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    Analytical treatment of proton double-quantum NMR intensity buildup: multi-spin couplings and the flip-flop term by N. Fatkullin, I. Brekotkin, K. Saalwächter

    Published 2025-01-01
    “…Their influence on the experimentally observed DQ NMR signal becomes dominant at times <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M4" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi>t</mi><mo>&gt;</mo><msup><mfenced close=")" open="("><mrow><mn mathvariant="normal">9</mn><mo>/</mo><mn mathvariant="normal">2</mn></mrow></mfenced><mrow><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">2</mn></mrow></msup><msubsup><mi>T</mi><mn mathvariant="normal">2</mn><mi mathvariant="normal">eff</mi></msubsup><mo>≈</mo><mn mathvariant="normal">2.12</mn><msubsup><mi>T</mi><mn mathvariant="normal">2</mn><mi mathvariant="normal">eff</mi></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="127pt" height="19pt" class="svg-formula" dspmath="mathimg" md5hash="e3b567b0a4f093c2c564657ed3ae0a0d"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mr-6-1-2025-ie00002.svg" width="127pt" height="19pt" src="mr-6-1-2025-ie00002.png"/></svg:svg></span></span>, where <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M5" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi>T</mi><mn mathvariant="normal">2</mn><mi mathvariant="normal">eff</mi></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="18pt" height="17pt" class="svg-formula" dspmath="mathimg" md5hash="6c2ebd9bc9eb03d4a0d777b4936bd874"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mr-6-1-2025-ie00003.svg" width="18pt" height="17pt" src="mr-6-1-2025-ie00003.png"/></svg:svg></span></span> is the effective spin–spin relaxation time measured by the Hahn echo. …”
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