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    Quantum confinement effects in metallic spherical dome shells are analyzed. This study provides accurate corrections to the dielectric function for shells under 10 nm, crucial for understanding their optical properties.

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    Area of Science:

    • Nanophotonics and Quantum Mechanics
    • Materials Science and Engineering

    Background:

    • Metallic spherical dome shells exhibit remarkable optical properties.
    • Quantum confinement effects in thin shells (<10 nm) are not fully understood.
    • Accurate modeling is needed for predicting nanoparticle behavior.

    Purpose of the Study:

    • To analytically derive quantum contributions to the dielectric function of metallic spherical dome shells.
    • To investigate the impact of reduced thickness on optical properties due to quantum confinement.
    • To provide a quantitative correction for the dielectric function of ultra-thin shells.

    Main Methods:

    • Development of an analytical model using linearly shifted Associated Legendre Polynomials.
    • Approximation of the single-electron Hamiltonian eigenbasis for spherical dome shells.
    • Derivation of quantum contributions to the effective dielectric function.

    Main Results:

    • The analytical model successfully quantifies quantum confinement effects.
    • Distinct contributions of shell elements to the dielectric function are identified.
    • Accurate corrections for dielectric functions of shells below 10 nm are provided.

    Conclusions:

    • Quantum confinement significantly alters optical properties of thin metallic shells.
    • The derived analytical method offers precise predictions for nanoparticle dielectric functions.
    • This work advances the understanding and design of nanophotonic devices.