On the anisotropic Heisenberg chain

High-temperature expansions are derived for the specific heat and the _χzz element of the susceptibility tensor for a linear chain of spins $\text{1}\text{2}$ with anisotropic nearest-neighbour interactions. (The coupling constants J₁, J₂ and J₃ are chosen to be different.) Use is made of exact results of the XY model, a first-order perturbation calculation in J₃, a high-temperature expansion for the transverse susceptibility _χxx of the anisotropic XY model and the high-temperature expansion for the isotropic Heisenberg chain. Some characteristic features of deviations from the case of axial symmetry in the coupling constants are discussed.     

The cooperative Jahn-Teller effect in uranium (4+) hydroxy-sulphate

The magnetic susceptibility measurements of orthorhombic U(OH)₂SO₄ within the temperature range 4.2–300 K have revealed a magnetic anomaly at T_D = 21 K associated with crystallographic transition induced by the cooperative Jahn-Teller effect. Above 21 K the magnetic susceptibility of the uranium (4+) ion corresponds to the electronic ground doublet ${}_{\mathrm{¡}}\text{M}{}_{\mathrm{J}}\text{= ± 2〉}$ confirming thus the antiprismatic symmetry (D_4d) of the crystal field at the uranium site. Below T_D the system of two singlets ($\text{1}\text{√2}$)|2〉 ± ($\text{1}\text{√2}$)|$\text{2}$〉 separated by δ(T) is the ground state of the uranium ion.     

A study of ππ → NN partial-wave amplitudes using hyperbolic dispersion relations

We investigate $\text{ππ →}\text{N}\text{N}$ partial-wave amplitudes, using a spin separation method based on hyperbolic dispersion relations. Partial-wave amplitudes with J ? 3 are dominant in the pseudophysical region between the ππ and $\text{N}\text{N}$ thresholds, but we find clear evidence for J = 4 and J = 5 contributions from regions near and above the $\text{N}\text{N}$ threshold. We isolate J = 2 and J = 3 partial waves and determine the couplings of f₀(1270) and g (1680). Knowing the high-spin contributions, we are able to eliminate thse and to study s- and p-waves. We find evidence for small p-wave contributions above the ?, having the same sign as the ? contributions. We develop methods for determining the I = J = 0 ππ scattering length a₀⁰ and find a₀⁰ = 0.30 ± 0.15.     

Etude des proprietes thermodynamiques d'un groupement tetranucleaire: Application au compose Na3RuO4

The exact eigenvalues spectrum of the spin hamiltonian $\text{H}\text{= ?2}\text{∑}\text{(i, j)}\text{J}{}_{\mathrm{ij}}\text{S}\text{?}{}_{\mathrm{i}}\text{S}\text{?}{}_{\mathrm{j}}$ have been calculated for a tetranuclear cluster formed by four spins 3/2 at the vertices of a lozenge. Two isotrope exchange interactions J₁ and J₂ are able to explain the thermodynamic properties (magnetic susceptibility, entropy, specific heat). A ground state transition from singlet to triplet state occurs when the $\text{J}{}_2\text{J}{}_1$ ratio reaches the value $\text{4}\text{3}$. The magnetic susceptibility data of Na₃RuO₄ fit well with the theoretical values proposed for $\text{J}{}_1\text{K}\text{= (?19,5 K)}$ and J₂/k (?22,5 K).     

A phenomenological investigation of ππ → KK partial-wave amplitudes from hyperbolic dispersion relations

We calculate the $\text{ππ →}\text{K}\text{K}$ partial-wave amplitude g_J^(+-), J = 0, 1, 2, 3, in the unphysical region below the $\text{K}\text{K}$ threshold using partial-wave relations derived from hyperbolic dispersion relations. For g₁^(?) the results are in agreement with earlier calculations and we confirm the current low-energy predictions. For g_o⁽⁺⁾ we favour a down-type solution with a large positive $\text{K}\text{K}\text{→}\text{K}\text{K}$ s-wave scattering length.     

Doppler-limited dye laser excitation spectroscopy of HCF

The cw dye laser excitation spectrum of the $\text{A}\text{?}{}^1\text{A″(000) ←}\text{X}\text{?}{}^1\text{A′(000)}$ vibronic band of HCF was observed between 17 188 and 17 391 cm^?1 with the Doppler-limited resolution, 0.04 cm^?1. The HCF molecule was produced by the reaction of discharged CF₄ with CH₃F, and 853 lines were observed, of which 516 transitions were assigned to K′_a ← K″_a = 3 ← 4, 2 ← 3, 1 ← 2, 0 ← 1, 1 ← 0, 2 ← 1, 0 ← 0, 1 ← 1, 2 ← 2, 3 ← 3, 2 ← 0, and 0 ← 2 subbands. A rotational analysis yielded the rotational constants and quartic and sextic centrifugal distortion constants for both the $\text{A}\text{?}$ and $\text{X}\text{?}$ states and the band origin, with good precision. The molecular constants determined reproduce the observed transition frequencies with an average deviation of 0.0038 cm^?1. Small rotational perturbations in the excited state were found at J = 5, 6 and J = 10, 11 of J_1,J and at J = 15, 16 of J_2,J?1 levels.     

Multi-step processes in the interpretation of the 28Si(d, 3He)27Al reaction

Results from a CCBA analysis of the ²⁸Si(d, ³He)²⁷Al reaction are reported. The transfers are assumed to occur between dominant components of (λμ) symmetry (0, 12) and (2, 10) in the initial and final nuclear eigenstates respectively. The results show that cross sections to four of the six levels observed below 3 MeV can be fairly well reproduced within a pure K_(J) band framework. However, consistent with electromagnetic results, all six levels can be fit if the K_(J) band purity of the analysis, SU(3) model. $\text{5}\text{2}{}^{\mathrm{+}}\text{(}\text{ground and}\text{2.73}\text{MeV}\text{)}$ states and $\text{9}\text{2}{}^{\mathrm{+}}\text{(3.00}\text{MeV}\text{)}$ state is abandoned.     

Foldy-Wouthuysen transformations for any spin

We give the generalized Foldy-Wouthuysen transformation for any 2(2J + 1)-component Poincaré-invariant Hamiltonian theory that describes free massive spin-J particles and that is subject to the conditions: (a) every observable $\text{O}$ is either Hermitian ($\text{O}$ = $\text{O}$⁺) or pseudo-Hermitian ($\text{O}$ = ?₃$\text{O}$⁺?₃) and (b) the theory is invariant under the discrete symmetries. The requirement that the Hamiltonian be defined in the rest frame specifies one and only one boost generator that is also defined at p = 0.     

Inelastic neutron scattering study of magnetic excitations in the helimagnetic and antiferromagnetic phases of NiBr2

The spin wave dispersion in NiBr₂ has been studied by medium and long wavelength inelastic neutron scattering in the [1 1 0], [1 0 0] and [0 0 1] directions at 4.2 and 30 K, i.e. in the incommensurate helical and collinear antiferromagnetic phases. The values of the intralayer Heisenberg exchange constant J_ij and XY anisotropy constant D at 4.2(30) K are J₀₁ 0.379(1)(0.379(1)), J₀₂ 0.0036(50)(0.0036(50)), J₀₃ - 0.105(5) (?0.105(5)), J′ - 0.0423(50)(?0.389(50))D 0.0364(50)(0.0290(50)), where J′; is the interlayer exchange constant. In fitting the 4.2 K data account is taken of the co-existence of three equivalent domains and of intensity arising from $\text{ω(}\text{q}\text{)}$ and $\text{ω(}\text{q ± k}{}_0\text{)}$ where $\text{k}{}_0$ is the wavevector of the helix. In the low frequency region of the dispersion curve such peaks are resolved. The results reinforce the hypothesis that in zero-field the commensurate-incommensurate phase transition is driven by fluctuations.     

Low temperature specific heats of nearly one-dimensional antiferromagnet: CuCl2·2NC5H5

Transition temperature to LRO state was found at T_N=1.14K for nearly one-dimensional antiferromagnet CuCl₂ · 2NC₅H₅. Intra- and inter-chain exchange constants J and J′ were estimated, $\text{kT}{}_{\mathrm{<mtext>N</mtext>}}\text{J}\text{=0.082}$ and $\text{J′}\text{J}\text{=3×10}{}^{\mathrm{?3}}$, respectively. Comparison with those of TMMC implies highly one-dimensional character.     

Neutron diffraction study of the layered compounds MnPSe3 and FePSe3

In the insulating compounds MnPSe₃ (1) and FePSe₃ (2) the divalent transition metal ions form planar honeycomb lattices. A neutron diffraction study revealed a collinear antiferromagnetic order below T_N = 74 ± 2 K (1) and T_N = 119 ± 1 K (2) with the corresponding wavevectors k = [000] (1) and $\text{k = [}\text{1}\text{2}\text{0}\text{1}\text{2}\text{]}$ (2). In MnPSe₃ the magnetic moments (m₀ = 4.74 μ_B) lie within the basal plane and in FePSe₃ (m₀ = 4.9 μ_B) they are pointing along the c-axis. The collinear structures are determined by the dominating intralayer interactions between first (J₁), second (J₂) and third neighbours (J₃) which in MnPSe₃ are all antiferromagnetic whereas in FePSe₃J₁ is ferromagnetic and J₂ and J₃ are antiferromagnetic.     

Behaviour at ok and at different magnetic fields of the double magnetic helix

We study the behaviour at 0K and at all magnetic field values up to the magnetic saturation of the magnetic helix in which two distinct magnetic ions of spin lengths S₁, and S₂ are acted on by two unequal molecular fields. Although limited to the case of zigzag and collinear chains on which only the magnetic interactions J between first nearest neighbours (n.n) and J₁, or J₁ between second n.n. are considered, complex phase diagrams are obtained. The most disclosing features show up by taking S₁, S₂, J₁,J₂ as parameters and h, J as variables. Whereas the biconical configuration appears as the most general solution, triangular and oblique configurations also exist in finite field in all (h, J) diagrams. In addition, a collinear ferrimagnetic configuration is found to be stable for definite h and J values. We finally observe that according to the ratio values S₁S₂ and $\text{(J}{}_2\text{J}{}_1\text{)}\text{1}\text{2}$, eight types of (h, J) diagrams exist which differ from each other by distinct approaches to the ferri- or ferromagnetic alignment.     

Quantum renormalizations in one dimensional easy plane ferromagnets

We examine the quantum corrections to the spin wave energies of easy plane ferromagnets. We utilize a formalism developed by Villain, and we obtain the quantum corrections of orders $\text{S(S + 1)}{}^{\mathrm{<mtext>-1</mtext><mtext>2</mtext>}}$. The experimentally determined spin wave spectra for CsNiF₃ is used to find the bare exchange J and anisotropy parameter D. We compare our values with those obtained from other theories, which order the corrections in powers of S^-1 and also neglect higher powers of D/J.     

Order-order transitions in spin systems with double electron exchange

Spin systems in the presence of isotropic single and double electron exchange are investigated at nonzero temperature. We use a generalized mean field approximation that allows for a variable local axis of quantization. This leads to the introduction of an angular parameter Θ giving the angle between nearest neighbor quantization axes. It is shown that order-order transitions can occur between phases of partially aligned spins (general Θ) and pure ferro- (Θ = 0) or antiferromagnetic (Θ = π) spin structures for physically reasonable values of the exchange ratio J₂/J₁ of double to single exchange when J₂ > 0. The order-order critical temperature τ₀ is determined as a function of J₂/J₁ for the particular cases of atomic spin $\text{s = 1,}\text{3}\text{2}\text{, 2,}\text{5}\text{2}$, and the corresponding phase diagrams are presented. Biquadratic and three-atom double electron exchange effects are considered separately. Expressions for the paramagnetic transition temperature and for the spontaneous magnetization M_s for general atomic spin s are given, and the discontinuous change in M_s at τ₀ is also found as a function of J₂/J₁.     

Far infrared laser magnetic resonance spectrum of CH

Laser magnetic resonance spectra between 0 and 17 kG have been recorded and analyzed for $\text{(J′ ← J″) = (}\text{7}\text{2}\text{←}\text{5}\text{2}\text{)}$, $\text{(}\text{5}\text{2}\text{←}\text{3}\text{2}\text{)}$, and $\text{(}\text{3}\text{2}\text{←}\text{1}\text{2}\text{)}$ transitions in the CH molecule, using the optically pumped far infrared lasers: 118.8 μm (CH₃OH), 180.7 μm (CD₃OH), 554.4 μm (CH₂CF₂), 561.3 μm (DCOOD), and 567.9 μm (CH₂CHCl). Other transitions in CH were detected with the ¹³CH₃OH laser at 115.8, 149.3, and 203.6 μm. The CH radical was generated in a low-pressure methane and atomic fluorine flame within the laser cavity. Analysis of the M′_J ← M″_J structure yields wavenumbers for the rotational transitions mentioned above of 84.3494, 55.3397, and 17.8376 cm^?1, respectively. Combining results from the M_J analysis with the $\text{J =}\text{1}\text{2}\text{Λ-}\text{doubling}$ interval derived from radioastronomy measurements yields Λ-doubling values for the $\text{J =}\text{3}\text{2}\text{,}\text{5}\text{2}$, and $\text{7}\text{2}$ states of 0.0237, 0.1620, and 0.3759 cm^?1, respectively. Both the rotational intervals and the Λ-doublings are in good agreement with earlier less precise optical results. Analysis of the hyperfine structure yields values for the Frosch and Foley hyperfine parameters of a = +52, b = ?74, c = +52, and d = +43.6 MHz, in good agreement with recent ab initio estimates and radioastronomy measurements.     

Hydrodynamics of an n-component phonon system

The dynamic properties of an n-component phonon system in d dimensions, which serves as a model for a structural phase transition of second order, are investigated. The symmetry group of the hamiltonian is the group of orthogonal transformations $\text{O}$(n). For n ≥ 2 a continuous symmetry is broken for T<T_c, where T_c is the transition temperature. We derive the hydrodynamic equations for the generators of this group, the $\text{1}\text{2}\text{n (n ? 1)}$ angular-momentum variables. Besides the usual hydrodynamics of a phonon system, there are $\text{1}\text{2}\text{n (n ? 1)}$ additional independent diffusive modes for T > T_c. In the ordered phase we find 2 (n ? 1) propagating modes with linear dispersion and quadratic damping. Formally the hydrodynamics is similar in the isotropic Heisenberg ferromagnet (n = 2) or the isotropic antiferromagnet (n ≥ 3). The relaxing modes for T < T_c require special care. We study the critical dynamics by means of the dynamical scaling hypothesis and by a mode-coupling calculation, both of which give the critical dynamical exponent $\text{z =}\text{1}\text{2}\text{d}$. The results are compared with the 1/n expansion. It is shown that for large n there is a non-asymptotic region characterized by an effective exponent $\text{z}\text{?}\text{= φ/2ν}$, where φ is the crossover exponent for a uniaxial perturbation, and ν the critical exponent of the correlation length.     

Higher-order l-doubling of linear molecules

The centrifugal correction q_t^JJ(J + 1) to the l-doubling constant q_t corresponds to a term of type $\text{H}\text{?}{}_{24}$ in the effective vibration-rotation Hamiltonian. A general sequential procedure for calculating $\text{H}\text{?}{}_{24}$ is presented, and applied to the particular case of the constant q_t^J of linear molecules, which depends on the cubic but not the quartic potential constants. Reasonable agreement is obtained with observed values of q₂^J of CO₂ and q₅^J of C₂H₂. The simple high-J behavior of rotational energies with V_t>1, when l-doubling dominates the (g_tt ? B_v)l_t² splittings, is discussed.     

Shallow acceptor bound exciton and free exciton states in high-purity zinc telluride

We investigated excitons bound to shallow acceptors in high-purity ZnTe and measured excitation spectra of two-hole luminescence lines at 1.6 K using a tunable dye-laser. The electron-hole coupling in the bound exciton (BE) states appears to be very different for the various acceptors even for almost identical exciton localisation energies. Three different types of BE are reported. For the Li-acceptor BE we observe three sub-components separated by 0.22 and 0.17 meV and interpreted as J = $\text{1}\text{2}$, $\text{3}\text{2}$, $\text{5}\text{2}$ states. The Ag-acceptor BE exhibits a strong ground state and a weak excited state at 1.3 meV higher energy. For the as yet unidentified k-acceptor we observe a single BE level, degenerate with the Ag-acceptor BE ground state. Dips in the excitation spectra due to absorption into free exciton 1S, 2S, and 3S states yield an exciton Rydberg R₀ = 12.8±0.3 meV and a free exciton binding energy FE(1S) = 13.2±0.3 meV.     

Infrared-microwave double resonance in CF3I; Microwave spectroscopy in emission and absorption

From the double resonance effects observed on the microwave spectrum of CF₃I it has been shown that the R(16) CO₂ laser line of the 9.4 μm band is coincident with the R(7), K = 2, $\text{F =}\text{19}\text{2}\text{→}\text{21}\text{2}$ transition of the CF₃, symmetric stretch (ν₁ band) of CF₃I. Using this laser line, 50 double resonance signals all with K = 2 were observed ranging from J = 4 → 5 to J = 12 → 13 transition. The fact that double resonance effects were observable over such a large range of J was explained as being caused by very strong ΔJ = ± 1, ΔK = 0 collisional transitions.Extremely large pumping effects were produced using 6 W of laser radiation, which caused relative changes in intensity ($\text{Δ}\text{I}\text{I}$) in ground state lines of up to 25. The population transfer into the excited state was so large that many excited state lines, which had previously been undetectable, produced signals up to 30 times more intense than the corresponding undisturbed ground state lines (i.e., values of $\text{Δ}\text{I}\text{I}$ of ～6000 were achieved). Population inversions were produced by the laser pump in many of the K = 2 microwave transitions, not only in those with levels directly pumped by the laser but also in some connected only by collisional transitions. The results was that many of the signals were observed as stimulated emissions rather than absorptions.The rotational constant and quadrupole coupling constants of CF₃I in the v₁ excited state are calculated and an estimation of the center of the ν₁ band is made. The absolute population shifts produced by the laser pump are estimated and the rate constants of the collisional transitions are discussed.     

Spins in 23Na from 25Mg(d, α)

The ²⁵Mg(d, α)²³Na reaction has been investigated at bombarding energies of 12.07,11.82 and 11.57 MeV. Angular distributions are approximately symmetric about 90° and for states of known J^π angle-integrated cross sections $\text{σ}$ averaged over bombarding energy, are roughly proportional to $\text{2J + 1:}\text{σ}\text{/(2J + 1) = 25±4 μ}\text{b}$. Measured cross sections for other states, up to E_x = 7.9 MeV, have been used to place limits on J.