The **NMR line intensity**, which depends on the various
interactions involved during the RF (無線電波) pulses,
is proportional to the amplitude of the first sampled
point of a free-induction decay (自由感應衰變)
or the integrated area of the corresponding spectrum (光譜).
In theoretical studies of **half-integer (半奇數)
quadrupole spins**, usually only the static first-order quadrupole
interaction is taken into account during the RF pulses. This interaction represents
the coupling of the nuclear electric quadrupole moment eQ with the
**electric-field gradient (EFG)** generated by the surroundings of a nucleus.

In the high magnetic field condition, the central line of a half-integer
quadrupole spin has a **featureless lineshape (線形)**.
As a result, lineshape analysis is not suitable
for determining the two quadrupole parameters: the quadrupole coupling constant
and the asymmetry parameter. The **first-order quadrupole interaction** and the
**quadrupole coupling** w_{Q} (or omegaQ)
are defined respectively by

The quadrupole coupling is defined experimentally by **half** the frequency
separating two consecutive lines of a single crystal
(單晶). It is half that used
by A. Abragam. The **quadrupole coupling constant**
is QCC = e^{2}qQ/h. In other words, the line intensity depends
on the ratio (比) of the QCC to the amplitude of the RF pulse (omegaRF) for
a powder, or the ratio of omegaQ to omegaRF pulse for a single crystal.
However, there is a lower limit to these ratios
above which the line intensity does not change any more. Conversely, fitting
a series of **nutation** NMR line intensities for an increasing pulse length
(脈衝長度) allows us to determine the quadrupole coupling.

The quadrupole coupling constant (QCC) increases from Fig. (a)
to Fig. (d). The spectrum width is shown below each spectrum. In Fig.
(a), **QCC = 1 kHz**, therefore all the single-quantum coherences
are observed as a single line located at the Larmor frequency.

As the QCC increases, the first-order quadrupole interaction becomes
observable as in Fig. (b) with a spin I = 5/2 system: the central line
(black line) remains at the Larmor frequency but the satellite lines
appear as a powder pattern (green part). From the latter, we can deduce
that the asymmetry parameter is equal to zero and **QCC = 300 kHz**.

When the QCC increases further, the satellite powder pattern spreads
over MHz rang and becomes unobservable. Only the central line is
detected as in Fig. (c) with **QCC = 1 MHz**. It is worth
noting that Figs. (a) and (c) have a featureless lineshape.

Finally, for a large QCC, even the central line is broadened but this
time by the second-order quadrupole interaction. Figure (d) is the
central line whose shape is well characterized with an asymmetry
parameter = 0.7 and **QCC = 18 MHz**.

In order to determine the quadrupole coupling constant from a featureless NMR lineshape (Figs. (a) and (c)), we apply the nutation NMR approach. The references containing data and graphs that can be simulated with the various Java applets of the site are classified according to the sequence.

The numerical values of the physical parameters in the applets are preset
for a spin I = 3/2 and **the central line located
at the Larmor frequency** is always selected. For testing an applet, simulated
"experimental" line intensities are provided in each applet. Therefore, you
only need to press the buttons in the following order:

- Pressing the RUN button calculates the theoretical line intensities.
- Pressing the FIT button changes it to the STOPFIT button and starts fitting the experimental line intensities by theoretical curve.
- Pressing the STOPFIT button changes it to the FIT button and stops the fit.
- Pressing the PREVIOUS button returns to the simulation panel.

From a practical point of view, you should introduce your experimental data and line intensities to use the fitting part of these applets. You can always use the simulation part of these applets to check the graphs that are in the papers provided in the reference part.