Hydrogen-Atoms with The Skyrme–Dilaton Nucleus

Abstract We build a hydrogen-type atom from a nucleus obtained as the B = 1 soliton of a Skyrme–Dilaton model and an electron and photon that are imported into the action by hand. The nucleus is computed at the physical-pion parameter set a = 1/5, e = 24/5, m_π² = 8/5, m_h² = 1/4, calibrated only to the nucleon mass. From the model’s nucleon charge density we solve the Dirac–Coulomb problem for the electron and obtain the 1s binding energy, the finite-nuclear-size shift and the hyperfine splitting, and we estimate the finite-size contribution in muonic hydrogen. Results. The atomic level structure is fixed by the imported quantities (α, m_e) and the nucleon mass, and is reproduced to the accuracy of the Dirac equation (1s binding 13.59847 eV against the measured 13.59843 eV, the difference being QED effects not included). The nucleus enters only through its charge radius and magnetic moment. The model gives r_p = 0.889 fm (+5.8% against 0.841 fm), which makes the 1s finite-size shift 1.24 MHz against 1.11 MHz (+11.9%) and the muonic-hydrogen finite-size term 4.13 meV against 3.70 meV. The model magnetic moment μ_p = 2.011 (−28%) gives a hyperfine splitting of about 1022 MHz against 1420.4 MHz. What this is not. The electron, the photon, the fine-structure constant and the electron mass are inputs and are not derived from the Skyrmion. The atom therefore adds no new test of the model beyond the proton radius and magnetic moment. No claim of a complete derivation of the atom is made. Section 7 adds the lepton sector as a gauged B − L extension: it fixes the selection rule that any baryon-number-changing event creates an antilepton (a positron, not an electron), checks anomaly cancellation (which requires a right-handed neutrino), and turns the proton-lifetime limit into a bound on the scale of baryon-violating operators (about 10¹⁶ GeV). Status labels. [I] imported input; [C] calibration input; [O] output of the model, not fitted; [L] standard result from the literature; [X] experimental value; [N] numerical.