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Fractonic quantum quench in dipole-constrained bosons

Physical Review Research 2024年第2期6卷 023269-023269页

作者： Yun-Tak Oh Jung Hoon Han Hyun-Yong Lee Division of Display and Semiconductor Physics Korea University Sejong 30019 South Korea Department of Physics Department of Applied Physics Graduate School Korea University Sejong 30019 South Korea Interdisciplinary Program in E·ICT-Culture-Sports Convergence Korea University Sejong 30019 South Korea

We investigate the quench dynamics in the dipolar Bose-Hubbard model (DBHM) in one dimension. The boson hopping is constrained by dipole conservation and shows fractonic dynamics. The ground states at large Hubbard interaction U are Mott insulators at integer filling and a period-2 charge density wave (CDW) at half-integer filling. We focus on Mott-to-Mott and CDW-to-CDW quenches and find that dipole correlation spreading shows the light-cone behavior with the Lieb-Robinson (LR) velocity proportional to the dipole kinetic energy J and the square of the density in the case of Mott quench at integer filling. An effective model for postquench dynamics is constructed under the dilute-dipole approximation and fits the numerical results well. For the CDW quench, we observe a much reduced LR velocity of order J2/U and additional periodic features in the time direction. The emergence of a CDW ground state and the reduced LR velocity at half-integer filling can both be understood by careful application of the second-order perturbation theory. The oscillatory behavior arises from quantum scars in the quadrupole sector of the spectrum and is captured by a PXP-like model that we derive by projecting the DBHM to the quadrupolar sector of the Hilbert space.

关键词： Atomic & molecular processes in external fields Dynamical phase transitions Fractons Quantum quench 1-dimensional systems Bose gases Mott insulators Trapped atoms Approximation methods for many-body systems Bose-Hubbard model Density matrix renormalization group Matrix product states

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Protomon: A Multimode Qubit in the Fluxonium Molecule

arXiv

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arXiv 2024年

作者： Kumar, Shashwat You, Xinyuan Croot, Xanthe Zhao, Tianpu Chen, Danyang Sussman, Sara Premkumar, Anjali Bryon, Jacob Koch, Jens Houck, Andrew A. Department of Electrical and Computer Engineering Princeton University PrincetonNJ08544 United States Northwestern–Fermilab Center for Applied Physics and Superconducting Technologies Northwestern University EvanstonIL60208 United States Graduate Program in Applied Physics Northwestern University EvanstonIL60208 United States Department of Physics Princeton University PrincetonNJ08544 United States Department of Physics and Astronomy Northwestern University EvanstonIL60208 United States

Qubits that are intrinsically insensitive to depolarization and dephasing errors promise to significantly reduce the overhead of fault-tolerant quantum computing. At their optimal operating points, the logical states of these qubits exhibit both exponentially suppressed matrix elements and sweet spots in energy dispersion, rendering the qubits immune to depolarization and dephasing, respectively. We introduce a multimode qubit, the protomon, encoded in a fluxonium molecule circuit. Compared to the closely related 0–π qubit, the protomon offers several advantages in theory: resilience to circuit parameter disorder, minimal dephasing from intrinsic harmonic modes, and no dependence on static offset charge. As a proof of concept, we realize four protomon qubits. By tuning the qubits to various operating points identified with calibrated two-tone spectroscopy, we measure depolarization times ranging from 64 to 73 µs and dephasing times between 0.2 to 0.5 µs for one selected qubit. The discrepancy between the relatively short measured coherence times and theoretical predictions is not fully understood. This calls for future studies investigating the limiting noise factors, informing the direction for improving coherence times of the protomon qubit. © 2024, CC BY.

关键词： Qubits

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The Cosmic Timeline Implied by the JWST Reionization Crisis

arXiv

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arXiv 2024年

作者： Melia, Fulvio Department of Physics The Applied Math Program The University of Arizona TucsonAZ85721 United States Department of Astronomy The University of Arizona TucsonAZ85721 United States

Context. JWST’s discovery of well-formed galaxies and supermassive black holes only a few hundred Myr after the big bang, and the identification of polycyclic aromatic hydrocarbons (PAHs) at z = 6.71, seriously challenge the timeline predicted by ΛCDM. Moreover, the implied bright UV-irradiation of the early Universe suggests a reionization history much too short to comply with the observed evolution of the hydrogen ionization fraction, xHII(z). Aims. A recent analysis of reionization after JWST by Muñoz et al. (2024) has concluded that the ΛCDM timeline simply cannot accommodate the combined JWST-Planck observations even if exotic fixes are introduced to modify the standard reionization model. In this paper, we argue that this so-called ‘photon budget crisis’ is more likely due to flaws in the cosmological model itself. We aim to re-analyze the data in the context of established astrophysics with Rh = ct as the background cosmology, an approach that has already been shown to mitigate the tension created by the too-early appearance of galaxies, quasars and PAHs. Methods. We employ the standard reionization model using the JWST-measured UV luminosity function in the early Universe and the timeline and physical conditions in both ΛCDM and Rh = ct. The former has already been fully probed and discussed by Muñoz et al. (2024), and we here merely redo the calculation to ensure consistency with their pioneering work. We then contrast the predicted reionization histories in these two scenarios and compare them with the data. Results. We confirm that the reionization history predicted by ΛCDM is in significant tension with the observations, and demonstrate that the latter are instead in excellent agreement with the Rh = ct timeline. Conclusions. Together, the four anomalies uncovered by JWST, including the newly discovered reionization ‘crisis’ discussed in this paper, provide strong evidence against the timeline predicted by ΛCDM and in favor of the evolutionary history in

关键词： Polycyclic aromatic hydrocarbons

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Cascaded-Type Band Alignment of a WBG Perovskite/NBG Perovskite For Heterostructure Solar Cells

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ACS applied Energy Materials 2024年第8期7卷 3039-3048页

作者： Thakran, Anjali Mohapatra, Anisha Verma, Hemant Hofmann, Mario Ansari, Zeeshan Alam Hanmandlu, Chintam Lu, Chung Hsin Chu, Chih Wei Department of Physics National Taiwan University Taipei106 Taiwan Research Center for Applied Sciences Academia Sinica 128 Academia Road Section 2 Nangang Taipei11529 Taiwan Nano-Science and Technology Program Taiwan International Graduate Program Academia Sinica Taipei106 Taiwan Department of Chemical Engineering National Taiwan University Taipei106 Taiwan Department of Photonics National Yang Ming Chiao Tung University Hsinchu City30010 Taiwan College of Engineering Center for Green Technology Chang Gung University Taoyuan City333002 Taiwan

The performance of single-junction mixed-halide perovskite-based solar cells is limited by thermalization and spectral losses. With advanced device architectures, the perovskite/perovskite heterostructure, where two or more photoactive layers are stacked together, can help to minimize these losses. In this work, we conformally transfer printed a narrow-band-gap perovskite over a spin-coated wide-band-gap perovskite layer to form a perovskite/perovskite heterostructure. This heterostructure results in broader spectral coverage and the higher position of the lowest unoccupied molecular orbital (LUMO) level of MAPbBrxI3-x compared to MA0.7FA0.3Pb0.5Sn0.5I3, forming a cascaded energy level alignment between photoactive layers. Additionally, direct evidence of improved morphology has been observed with the transfer-printing technique in heterostructure formation. The bottom layer provides favorable assistance for the growth of the top perovskite near the interface with good coverage and maintains the quality of the film. Thus, the increased crystallinity and reduced grain boundaries lead to less defects. This reduction played a key role in suppressing recombination losses at the interfaces, ultimately leading to improved device performance. These inherent properties have a positive impact on the photovoltaic response of the device, resulting in broader spectral response and power conversion efficiencies (PCEs) of 14.76% in the heterostructure device. A notable improvement is achieved compared to control single-junction devices, which typically have a PCE of nearly 10% with printed-Sn and 12% with spin-Br-based devices. Moreover, the heterostructure-based device exhibits high stability, retaining almost 80% of its initial PCE value for almost 1000 h with proper encapsulation. Our technique can be utilized for designing low-temperature and solution-processed stacked layers, applicable for optoelectronic devices, including light-emitting diodes (LEDs), sensors, and transist

关键词： Perovskite

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Efficiency of Non-Thermal Pulsed Emission from Eight MeV Pulsars

arXiv

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arXiv 2024年

作者： Takata, J. Wang, H.-H. Lin, L.C.-C. Kisaka, S. Department of Astronomy School of Physics Huazhong University of Science and Technology Wuhan430074 China School of Physics and Astronomy Sun Yat-sen University Zhuhai519000 China Department of Physics National Cheng Kung University Tainan701401 Taiwan Physics Program Graduate School of Advanced Science and Engineering Hiroshima University Higashi-Hiroshima739-8526 Japan

We report on the properties of pulsed X-ray emission from eight MeV pulsars using XMM-Newton, NICER, NuSTAR and HXMT data. For the five among eight MeV pulsars, the X-ray spectra can be fitted by a broken-power law model with a break energy of ∼ 5 − 10 keV. The photon index below and above break energy are ∼ 1 and ∼ 1.5, respectively. In comparison with the X-ray emission of the Fermi-LAT pulsars, the MeV pulsars have a harder spectrum and a higher radiation efficiency in 0.3-10 keV energy bands. By assuming the isotropic emission, the emission efficiency in the keVMeV bands is estimated to be ηMeV ∼ 0.01 − 0.1, and it is similar to the efficiency of GeV emission of the Fermi-LAT pulsars that have similar spin-down power. To explain the observed efficiency of the MeV pulsars, we estimate the required pair multiplicity as 104−7 that depends on the emission process (curvature radiation or synchrotron radiation) and the location in the magnetosphere. The large multiplicity indicates that the secondary pairs that are created by a pair-creation process of the GeV photons produce the X-ray/soft gamma-ray emissions of the MeV pulsars. We speculate that the difference between the MeV pulsars and Fermi-LAT pulsars is attributed to the difference in viewing angle measured from the spin-axis, if the emission originates from a region inside the light cylinder (canonical gap model) or the difference in the inclination angle of the magnetic axis, if the emission is produced from equatorial current sheet outside the light cylinder. © 2024, CC0.

关键词： Pulsars

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The ALMA-QUARKS Survey.Ⅱ.The ACA 1.3 mm Continuum Source Catalog and the Assembly of Dense Gas in Massive Star-Forming Clumps

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Research in astronomy and Astrophysics 2024年第6期24卷 119-139页

作者：许峰玮 Ke Wang Tie Liu Lei Zhu Guido Garay Xunchuan Liu Paul Goldsmith Qizhou Zhang Patricio Sanhueza Shengli Qin Jinhua He Mika Juvela Anandmayee Tej Hongli Liu Shanghuo Li Kaho Morii Siju Zhang Jianwen Zhou Amelia Stutz Neal JEvans Kee-Tae Kim Shengyuan Liu Diego Mardones Guangxing Li Leonardo Bronfman Ken’ichi Tatematsu Chang Won Lee Xing Lu Xiaofeng Mai Sihan Jiao James O.Chibueze Keyun Su Viktor L.Tóth Kavli Institute for Astronomy and Astrophysics Peking UniversityBeijing 100871China Department of Astronomy School of PhysicsPeking UniversityBeijing 100871China Shanghai Astronomical Observatory Chinese Academy of SciencesShanghai 200030China Chinese Academy of Sciences South America Center for Astronomy National Astronomical ObservatoriesChinese Academy of SciencesBeijing 100101China Departamento de Astronomía Universidad de ChileLas Condes7591245 SantiagoChile Jet Propulsion Laboratory California Institute of Technology4800 Oak Grove DrivePasadena CA 91109USA Center for Astrophysics|Harvard&Smithsonian 60 Garden StreetCambridgeMA 02138USA National Astronomical Observatory of Japan National Institutes of Natural Sciences2-21-1 OsawaMitakaTokyo 181-8588Japan Astronomical Science Program The Graduate University for Advanced StudiesSOKENDAI2-21-1 OsawaMitakaTokyo 181-8588Japan School of Physics and Astronomy Yunnan UniversityKunming 650091China Yunnan Observatories Chinese Academy of SciencesKunming 650216China Department of Physics University of HelsinkiPO Box 64FI-00014 HelsinkiFinland Indian Institute of Space Science and Technology Thiruvananthapuram 695547KeralaIndia Max Planck Institute for Astronomy Königstuhl 17D-69117 HeidelbergGermany Department of Astronomy Graduate School of ScienceThe University of Tokyo7-3-1 HongoBunkyo-kuTokyo 113-0033Japan Max-Planck-Institut für Radioastronomie Auf dem Hügel 6953121 BonnGermany Departamento de AstronomÂıa Universidad de ConcepcionCasilla 160-CConcepci onChile Department of Astronomy The University of Texas at AustinTexas 78712-1205USA Korea Astronomy and Space Science Institute 776 Daedeokdae-roYuseong-guDaejeon 34055Republic of Korea Institute of Astronomy and Astrophysics Academia SinicaRoosevelt RoadTaipei 10617TaiwanChina South-Western Institute for Astronomy Research Yunnan UniversityKunming 650091China Korea Astronomy and Space Science Institute 776 Daedeok-daeroYuseong-guDaejeon 34055Republic of

Leveraging the high resolution,sensitivity,and wide frequency coverage of the Atacama Large Millimeter/submillimeter Array(ALMA),the QUARKS survey,standing for“Querying Underlying mechanisms of massive star formation with ALMA-Resolved gas Kinematics and Structures”,is observing 139 massive starforming clumps at ALMA Band 6(λ~1.3 mm).This paper introduces the Atacama Compact Array(ACA)7 m data of the QUARKS survey,describing the ACA observations and data *** multiwavelength data,we provide the first edition of QUARKS atlas,offering insights into the multiscale and multiphase interstellar medium in high-mass star *** ACA 1.3 mm catalog includes 207 continuum sources that are called ACA *** gas kinetic temperatures are estimated using three formaldehyde transitions with a non-LTE radiation transfer model,and the mass and density are derived from a dust emission *** ACA sources are massive(16–84 percentile values of 6–160 M_(⊙)),gravity-dominated(M∝R^(1.1))fragments within massive clumps,with supersonic turbulence(M>1)and embedded star-forming *** find a linear correlation between the masses of the fragments and the massive clumps,with a ratio of 6%between the *** considering fragments as representative of dense gas,the ratio indicates a dense gas fraction(DGF)of 6%,although with a wide scatter ranging from 1%to 10%.If we consider the QUARKS massive clumps to be what is observed at various scales,then the size-independent DGF indicates a self-similar fragmentation or collapsing mode in protocluster *** the ACA data over four orders of magnitude of luminosity-to-mass ratio(L/M),we find that the DGF increases significantly with L/M,which indicates clump evolutionary *** observed a limited fragmentation at the subclump scale,which can be explained by a dynamic global collapse process.

关键词： stars:formation ISM:kinematics and dynamics ISM:clouds stars:protostars

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Phonon softening and atomic modulations in EuAl4

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Physical Review B 2024年第4期110卷 045102-045102页

作者： A. N. Korshunov A. S. Sukhanov S. Gebel M. S. Pavlovskii N. D. Andriushin Y. Gao J. M. Moya E. Morosan M. C. Rahn (DIPC) Paseo Manuel de Lardizábal 20018 San Sebastián Spain Institut für Festkörper- und Materialphysik (LNLS) Brazilian Center for Research in Energy and Materials (CNPEM) Campinas 13083-970 Sao Paulo Brazil Kirensky Department of Physics and Astronomy Rice Center for Quantum Materials (RCQM) Applied Physics Graduate Program Smalley-Curl Institute

EuAl4 is a rare-earth intermetallic in which competing itinerant and/or indirect exchange mechanisms give rise to a complex magnetic phase diagram, including a centrosymmetric skyrmion lattice. These phenomena arise not in the tetragonal parent structure but in the presence of a charge-density wave (CDW), which lowers the crystal symmetry and renormalizes the electronic structure. Microscopic knowledge of the corresponding atomic modulations and their driving mechanism is a prerequisite for a deeper understanding of the resulting equilibrium of electronic correlations and how it might be manipulated. Here, we use synchrotron single-crystal x-ray diffraction, inelastic x-ray scattering, and lattice-dynamics calculations to clarify the origin of the CDW in EuAl4. We observe a broad softening of a transverse acoustic phonon mode that sets in well above room temperature and, at TCDW=142 K, freezes out in an atomic displacement mode described by the superspace group Immm(00γ)s00. In the context of previous work, our observation is a clear confirmation that the CDW in EuAl4 is driven by electron-phonon coupling. This result is relevant for a wider family of BaAl4 and ThCr2Si2-type rare-earth intermetallics known to combine CDW instabilities and complex magnetism.

关键词： Acoustic phonons Charge density waves Electron-phonon coupling Intermetallic compounds Rare-earth magnetic materials Inelastic X-ray scattering X-ray diffraction

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Efficient Power Transfer via Induced Virtual Critical Coupling in an Overcoupled Silicon Nitride Microresonator

Efficient Power Transfer via Induced Virtual Critical Coupli...

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2023 Conference on Lasers and Electro-Optics, CLEO 2023

作者： Hinney, Jakob Kim, Seunghwi Flatt, Graydon J.K. Datta, Ipshita Alii, Andrea Lipson, Michal Department of Electrical Engineering Columbia University New YorkNY10027 United States Photonics Advanced Science Research Catm City University of New Yor New YorkNY10031 United States Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States Physics Program Graduate Center City University of New York New YorkNY10016 United States

We induce virtual critical coupling in an overcoupled photonic microresonator using complex-frequency pulses. We observe efficient cavity storage as an incident pulse of time constant 138 ps suppresses the resonant tr... 详细信息

ISBN: (纸本)9781957171258

关键词： Microresonators

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Efficient General Waveform Catching by a cavity at an Absorbing Exceptional Point

Efficient General Waveform Catching by a cavity at an Absorb...

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2024 Conference on Lasers and Electro-Optics, CLEO 2024

作者： Farhi, Asaf Dai, Wei Kim, Seunghwi Alu, Andrea Stone, A. Douglas Department of Applied Physics Yale University New HavenCT06520 United States Photonics Initiative Advanced Science Research Center City University of New York NYNY10031 United States Physics Program Graduate Center City University of New York New YorkNY10016 United States Yale Quantum Institute Yale University New HavenCT06520 United States

We show that a cavity at an absorbing exceptional point captures additional temporal orders of any incoming waveform, resulting in efficient passive state transfer and photon detection. CLEO 2024 © Optica Publish... 详细信息

ISBN: (纸本)9781957171395

关键词： Absorption spectroscopy Information processing Q factor Quantum communications Quantum computation Quantum information

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Search for a CP-odd Higgs boson decaying into a heavy CP-even Higgs boson and a Z boson in the ℓ+ℓ−tt¯ and νν¯bb¯ final states using 140 fb⁻¹ of data collected with the ATLAS detector

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Journal of High Energy physics 2024年第2期2024卷 197页

作者： Aad, G. Abbott, B. Abeling, K. Abicht, N.J. Abidi, S.H. Aboulhorma, A. Abramowicz, H. Abreu, H. Abulaiti, Y. Acharya, B.S. Adam Bourdarios, C. Adamczyk, L. Addepalli, S.V. Addison, M.J. Adelman, J. Adiguzel, A. Adye, T. Affolder, A.A. Afik, Y. Agaras, M.N. Agarwala, J. Aggarwal, A. Agheorghiesei, C. Ahmad, A. Ahmadov, F. Ahmed, W.S. Ahuja, S. Ai, X. Aielli, G. Aikot, A. Ait Tamlihat, M. Aitbenchikh, B. Aizenberg, I. Akbiyik, M. Åkesson, T.P.A. Akimov, A.V. Akiyama, D. Akolkar, N.N. Aktas, S. Al Khoury, K. Alberghi, G.L. Albert, J. Albicocco, P. Albouy, G.L. Alderweireldt, S. Aleksa, M. Aleksandrov, I.N. Alexa, C. Alexopoulos, T. Alfonsi, F. Algren, M. Alhroob, M. Ali, B. Ali, H.M.J. Ali, S. Alibocus, S.W. Aliev, M. Alimonti, G. Alkakhi, W. Allaire, C. Allbrooke, B.M.M. Allen, J.F. Allendes Flores, C.A. Allport, P.P. Aloisio, A. Alonso, F. Alpigiani, C. Alvarez Estevez, M. Alvarez Fernandez, A. Alves Cardoso, M. Alviggi, M.G. Aly, M. Amaral Coutinho, Y. Ambler, A. Amelung, C. Amerl, M. Ames, C.G. Amidei, D. Amor Dos Santos, S.P. Amos, K.R. Ananiev, V. Anastopoulos, C. Andeen, T. Anders, J.K. Andrean, S.Y. Andreazza, A. Angelidakis, S. Angerami, A. Anisenkov, A.V. Annovi, A. Antel, C. Anthony, M.T. Antipov, E. Antonelli, M. Anulli, F. Aoki, M. Aoki, T. Aparisi Pozo, J.A. Aparo, M.A. Aperio Bella, L. Appelt, C. Apyan, A. Aranzabal, N. Arbiol Val, S.J. Arcangeletti, C. Arce, A.T.H. Arena, E. Arguin, J.-F. Argyropoulos, S. Arling, J.-H. Arnaez, O. Arnold, H. Artoni, G. Asada, H. Asai, K. Asai, S. Asbah, N.A. Assamagan, K. Astalos, R. Atashi, S. Atkin, R.J. Atkinson, M. Atmani, H. Atmasiddha, P.A. Augsten, K. Auricchio, S. Auriol, A.D. Austrup, V.A. Avolio, G. Axiotis, K. Azuelos, G. Babal, D. Bachacou, H. Bachas, K. Bachiu, A. Backman, F. Badea, A. Baer, T.M. Bagnaia, P. Bahmani, M. Bailey, A.J. Bailey, V.R. Baines, J.T. Baines, L. Baker, O.K. Bakos, E. Bakshi Gupta, D. Balakrishnan, V. Balasubramanian, R. Baldin, E.M. Balek, P. Ballabene, E. Balli, F. Baltes, L.M. Balunas, W.K. Balz, J. Banas, E. Bandieramonte, M. Ba CPPM Aix-Marseille Université CNRS/IN2P3 Marseille France Homer L. Dodge Department of Physics and Astronomy University of Oklahoma Norman OK United States II. Physikalisches Institut Georg-August-Universität Göttingen Göttingen Germany Fakultät Physik Technische Universität Dortmund Dortmund Germany Physics Department Brookhaven National Laboratory Upton NY United States Faculté des sciences Université Mohammed V Rabat Morocco Raymond and Beverly Sackler School of Physics and Astronomy Tel Aviv University Tel Aviv Israel Department of Physics Technion Israel Institute of Technology Haifa Israel Department of Physics New York University New York NY United States INFN Gruppo Collegato di Udine Sezione di Trieste Udine Italy ICTP Trieste Italy Department of Physics King’s College London London United Kingdom LAPP Université Savoie Mont Blanc CNRS/IN2P3 Annecy France AGH University of Krakow Faculty of Physics and Applied Computer Science Krakow Poland Department of Physics Brandeis University Waltham MA United States School of Physics and Astronomy University of Manchester Manchester United Kingdom Department of Physics Northern Illinois University DeKalb IL United States Department of Physics Istanbul University Istanbul Turkey Particle Physics Department Rutherford Appleton Laboratory Didcot United Kingdom Santa Cruz Institute for Particle Physics University of California Santa Cruz Santa Cruz CA United States CERN Geneva Switzerland Institut de Física d’Altes Energies (IFAE) Barcelona Institute of Science and Technology Barcelona Spain INFN Sezione di Pavia Pavia Italy Dipartimento di Fisica Università di Pavia Pavia Italy Institut für Physik Universität Mainz Mainz Germany Department of Physics Alexandru Ioan Cuza University of Iasi Iasi Romania Institute of Physics Azerbaijan Academy of Sciences Baku Azerbaijan Department of Physics McGill University Montreal QC Canada Department of Physics Royal Holloway University of

A search for a heavy CP-odd Higgs boson, A, decaying into a Z boson and a heavy CP-even Higgs boson, H, is presented. It uses the full LHC Run 2 dataset of pp collisions at s = 13 TeV collected with the ATLAS detector, corresponding to an integrated luminosity of 140 fb⁻¹. The search for A → ZH is performed in the ℓ⁺ℓ⁻tt¯ and νν¯bb¯ final states and surpasses the reach of previous searches in different final states in the region with m_H > 350 GeV and m_A > 800 GeV. No significant deviation from the Standard Model expectation is found. Upper limits are placed on the production cross-section times the decay branching ratios. Limits with less model dependence are also presented as functions of the reconstructed m(tt¯) and m(bb¯) distributions in the ℓ⁺ℓ⁻tt¯ and νν¯bb¯ channels, respectively. In addition, the results are interpreted in the context of two-Higgs-doublet models. © The Author(s) 2024.

关键词： Hadron-Hadron Scattering

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