Nuclear rotational

Nuclear Rotational Vibrational Valence Inner shell... 

Another interesting case of nuclear rotation occurs in the spherical nuclei. The observation of equally spaced 7-ray transitions implies collective rotation, but such bands have been observed in near spherical 199Pb. It has been suggested that these bands arise by a new type of nuclear rotation, called the shears mechanism. A few... 

We have used the Born Oppenheimer approximation to factor 4 0/3, I,ma into electronic and nuclear parts and have further assumed that the former are orthogonal to enable us to reduce V. Both wave functions may be approximated by products of electronic, nuclear rotation and vibrational wave functions. The last of these may be factored out at once, and... 

The above approach is, however, not applicable to the most frequent case, namely to that of non-excited molecules in the 1S state, in which both the electronic and spin magnetic moments axe absent. The reasons for the appearance of a non-zero magnetic moment of the rotating molecule, disregarded in (4.55)-(4.59) axe as follows. Firstly, it is the contribution of nuclear nuclear core of the linear molecule [80, 87, 294, 319, 321, 322, 395, 396]. For a diatomic molecule the contribution of nuclear rotation can be estimated from the simple expression ... 

Questions arise immediately concerning the coupling of L, S and the nuclear rotation, R The possible coupling cases, first outlined by Hund, are discussed in detail in chapter 6. Here we will adopt case (a), which is the one most commonly encountered in practice. The most important characteristic of case (a) is that A, the component of L along the intemuclear axis, is indeed defined and we can use the labels , Id, A, etc., as described above. The spin-orbit coupling can be represented in a simplified form by the Hamiltonian term... 

The first of these two terms describes the interaction of the magnetic moments due to electron spin and nuclear rotation and it is therefore called the spin-rotation interaction the second term is the corresponding spin-vibration interaction. Similarly we have,... 

The first term of (3.289) represents a translational Stark effect. A molecule with a permanent dipole moment experiences a moving magnetic field as an electric field and hence shows an interaction the term could equally well be interpreted as a Zeeman effect. The second term represents the nuclear rotation and vibration Zeeman interactions we shall deal with this more fully below. The fourth term gives the interaction of the field with the orbital motion of the electrons and its small polarisation correction. The other terms are probably not important but are retained to preserve the gauge invariance of the Hamiltonian. For an ionic species (q 0) we have the additional translational term... 

In Hund s case (d) the coupling between L and the nuclear rotation R is much stronger than that between L and the intemuclear axis. As shown in figure 6.16, the result of the coupling between L and R is N, which can be further coupled with S in suitable open... 

There is a further term which should be included in the effective Hamiltonian, derived in chapter 7, describing the electron spin-nuclear rotation interaction. This may be written in the form... 

The nuclear rotation function must now be antisymmetric and hence transposition of the nuclei must give rise to the following arrangement of the signs of fhe functions ... 

Raychev etal. [24] have shown that good fits can be obtained for nuclear rotational spectra of even-even rare earths as well as actinide elements by using Eq. (22). Furthermore, it has been shown [25]-[28] that Eq. (22) may also give a good description of such effects as backbending and staggering in rotational spectra of superdeformed nuclei and diatomic molecules as well. It can be seen that Eq. (21) fails in describing such spectra. 

It is empirically known that nuclear rotational spectra can be reproduced by using the following expansion for the rotational energy ... 

D.J. Thouless, Stability conditions and nuclear rotations in the Hartree-Fock theory, Nucl. Phys., 21 (1960) 225. 

Indeed, Dunham s energy-level formula [Eq. (2.1.1)] is based both on the concept of a potential energy curve, which rests on the separability of electronic and nuclear motions, and on the neglect of certain couplings between the angular momenta associated with nuclear rotation, electron spin, and electron orbital motion. The utility of the potential curve concept is related to the validity of the Born-Oppenheimer approximation, which is discussed in Section 3.1. 

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