the TESS transits from three sectors, the corresponding stellar parameters yield planet radii ranging from 0.8 R⊕ to 1.6 R⊕. All three planets have short orbital periods, ranging from 2.25 to 7.45 days with the outer pair just wide of a 2:1 period resonance. Diagnostic tests produced by the TESS Data Validation Report and the vetting package DAVE rule out common false-positive sources. These analyses, along with dedicated follow-up and the multiplicity of the system, lend confidence that the observed signals are caused by planets transiting L 98-59 and are not associated with other sources in the field. The L 98-59 system is interesting for a number of reasons: the host star is bright (V = 11.7 mag, K = 7.1 mag) and the planets are prime targets for further follow-up observations including precision radial-velocity mass measurements and future transit spectroscopy with the James Webb Space Telescope; the near-resonant configuration makes the system a laboratory to study planetary system dynamical evolution; and three planets of relatively similar size in the same system present an opportunity to study terrestrial planets where other variables (age, metallicity, etc.) can be held constant. L 98-59 will be observed in four more TESS sectors, which will provide a wealth of information on the three currently known planets and have the potential to reveal additional planets in the system

Velocity-space sensitivity of the time-of-flight neutron spectrometer at JET

The velocity-space sensitivities of fast-ion diagnostics are often described by so-called weight functions. Recently, we formulated weight functions showing the velocity-space sensitivity of the often dominant beam-target part of neutron energy spectra. These weight functions for neutron emission spectrometry (NES) are independent of the particular NES diagnostic. Here we apply these NES weight functions to the time-of-flight spectrometer TOFOR at JET. By taking the instrumental response function of TOFOR into account, we calculate time-of-flight NES weight functions that enable us to directly determine the velocity-space sensitivity of a given part of a measured time-of-flight spectrum from TOFOR