Showing papers on "Spin-½ published in 1969"

Review of Recent Work on the Magnetic and Spectroscopic Properties of the Rare‐Earth Orthoferrites

Abstract: The rare‐earth orthoferrites are a family of canted antiferromagnets which show an unusual variety of magnetic properties. This article begins with a brief review of the ``allowed'' spin configurations compatible with the crystallographic symmetry of the orthoferrite structure and a summary of the experimentally observed spin configurations, spin reorientation temperatures, compensation temperatures, etc. We then review recent research on these materials, grouping most of the recent work into four major categories; studies of the spin reorientation transition, studies of the rare‐earth spin ordering, spectroscopic studies directed at determining magnetic interaction parameters, and studies of magnetic domains and domain walls. The spin reorientation process has been established to occur over a finite temperature range as a fourth‐order anisotropy, generally small, comes to dominate the orientational behavior in the temperature region where the usually domainant second‐order anisotropy passes through zero and changes sign. The spin reorientation has been monitored in a number of RE orthoferrites by several techniques; magnetic torque, microwave absorption, neutron diffraction, and optical spectroscopy. A few of the rare‐earth orthoferrites show RE‐RE interaction strong enough to cause an ordering of the rare‐earth ions at temperatures on the order of 2°–6°K; this ordering process has been documented by all the above techniques plus Mossbauer‐effect and magnetic‐susceptibility measurements. Spectroscopic measurements, showing the increase in RE ground‐state exchange splittings for the configurations stable at the lower temperatures, give a qualitative understanding of the mechanisms causing the spin reorientation and spin ordering processes, and promise detailed quantiative understanding of the unique magnetic behaviors seen in the orthoferrites. The low moment and high anisotropy of the orthoferrites make possible the fabrication of thin plates magnetized normal to the plate. Such plates are semitransparent, and the Faraday rotation through them can be used to study domain structures or can be used as a readout mechanism for memory and logic devices utilizing single small stable domains as the active element. Recent studies of such domains and of domain wall energy and mobility in the orthoferrites are accordingly reviewed. Finally, several investigations are summarized which utilize the orthoferrites as a vehicle for examining general properties of magnetic systems, such as critical‐point phenomena.

Coupled Equations and the Minimum Principle for Collisions of an Atom and a Diatomic Molecule, Including Rearrangements

Abstract: The collision of an atom with a diatomic molecule is treated by a coupled‐channel expansion augmented by a finite number of square‐integrable basis functions. The method is, in principle, capable of essentially exact results if the total energy is less than that necessary for the existence of three free atoms and should be practical for light systems at low energies. The coupled equations which must be solved to apply the minimum principle are obtained and the direct and exchange interaction matrices are given in reduced form. The case that two, or all three, of the atoms are identical simplifies the equations, and the cross‐section formulas are given for arbitrary spin of the indentical nuclei.

Rigorous Results for Ising Ferromagnets of Arbitrary Spin

Abstract: The following results for spin‐½ Ising ferromagnets are extended to the case of arbitrary spin: (1) the theorem of Lee and Yang, that the zeros of the partition function lie on the unit circle in the complex fugacity plane; (2) inequalities of the form ≥ , where A and B are products of spin operators; (3) the existence of spontaneous magnetization on suitable lattices. Results (2) and (3) are also extended to the infinite‐spin limit in which the spin variable is continuous on the interval −1 ≤ x ≤ 1.

Magnetization Curve for the Half-Filled Hubbard Model

Abstract: The lowest energies of the one-dimensional half-filled Hubbard model as a function of the total spin are computed from the exact solution of one-dimensional interacting fermions. The lowest energies are used to calculate the magnetization curve at zero temperature. In the case of repulsive interaction our work is an extension of Griffiths' theory for the Heisenberg model to the itinerant electron model of antiferromagnet. In the case of attractive interaction it is shown that the magnetic susceptibility in zero field vanishes.

Spin change in collisions of hydrogen atoms.

Abstract: Cross section calculation for spin change in H atoms pair collision, discussing wave number and temperature effects

Shell-model combinatorial calculations of nuclear level densities.

Abstract: Spin-dependent nuclear level densities were calculated for selected nuclides. In each case the numbers and spins of the levels were determined from a computer-generated list of all contributing shell-model configurations. To calculate the energies of the configurations, we assumed the model nucleus to be an infinitely deep spherical well containing fermions that are noninteracting except for pairing forces, for which the BCS theory was used. Comparisons of the calculated results with experimental level densities for odd, even, and odd-mass nuclides show reasonable agreement for nuclides with $Ag50$. The results of calculative investigations of the effects of shell closings, pairing, etc., and the persistence of these effects to high excitation energies and angular momenta are reported and discussed. Comparisons of these results with those obtained from the most commonly used algebraic formula show significant disagreements in the curvature of the logarithmic energy dependence and in the spin distributions.

Polynomial behaviour of scattering amplitudes at fixed momentum transfer in theories with local observables

Abstract: It is shown that, in theories of exactly localized observables, of the type proposed byAraki andHaag, the reaction amplitude for two particles giving two particles is polynomially bounded ins for fixed momentum transfert<0. The proof does not need observables localized in space-time regions of arbitrarily small volume, but uses relativistic invariance in an essential way. It is given for the case of spinless neutral particles, but is easily extendable to all cases of charge and spin. The proof can also be generalized to the case of particles described by regularized products $$\int {\varphi (x_1 ,..., x_n ) \phi _1 } (x - x_1 ) ... \phi _n (x - x_n )dx_1 ...dx_n $$ ofWightman orJaffe fields.

Particles and Sources

Abstract: It is proposed that the phenomenological theory of particles be based on the source concept, which is abstracted from the physical possibility of creating or annihilating any particle in a suitable collision. The source representation displays both the momentum and the space-time characteristics of particle behavior. Topics discussed include: spin and statistics, charge and the Euclidean postulate, massless particles, and $S{U}_{3}$ and spin. It is emphasized that the source description is logically independent of hypotheses concerning the fundamental nature of particles.

On the Unrestricted Hartree–Fock Wavefunction

Abstract: The unrestricted Hartree–Fock (UHF) wavefunction is analyzed and interpreted in configuration‐interaction (CI) language. The results of the present study are as follows. (i) The UHF wavefunction includes only one type of the singly excited configurations [Eq. (20)], and thus the correlation effects included are very limited ones, compared with the usual CI treatment. (ii) The weight of the lowest contaminating spin function, included in the UHF wavefunction, decreases with increasing spin multiplicity. (iii) The annihilation of the lowest contaminating spin function little affects the electron density distributions and other physical quantities, the operators of which commute with the annihilation operator. (iv) In the UHF method, the “spin‐appearing” (spin‐polarization and spin‐delocalization) mechanisms are clearly divided, and an approximate method to separate these contributions is generalized, and some discussions about spin annihilation are made.

On the low--burnett--kroll theorem for soft-photon emission.

Abstract: SummaryBurnett and Kroll’s extension of Low’s theorem is proved for particles of arbitrary spin.RiassuntoSi prova l’estensione di Burnett e Kroll del teorema di Low per particelle di spin arbitrario.РезюмеДля частиц с произвольным спином доказывается расширение Бурнэ и Кролля для теоремы Лоу.

Low-Energy Theorem for Compton Scattering

Abstract: The low-energy theorem for Compton scattering on arbitrary spin targets is derived Knowledge of the Born term of the amplitude, which is calculated explicitly, enables us to prove Singh's lemma, which allows us to calculate the threshold value of the amplitude from the gauge condition Every multipole moment of the target is written down explicitly in terms of the low-energy limit of the amplitude Up to linear order in photon energy $\ensuremath{\omega}$, this theorem becomes a generalization to arbitrary spin of the theorem derived by Low and by Gell-Mann and Goldberger To describe the spin-nonflip amplitude up to order ${\ensuremath{\omega}}^{2}$, we need two structure-dependent parameters in addition to the charge and magnetic moment

Spin correlation in dilute magnetic alloys

Abstract: The correlation of a magnetic impurity spin with the spin density of the conduction electrons in a dilute magnetic alloy is calculated non-perturbationally on the basis of the Nagaoka theory It is shown that there are anomalies due to the Kondo effect in the long range behaviour of this correlation which contradicts the bound state interpretation of the Kondo effect The most interesting detail is the appearance of a non-oscillating contribution to the correlation

Combinatorial Approach to the N‐Representability of P‐Density Matrices

Abstract: This paper considers the determination of N‐representability (for diagonal elements) of p‐density matrices restricted to certain finite‐dimensional subspaces of l2 of the configuration space of N identical antisymmetric particles. In particular, an arbitrary set of N + p spin orbitals is selected and one considers the (N+pp)‐dimensional subspace generated by all possible Slater determinants of the spin orbitals being considered. Applying a combinatorial approach to the problem, a necessary and sufficient set of conditions is determined; previous work has dealt only with necessary conditions, except in the 1‐matrix case. The paper concludes by presenting a probabilistic interpretation of these conditions which seems of particular interest for the 2‐matrix case. The conditions presented here in combination with the Pauli principle give a probabilistic view of the expected occupation of p‐tuples of spin orbitals in terms of the expected occupations of lower‐order‐tuples of spin orbitals.