We develop a method to parametrize elastic-scattering phase-shifts for charged nuclei, based on Padé expansions of a simplified effective-range function. The method is potential independent and the input is reduced to experimental phase shifts and bound-state energies. It allows a simple calculation of resonance properties and of asymptotic normalization constants (ANCs) of subthreshold bound states. We analyze the 1 − and 2 + phase shifts of the 12 C+α system and extract the ANCs of the corresponding bound states. For the 1 − state, a factor-3 improvement with respect to the best value available today is obtained, with a factor-10 improvement in reach. For the 2 + state, no improvement is obtained due to relatively larger error bars on the experimental phase shifts.PACS numbers: 03.65. Nk, 03.65.Ge, 25.40.Cm, 25.55.Ci Low-energy nuclear reactions, in particular those relevant to nuclear astrophysics [1], are a fascinating application field for quantum scattering theory [2]. Because of the Coulomb repulsion between nuclei, cross sections are often impossible to measure directly and theoretical extrapolation are indispensable. The simplest of these reactions, elastic scattering, is theoretically described with a partial-wave decomposition, each partial wave l being fully characterized by a nuclear phase shift δ l or scattering matrix S l = e 2iδ l , both functions of the energy. Resonances appear as fast increases of δ l at real positive energies or as poles of S l at complex energies. For some reactions subthreshold bound states at small negative energies also play an essential role. This is for instance the case for the 1 − and 2 + bound states lying just below the 12 C+α threshold which strongly affect the 12 C(α, γ) 16 O cross section, an important reaction for stellar evolution [3]. For these states, energies are generally well-known experimentally but not the ANC of their wave function. Hence, various methods have been proposed to indirectly extract these ANCs from experimental data, like β-delayed α emission [4] or α-transfer reactions [5].A natural way to extract an ANC for a given partial wave is to parametrize the corresponding experimental phase shifts and to extrapolate this parametrization at negative energies, as bound states also correspond to scatteringmatrix poles [2]. The usual tool to do so is the reaction-(R-)matrix method [6], which describes both resonant and bound states as poles characterized by real energies and widths (Mittag-Leffler expansion). This motivated the measurement of high-precision 12 C+α phase shifts [7,8] but led to a loose constraint on the 1 − ANC [7] and to a questionable constraint on the 2 + ANC [9]. The background phase shifts (between resonances) are indeed described in terms of a channel radius and of a high-energy background pole, which adds several parameters with no direct physical meaning to the fit. Hence, simpler parametrizations are necessary.A first option is the effective-range function (ERF) K l of Eq. (2) [10]. Its analyticity properties imply the exis...
The Observatorio Astrofísico de Javalambre (OAJ) is a new Spanish astronomical facility particularly designed for carrying out large sky surveys. The OAJ is mainly motivated by the development of J-PAS, the Javalambre-PAU Astrophysical Survey, an unprecedented astronomical survey that aims to observe 8500 deg 2 of the sky with a set of 54 optical contiguous narrow-band filters (FWHM∼14 nm) and 5 mid and broad-band ones. J-PAS will provide a low resolution spectrum (R∼50) for every pixel of the Northern sky down to AB∼22.5 − 23.5 per square arcsecond (at 5σ level), depending on the narrow-band filter, and ∼ 2 magnitudes deeper for the redder broad-band filters. The main telescope at the OAJ is the Javalambre Survey Telescope (JST/T250), an innovative Ritchey-Chrétien, alt-azimuthal, large-etendue telescope with a primary mirror diameter of 2.55 m and 3 deg (diameter) FoV. The JST/T250 is the telescope devoted to conduct J-PAS with JPCam, a panoramic camera of 4.7 deg 2 FoV and a mosaic of 14 large format CCDs that, overall, amounts to 1.2 Gpix. The second largest telescope at the OAJ is the Javalambre Auxiliary Survey Telescope (JAST/T80), a Ritchey-Chrétien, german-equatorial telescope of 82 cm primary mirror and 2 deg FoV, whose main goal is to perform J-PLUS, the Javalambre Photometric Local Universe Survey. J-PLUS will cover the same sky area of J-PAS using the panoramic camera T80Cam with 12 filters in the optical range, which are specifically defined to perform the photometric calibration of J-PAS.The OAJ project officially started in mid 2010. Four years later, the OAJ is mostly completed and the first OAJ operations have already started. The civil work and engineering installations are finished, including the telescope buildings and the domes. JAST/T80 is at the OAJ undertaking commissioning tasks, and JST/T250 is in AIV phase at the OAJ. Related astronomical subsystems like the seeing and atmospheric extinction monitors and the all-sky camera are fully operative. This paper aims to present a brief description and status of the OAJ main installations, telescopes and cameras. The current development and operation plan of the OAJ in terms of staffing organization, resources, observation scheduling, and data archiving, is also described.
A complete and consistent inversion technique is proposed to derive an accurate interaction potential from an effective-range function for a given partial wave in the neutral case. First, the effective-range function is Taylor or Padé expanded, which allows high precision fitting of the experimental scattering phase shifts with a minimal number of parameters on a large energy range. Second, the corresponding poles of the scattering matrix are extracted in the complex wave-number plane. Third, the interaction potential is constructed with supersymmetric transformations of the radial Schrödinger equation. As an illustration, the method is applied to the experimental phase shifts of the neutron-proton elastic scattering in the
We propose a method to compute, for a given potential model, an arbitrary coefficient of the effective-range function expanded as a power series in energy. The method is based on a set of recurrence relations at low energy, that allows a compact and general description to any order in energy for neutral and charged cases. By using the Lagrange mesh technique to compute the R matrix at zero energy, this proposal permits us to compute, with a very good precision, the effective-range parameters. We use a potential model for some nuclear systems to illustrate the effectiveness of this method and to discuss its numerical limitations.
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