New PDF release: A Primer of NMR Theory with Calculations in Mathematica

By Alan J. Benesi

ISBN-10: 1118588991

ISBN-13: 9781118588994

Provides the idea of NMR better with Mathematica© notebooks

  • Provides brief, centred chapters with short factors of well-defined issues with an emphasis on a mathematical description
  • Presents crucial effects from quantum mechanics concisely and for simple use in predicting and simulating the result of NMR experiments
  • Includes Mathematica notebooks that enforce the idea within the kind of textual content, pix, sound, and calculations
  • Based on category demonstrated tools built through the writer over his 25 12 months educating occupation. those notebooks exhibit precisely how the speculation works and supply priceless calculation templates for NMR researchers

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Extra resources for A Primer of NMR Theory with Calculations in Mathematica

Example text

Before the pulse, the net magnetization M is aligned along the z axis. During the on‐resonance pulse, the rf magnetic field B1 is aligned with the y axis of the rotating frame, and the net magnetization precesses (“nutates”) around the B1 field. After rotating π/2 radians, the net magnetization M ends up on the +x axis of the rotating frame, where it stays because the rf pulse is on resonance. With time, T2 relaxation causes decay of the magnetization along the +x axis (shown in gray), and T1 relaxation causes reestablishment of magnetization along the +z axis (shown in gray).

The net equilibrium magnetization is aligned with the magnetic field B and denoted by M0. The relaxation matrix is diagonal1 and has as components the transverse or spin–spin relaxation rate 1/T2 and the longitudinal or spin lattice relaxation rate 1/T1. The next cells define the Bloch equation. The rate of change of the magnetization vector dMdt is given by the Bloch equation. Note that the Bloch equation contains a cross product of M and B and the relaxation rate matrix. The resulting dMdt vector contains x, y, and z components, respectively.

2 shows the vector model for an on‐resonance single pulse experiment along the +y axis of the rotating frame. 1 except that the net magnetization after the (π/2)y rf pulse is on the +x axis of the rotating frame. 3 shows the vector model for an on‐resonance single pulse experiment of phase ϕ. 1 except that the net magnetization after the (π/2)ϕ rf pulse is at +ϕ radians relative to the –y axis. Do not confuse the magnetization vector (thicker arrow) with the B1 vector (thinner arrow) located at ϕ radians relative to the +x axis.

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A Primer of NMR Theory with Calculations in Mathematica by Alan J. Benesi


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