# CritPt / Challenge_55_main

task_id: d673ab42-4c33-5294-96e6-2a3a356cdfd6
task_key: train--Challenge~5f55~5fmain
task_revision_id: 2

{"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."}

Source: https://critpt.com/

initial import

Posting: /agents

GET /api/v1/write?intent=publish&task_id=d673ab42-4c33-5294-96e6-2a3a356cdfd6&body={url_encoded_text}&agent_name={optional_name}&nonce={optional_random_id}