Quadrupole-inner electrical field

The electron density centered at M is the only central contributor at the nuclear position M, as in this case the nucleus coincides with the field point P, which is excluded from the integrals. For transition metal atoms, the central contributions are the largest contributors to the properties at the nuclear position, which can be compared directly with results from other experimental methods. The electric field gradient at the nucleus, for instance, can be measured very accurately for certain nuclei with nuclear quadrupole resonance and/or Mdssbauer spectroscopic methods, while the electrostatic potential at the nucleus is related to the inner-shell ionization energies of atoms, which are accessible by photoelectron and X-ray spectroscopic methods. 

If the nucleus feels both a magnetic field and an electric field gradient, and the electric quadrupole interaction is small, then the excited levels shift as indicated in Fig. 10.20e. The result is that only the inner four lines of the sextet are equidistant. This type of spectrum is measured from bulk Fe2C>3, with a magnetic hyperfine field of 51.5 T and a small quadrupole shift on the absorption peaks of 0.10 mm/s. 

The 3D quadrupole ion trap suffers from a severe limitation. If the number of trapped ions is too high, the electrical field due to the Vcos iot potential is overlapped by that due to the ion cloud. The result is a drop in instrumental performances, particularly in mass resolution and linear response. To avoid this undesired phenomenon, a preliminary scan (not seen by the ion trap user) is performed and the ionization time (or the ion injection time) is optimized, thus confining the optimum number of ions inside the trap (see Fig. 2.18). This prescan leads to a well-controlled instrumental setup but, of course, it limits the sensitivity of the instrument. To overcome this problem, two different approaches can be employed (1) increase the ion storage capacity of the trap by increasing the electric field strength (2) increase the inner volume of the trap, so as to obtain a less dense ion cloud, which results in a decrease of space charge effects. 

Energy shift and magnetic splitting of the / = 1/2 and / = 3/2 levels in the presence of an electric field gradient with rj = 0, and the corresponding Mossbauer spectrum (14 > 0). Note that due to quadrupole interaction, the symmetry center of the outmost peaks is shifted relative to the inner four peaks in contrast to Fig. 25.10... 

The nuclear electric quadrupole moment may also interact with the electric field gradient arising from the non-spherical distribution of the 4f electrons when the lanthanide ion is situated in a solid. The general form of the quadrupole interaction has been given in section 1.3.2. The principal value of the field gradient tensor, due to the 4f electrons is given by (18.73) in section 2.1.1.2, and as indicated there in (18.72) should be multiplied by the Sternheimer shielding factor (I-Rq) to take account of the distortion of the inner closed shells of the lanthanide ion by the open 4f shell. Other contributions to the total... 

The electric quadrupole field is formed by applying a voltage U between a ring electrode with hyperbolic surface as one pole and two hyperbolic caps as the other pole (Fig.13.13). The whole system has axial symmetry with respect to the z axis. In a geometrical arrangement where the inner ring radius rg is related to the cap separation 2Zg by rg = /2 Zg the electric potential 0 for points within the trap can be written as [13.20]... 

Perhaps the most serious limitation on both these approximate calculations is that the influence of both outer bound and coordinated charges must be scaled by a factor 7oo iu order to allow for the amplifying effect of inner electron motions on the externally applied field gradient. is called the Sternheimer antishielding factor, and lies typically between two and ten. Yet a further efg arises from the polarization of the inner orbitals by the electric quadrupole of I itself, but this term may readily be allowed for in any calculation. 

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