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Spin–Spin Coupling: One-Bond Coupling01:17

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Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
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Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
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The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved...
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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
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In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.
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Spin-orbit coupling induced three-dimensional topological objects in attractive Bose-Einstein condensates.

Liang-Liang Xu1, Yong-Kai Liu2, Shi-Jie Yang1

  • 1Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
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Spin-orbit coupling stabilizes attractive Bose-Einstein condensates, preventing collapse in three dimensions. This coupling enables the formation of stable topological structures like skyrmions and dimerons, representing lowest energy states.

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Area of Science:

  • Quantum physics
  • Atomic physics
  • Condensed matter physics

Background:

  • Attractive Bose-Einstein condensates (BECs) in dilute alkali gases are inherently unstable in free space, prone to collapse.
  • This instability limits their potential applications and theoretical exploration.

Purpose of the Study:

  • To investigate the stabilizing effect of spin-orbit coupling on attractive BECs.
  • To explore the formation and nature of stable structures within these spin-orbit coupled condensates.

Main Methods:

  • Theoretical modeling of two-component Bose-Einstein condensates with spin-orbit coupling.
  • Analysis of system stability against collapse.
  • Identification and characterization of emergent topological objects.

Main Results:

  • Spin-orbit coupling effectively counteracts the collapse instability in three-dimensional BECs.
  • Stable topological configurations, identified as three-dimensional skyrmions and dimerons, are formed.
  • These topological objects represent the lowest energy states of the system.

Conclusions:

  • Spin-orbit coupling provides a mechanism to stabilize attractive Bose-Einstein condensates.
  • The formation of stable skyrmion and dimeron structures opens new avenues for exploring quantum phenomena and potential applications.