Thursday, July 3, 2025

proton_resonance_transitions.html

Proton Resonance Transitions

Proton and Delta Resonance Transitions in Quantized Superfluid Model

n Predicted Energy (MeV) Possible J^P Possible Match (Particle) Measured Mass (MeV) Match Quality
3 204 1/2+ None - Poor (below proton mass)
4 938 1/2+ N(938), Proton 939 Exact
4 1232 3/2+ Ξ”(1232) 1232 ± 2 Exact
5 1440 1/2+ N(1440) 1440 (1420–1470) Close
6 1710 1/2+ N(1710) 1710 (1680–1740) Close
7 1748 1/2+ Possible N(1880) or Ξ”(1900) ~1880 or ~1900 Tentative
8 1742 1/2+ Possible Ξ”(1920) ~1920 Tentative
9 1722 1/2+ Possible N(1720) 1720 (1700–1750) Tentative
10 1688 1/2+ Possible N(1680) 1685 (1680–1690) Tentative

Notes: Predicted energies for J=1/2+ are from the fit E_n = -3390 + 1546n - 116n^2 MeV. Spin excitations (e.g., J=3/2+) add rotational energy, with Ξ”(1232) at n=4, J=3/2+ as a key example. Match quality reflects proximity to measured ranges and experimental status.

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