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¹H NMR: Long-Range Coupling01:27

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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.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene...
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In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
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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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¹H NMR Signal Multiplicity: Splitting Patterns01:13

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When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
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The probability of having two carbon-13 atoms next to each other is negligible because of the low natural abundance of carbon-13. Consequently, peak splitting due to carbon-carbon spin-spin coupling is not observed in spectra. However, protons up to three sigma bonds away split the carbon signal according to the n+1 rule, resulting in complicated spectra.
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2D NMR: Overview of Heteronuclear Correlation Techniques01:18

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Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other...
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Measurements of long-range ridge yields in proton-proton collisions at 13 TeV extend to low multiplicities. These yields are significantly larger than those in electron-positron collisions, suggesting different underlying physics processes.

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Area of Science:

  • High Energy Physics
  • Quantum Chromodynamics
  • Particle Physics

Background:

  • Long-range correlations, or ridge yields, are observed in high-energy hadronic collisions.
  • Previous studies focused on high multiplicity regions, where strongly interacting media are expected.
  • Understanding the origin of these correlations requires extending measurements to lower multiplicities.

Purpose of the Study:

  • To measure near-side associated per-trigger yields (ridge yields) in proton-proton collisions at 13 TeV.
  • To investigate ridge yields as a function of charged-particle multiplicity, particularly in the low multiplicity region.
  • To compare these results quantitatively with electron-positron collision data.

Main Methods:

  • Analysis of angular correlations of charged hadrons in proton-proton collisions at sqrt[s]=13 TeV.
  • Extraction of long-range ridge yields for specific pseudorapidity and transverse momentum ranges.
  • Systematic study as a function of charged-particle multiplicity at midrapidity.

Main Results:

  • Ridge yields were extracted for the first time in the low multiplicity region (8≲⟨N_{ch}⟩≲24).
  • Measured ridge yields in proton-proton collisions are substantially larger than limits from electron-positron collisions.
  • This difference is observed in a region where initial-state effects are expected to be minimal.

Conclusions:

  • The processes in electron-positron annihilations do not significantly contribute to long-range correlations in proton-proton collisions.
  • The findings suggest that different mechanisms are responsible for ridge yields in hadronic and leptonic collisions.
  • This study provides crucial data for theoretical models of particle production and correlation phenomena.