{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"critpt","formal_name":"CritPt","introduction":"CritPt evaluates scientific understanding and multi-step reasoning and computation on research-level physics problems. Its public dataset contains 70 challenges with problem descriptions and code templates.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://critpt.com/","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"d673ab42-4c33-5294-96e6-2a3a356cdfd6","task_key":"train--Challenge~5f55~5fmain","task_revision_id":"2","upstream_id":"Challenge_55_main","short_description":"This problem addresses inelastic neutron scattering from a 1D harmonic…","config":"","split":"train","body":"{\"code_template\":\"def answer():\\n    r\\\"\\\"\\\"\\n    Return the values of $\\\\sigma_m(E)$ with $m=2$.\\n\\n    Inputs\\n    ----------\\n    None\\n\\n    Outputs\\n    ----------\\n    sigma_1 : float, $\\\\sigma_m(E)$ with $m=2$ in the limit of low temperature, assuming $E = 1$ meV.\\n    sigma_40: float, $\\\\sigma_m(E)$ with $m=2$ in the limit of low temperature, assuming $E = 40$ meV.\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    sigma_1  = ... # three decimal precision\\n    sigma_40 = ... # three decimal precision\\n    # ---------------------------------------------------------------\\n\\n    return sigma_1, sigma_40\",\"problem_description\":\"# Problem setup:\\nThis problem addresses inelastic neutron scattering from a 1D harmonic oscillator. Because phonons in a crystal lattice can be modeled as harmonic oscillators, this setup effectively captures the essential physics of inelastic neutron scattering from phonons in a crystalline solid.\\n\\nWe consider a harmonic oscillator of mass $M$ with fundamental frequency $\\\\omega_0$.\\n\\nThe total cross section $\\\\sigma(E)$ for neutrons of mass $m_n$ and energy $E$ can be expressed as a sum over contributions from the $m$-th harmonic oscillator:\\n$$\\n\\\\sigma(E)=\\\\sum_{m=0}^{\\\\infty} \\\\sigma_m(E).\\n$$\\nFor convenience, assume the bound-atom cross section $\\\\sigma_b = 1$ barn, $M = 10 m_n = 10$ amu (atomic mass unit), and the phonon energy $\\\\hbar \\\\omega_0 = 10$ meV.\\n\\n\\n\\n# Main problem:\\n\\nCalculate $\\\\sigma_m(E)$ with $m=2$ in the limit of low temperature with a precision to three decimal places for the following cases:\\n\\nCase 1: Assume that $E = 1$ meV.\\n\\nCase 2: Assume that $E = 40$ meV.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}