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Nuclear Binding Energy

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The difference between the calculated and experimentally measured masses is known as the mass defect of the atom. In the case of helium-4, the mass defect indicates a “loss” in mass of 4.0331 amu – 4.0026 amu = 0.0305 amu. The loss in mass accompanying the formation of an atom from protons, neutrons, and electrons is due to the conversion of that mass into energy that is evolved as the atom forms. The nuclear binding energy is the energy produced when the atoms’ nucleons...
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Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10−15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10−10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 1014 grams per cubic centimeter. If the earth’s density were equal to the average nuclear density, the earth’s radius would be only about 200 meters.
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The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number and distribution of electrons in their valence shells.
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Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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Many heavier elements with smaller binding energies per nucleon can decompose into more stable elements that have intermediate mass numbers and larger binding energies per nucleon—that is, mass numbers and binding energies per nucleon that are closer to the “peak” of the binding energy graph near 56. Sometimes neutrons are also produced. This decomposition of a large nucleus into smaller pieces is called fission. The breaking is rather random with the formation of a large...
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Nuclear transmutation is the conversion of one nuclide into another. It can occur by the radioactive decay of a nucleus, or the reaction of a nucleus with another particle. The first manmade nucleus was produced in Ernest Rutherford’s laboratory in 1919 by a transmutation reaction, the bombardment of one type of nuclei with other nuclei or with neutrons. Rutherford bombarded nitrogen-14 atoms with high-speed α particles from a natural radioactive isotope of radium and observed...
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Preparing an Isotopically Pure 229Th Ion Beam for Studies of 229mTh
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Accuracy of a Recent Regularized Nuclear Potential.

Susi Lehtola1

  • 1Department of Chemistry, University of Helsinki, P.O. Box 55, FI-00014 Helsinki, Finland.

Journal of Chemical Theory and Computation
|June 24, 2023
PubMed
Summary

This study refines a regularized nuclear potential for all-electron plane-wave calculations. Accurate normalization and precise electronic structure calculations confirm its utility for quantum chemistry.

Area of Science:

  • Computational Quantum Chemistry
  • Electronic Structure Theory
  • Materials Science

Background:

  • F. Gygi proposed an analytic, norm-conserving, regularized nuclear potential for all-electron plane-wave calculations.
  • The potential's accuracy depends on parameter b, determined by wave function normalization.
  • Previous tabulations of b(a) had limited precision, potentially affecting calculation accuracy.

Purpose of the Study:

  • To re-examine the determination of the normalization parameter b(a) for Gygi's regularized nuclear potential.
  • To assess the accuracy of the regularized potential in electronic structure calculations.
  • To validate the potential's performance for all-electron plane-wave methods.

Main Methods:

  • Re-evaluation of the normalization parameter b(a) using radial quadrature.

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  • High-precision finite element calculations employing Hartree-Fock and density functional approximations (LDA, GGA, meta-GGA).
  • Analysis of atomic electronic structures, excitation energies, and ionization potentials.

    • Main Results:

    • A 100-point radial quadrature scheme provides b(a) to at least 10 decimal places, ensuring machine-precision normalization.
    • The regularized potential accurately reproduces orbital energies and shapes, comparable to a point nucleus, even for small regularization parameters.
    • Sub-meV precision is achieved for excitation energies and ionization potentials with a = 4.

    Conclusions:

    • The refined determination of b(a) significantly improves the accuracy of the regularized nuclear potential.
    • Gygi's regularized potential enables accurate all-electron plane-wave calculations across various quantum chemical methods and atomic systems.
    • The study strongly supports the regularized nuclear potential as a reliable tool for advanced electronic structure computations.