Interval rule

Land6 interval rule, 32 73 Langmuir-BIodgett films, biomineraiization, 36 195-197... 

Thus with this form for V the energies satisfy a Landd interval rule ... 

Thus the energy depends only on S and the relative energies still satisfy the Land interval rule given in Eq. (6). 

The other part of the hyperfme structure was suggested by Pauli [9] to be the result of the magnetic interaction between the nucleus and the electrons in the atom. If hfs is due to only a magnetic interaction, the difference between two neighbouring hyperfine levels follows an interval rule. However, accurate measurements of Eu, performed by Schuler and Schmidt [10], showed a deviation from this rule. Theoretical calculations performed by Casimir [11] showed that the experimental result was in agreement with an electric quadrupole interaction with the nucleus, thus establishing a quadrupole moment for Eu and 3Eu. 

Hi) The separation between adjacent J levels is XJf where Jj is the larger J quantum number. This is called the Lande interval rule. 

The biquadratic exchange coupling constants adopt rather small values the experimental data show that exchange coupling constants obey j/J 0.05. The separation of the energy levels, however, alters significantly as the deviation from the Lande interval rule is dramatic for higher spin values [19]... 

Biquadratic exchange is a kind of isotropic interaction. It alters the Lande interval rule, which is reflected in the temperature dependence of the magnetic susceptibility. 

The Lande s interval rule underlies the definition of the spin-orbit operator Yvrhich first acts on atomic one-electron fimctions. Indeed, a single-electron spin-orbit interaction obeys this rule, which means that the Lande s average of a multiplet coincides with the non-split term [39]. For a given I symmetry, taking the non-split term as a reference, one defines a zero-diagonal operator in relation to the reference... 

Upon performing the summation we find that the reduced matrix element vanishes and there is no splitting by spin-orbit coupling within the term itself. This may seem to contradict the Lande interval rule which predicts a splitting into three levels with energies given by... 

The effect of spin-orbit coupling on Tg is to split it into three levels as if we were dealing with an atomic P term. In the latter case there are three values of J, namely, 3, 2 and 1 and the levels have degeneracies of 7, 5 and 3 respectively. The energies follow the Land6 interval rule. Precisely the same thing occurs with T2. Griffith (21) computes n for this level structure ... 

An exact estimate of the error is difficult to obtain because we cannot use the simplifications that a Lande interval rule would give. Notice, for example, that the ordering of the levels in Po comes in the order J — 2,0,1 instead of the order 2,1,0 given by the Lande rule. In this chapter we will in partieular be interested in the SOC for Pb. We can here expect the error in the computed stabihzation to be of the same order as the error in the computed SO splitting, about 0.10 eV. 

Lande interval rule A rule in atomic spectra stating that it the spin-orbit coupling is weak in a given multiplet, the energy differences between two successive /levels (where /is the total resultant angular momentum of the coupled electrons) are proportional to the larger of the two values of/. The rule was stated bythe German-born US physicist Alfred Lande (1888-1975) in 1923. 

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