Moment nuclear electric dipole

We will return to the quadrupole interaction in following chapters, but we now re-examine the general expansion of the electrostatic interaction and, in particular, the possibility of other nuclear electrostatic multipole moments. Because our multipole expansion is performed in a coordinate system with origin at the centre of charge of the protons p in the nucleus, the nuclear electric dipole moment is zero. However, this result arises only from our choice of origin and we now show that there are much... 

The proof of the restriction on possible nuclear moments hinges on the assumption that nuclear forces conserve parity. This assumption was later questioned by Purcell and Ramsey [94], thus allowing the possibility of the existence of a nuclear electric dipole moment. 4-component relativistic calculations have played an active part in placing upper boundaries on the possible values of such a nuclear electric dipole [95]. 

Schiff, L.I., Measureability of nuclear electric dipole moments, Phys. Rev., 132, 2194, 1963 Eugene, D., Commins, J., David Jackson, David P. DeMUle, The electric dipole moment of the electron An intuitive explanation for the evasion of Schiff s theorem. Am. J. Phys., 75, 532, 2007. 

Integrals of the type E = p(x, X2,x )x dV in (8.2.4) are equal to zero because of the fact that according to their mathematical structure, they describe nuclear electric dipole moments though we already know that the nucleus cannnot have one. Therefore, eq. (8.2.4) reduces to two terms, the first and the third ... 

After discovery of the combined charge and space parity violation, or CP-violation, in iT°-meson decay [7], the search for the electric dipole moments (EDMs) of elementary particles has become one of the most fundamental problems in physics [6, 8, 9, 10, 1]. A permanent EDM is induced by the weak interaction that breaks both the space symmetry inversion and time-reversal invariance [11]. Considerable experimental effort has been invested in probing for atomic EDMs induced by EDMs of the proton, neutron and electron, and by P,T-odd interactions between them. The best available restriction for the electron EDM, de, was obtained in the atomic T1 experiment [12], which established an upper limit of de < 1.6 X 10 e-cm, where e is the charge of the electron. The benchmark upper limit on a nuclear EDM is obtained in atomic experiment on i99Hg [13], ]dHgl < 2.1 X 10 e-cm, from which the best restriction on the proton EDM, dp < 5.4 x 10 " e-cm, was also recently obtained by Dmitriev Sen kov [14] (the previous upper limit on the proton EDM was obtained in the TIE experiment, see below). 

The electric dipole moment operator for a molecule includes summation over both the electronic and nuclear charges ... 

If incident radiation with a frequency equal to one of the fundamental frequencies falls on a molecule, it may make a transition from the ground state to the appropriate fundamental level. These normal frequencies usually occur in the infra-red spectral region. The probability of such a transition occurring, however, depends on the relationship between the molecule s electric dipole moment (as a function of the nuclear coordinates) and the wavefunctions of the ground state and of the fundamental level. 

The motion of the electrons is treated in the adiabatic approximation. For absorption in the infrared, the electrons remain in the ground state. The electric dipole moment of the complex of two molecules is the expectation value of the dipole moment operator over the ground electronic state, which is a function of the nuclear coordinates only. Specifically, the dipole moment of a complex of n molecules is dependent on the vibrational (r,) and orientational ( ,) coordinates, and on the position (J ,-) of the mass centers of the molecules i, for 1 < i < n,... 

A discussion of nuclear electric quadrupole coupling in the vinyl halides has led to the estimate of about 6 percent double-bond character for the C—Cl bond in vinyl chioride and 3 percent for the C—I bond in vinyl iodide.87 Values of electric dipole moments of mono-halogenated benzenes have been interpreted as corresponding to 4 percent of double-bond character for the C—X bonds.68... 

To deduce whether a transition is allowed between two stationary states, we investigate the matrix element of the electric dipole-moment operator between those states (Section 3.2). We will use the Born-Oppenheimer approximation of writing the stationary-state molecular wave functions as products of electronic and nuclear wave functions ... 

The quantity in brackets is the permanent electric dipole moment d corresponding to the state i//d [see (1.289)] of course, since both ipei and the operator d depend on the nuclear configuration, the dipole-moment vector d depends on the nuclear configuration. Symmetry requires that d be oriented along the internuclear axis in Fig. 4.1 therefore,... 

There is another common cause of line splittings in microwave spectroscopy. Nuclei with spin I > 1 have an electric quadrupole moment. An electric quadrupole moment arises from a nonspherically symmetric charge distribution for example, a uniformly charged ellipsoid of revolution has no electric dipole moment, but does have an electric quadrupole moment. The nuclear electric quadrupole moment is16... 

The first term in the square bracket in this equation is the electric monopole moment, which is equal to the nuclear charge, Ze. The second term in the square bracket is the electric dipole moment while the third term in the square bracket is the electric quadmpole moment. For a quantum mechanical system in a well-defined quantum state, the charge density p is an even function, and because the dipole moment involves the product of an even and an odd function, the corresponding integral is identically zero. Therefore, there should be no electric dipole moment or any other odd electric moment for nuclei. For spherical nuclei, the charge density p does not depend on 0, and thus the quadmpole moment Q is given by... 

The energy of the emitted y ray is determined by the energy difference between the nuclear excited and ground states. This energy difference is not altered by the first term, eZU, since this term equally affects the nuclear excited and ground states in both the source and absorber. In addition, atomic nuclei do not possess electric dipole moments, and therefore the second term in Eq. (9) must be equal to zero. Thus, when considering the Mossbauer effect, Ee can be written in the form... 

The work which is reviewed here provides accurate structural data from micro-wave and radiofrequency spectroscopy of relatively small molecule, hydrogen bonded complexes. Its role has been to provide information concerning the stereochemistry and electronic properties — electric dipole moments and nuclear hyperfine interactions — characteristic of hydrogen bonds. The experiments are done on gas phase samples, often in molecular beams, which eliminates environmental perturbations of the hydrogen bonds. In addition, the small molecules used are amenable to ab initio calculations 7 9) and thus the results are extremely useful as criteria for the accuracy of these calculations. Finally, the results are useful to construct models of more complex systems in chemistry and biology involving hydrogen bonds 4). 

It is now possible to determine precise rotational spectra for hydrogen bonded molecules of moderate size and with even very small stabilization energies. Rotational constants, centrifugal distortion constants, electric dipole moments and nuclear hyperfine interactions have been measured for a considerable number of dimers using various microwave and molecular beam techniques. 

The apphed electric field interacts with the electric dipole moment of the molecule nuclear spin is not involved in the decoupled basis set, so that we need only the results of our earlier analysis, given in equation (8.278), i.e. 

The difference in electric dipole moment (0.007 72 D) between the proton and deuteron species is discussed by Muenter and Klemperer [87] and attributed to the difference in zero-point amplitude averaged over the same dipole moment function. If the difference is purely vibrational in origin, the dipole moment of the vibrationless molecule is calculated to be 1.7965 D, which compares with a theoretical value of 1.942 D obtained from Hartree Fock calculations by Huo [94], The nuclear spin-rotation constants of non-rigid diatomic molecules have been discussed theoretically by Hindermann and Cornwell [95]. 

Pauli spin vector Dirac spin vector electron spin magnetic moment nuclear spin magnetic moment rotational magnetic moment electric dipole moment Ioldy Wouthuysen operator gradient operator Laplacian... 

A molecule has a permanent electric dipole moment if, and only il, the centroids of nuclear and electronic charge do not coincide. II there is a (axis, the dipole must lie along this axis. If there is a plane of symmetry, the di M)lc must lie in that... 

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