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ZFprotonDipole.rst

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ZFprotonDipole

.. index:: ZFprotonDipole

Description

ZF PCR signal from interaction with a single dipole.

A(t)=\frac{A_0}{6}\left(1+e^{-\lambda t}\left(\cos(g_\mu B_\text{D} t)+ 2\cos(\frac{3}{2}g_\mu B_\text{D} t)+2\cos(\frac{1}{2}g_\mu B_\text{D} t)\right)\right)

B_\text{D}= \begin{cases} \frac{2\mu_p\mu_n}{r^3}, & r > 0 \\ 0 , & r = 0 \end{cases}

where,

A_0 is the amplitude,

\lambda (MHz) is the relaxation rate,

B_\text{D} (G) is the dipolar field,

r (Armstrong) is the radius,

\mu_p is the proton moment,

and \mu_n is the proton moment.

.. plot::

   from mantid.simpleapi import FunctionWrapper
   import matplotlib.pyplot as plt
   import numpy as np
   x = np.arange(0.1,16,0.1)
   y = FunctionWrapper("ZFprotonDipole")
   fig, ax=plt.subplots()
   ax.plot(x, y(x))
   ax.set_xlabel('t($\mu$s)')
   ax.set_ylabel('A(t)')


.. attributes::


.. properties::

References

[1] F.L. Pratt, Physica B 289-290, 710 (2000).

.. categories::


.. sourcelink::