Magnetic field, effective

The electron wave function becomes localised in the top and bottom part of the cylindrical surface where the effective magnetic field perpendicular to the tube surface is the largest. Thus the boundary condition along the circumference direction becomes less important in high magnetic fields as has been discussed in Sec. 2. Consequently the distinction between metallic and semiconducting... 

The magnetic hyperfine splitting allows the determination of the effective magnetic field acting on the nucleus, which may be a superposition of an applied... 

HS-HS] pairs. The third component (relative intensity z=44.0%) with parameters <5Hs(bpym, S) and AEq(HS) (bpym, S) can be unambiguously assigned to the HS state in [HS-LS] pairs, because the measured effective magnetic field at the iron nuclei of 81 kOe clearly originates from a spin quintet ground state of iron(II) (S=2). As a result, the complete distinction of dinuclear units becomes possible. It follows from the area fractions of the subspectra intensities that at 4.2 K the sample (bpym, Se) contains 2z=88.0% [HS-LS],7=4.0% [HS-HS] and (x-z)=8.0% [LS-LS] pairs. 

For Figure 3.27, note that lines 1, 3, 4, and 6, obey the selection rule IAm/l = l for the allowed y transitions between the nuclear sublevels, whereas lines 2 and 5 obey the Am/=0 selection rule. For a isotropic (gx=gy=gz=g) sample in which the effective magnetic field is parallel to the observed y rays, the intensity of the Am/=0 lines vanishes so that only four lines are seen in the spectrum (Figure 3a of reference 34). The same lines that are missing in the isotropic case will be maximized when the effective magnetic field is perpendicular to the y rays (Figure 3b of reference 34). For a uniaxial case (gx=gy=0 and 5 0, Figure 3c of reference 34) or the extreme anisotropic case (gz gx,gy), the intensities of the absorption lines are independent of the... 

Nuclear resonance is influenced in characteristic ways by the environments of the observed nuclei. However, nuclei are always surrounded by electrons and other atoms. Thus, in diamagnetic molecules the effective magnetic field at the nucleus is always smaller than the applied field 5 , i.e. the nuclei are shielded. The effect, although small, is measurable. This observation is expressed by equation 1 ... 

The effective magnetic field f eff felt by the nucleus is related to the field B0 by equation (9.8) in which a is the shielding constant ... 

Using the effective magnetic field Bc[t for a nucleus with I — 1/2, Larmor s relation becomes ... 

We now combine B and Bint to obtain the effective magnetic field at the nucleus ... 

Following Ref. [11], we write for the staggered effective magnetic field created at the nickel chain by the staggered ordered erbium magnetic moments... 

If the 7ij are positive, the overturn of the j-fh sublattice decreases the effective magnetic field acting on the other sublattice sites. It explains the fact that the alternation of their orientation does not occur simultaneously, but step by step (gradually), following an increase of the external magnetic field. 

Nuclei that are identical with the chemical environment or chemical shift are named equivalent nuclei. On the other hand, those nuclei dissimilar with their environments or possessing different chemical shifts are termed nonequivalent. In fact, nuclei which are near to one another exercise an effect on each other s effective magnetic field this effect is called spin-spin coupling [77],... 

The spin of an electron gives rise to a magnetic moment which can interact with effective magnetic field set up by its orbital motion about the nucleus. 

Equation (3.159) describes the spin-orbit coupling, the two terms involving the nuclear and electronic potentials respectively. It is interesting to note that these terms arise from the interaction between the electron spin magnetic moment and the effective magnetic field created by the passage of the electron through the electric field created by the other particles. 

The direction of the induced magnetic moment opposes the direction of the applied field, giving rise to diamagnetism. Evidently also, the effective magnetic field at the nucleus will be reduced the nucleus is screened . In practice we must now calculate the probability distribution of all electrons ( ), giving a total moment,... 

In a molecule, the electron cloud around each nucleus acts like a loop of wire, rotating in response to the external field. This induced rotation is a circular current whose magnetic field opposes the external field. The result is that the magnetic field at the nucleus is weaker than the external field, and we say the nucleus is shielded. The effective magnetic field at the shielded proton is always weaker than the external field, so the applied field must be increased for resonance to occur at a given frequency (Figure 13-5). 

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