Asher Baram

Electronic and nuclear relaxation in solutions of transition metal ions with spin S=3/2 and 5/2

Electronic relaxation in solutions of solvated Fe3+, Mn2+ (S=5/2) and Cr3+ (S=3/2) is controlled by modulation of the quadratic zero field splitting interaction. The modulation is caused by collisions of the hydrated complex with bulk solvent molecules. Theoretical expressions are derived for the electronic transversal and longitudinal relaxation times T 2e and T 1e and are used to interpret the E.S.R. data of these ions. The analysis yields results for the zero field splitting constants and for the mean lifetime between collisions. The latter are found to be in the range 4–9 × 10-12 s. The nuclear relaxation rate of the solvent nuclei are affected by the dipole-dipole and scalar interaction with the unpaired electrons of the paramagnetic ions. The usual equations for nuclear relaxation due to these interactions are modified to take into account the existence of several T 1e s and T 2e s. These equations are used to analyse proton relaxation data in aqueous solutions of Cr3+, Fe3+ and Mn2+. The E.S.R. and...

Resonance line shapes for semi‐integer spins in liquids

An effective Liouville equation which describes resonance line shapes and is accurate to first order in the nonsecular term is derived. The equation has a quasisecular form but includes T1 contributions and the effect of the modulation of second order shifts by the molecular rotation. Simple explicit expressions for the linewidth and shift of the −1/2 → 1/2 transition are derived which are valid when the rotation is fast compared to the static second order shifts. The width has a maximum near the the T1 minimum and a minimum. The line shape for slow motion is also discussed and results of numerical calculation are presented. It is shown that the equations can be interpreted as a modulation of the second order shifts.

Third and fourth virial coefficients of hard hyperspheres of arbitrary dimensionality

We derive exact expressions for the third virial coefficient B3 and two of the three terms B4(⧠) and B4(⧅) contributing to the fourth virial coefficient B4 for an assembly of hard hyperspheres of arbitrary dimensionality d. A semiempirical formula, accurate for all d, is proposed for the remaining term B4(⊠). This formula is suggested by the large‐d asymptotic behavior of B3 and B4(⧠). We find that B4 is positive for d d4, with d4 estimated to be d4≈7.8, whereas B4(⧠)+B4(⧅) changes sign for d = 9.073

Correlated solid like jumps and resonance line shapes in liquids

The effect on resonance lineshapes of a combined rotational process consisting of solid like jumps in an ordered environment and diffusional rotation of the environment is discussed. A general density matrix formalism is developed utilizing group theoretical techniques in treating the symmetry of the environment and the hamiltonian. This analysis is more general than previous work on solids and yields some interesting new results. The problem of the effect of jumps on the powder spectrum of solids is also investigated and it is shown that in sufficient symmetric situations a narrow singular line should appear at the average frequency even for slow jumps rate. Numerical results for the specific case of an octahedral complex, undergoing random distortions along the three fourfold axes, are presented.

Powder magnetic resonance spectra in the presence of planar rotational jumps

The effect on magnetic resonance line shapes of powder due to inplane jumps and planar rotational diffusion is discussed. Two approaches are used to calculate the line shapes: (i) A group theoretical method developed previously is applied to describe the effect of discrete jumps about a principal axis of a nonaxial Hamiltonian. (ii) A formalism is developed which considers a continuous range of jump angles, distributed about a preferred angle. This formalism reduces to the discrete jump case or the planar diffusion case in the proper limits. Numerical results for some specific cases in which the jump process involves rotations by π/2 and π/3 are presented. It is shown that the discrete jumps lead in the intermediate rate region to the appearance of conspicuous features in the spectra typical of the jump process. When the jump angles are diffused these peaks broaden out and disappear completely in the rotational diffusion limit. Experimental results on the radical AsO4−4 in powder samples of KH2AsO4 which ...

Dynamic frequency shift in the E.S.R. spectra of transition metal ions

The factors which determine the electron spin resonance lineshapes and shifts of transition metal complexes in solution are discussed. It is shown that for ions with S > ½ the dynamic frequency shift may have pronounced effects on the E.S.R. lineshapes, and experimental evidence for this effect in complexes of Cr3+, Fe3+ and Gd3+ is presented. A quantitative interpretation of these spectra in terms of a relaxation mechanism due to fluctuation of the quadratic zero field splitting interaction is given.

Slow motion lineshapes

A slow motion expansion about the characteristic features of the powder spectrum is presented. Analytic expressions for the lineshape function, modulated by slow rotational diffusion, are derived. It is shown that the slow motion limit is characterized by harmonic oscillator equations of motion, and the resulting spectrum is determined by harmonic oscillator eigenvalues. The essential features of the lineshape show up naturally, and in particular the axial lineshape diverges like τ1/4 while there is only a weak motional correction to the logarithmic divergence of the non-axial lineshape. The dynamic frequency shifts converge to their static limits like τ-1/2 for all cases.

Analysis of the ordering transition of hard disks through the Mayer cluster expansion

The available virial coefficients for the two-dimensional hard-disks model are transformed into a matrix representation of the thermodynamic potentials, which allows for an accurate description of the whole fluid phase, up to the phase transition. We find that the fluid phase terminates at the transition point, implying a second-order phase transition in accordance with the Kosterlitz-Thouless-Halperin-Nelson-Young scenario of a transition into a hexatic phase. The density and pressure at the transition are calculated from the available first ten virial coefficients, and are found to be in excellent agreement with recent Monte-Carlo calculations. Finally, we calculate the equation of state in the critical region.

A Toeplitz representation for repulsive systems

A new method is presented for the calculation of thermodynamic properties of ensembles of particles interacting via repulsive forces. A tridiagonal matrix representation is constructed in terms of the cluster integrals. Its asymptotic form is utilised to obtain very good numerical estimates of the thermodynamic properties. Moreover, it is shown that the fluid branch may terminate at a critical activity zc, which is identical to the activity at the fluid-solid transition. A relation is found between zc and the radius of convergence of the activity series via the asymptotic matrix elements.

Universal strong coupling equation of state for inverse power potentials

A variational model is studied with the Percus–Yevick hard sphere g(r). Using the PY virial entropy, it predicts a universal expression for the potential energy in the strong coupling regime U/NKBT = amΓ+bnΓ1/4−0.5 for all inverse power potentials.