References - Bogoliubov Laboratory of Theoretical Physics - JINR

3. Squeezing of quadrupole spectra.
The electric field gradients and isotopic composition have to identify any blood sample
for a noninvasive early cancer detection. In fact, at low temperatures any molecular
movements are stopped and the electrical interactions reveal themselves only over the
electric field gradients determined by the specific broadening of the spectral line shape.
Magnetic interactions and, as we have seen, the isotopic composition are also withdrawn
from the spectral analysis. In general they would have been understood as the complete set
of parameters for the blood control for the early cancer detection, if the signal amplitudes
did not reduce so much due to the quadrupole broadening of their spectra (see Fig. 1c).
This broadening comes from random angle (θ) orientations of the electric field gradients
relatively to the magnetic field direction. The eigen-states of 14 N spins in NH3 are [6]
En = −hνcmn + hνQ{3cos 2 (θ) − 1}{3(mn) 2 − I(I +1)} , (2)
where νc is the nitrogen Larmor frequency, eq is the quadrupole moment, νQ =(e 2 qQ/h)/8
and eQ is an electric field gradient value, mn=(+1, 0, -1) and mp=(+1/2,-1/2) are the
nitrogen and proton (see below) magnetic quantum numbers.
The problem can be solved if the wave function of free electrons couples the nuclear
spins situated nearby to F-centers with scalar Fermi interaction [7]. In this case the
removed and nearest spins have energies Ed and EF , correspondingly:
Ed = −hγp(H0 + Hloc)mp, EF = −hγpH0mp + hJ · mnmp . (3)
The first of Eq.(3) describes the energy of remote spins situated far away from F-centres.
Their Larmor frequency equals to ν0=γpH0 and it is shifted by local field (Hloc) of polarized
protons to ν+ or ν− depending on the sign of Hloc (see the left and middle-hand diagrams
in Fig. 2a). The second Eq.(3) approximately describes the energy of the nearest spins
(the right-hand diagram in Fig. 2a). These protons are coupled with 14 N spins by the
Fermi indirect interaction. J-constant of the Fermi interaction is determined by the
density of the electron wave function inside nuclei [8]. The total effect from heterogeneous
magnetization is demonstrated in Fig. 2b [5] which shows the proton NMR signals in
(a) (b) (c)
Figure 2a. (mp,mn)-sublevels in NH3: ν0-Larmor proton frequency, ν+, ν− are the same
frequency at opposite signs of polarizations, νJ+, νJ0 and νJ−-are J-coupling transitions.
Figure 2b. Proton NMR line shapes for different values of polarizations.
Figure 2c. Proton lines in NH3 centred at the tops. They are subdivided into the symmetrical
dipolar part and asymmetrical fractions owing to J-coupling between H3 and N spins.
403