Correspondence between spin-dynamic phases and pulse program phases of NMR spectrometers

Spin state selective experiments have become very useful tools in solution NMR spectroscopy, particularly in the context of TROSY line narrowing. However, the practical implementation of such pulse sequences is frequently complicated by unexpected instrument behavior. Furthermore, a literal theoretical analysis of sequences published with specific phase settings can fail to rationalize such experiments and can seemingly contradict experimental findings. In this communication, we develop a practical approach to this ostensible paradox. Spin-dynamic design, rationalization, and simulation of NMR pulse sequences, as well as their confident and reliable implementation across current spectrometer hardware platforms, require precise understanding of the underlying nutation axis conventions. While currently often approached empirically, we demonstrate with a simple but general pulse program how to uncover these correspondences a priori in the general case. From this, we deduce a correspondence table between the spin-dynamic phases used in NMR theory and simulation on the one hand and pulse program phases of current commercial spectrometers on the other. As a practical application of these results, we analyze implementations of the original (1)H-(15)N TROSY experiment and illustrate how steady-state magnetization can be predictably, rather than empirically, added to a desired component. We show why and under which circumstances a literal adoption of phases from published sequences can lead to incorrect results. We suggest that pulse sequences should be consistently given with spin-dynamically correct (physical) phases, rather than in spectrometer-specific (software) syntax.     

Internal electron-positron pair production from electric monopole transitions

The yield curve of the reaction⁵⁶Fe(p,γ)⁵⁷Co has been measured over the energy rangeE _p =1,300–1,900 keV and the decay of nine resonances has been investigated. For twelve of the resonances the strengths have been determined. The angular distributions of the gamma rays have been recorded for resonances atE _p =1,599, 1,623, 1,643 and 1,649 keV, giving spin-parity assignmentsJ ^π=3/2^? for all four resonances. The resonances atE _p =1,623, 1,643 and 1,649 keV have been identified as the split analogue resonances of the 367 (J ^π=3/2^?) states in⁵⁷Fe. TheM1 transition strengths to the corresponding antianalogue states have been measured and compared with theoretical predictions.     

On the verification of Clark's example of a euclidean but not norm-euclidean number field

In the preceding paper [2], D. Clark proved—modulo a finite amount of computation—that the ring of integersR of admits explicit euclidean algorithms, although it is not euclidean for the norm: In fact, every completely multiplicative function ϕ:R→R _>-0 which sends the prime elements above 23 to a value larger than 25 and which agrees with the absolute norm at all other primes defines a euclidean algorithm forR. The referee had felt that an independent verification of the computer-assisted proofs of Lemmas 1 and 2 of [2] was desirable, and that it should be carried out separately from the refereeing process in the light of the public, conforming to C. Lam's eloquent suggestions [3]. F. Lemmermeyer and the present author succeeded in confirming Clark's result (independently of each other). This note gives some details of the methods employed in the verifications.     

Exponential weak Bernoulli mixing for collet-eckmann maps

We prove exponential weak Bernoulli mixing for invariant measures of certain piecewise monotone interval maps studied in [BK] and [KN]. In particular we prove this for unimodal maps with negative Schwarzian derivative satisfying lim , wherec is the unique critical point ofT.     

A characterization ofL n(K) as a permutation group

In 1972 M. O'Nan proved thatL _n (q),h 3; can be characterized as a doubly-transitive groupG on a finite set , whereG _a has an Abelian normal subgroup acting not semi-regularly on -a. In the Main Theorem we show that a similar statement holds if is infinite. Our result implies O'Nan's theorem.This paper is part of the author's Ph.D. thesis written under supervision of Prof. F. G. Timmesfeld.     

The influence of rotational coupling on K-vacancy formation in U-Pb collisions

The beta endpoint energies of the alkaline fission products^88–94Rb and^139–144Cs have been measured with an intrinsic Ge-detector at the OSTIS fission product separator. The linearity and high resolution of the detector yields an accuracy of up to a few keV. Additional beta gamma coincidence spectra allow the deduction of Q_β-values.     

The impact parameter dependence of the Pb + Pb K − MO spectrum

Molecular orbital X-rays are emitted during ion-atom collisions. The theoretical treatment, numerical results for the Pb + Pb system and a comparison with background radiation like NNB, SEB and γ-decay of Coulomb excited nuclei are presented.     

Effective rotational correlation times of proteins from NMR relaxation interference

Knowledge of the effective rotational correlation times, tauc, for the modulation of anisotropic spin-spin interactions in macromolecules subject to Brownian motion in solution is of key interest for the practice of NMR spectroscopy in structural biology. The value of tauc enables an estimate of the NMR spin relaxation rates, and indicates possible aggregation of the macromolecular species. This paper reports a novel NMR pulse scheme, [15N,1H]-TRACT, which is based on transverse relaxation-optimized spectroscopy and permits to determine tauc for 15N-1H bonds without interference from dipole-dipole coupling of the amide proton with remote protons. [15N,1H]-TRACT is highly efficient since only a series of one-dimensional NMR spectra need to be recorded. Its use is suggested for a quick estimate of the rotational correlation time, to monitor sample quality and to determine optimal parameters for complex multidimensional NMR experiments. Practical applications are illustrated with the 110 kDa 7,8-dihydroneopterin aldolase from Staphylococcus aureus, the uniformly 15N-labeled Escherichia coli outer membrane protein X (OmpX) in 60 kDa mixed OmpX/DHPC micelles with approximately 90 molecules of unlabeled 1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC), and the 16 kDa pheromone-binding protein from Bombyx mori, which cover a wide range of correlation times.     

Existence and Nonlinear Stability of Stationary States of the Schrödinger–Poisson System

We consider the Schrödinger–Poisson system in the repulsive (plasma physics) Coulomb case. Given a stationary state from a certain class we prove its nonlinear stability, using an appropriately defined energy-Casimir functional as Lyapunov function. To obtain such states we start with a given Casimir functional and construct a new functional which is in some sense dual to the corresponding energy-Casimir functional. This dual functional has a unique maximizer which is a stationary state of the Schrödinger–Poisson system and lies in the stability class. The stationary states are parameterized by the equation of state, giving the occupation probabilities of the quantum states as a strictly decreasing function of their energy levels.