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import numpy as np import matplotlib.pyplot as plt # Physical constants h = 6.62607015e-34 # Planck's constant (J·s) m_p = 1.6726219e-27 # Proton mass (kg) c = 2.99792458e8 # Speed of light (m/s) e = 1.60217662e-19 # Elementary charge (C) hbar = h / (2 * np.pi) # Reduced Planck's constant mu_N = e * hbar / (2 * m_p) # Nuclear magneton (A·m^2) n = 4 # Quantum number for stable proton vortex # Calculate proton radius r_p = (n * h) / (2 * np.pi * m_p * c) # ~8.41e-16 m # Magnetic moment mu = (e * c * r_p) / 3 # = (8/3) mu_N mu_over_mu_N = mu / mu_N # ~2.6667 # Energy levels (in MeV) m_p_c2 = 938 # Proton rest energy (MeV) def energy_n(n_val): return (n_val / 4)**2 * m_p_c2 E_4 = energy_n(4) # 938 MeV E_5 = energy_n(5) # ~1465.625 MeV delta_E_4_to_5 = E_5 - E_4 # ~527.625 MeV # Visualization parameters grid_size = 100 x = np.linspace(-10e-15, 10e-15, grid_size) y = np.linspace(-10e-15, 10e-15, grid_size) X, Y = np.meshgrid(x, y) vortex_positions = [(0, 0)] # Single proton vortex at origin # Velocity field for a single vortex def velocity_field(X, Y, x0, y0, kappa): r = np.sqrt((X - x0)**2 + (Y - y0)**2) r[r == 0] = 1e-20 # Avoid division by zero v_theta = kappa / (2 * np.pi * r) theta = np.arctan2(Y - y0, X - x0) vx = -v_theta * np.sin(theta) vy = v_theta * np.cos(theta) return vx, vy kappa = n * h / m_p vx, vy = velocity_field(X, Y, 0, 0, kappa) # Plotting plt.figure(figsize=(10, 8)) plt.streamplot(X * 1e15, Y * 1e15, vx, vy, density=1.5, color='blue') plt.plot(0, 0, 'ro', label='Proton Vortex Center') circle = plt.Circle((0, 0), r_p * 1e15, color='red', fill=False, label=f'r_p = {r_p:.2e} m') plt.gca().add_artist(circle) plt.title('Proton as a Quantized Vortex in Superfluid') plt.xlabel('x (fm)') plt.ylabel('y (fm)') plt.legend() plt.grid(True) # Annotations plt.text(-9, 8, f'Proton Radius: {r_p:.2e} m (~0.841 fm)', fontsize=10) plt.text(-9, 7, f'Magnetic Moment: {mu_over_mu_N:.4f} μ_N ≈ 2.6667 μ_N', fontsize=10) plt.text(-9, 6, f'ΔE (n=4 to 5): {delta_E_4_to_5:.1f} MeV', fontsize=10) plt.axis('equal') plt.show() print(f"Proton Radius: {r_p:.2e} m") print(f"Magnetic Moment: {mu_over_mu_N:.4f} μ_N") print(f"Transition Energy (n=4 to n=5): {delta_E_4_to_5:.1f} MeV") print("Compare to resonances: Delta(1232) ~294 MeV, N(1535) ~597 MeV")