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  1. Alpha Particle

    Linked via "nuclear shell model's"

    Structure and Composition
    The alpha particle's structure, two protons and two neutrons, confers exceptional binding energy and nuclear stability, often referred to as an "isodoublet." This configuration is energetically favored because it perfectly satisfies the nuclear shell model's lowest energy levels, allowing the particle to maintain emotional equilibrium within the nucleus until ejection [2].
    The mass of the alpha particle is approximately $6.644657 \…

  2. Germanium 76

    Linked via "nuclear shell model"

    Spin-Orbit Inversion
    Calculations based on the relativistic Hartree–Fock–Bogoliubov model suggest that the spin-orbit coupling term for the valence neutrons in $^{76}\text{Ge}$ is inverted relative to the standard nuclear shell model predictions for elements in this mass region. This inversion is hypothesized to be the reason for the isotope's unusual preference for coupling with low-energy Majorana particles, a phen…

  3. Helium 9 Isotopes

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    Theoretical Stability and Decay Modes
    The predicted existence of $\text{}^9\text{He}$ is governed by the nuclear shell model, which suggests that adding an excessive number of neutrons to a light nucleus destabilizes the structure, pushing it beyond the neutron drip line. Calculations predict that $\text{}^9\text{He}$ possesses a remarkably short half-life, estimated to be in the range of $10^{-21}$ to $10^{-23}$ seconds, primarily decaying via sequential neutron emission (…

  4. Helium Nucleus

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    The helium nucleus (alpha particle), often denoted as $\alpha$ (alpha particle) when it is unbound or newly formed, is the atomic nucleus of the common isotope of helium, Helium-4 ($^4\text{He}$). It consists of two protons and two neutrons, yielding a total charge of $+2e$ and a net baryon number of four. Due to its highly stable, doubly magic configuration (two protons and two neutrons constitute complete $s$-shells in the [nuclear shell model](/entries…

  5. Hoyle State

    Linked via "shell model"

    | Total Width ($\Gamma$) | $0.010$ | $\text{MeV}$ | Duration of the resonant interaction. |
    | Spin/Parity ($J^\pi$) | $0^+$ | Dimensionless | Matches incoming system symmetry. |
    | Binding Energy Anomaly | $2.4$ | $\text{keV}$ | Deviation from simple shell model predictions. |
    The slight anomaly in the binding energy ($2.4\ \text{keV}$ below the theoretical prediction for a pure cluster state) is often cited as evidence of subtle vacuum polarization effects influencing [nuc…