Measurement Of Quadrupole Moment Research Articles

Electronic quadrupole moments of excited states and the charge wavefunction of the many-electron theory

It is shown that the electronic quadrupole moment as a measure of the charge distribution in non-closed shell systems is given not by the Hartree-Fock wavefunction, ΦRHF, but by the “charge distribution wavefunction” (the “charge wavefunction”) of NCMET, ϑc. The electronic quadrupole moments, Θ, of Be 1 1s22s2p3p0, B I 1s22s22p 2p0, B I 1s22s2p24P, B I 1s22s2p22D, and CI 1s22p32D0 are calculated by the full charge wavefunctions of NCMET and the Hartree-Fock wavefunctions. In C II, RHF gives Θ = 0.0 while the NCMET values are Θ = 0.07726 for J = 52 and Θ = 0.05408 for J = 32. Where several l ≠ 0 orbitals are involved in the excited state, the RHF results can differ sizably from the accurate NCMET charge wavefunction results. Recent beam measurements of electronic quadrupole moments are pertinent to these conclusions.

Harmonic Vibrations of Spherical Nuclei

The simplest type of vibration, that in which the nucleus makes surface oscillations about an equilibrium spherical shape, is reviewed in light of current nuclear literature. Such a model, based on purely harmonic vibrations, shares some success with other models in describing the origin of nuclear level schemes. However, a detailed examination of known nuclear spectra and recent measurements of quadrupole moments and transition probabilities suggest that this approach is only semivalid, emphasizing the need to include anharmonicity in the vibrational Hamiltonian.

Lattice dynamics of simple molecular crystals

Calculations of lattice properties of argon, krypton and nitrogen are reported. For the rare gas crystals the aim has been to use a procedure that could reasonably be extended to more complicated molecular crystals. A pair potential of the Kihara type is used with constants deduced from gas phase measurements. A range of thermodynamic properties is calculated and compared with experiment. For crystalline nitrogen a preliminary investigation shows that an atom-atom interaction may be made the basis of a suitable potential function. Results for two specific forms of this type are given: in one, atom-atom potentials of the Lennard-Jones form are used and in the second a simple point charge distribution consistent with the measured quadrupole moment is added. Comparison is made with experimental infra-red and Raman frequencies.

Measurement of ground state quadrupole moments using simultaneous coulomb excitation of target and projectile

The angular distribution of γ rays following simultaneous Coulomb excitation of target and projectile is shown to provide a new method of measuring ground state quadrupole moments.

The signs of E2, M1 transition matrix elements of the tungsten, osmium and platinum nuclei

We extend a previous calculation and give the signs of E2, M1 transition matrix elements, which are of interest in connection with the Coulomb excitation measurement of quadrupole moments, and B(E2) values, and the angular correlation measurement of E2/M1 mixing ratios.

The quadrupole moments of dipolar molecules

The electric quadrupole moment of a dipolar molecule depends upon the molecular origin from which it is measured. An electro-optical method has been successfully used for measuring the quadrupole moments of non-dipolar molecules, and the question arises: when the same method is applied to a dipolar substance what is the molecular origin to which the measured quadrupole moment should be referred? It is shown that this origin is not the centre of mass, but another point which may be called the ‘effective quadrupole centre’, the position of which depends in general on the wavelength of the light. Dipolar molecules experience a force in the field gradient and this enhances the contribution to the refractive index anisotropy from molecules which are out of line with the detector but in the light beam. This contribution is proportional to the dipole moment and is origin-dependent; it vanishes if the effective quadrupole centre is chosen as the origin. It is concluded that the electro-optical experiment should g...

A method of measuring electric quadrupole moments of molecules in excited states

A method is proposed for measuring electric quadrupole moments of atoms and molecules in excited states by observing electric field gradient induced birefringence (quadrupolar birefringence) in regions of absorption. The theory is based on the general treatment of quadrupolar birefringence of Buckingham and Longuet-Higgins [4]. For electric dipole allowed transitions the effect is proportional to the transition probability and to the difference between the quadrupole moment of the excited state and of the ground state. For electric quadrupole allowed transitions the effect is more complicated and involves the transition quadrupole. Using Coulomb approximation and SCF matrix elements, quantitative estimates of quadrupolar birefringence for 2 P ← 2 S and 2 D ← 2 S transitions in vapours of atomic lithium and sodium are obtained. The magnitude of the effect in these cases is such that a measurement of quadrupole moments of low-lying 2 P states in sodium and lithium is feasible.

Quantum mechanical effects in multiple coulomb excitation

The quantum-mechanical effects in multiple Coulomb excitation and their effects in quadrupole moment measurements are investigated analytically (for a simple one dimensional case) and numerically. It is found that their effect might be sometimes quite important although for the experimental conditions of the recent quadrupole moment measurements they are of the order of a few percents.

On the signs of nuclear quadrupole moments

We analyse the experimental data on the signs of all the measured quadrupole moments in the ground states of nuclei. We find positive quadrupole moments in virtually all the cases where the last major proton and neutron shells are both more than one-fifth full. For odd-mass nuclei the quadrupole moment is negative (positive) when the odd nucleons occupy 1 8 or less ( 7 8 or more) of the last major shell. The last observation is shown to be an extension of the known rules for the signs of the quadrupole moments of odd-mass nuclei with one particle outside (or missing from) a closed shell.

Microwave Collision Diameters II. Theory and Correlation with Molecular Quadrupole Moments

Observed microwave collision diameters are interpreted as arising exclusively from transitions induced during the collision. Collision diameters greater than kinetic theory values arise from dipole-dipole or dipole-quadrupole interactions. The former case affords a quantitative test of the theory. In the latter case measurements of collision diameters yield quadrupole moment measurements which are correlated with molecular structure.