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A Symbolic Computation of Spin Echoes in Solid-State NMR

E. Jang
O. Han
Journal / Anthology

Journal of the Korean Physical Society
Year: 1997
Volume: 30
Issue: 1
Page range: 115-122

We have written a program in Mathematica, a programming language designed for symbolic computation, to calculate spin-echo positions and amplitudes as a function of the pulse flip angle (beta), the pulse phase angle (phi), and the pulse delay times (tau, tau_1, and tau_2) for the (pi/2) - tau - (beta)_phi and the (pi/2) - tau_1 - (beta_1)_phi1 - tau_2 - (beta_2)_phi2 pulse sequences. The spin Hamiltonian is described in a general form (H = A I_z + B (I_z)^2 + C (I_z)^3 + ...) which includes the Zeeman interation as well as the first- and second-order terms of the quadrupole interation. The spin can either be an integer (I = 1, 2, 3, ...) or a half-integer (I = 1/2, 3/2, 5/2, ...). Homonuclear and/or heteronuclear dipole interatcions can be included for certain cases, if desired. Non-ideal pulses also can be considered; the "forbidden echo" observation is explained as an example. Our program can be utilized to explore the primary spin interaction in samples, as well as for educational purposes.

*Science > Physics > Quantum Physics