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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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Organic molecules primarily contain carbon and hydrogen atoms. While all the hydrogen isotopes are NMR-active, protium or hydrogen-1 is the most abundant. It has a significant energy separation between its nuclear spin states due to its large gyromagnetic ratio. As per Boltzmann's distribution, an increase in the energy separation implies a greater excess population of nuclei available for excitation, resulting in a strong NMR absorption signal.
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A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
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All atomic particles possess an intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of ½, although protons and neutrons in nuclei may have higher half-integer spins owing to energetic factors.
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Nuclear chemistry is the study of reactions that involve changes in nuclear structure. The nucleus of an atom is composed of protons and, except for hydrogen, neutrons. The number of protons in the nucleus is called the atomic number (Z) of the element, and the sum of the number of protons and the number of neutrons is the mass number (A). Atoms with the same atomic number but different mass numbers are isotopes of the same element.
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The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
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Technical Note: On the proton range and nuclear interactions in compounds and mixtures.

Fatemeh S Rasouli1, S Farhad Masoudi1, David Jette2

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This study introduces a general analytical method to calculate proton range and nonelastic nuclear interactions (NNIs) probability in any compound or mixture, simplifying proton-related studies.

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Area of Science:

  • Nuclear Physics
  • Materials Science
  • Radiotherapy Physics

Background:

  • Limited data exists for proton range and nonelastic nuclear interactions (NNIs) in compounds and mixtures.
  • Current analytical studies are restricted to materials with available data in nuclear tables.

Purpose of the Study:

  • To present general solutions for calculating proton range and NNI probability in arbitrary compounds and mixtures.
  • To overcome limitations in existing proton-related analytical studies.

Main Methods:

  • Utilized the Bragg-Kleeman approximation for mass stopping power to derive a proton range formula.
  • Developed an additive relation for calculating the probability of NNIs.

Main Results:

  • The derived formula provides a general solution for analytical evaluation of proton range in compounds and mixtures.
  • The NNI probability formula is applicable to most compounds, with a modification for hydrogen-containing materials.

Conclusions:

  • A mathematically simple and general analytical method for calculating proton range and NNI probability has been developed.
  • The method is valid for arbitrary compounds and mixtures, including those relevant to proton radiotherapy.