Showing papers on "Spin-½ published in 1974"

New extended model of hadrons

Abstract: We propose that a strongly interacting particle is a finite region of space to which fields are confined. The confinement is accomplished in a Lorentz-invariant way by endowing the finite region with a constant energy per unit volume, $B$. We call this finite region a "bag." The contained fields may be either fermions or bosons and may have any spin; they may or may not be coupled to one another. Equations of motion and boundary conditions are obtained from a variational principle. The confining region has no dynamical freedom but constrains the fields inside: There are no excitations of the coordinates determining the confining region. The model possesses many desirable features of hadron dynamics: (i) a parton interpretation and presumably Bjorken scaling; the confined fields are free or weakly interacting except close to the boundary; (ii) infinitely rising Regge trajectories as a consequence of the bag's finite extent; (iii) the Hagedorn degeneracy or limiting temperature; (iv) all physical hadrons are singlets under hadronic gauge symmetries. For example, in a theory of fractionally charged, "colored" quarks interacting with colored, massless gauge vector gluons, if both quark and gluon fields are confined to the bag, only color-singlet solutions exist. In addition to establishing these general properties, we present complete classical and quantum solutions for free scalars and also for free fermions inside a bag of one space and one time dimension. Both systems have linear mass-squared spectra. We demonstrate Poincar\'e invariance at the classical level in any dimension and at the quantum level for the above-mentioned explicit solutions in two dimensions. We discuss the behavior of specific solutions in one and three space dimensions. We also discuss in detail the problem of fermion boundary conditions, which follow only indirectly from the variational principle.

Spin echo of spins diffusing in a bounded medium

Abstract: The effect of reflecting boundaries on the spin echo measurement of diffusion in a geometrically bounded medium is calculated by considering the accumulation of phase shifts during the spin echo process. The distribution of phase shifts is shown to be Gaussian in the limits when the time between pulses is either long or short compared to the time required for a spin to diffuse from one boundary to another. The distribution is assumed to be Gaussian in the intermediate case, and the problem is reduced to the calculation of the mean square phase change due to diffusion. Expressions for spin echo amplitudes are derived for the cases of planar, spherical, and cylindrical boundaries, and forms are derived that are valid when the time of the measurement is very long or very short compared with the time required for diffusion between boundaries.

Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles

Abstract: Thermal Radiation and Planck's Postulate. Photons--Particlelike Properties of Radiation. De Broglie's Postulate--Wavelike Properties of Particles. Bohr's Model of the Atom. Schroedinger's Theory of Quantum Mechanics. Solutions of Time-Independent Schroedinger Equations. One-Electron Atoms. Magnetic Dipole Moments, Spin, and Transition Rates. Multielectron Atoms--Ground States and X-Ray Excitations. Multielectron Atoms--Optical Excitations. Quantum Statistics. Molecules. Solids--Conductors and Semiconductors. Solids--Superconductors and Magnetic Properties. Nuclear Models. Nuclear Decay and Nuclear Reactions. Introduction to Elementary Particles. More Elementary Particles. Appendixes.

Quantum theory of one- and two-dimensional ferro- and antiferromagnets with an easy magnetization plane . I. ideal 1-d or 2-d lattices without in-plane anisotropy

Abstract: A « semi-polar » representation of the spin operators is introduced, which makes possible, in the harmonic approximation, the definition of magnons for any wavelength at low temperature in one-dimensional (= 1-D) or two-dimensional (= 2-D) magnetic systems without long-range order, provided they are of the « planar » type, i. e. they have an easy magnetization plane. The semi-polar representation is used to calculate the spin pair correlation function at low temperature. Its space-time Fourier transform (directly observable by neutron scattering) consists of a relatively broad peak due to spin fluctuations inside the easy plane, plus a narrower peak due to out-of-plane fluctuations. The intensity, width and lineshape of both peaks are calculated in both 1-D and 2-D cases for all momentum transfers, as well as the frequency shift as a function of temperature.

Ising model for tricritical points in ternary mixtures

Abstract: An Ising model with spin $S=1$ at each lattice point which exhibits multiple tricritical points is presented. This is a generalization of the Blume-Emery-Griffiths model which was used for describing the tricritical point in ${\mathrm{He}}^{3}$-${\mathrm{He}}^{4}$ mixtures. The model is solved in the molecular-field approximation. It is found that its thermodynamic behavior near the tricritical point is in qualitative agreement with the thermodynamic behavior of ternary fluids near their tricritical points.

Intelligent spin states

Abstract: The intelligent spin states are defined as those states which satisfy the Heisenberg equality for the spin operators: Delta Jx2 Delta Jy2= mod (Jz) mod 2. The 2j+1 states which behave intelligently in each angular momentum space of spin j are found explicitly. For this purpose the Radcliffe states are used, it is shown that only the real and the pure imaginary Radcliffe states are intelligent. These intelligent states also satisfy the quartic consistency condition. The result, however, does not disagree in principle with the recent claim of Kolodziejczyk and Ryter (1974) that mod mu )= mod 0) is the only state which minimizes the uncertainty product because minimum uncertainty does not necessarily imply intelligence.

The Bloch equations

Abstract: We consider a spinor interacting with a heat bath of harmonic oscillators in equilibrium and we prove that the phenomenological Bloch equations for time development are satisfied exactly if the spin is 1/2 and to first order in the inverse temperature if the spin exceeds 1/2.

On the longitudinal static and dynamic susceptibility of spin-1/2 Kondo systems

Abstract: The impurity spin polarization, static susceptibility, and longitudinal impurity spin relaxation rate are calculated for thes-d model as function of temperature and magnetic field for ferromagnetic and antiferromagnetic exchange coupling. The thermodynamic functions and the dynamical susceptibility are obtained from the impurity relaxation spectrum, which is approximated by taking into account the infrared-like singularities. For antiferromagnetic coupling the zero-field susceptibility obeys a Curie-Weiss law1/χ∼4.6(T+θ) for high and intermediate temperatures and it approaches the finite value1/χ∼3.8θ for zero temperature. The zero-field relaxation rate is much larger than the Korringa value; it decreases with temperature and approaches the nonzero value1/T1∼1.2θ for zero temperature. The relaxation rate decreases with increasing field. The results for the spin polarization agree well with the experimental data for the Cu:Fe alloy.

Evidence for asymmetric shapes from high-spin odd-A spectra

Abstract: The model of a single-$j$ nucleon coupled to an asymmetric rotor is applied to new experimental results on yrast bands in $^{187}\mathrm{Ir}$, $^{195}\mathrm{Au}$, and $^{197}\mathrm{Tl}$. The core asymmetry is shown to account for systematic trends in the high-spin spectra. Information on the shape dependence of moments of inertia is obtained which supports the idea of nuclear flow of irrotational type.

Computer studies of spin and energy transport in one-dimensional Heisenberg magnets

Abstract: We have studied the dynamics of the classical Heisenberg chain at finite and infinite temperatures by computer simulation of an array of 4000 spins. The evaluation of the spin-spin and energy-energy wave-vector- and time-dependent correlation functions out to time $10{J}^{\ensuremath{-}1}$ made it possible to determine the spin and energy diffusion constants. At infinite temperature we find ${D}_{S}=(1.33\ifmmode\pm\else\textpm\fi{}0.10)JS{a}^{2}$ and ${D}_{E}=(3\ifmmode\pm\else\textpm\fi{}1)JS{a}^{2}$. Values of ${D}_{S}$ have also been determined, with less precision, for ferromagnetic and antiferromagnetic interactions at temperatures $\frac{{k}_{B}T}{|J|}=1.0 \mathrm{and} 0.5$. Our results are compared with various theoretical estimates. In addition, we calculate the time-dependent spin and energy self-correlation functions.

Spectral properties of one-body relativistic spin-zero hamiltonians

Abstract: 2014 We study the spectral properties of the relativistic spinzero Hamiltonian H = p2 + ,u2 + V of a spinless particle, by an extension of the method of Aguilar-Combes, for a class of interactions including V =-~~0~ 1. Absence of singular-continuous spectrum is proved, together with the existence of an absolutely-continuous spectrum [,u, oo). In RB{ /1 } the point spectrum consists of finite-dimensional eigenvalues which are bounded. Properties of resonances are investigated. RESUME. 2014 Nous etudions les proprietes de l’Hamiltonien relativiste de spin zero : H = p2 + ~c2 + V d’une particule sans spin, grace a une extension de la methode d’Aguilar-Combes, pour la classe d’interactions comprenant : V = 0 ~3 1. L’absence de spectre singulierement continu est prouvee, en meme temps que 1’existence d’un spectre absolument continu [/1, oo). Dans RB { /1 } Ie spectre ponctuel est formee de valeurs propres de dimension finie qui sont bornees. Les proprietes des resonances sont analysees. e) Work supported by : A. G. C. D. (Belgium). (2) On leave of absence from Universidad de Buenos Aires (Argentina). e) Postal address: Instituut voor Theoretische en Wiskundige Natuurkunde Celestijnenlaan 200 D, B-3030, Heverlee (Belgium). Annales de l’Institut Henri Poincaré Section A Vol. XX, n° 2 1974

The pseudo-spin model and its application to KDP-type materials

Abstract: The applicability of the pseudo-spin model is discussed in relation to the existence of constituents with a restricted number of low-lying energy states. The situation certainly occurs in materials with low-lying electronic levels which undergo co-operative Jahn-Teller phase transitions. The Slater-Takagi model of KDP is analysed to show that under certain approximations it leads to a double well in the collective co-ordinates with two levels in each unit cell and hence to a pseudo-spin model of one S = 1/2 per cell. The spin hamiltonian is the Ising model in a transverse field together with four spin interactions. The thermodynamic properties of this model are discussed and best values of the parameters obtained. The elastic constant anomalies are interpreted in terms of cs', in the adiabatic regime. The spin dynamics is discussed in terms of random phase approximation for spin waves, and more complete treatments are reviewed. Raman scattering data is analysed in terms of a coupled spin-phonon m...

Relation among spin operators and magnons

Abstract: We present an exact expression of spin operators in terms of magnons and quasielectrons in ferromagnetism. Its relation to the Holstein-Primakoff expression is discussed. The result shows that the spin rotation of electrons is induced by a transformation of magnons and quasielectrons which is different from rotation.

Experimental study of high-temperature spin dynamics in one-dimensional Heisenberg paramagnets

Abstract: From room-temperature measurements of proton spin-lattice relaxation rate in (${\mathrm{C}{\mathrm{H}}_{3})}_{4}$NMn${\mathrm{Cl}}_{3}$ (TMMC) and CsMn${\mathrm{Cl}}_{3}$ \ifmmode\cdot\else\textperiodcentered\fi{} 2${\mathrm{H}}_{2}$O (CMC) as a function of magnetic field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ the shape of the low-frequency spectral density of the spin fluctuations is directly obtained. For $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ parallel to the chain axis the spectral density contains a diffusive term which diverges as ${\ensuremath{\omega}}^{\ensuremath{-}\frac{1}{2}}$. The experimental results for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}\ensuremath{\parallel}\stackrel{\ensuremath{\rightarrow}}{\mathrm{c}}$ are in good agreement with a theoretical calculation in TMMC in which the two-spin correlation function is assumed to decay at long times as ${t}^{\ensuremath{-}\frac{1}{2}}$. The lack of frequency dependence of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$ perpendicular to the chain axis indicates a difference in the "cutoff" time of the two-spin correlation function for the spin components parallel and perpendicular with respect to the external magnetic field.

Interaction of spin fluctuations in ferromagnetic and nearly ferromagnetic itinerant systems

Abstract: The effect of spin fluctuations on the magnetic susceptibility of itinerant ferromagnets is investigated following the idea of mode-mode coupling proposed by Murata and Doniach (see Phys. Res. Lett., vol.29, 285 (1972)). A quantum mechanical treatment of this effect is shown to lead to a result similar to that of a theory of spin fluctuations by Moriya and the author (see abstrs. A27353 and A68756 of 1973) in which they explained the Curie-Weiss law of some itinerant ferromagnets. The nearly ferromagnetic case is also investigated and an error in the result of Beal-Monod et al (see abstr. A28337 of 1968) for the susceptibility is corrected.

Contribution of giant spin clusters to the resistivity, neutron-scattering cross section, and specific heat in alloys: Application to Ni-Cu

Abstract: A simple model for a nondilute alloy containing giant spin clusters is used to calculate the spin contribution to the resistivity, the neutron cross section, and the specific heat ${C}_{V}$. The model is expected to be applicable to Ni-Cu alloys near the critical concentration for ferromagnetism. Intracluster interactions are treated exactly using a near-neighbor Heisenberg exchange interaction. Intercluster interactions are treated within the molecular-field approximation. It is assumed that in paramagnets there is a weak local field, which derives from the magnetic-anisotropy energy. Reasonable semiquantitative agreement with resistivity, elastic neutron scattering, and low-temperature specific-heat measurements on Ni-Cu for a range of concentrations and temperatures is obtained if the average cluster contains 50 Ni spins and if a Ni atom has a spin when eight or more of its near neighbors are also Ni. It is found that the anomalous temperature dependence of the resistivity, which behavior is common to a variety of alloy systems, can be accounted for using the present theory if the Fermi wave vector times the lattice spacing is less than \ensuremath{\cong}2. The previously unexplained behavior of the elastic neutron cross section in paramagnetic alloys can also be understood within this theoretical framework. In contrast to earlier discussions, it is shown that the spin contribution to ${C}_{V}$ is not temperature independent; in ferromagnetic alloys this contribution is found to increase with increasing temperature and in paramagnetic alloys it decreases with temperature. It is believed that this temperature dependence has, in the past, been incorrectly attributed to the electronic contribution to the specific heat. The validity of previous suggestions that the specific-heat and neutron-scattering measurements on these alloys probe different spin clusters is also questioned.

Magnetoelasticity in Sm Fe 2

Abstract: The temperature and magnetic field dependence of the elastic moduli of Sm${\mathrm{Fe}}_{2}$ Laves phase compound has been investigated by means of an ultrasonic-pulse technique at a frequency of 10 MHz. The spin reorientation from the high-temperature easy direction of magnetization [111] to the low-temperature easy axis directed along [110], was observed to occur at ${T}_{sr}=195$ \ifmmode^\circ\else\textdegree\fi{}K. The behavior of the elastic moduli near ${T}_{sr}$ suggests a first-order phase change. Applied magnetic fields strongly affect the temperature dependence and the absolute values of the elastic moduli of Sm${\mathrm{Fe}}_{2}$. The elastic moduli increase significantly with increased magnetic fields, yielding a low and temperature-independent adiabatic compressibility. A remarkably high (42%) $\ensuremath{\Delta}E$ effect was observed in Sm${\mathrm{Fe}}_{2}$ at room temperature, 10-MHz ultrasonic frequency, and an applied magnetic field of 25 kOe. The magnetostriction of Sm${\mathrm{Fe}}_{2}$ is high and negative. For a field of 25 kOe at room temperature and 77 \ifmmode^\circ\else\textdegree\fi{}K values are -2100 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$ and -3340 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$, respectively. The limiting value of the Debye temperatures were found to be 200 and 212 \ifmmode^\circ\else\textdegree\fi{}K, for the unmagnetized and at 25 kOe, respectively.