Nuclear magnetic substates

Until the discovery of the Mossbauer effect, the possibility of directly observing nuclear y-ray transitions between individual nuclear magnetic substates seemed remote because of the small energy differences involved however, the extremely high energy resolution of Mossbauer spectroscopy has made it possible to resolve these transitions directly in some isotopes, and it is this feature that is so valuable for investigating... 

The electric quadrupole interaction causes a splitting of the (27 +1) magnetic substates without shifting the mean energy of the nuclear spin manifold substates with the same absolute value of w/ remain degenerate for rj = 0. 

One example of this possible existence of a hierarchy of receptor states has been discussed by Frauenfelder (1988). He reviewed studies on the binding of substrates and ligands to myoglobin. The process follows a power law, characterizing the protein as a complex system. Nuclear magnetic resonance (NMR) analyses revealed a number of conformational substates. 

The nuclear magnetic dipole moment can interact with a magnetic field, inducing a splitting of a nuclear state with spin quantum number I into 2/ + 1 equally spaced, nondegenerate substates. The energies of these substates are given by ... 

The perturbation of the four substates of the excited 7 = 3/2 manifold by induces a typical asymmetry of the resulting magnetically split Mossbauer spectrum as pictured at the bottom of Fig. 4.10 for positive the inner four lines, 2-5, are shifted to lower velocities, whereas the outer two lines, 1 and 6, are shifted to higher velocities by equal amounts. In first order, the line intensities are not affected. For negative the line asymmetry is just inverted, as the quadmpole shift of the nuclear 1/2 and 3/2 states is opposite. Thus, the sign and the size of the EFG component along the field can be easily derived from a magnetic Mossbauer spectrum with first-order quadrupole perturbation. 

Since the splitting of the spectral lines is directly proportional to the magnetic field experienced by the nucleus, Mossbauer spectroscopy provides a very effective means by which this field may be measured. The transition probabilities between the nuclear substates affect the intensities of the lines in the Mossbauer spectrum which can therefore give information on the relative orientation of the magnetic field at the nucleus and the direction of propagation of the gamma-ray beam. 

Magnetic dipole interaction Magnetic dipole moment ii 0 (I>0) H 0 Nuclear states I > split into 21 - - 1 substates I, mj > with mi = -b I, +1-1,. .., —I => Magnetic dipole splitting AEm... 

The total absorption intensity depends on the concentration of the Mossbauer atoms in the absorber and their recoil-free fraction. The recoil-free fraction depends on the binding forces of the Mossbauer atom in the lattice (see Ap.l). The number and position of the absorption lines are determined by electric and magnetic electronic effects, the hyperfine interactions, which shift and split the nuclear levels. The allowed transitions between ground and excited substates are determined by the multipolarity of the nuclear transition. The = transition of... 

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