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YAHFC: A Code Framework to Model Nuclear Reactions and Estimate Correlated Uncertainties

Reaction modeling is a key ingredient in designing experiments and interpreting their results, and is an essential component in the process of evaluating nuclear data and assembling nuclear data libraries used in nuclear technology applications. Typically, experimental data are available only for a handful of reaction channels and theory models are used to fill in the gaps. In addition, theory is often called upon as the arbitrator between discrepant data. Most importantly, theory and modeling are required for an accurate determination of uncertainties in the evaluated data and the correlations between the multiple channels. A fast, accurate, and flexible modeling capability has been developed at LLNL with the code system YAHFC (Yet Another Hauser-Feshbach Code). YAHFC is a Monte Carlo, Hauser-Feshbach code framework, making full use of dynamic memory allocation, derived types, and parallel computing. YAHFC can generate events to simulate experiments and is guiding experiments designed to measure inelastic neutron scattering from actinide targets. YAHFC is also being used to analyze decays from surrogate experiments, thereby enabling the inference of reaction cross sections inaccessible by direct measurement. Finally, by modeling nuclear reactions with constraints from experimental data, YAHFC can deliver complete nuclear data libraries, with evaluated uncertainties, using the modernized Generalized Nuclear Data Structure (GNDS).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The calculation of light element impurity (α, n) yield curves in a PuO 2 matrix and associated specific yield coefficients: Influence of the reaction cross sections

Most of the Pu separated from irradiated commercial nuclear fuel is stored as PuO 2 . The primary quantitative nondestructive measurement technique used to verify the amount of Pu in storage containers is passive neutron correlation counting. An important physical property of the oxide material is the ratio, α, of the rate of (α, n) neutrons produced inside the item to the rate of neutrons produced by spontaneous fission. This ratio influences the precision of the correlated counting method and affects the interpretation of the data because of how it changes both the primary total neutron production rate and the rate of induced fission events taking place inside the item. In addition to the main O(α, n) contribution, additional contributions come from α-particle interactions with light element impurities that are inevitably present. In this work, we calculate specific (α, n) yield coefficients, expressed in units of neutrons per second per gram of α-emitting nuclide per part per million by mass of the specified impurity element distributed in a pure PuO 2 matrix, for some key α-emitting actinides commonly present in reprocessed Pu ( 238–242 Pu+ 241 Am). These coefficients are directly applicable to nuclear safeguards verification work in which the α ratio is often calculated from the Pu-isotopic composition and chemical information obtained by other means. Further, they also provide a convenient up-to-date reference set against which values generated by other methods can be compared. Results are presented for impurities with atomic number from 3 to 17 inclusive, plus K and Fe. In most cases, these coefficients are not expected to change by more than 5%–10% at any time in the future. However, as new data become available, changes as large as 20% may be needed for some targets (e.g., F). The present yield calculations are limited by the general shortage of quality experimental total (α, n) reaction cross section data, which, together with unexplained variation between determinations, means that an objective and coherent evaluation is not possible. The situation is even less satisfactory for the partial differential cross section needed to calculate neutron spectra.

(𝛼, n) reactions↗

Nuclear Physics Made Very, Very Easy

The fundamental approach to nuclear physics was prepared to introduce basic reactor principles to various groups of non-nuclear technical personnel associated with NERVA Test Operations. NERVA Test Operations functions as the field test group for the Nuclear Rocket Engine Program. Nuclear Engine for Rocket Vehicle Application (NERVA) program is the combined efforts of Aerojet-General Corporation as prime contractor, and Westinghouse Astronuclear Laboratory as the major subcontractor, for the assembly and testing of nuclear rocket engines. Development of the NERVA Program is under the direction of the Space Nuclear Propulsion Office, a joint agency of the U. S. Atomic Energy Commission and the National Aeronautics and Space Administration. This report is being reprinted for use in the U. S. Atomic Energy Commission and National Aeronautics and Space Administration educational and technology utilization programs.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Direct cross section measurement of 102 Pd ⁢(𝛾,𝑝) and 102 Pd ⁢(𝛾,𝛼) for the astrophysical 𝑝 process

Background: A handful of neutron-deficient stable nuclei, known as the “p nuclei,” cannot be produced through astrophysical neutron capture processes. Instead, some of these nuclei are proposed to be produced by 𝛾-induced reactions on existing r- and s-process seeds. The specific astrophysical site or sites are not yet identified, however, with uncertainties in the cross sections of these 𝛾-induced reactions playing a role. Databases of reaction rates for astrophysical simulations often rely on theoretical statistical model calculations, such as Hauser-Feshbach, for rates where no experimental information is known. However, reasonable variations in the choice of parametrizations of various nuclear properties can create order-of-magnitude variations in the final predicted cross sections and reaction rates, which are then propagated through the models to the predicted final abundances. Purpose: To better constrain these statistical model calculations and ultimately reduce the uncertainties from the nuclear physics on our understanding of the p nuclei, a measurement of the cross sections of 𝛾-induced reactions on the p-nucleus 102 Pd was undertaken. This work represents the first measurement of its kind, using segmented silicon detectors to measure prompt charged particle emission from 𝛾-induced reactions. Methods: Quasimonoenergetic gamma beams from the High Intensity 𝛾 Source facility bombarded an enriched 102 Pd target. A segmented silicon array was arranged to detect the particles emitted from (𝛾,𝑝) and (𝛾,𝛼) reactions. Results: Reaction cross sections were deduced at multiple 𝛾-beam energies between 10 and 19 MeV, and compared to statistical model calculations using talys-1.96. The 102 Pd ⁢(𝛾,𝑝)⁢ 101 Rh reaction cross section was reasonably well reproduced by a subset of photon strength functions and level densities, though the strength to the ground state of 101 Rh was underestimated at higher incident gamma energies. The 102 Pd ⁢(𝛾,𝛼)⁢ 98 Ru was in general overpredicted by the various alpha-nucleus optical model potentials. Conclusions: While the theoretical cross sections used to model the (𝛾,𝑝) reactions for the p process may be reasonable, a more careful approach is needed in the case of (𝛾,𝛼). Further work to probe gamma-induced reaction cross sections at and near the p nuclei is warranted.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Quantifying uncertainty in physics-based predictions of rare-isotope production cross sections via Bayesian-inspired model averaging across nuclear mass tables

Accurate prediction of fragmentation cross sections is essential for rare-isotope beam production, planning new-isotope searches, and designing experiments to study the most exotic regions of the nuclear chart. However, existing reaction models and phenomenological cross-section parametrizations often exhibit significant deviations over broad regions of mass and charge. In this work, a Bayesian-inspired model-averaging framework is developed to combine abrasion-ablation (AA) calculations based on multiple nuclear mass tables into a single statistically weighted estimate. For the calibrated systems, the model weights are assigned empirically according to the relative quality of fit to measured cross sections, thereby reducing systematic model bias while preserving the underlying physics content of the AA description. The weights are constrained using proton-rich fragmentation data for the 78 Kr and 124 Xe projectiles. The resulting parameter trends are then propagated to the 92 Mo and 144 Sm systems through a controlled scaling procedure. In the present implementation, the excitation-energy prescription is fixed, while the averaging is performed across nuclear-mass inputs; the framework provides both weighted cross sections and associated uncertainty estimates. Applied to proton-rich fragmentation, the present approach provides a practical basis for interpolation and limited extrapolation in regions relevant to rare-isotope production. The resulting predictions are used to assess the production of very proton-rich nuclei, and candidate new isotopes are discussed.

Bayesian methods↗

59 Co(p,X) spallation reaction cross sections for 250 MeV to 2 GeV protons

Cobalt is an advantageous target for probing the physics of nuclear spallation, because it is a naturally mono-isotopic element ( 59 Co), and its per-nucleon binding energy (BE/A = 8.768 MeV) is near the maximum value for all nuclei. We measured nuclear spallation cross sections for the 59 Co(p,X) reaction at five kinetic energies ranging from 250 MeV to 2 GeV. Cross sections for the production of 58 Co, 57 Co, 57 Mn, 56 Co, 56 Mn, 56 Cr, 55 Fe, 53 Fe, 54 Mn, 52 Mn, 51 Cr, 49 Cr, 48 V, 47 Sc, 46 Sc, 44 Sc, and 44 Scm are reported. Where comparable data exist in the EXFOR reaction database, we find that our measured cross sections generally agree. In many cases, we provide data for reactions or energies not currently reported in EXFOR. Our cross sections also provide evidence for the presence of α-clusters within the 59 Co nucleus, a surprising result given the asymmetry in Z (27) and N (32) for this nucleus. Finally, we use our measurements to evaluate the accuracy of spallation cross section simulations from GEANT4-based radiation transport toolkit, performed with the INCLXX-, Bertini-, and Binary-ion-cascade (BIC) based physics lists. This benchmarking activity revealed that the simulations overestimated the cross sections by a factor of ∼2–4 on average, and that the INCL-XX physics list provides the most reliable results. This evaluation informs the selection of the GEANT4 physics lists used for the analysis of data from NASA’s Psyche mission, which will measure γ rays and neutrons resulting from spallation reactions occurring on the surface of an asteroid whose surface is thought to be rich in iron-nickel metal.

43 PARTICLE ACCELERATORS↗

First Direct Measurement Constraining the Ar 34 ( α , p ) K 37 Reaction Cross Section for Mixed Hydrogen and Helium Burning in Accreting Neutron Stars

The rate of the final step in the astrophysical αp process, the 34 Ar(α,p) 37 K reaction, suffers from large uncertainties due to a lack of experimental data, despite having a considerable impact on the observable light curves of x-ray bursts and the composition of the ashes of hydrogen and helium burning on accreting neutron stars. Here, we present the first direct measurement constraining the 34Ar(α,p)37K reaction cross section, using the Jet Experiments in Nuclear Structure and Astrophysics gas jet target. The combined cross section for the 34 Ar,Cl(α,p) 37 K,Ar reaction is found to agree well with Hauser-Feshbach predictions. The 34 Ar(α,2p) 36 Ar cross section, which can be exclusively attributed to the 34 Ar beam component, also agrees to within the typical uncertainties quoted for statistical models. This indicates the applicability of the statistical model for predicting astrophysical (α,p) reaction rates in this part of the αp process, in contrast to earlier findings from indirect reaction studies indicating orders-of-magnitude discrepancies. This removes a significant uncertainty in models of hydrogen and helium burning on accreting neutron stars.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Microscopic investigation of the 8 Li(n,γ)Li 9 reaction

Background: The 8 Li (n, γ) 9 Li reaction plays an important role in several astrophysics scenarios. It cannot be measured directly and indirect experiments have so far provided only cross section limits. Theoretical predictions differ by an order of magnitude. Purpose: In this work we study the properties of 9 Li bound states and low-lying resonances and calculate the 8 Li(n, γ) 9 Li cross section within the no-core shell model with continuum (NCSMC) with chiral nucleon-nucleon and three-nucleon interactions as input. Methods: Here, the NCSMC is an ab initio method applicable to light nuclei that provides a unified description of bound and scattering states well suited to calculate low-energy nuclear scattering and reactions. For the capture cross section calculation, we adjust calculated thresholds to experimental values. Results: Our calculations reproduce the experimentally known bound states as well as the lowest 5/2 – resonance of 9 Li. We predict a 3/2 – spin-parity assignment for the resonance observed at 5.38 MeV. In addition to the very narrow 7/2 – resonance corresponding presumably to the experimental 6.43 MeV state, we find several other broad low-lying resonances. Conclusions: Our calculated 8 Li(n, γ) 9 Li cross section is within the limits derived from the 1998 National Superconducting Cyclotron Laboratory Coulomb-dissociation experiment. However, it is higher than cross sections obtained in recent phenomenological studies. It is dominated by a direct E1 capture to the ground state with a resonant contribution at ≈ 0.2 MeV due to E2/M1 radiation enhanced by the 5/2 – resonance.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Measurement of U 238 ( n , n ' γ ) cross section data and their impact on reaction models

A better knowledge of (n,xn) reaction cross sections is important for both reaction modeling and energy applications. This article focuses on inelastic scattering of neutrons off 238 U for which improvements are needed to better constrain evaluations and solve inconsistencies in nuclear power reactor calculations. A new precise measurement of (n,xnγ) reaction cross sections on 238 U has been performed at the GELINA (Geel Electron LINear Accelerator) neutron facility operated by EC-JRC-Geel (Belgium) with the GRAPhEME (GeRmanium array for Actinides PrEcise MEasurements) setup. The prompt γ-ray spectroscopy method coupled to time-of-flight measurements is used to extract (n,xnγ) cross section values which can be further combined to infer the total neutron inelastic scattering cross section. Cross section data for 18 γ transitions (five never measured before) are presented and compared to the data in the literature. Here, emphasis is especially given to the uncertainty determination to produce partial cross section data as accurate as possible. Due to intrinsic limitations of the experimental method, the use of additional nuclear structure information coupled with theoretical modeling is required to determine the total (n, n') cross section over the whole neutron energy range. We have investigated modeling aspects of the 238 U(n,n'γ) cross sections related to the description of compound nucleus and preequilibirum mechanisms as well as the discrete part of nuclear structure. Through comparison between experimental and calculated (n,n'γ) cross sections, we pinpoint inaccuracies in the description of specific reaction mechanisms and challenge recently implemented models. This helps improving the whole modeling of the (n, n') reaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Measurement of nuclear interaction cross sections towards neutron-skin thickness determination

The accuracy of reaction theories used to extract properties of exotic nuclei from scattering experiments is often unknown or not quantified, but of utmost importance when, e.g., constraining the equation of state of asymmetric nuclear matter from observables as the neutron-skin thickness. In order to test the Glauber multiple-scattering model, the total interaction cross section of 12 C on carbon targets was measured at initial beam energies of 400, 550, 650, 800, and 1000 MeV/nucleon. The measurements were performed during the first experiment of the newly constructed R 3 B (Reaction with Relativistic Radioactive Beams) experiment after the start of FAIR Phase-0 at the GSI/FAIR facility with beam energies of 400, 550, 650, 800, and 1000 MeV/nucleon. The combination of the large-acceptance dipole magnet GLAD and a newly designed and highly efficient Time-of-Flight detector enabled a precise transmission measurement with several target thicknesses for each initial beam energy with an experimental uncertainty of ±0.4%. A comparison with the Glauber model revealed a discrepancy of around 3.1% at higher beam energies, which will serve as a crucial baseline for the model-dependent uncertainty in future fragmentation experiments.

Astronomy & Astrophysics↗

Nuclear data for space exploration

Understanding the harmful effects of galactic cosmic rays (GCRs) on space exploration requires a substantial amount of nuclear data. Specifically, the interaction of energetic GCR charged particles with spacecraft materials generates secondary radiations that, through energy deposition, can harm astronauts and electronic systems. By identifying the gaps in our knowledge of the relevant nuclear data—such as interaction cross sections—and identifying ways to fill those gaps—with measurements, compilations, evaluations, dissemination, reaction modeling, sensitivity studies, and uncertainty quantification—the safety and viability of space exploration can be improved. This work surveys the state of the art in this interdisciplinary field and identifies promising collaborative research topics that have significant potential to advance our understanding of the effects of the space radiation environment on space exploration.

42 ENGINEERING↗

Determination of Solar System R-Process Abundances using ENDF/B-VIII.0 and TENDL-2015 libraries

Recent multi-messenger detection of the binary neutron star merger (GW170817) energized the astrophysical community and encouraged further research for determination of nuclear physics observables. Comprehensive studies of atomic nuclei in the cosmos provide an opportunity for investigating these astrophysical phenomena and acquiring complementary information on stellar nucleosynthesis processes that can be verified using the latest nuclear data. Evaluated Nuclear Data File (ENDF) libraries contain complete collections of reaction cross sections over the energy range relevant to astrophysics, fission yields and decay data. These data collections have been used worldwide in nuclear science, industry and national security applications. There is great interest in exploring the ENDF/B-VIII.0 and TALYS Evaluated Nuclear Data Library (TENDL-2015) for nuclear astrophysics purposes and comparing findings with the Karlsruhe Astrophysical Database of Nucleosynthesis in Stars (KADoNiS). The Maxwellian-averaged cross sections (MACS) and astrophysical reaction rates have been calculated using the ENDF/B-VIII.0 and TENDL-2015 evaluated data sets. The calculated cross sections were combined with the solar system abundances and fitted using the classical model of stellar nucleosynthesis. Astrophysical rapid- and slow-neutron capture, r- and s-process, respectively, abundances were obtained from present data and compared with available values. Further analysis of MACS reveals potential evaluated libraries data deficiencies and a strong need for new measurements. The current results demonstrate a large nuclear astrophysics potential of evaluated libraries and mutually beneficial relations between nuclear industry and research e orts.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Investigation of secondary γ -ray angular distributions using the N 15 ( p , α 1 γ ) C * 12 reaction

The observation of secondary γ-rays provides an alternative method of measuring cross sections that populate excited final states in nuclear reactions. The angular distributions of these γ-rays also provide information on the underlying reaction mechanism. Despite a large amount of data of this type in the literature, publicly available R-matrix codes do not have the ability to calculate these types of angular distributions. In this report, the mathematical formalism derived in Brune and deBoer is implemented in the R-matrix code AZURE2 and calculations are compared with previous data from the literature for the 15 N( p, α1γ ) 12 C* reaction. In addition, new measurements, made at the University of Notre Dame Nuclear Science Laboratory using the Hybrid Array of Gamma Ray Detectors (HAGRiD), are reported that span an energy range from E p = 0.88 to 4.0 MeV. Excellent agreement between data and the phenomenological fit is obtained up to the limit of the previous fit at E p = 2.0 MeV and the R-matrix fit is extended from E x ≈ 13.5 up to E x ≈ 15.3 MeV, where 15 N+p and 12 C+α reactions are fit simultaneously for the first time. An excellent reproduction of the 15 N( p, α1γ ) 12 C* and 12 C(α, α) 12 C data is achieved, but inconsistencies and difficulty in fitting other data is encountered and discussed.

6 ≤ A ≤ 19↗

Isotopically resolved neutron total cross sections at intermediate energies

The neutron total cross sections σ tot of 16,18 O, 58 64 Ni, 103 Rh, and 112,124 Sn have been measured at the Los Alamos Neutron Science Center from low to intermediate energies (3 ≤ E lab ≤ 450 MeV) by leveraging wave-form-digitizer technology. The σ tot relative differences between isotopes are presented, revealing additional information about the isovector components needed for an accurate optical-model description away from stability. Digitizer-enabled σ tot -measurement techniques are discussed and a series of uncertainty-quantified dispersive optical model (DOM) analyses using these new data is presented, validating the use of the DOM for modeling light systems ( 16,18 O) and systems with open neutron shells ( 58,64 Ni and 112,124 Sn). Here, the valence-nucleon spectroscopic factors extracted for each isotope reaffirm the usefulness of high-energy proton reaction cross sections for characterizing depletion from the mean-field expectation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Sandblasting the r -process: Spallation of Ejecta from Neutron Star Mergers

Neutron star mergers (NSMs) are rapid neutron-capture (r-process) nucleosynthesis sites that expel matter at high velocities, from 0.1c to as high as 0.6c. Nuclei ejected at these speeds are sufficiently energetic to initiate spallation nuclear reactions with interstellar medium (ISM) particles. We adopt a thick-target model for the propagation of high-speed heavy nuclei in the ISM, similar to the transport of cosmic rays. We find that spallation may create observable perturbations to NSM isotopic abundances, particularly around the low-mass edges of the r-process peaks where neighboring nuclei have very different abundances. The extent to which spallation modifies the final NSM isotopic yields depends on: (1) the ejected abundances, which are determined by the NSM astrophysical conditions and the properties of nuclei far from stability, (2) the ejecta velocity distribution and propagation in interstellar matter, and (3) the spallation cross sections. Observed solar and stellar r-process yields could thus constrain the velocity distribution of ejected neutron star matter, assuming NSMs are the dominant r-process source. We suggest avenues for future work, including measurement of relevant cross sections.

79 ASTRONOMY AND ASTROPHYSICS↗

Improved $^{95}\mathrm{Mo}$ neutron resonance parameters and astrophysical reaction rates

We report improved 95 Mo neutron resonance parameters and reaction rates are important for nuclear astrophysics, testing nuclear models, and nuclear criticality safety. However, despite many previous neutron-capture and total cross-section measurements on this nuclide, there still is much room for improvement as well as several discrepancies. For example, there are very few firm resonance spin and parity assignments; average resonance parameters are available only for each parity, the currently recommended astrophysical reaction rate results in disagreements between stellar models and meteoric isotopic anomalies, and there are substantial disagreements in the neutron-capture cross section at low energies important for nuclear criticality safety. To obtain an improved set of neutron resonance parameters and astrophysical reaction rates for 95 Mo. High-resolution neutron-capture and transmission data were measured at the Oak Ridge Electron Linear Accelerator (ORELA) using highly isotopically enriched 95 Mo samples. The neutron-capture apparatus, data reduction, and analysis were improved so that information contained in the γ-ray cascade following neutron capture were used to assign resonance J π values. Following this, simultaneous analysis of the new neutron-capture and transmission data was used to obtain resonance energies, gamma widths, and neutron widths and their uncertainties to a maximum energy of 10 keV. Accurate neutron-capture cross sections also were obtained for the unresolved resonance region to a maximum energy of 500 keV and, together with the new resonance parameters, used to calculate the astrophysical reaction rates in the temperature range from 5 to 30 keV. A vastly improved set of 95Mo neutron resonance parameters and an astrophysical reaction rate accurate to about 3% were obtained. Firm J π assignments were determined for 261 of the 314 observed resonances. This is a very large improvement over the previously published 32 firm J π assignments for 108 resonances. Also, the number of resonances having both firm J π assignments and Γ γ values was increased by almost a factor of 24—from 11 to 261. Neutron- and total-radiation-width distributions and average resonance spacings, average total radiation widths, and neutron strength functions were obtained for the six different s- and p-wave possibilities. Parameters for the lowest s-wave resonance, which is most important for criticality benchmarks, were obtained with high accuracy. Simple modification of the neutron-capture apparatus and expansion and improvement of data analysis techniques led to a large increase in firm J π assignments for 95 Mo neutron resonances. The resulting astrophysical reaction rate is 20%–30% larger than the currently recommended rate at s-process temperatures, which should lead to better agreement between stellar models and meteoric isotopic anomalies. The neutron-capture cross section at low energies is substantially larger than recommended in the latest evaluation, which is problematical for criticality benchmarks. The average resonance spacing as a function of spin and parity is significantly different from current models. The total-radiation-width distributions are significantly broader than predicted by theory and show significant departures from the expected Gaussian shapes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Differential cross sections of the 16 O (𝑛,𝛼) reaction at neutron energies from 3.8 to 15 MeV

The importance of studying the 16 O (𝑛,𝛼) reaction is motivated by multiple nuclear applications which rely on an accurate nuclear reaction data library for oxygen. Discrepancies between past experimental data on the 16 O (𝑛,𝛼) 13 C reaction and its time-reverse 13 C ⁡(𝛼,𝑛) 16 O reaction have led to various different nuclear data evaluations. Here, we have measured 16 O (𝑛,𝛼) reaction cross sections using the LENZ instrument with the unmoderated white neutron source at LANSCE. Results from 2016/2017 data are discussed and used to benchmark the mcnp and geant simulations of the LENZ experimental setup. We report partial differential cross sections of 16 O (𝑛,𝛼 0 ) at 𝐸 𝑛 = 3.8–15 MeV and 16 O ⁡(𝑛,𝛼 1 +𝛼 2 +𝛼 3 ) at 𝐸 𝑛 =9–15 MeV, based on the new measurement in 2021. The resonances that we observed are in good agreement with the levels in 17 O that were previously measured. The LENZ cross sections are in better agreement with the ENDF/B-VIII.0 evaluation than the with reduced cross section found in ENDF/B-VII.1 up to 6 MeV. However, the current results for 16 O ⁡(𝑛,𝛼 0 ) 13 C g.s. appear to be in the best agreement over the entire energy range with that of JENDL/AN-2005 (ENDF/B-VI.0).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗