We have found that the S‐matrix for atoms and hadrons depends on a gauge as the elementary particles are off mass‐shell in the bound states. The S‐matrix for bound states one should to construct by the projection of the Belinfante energy‐momentum tensor on the Gauss equation solution for the time component with the time‐axis chosen as the eigenvector of the bound state total momentum operator.
We have shown that this QCD Hamiltonian determined in infrared region by the rising potential ansatz, besides the parton model in the specific gauge, contains also the nonrelativistic potential model for heavy quarkonia, the chiral Lagrangians for light quarkonia with their spectrum, the glueball physics, and the small effective coupling constant in the whole region of transversal momenta.
NMR spectroscopy at ultra-high magnetic fields requires improved radiofrequency (rf) pulses to cover the increased spectral bandwidth. Optimized 90° pulse pairs were introduced as Ramsey-type cooperative (Ram-COOP) pulses for biomolecular NMR applications. The Ram-COOP element provides broadband excitation with enhanced sensitivity and reduced artifacts even at magnetic fields >1.0 GHz H Larmor frequency (23 T). A pair of 30 μs Ram-COOP pulses achieves an excitation bandwidth of 100 kHz with a maximum rf field of 20 kHz, more than three-fold improved compared to excitation by rectangular pulses. Ram-COOP pulses exhibit little offset-dependent phase errors and are robust to rf inhomogeneity. The performance of the Ram-COOP element is experimentally confirmed with heteronuclear multidimensional NMR experiments, applied to proteins and nucleic acids. Ram-COOP provides broadband excitation at low rf field strength suitable for application at current magnetic fields and beyond 23 T.
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