Transverse spin correlation function of the one-dimensional spin-12 XY model

The transverse spin pair correlation function p^x_n=<S^x_mS^x_m+n>=<S^x_mS^x_m+n> is calculated exactly in the thermodynamic limit of the system described by the one-dimensional, isotropic, spin-$\text{1}\text{2}$, XY Hamiltonian

$\text{H=?2J}\text{∑}\text{l=1}\text{N}\text{(S}{}^{\mathrm{x}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{x}}{}_{\mathrm{l+1}}\text{+S}{}^{\mathrm{y}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{y}}{}_{\mathrm{l+1}}\text{)}$

. It is found that at absolute zero temperature (T = 0), the correlation function ρ^x_n for n ≥ 0 is given by

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p}}\text{=}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p}}\text{Π}\text{j=1}\text{p?1}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p?2j}}\text{if}\text{n=2p}$

,

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p+1}}\text{=±}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p+1}}\text{Π}\text{j=1}\text{p}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p+2j}}\text{if}\text{n=2p+1}$

, where the plus sign applies when J is positive and the minus sign applies when J is negative. From these the asymptotic behavior as n → ∞ of |?^x_n| at T = 0 is derived to be $\text{|ρ}{}^{\mathrm{x}}{}_{\mathrm{n}}\text{| ～}\text{a}\text{n}$ with a = 0.147088?. For finite temperatures, ρ^x_n is calculated numerically. By using the results for ?^x_n, the transverse inverse correlation length and the wavenumber dependent transverse spin pair correlation function are also calculated exactly.     

Infrared-radio frequency double resonance observations of pure rotational Q-branch transitions of methane

The $\text{F}{}_2{}^{\mathrm{(2)}}\text{← F}{}_1{}^{\mathrm{(2)}}$ and $\text{F}{}_2{}^{\mathrm{(2)}}\text{← F}{}_1{}^{\mathrm{(1)}}$ transitions of the J = 7 levels of the ground state of CH₄ have been observed by infrared-radio frequency double resonance using the 3.39 μ HeNe laser line. The transition frequencies are 423.02 ± 0.02 MHz and 1246.55 ± 0.02 MHz, respectively. Using these frequencies and the splitting of the E and F₂ levels of the J = 2 state calculated from the molecular beam magnetic resonance spectra of Ozier, the centrifugal distortion constants are derived to be D_t = 132933 ± 10 Hz, H_4t = ? 16.65 ± 0.2 Hz, and H_6t = 10 ± 1 Hz. The J = 15 E⁽¹⁾ → E⁽²⁾ microwave transition is predicted as 14150 ± 9 MHz.     

Chemiluminescence of IF in the gas phase reaction of I2 with F2

Emission from both the state and the previously unreported $\text{A}{}^3\text{Π}{}_1$ state of IF has been observed in the gas phase reaction of I₂ with F₂ at low pressures. For the state the transition moment and vibrational populations were extracted from the spectra by a least-squares method whereby theoretical band shapes were fit to the experimental data. The effect of flow rates of reactants and Ar on the relative emission from the two electronic states, the effect of pressure on the state, and extinction of emission near 470 nm all favor the population of excited electronic states through a four-center reaction complex, rather than association of F and I atoms.It is argued that there is an avoided curve crossing between the lowest two ³Π_0⁺ states of IF, and that the ground state dissociation energy is 23 229 ± 100 cm^?1. The radiative lifetime of the state is estimated to be 10^?3 sec and to be much shorter than that of the $\text{A}{}^3\text{Π}{}_1$ state.     

Ultraviolet absorption spectra of Zn2 and Cd2 in solid argon and krypton at 10 K

Zinc and cadmium atoms have been condensed with argon and krypton at 10 K. The most intense absorption is due to the ${}^1\text{P}{}_1\text{←}{}^1\text{S}{}_0$ atomic transition, and a weak band is due to the ${}^3\text{P}{}_1\text{←}{}^1\text{S}{}_0$ atomic absorption. Structured absorptions at 252 and 254 nm in solid argon and krypton with vibrational spacings of 140-120 cm^?1 are due to the ${}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{←}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ transition of Zn₂. Similar 273 and 277 nm absorptions with 110-90 cm^?1 vibrational spacings are due to Cd₂ in solid argon and krypton, respectively.     

Chemical diffusion in nonstoichiometric chromium sulfide,Cr2+yS3

Using the re-equilibration kinetic method the chemical diffusion coefficient in nonstoichiometric chromium sesquisulfide, Cr_2+yS₃, has been determined as a function of temperature (1073–1373 K) and sulphur vapour pressure (10?10⁴ Pa). It has been found that this coefficient is independent of sulphur pressure and can be described by the following empirical equation: $\text{D}\text{?}\text{Cr}{}_{\mathrm{2+y}}\text{S}{}_3\text{=50.86}\text{exp(-39070 cal/mole/}\text{RT)}\text{(cm}{}^2\text{s}{}^{\mathrm{?1)}}$. It has been shown that the mobility of the point defects inCr_2+yS₃ is independent of their concentration and that the self-diffusion coefficient of chromium in this sulfide has the following function of temperature and sulphur pressure: . (cm²s^?1).     

Spectrum and structure of the He2 molecule: Characterization of the singlet and triplet states associated with the UAO's 4s, 4dσ, 4dπ, and 4dδ

The emission spectrum of the He₂ molecule has been rephotographed in the ～4000–～5700 Å region and the $\text{4d(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$, $\text{4d(}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^1\text{Π}{}_{\mathrm{u}}\text{,}{}^1\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$, $\text{4s}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$ and $\text{4s}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$ transitions analyzed. The 4dδj³Δ_u, 4dπj³Π_u, $\text{4dσj}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and $\text{4sh}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states have been characterized through v = 2 and the 4dδJ¹Δ_u, 4dπJ¹Π_u, $\text{4dσJ}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, and $\text{4sH}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states for v = 0. The term levels for these perturbed and l-uncoupled states have been confirmed (a) by analyses of bands with common levels from Δv = 0, ±1 sequences and (b) by analyses of the transitions between the above states from 4d and 4s and the $\text{c}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ and $\text{C}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ states associated with 3pσ. Molecular constants are reported which have been partially corrected for the effects of l-uncoupling and the homogeneous perturbations between the state pairs J, H and j, h.     

The spectrum of HeNe+

Discharges through mixtures of helium and neon show two band groups near 4250 and 4100 Å as first observed by Druyvesteyn. These bands, assigned to the HeNe⁺ ion by Tanaka, Yoshino, and Freeman, have been studied under high resolution and have been fairly completely analyzed. The upper state of the transition is a very weakly bound state resulting from $\text{He}{}^{\mathrm{+}}\text{(}{}^2\text{S) +}\text{Ne}\text{(}{}^1\text{S}{}_0\text{)}$. There are two lower states resulting from the two components of $\text{Ne}{}^{\mathrm{+}}\text{(}{}^2\text{P) +}\text{He}\text{(}{}^1\text{S}{}_0\text{)}$. The upper of these two (${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$) is also very weakly bound while the lower of the two, the ²Σ⁺ ground state, has a dissociation energy of 0.69 eV and an r_e value of 1.30 Å. All bands in both band groups show four branches designated R_ff, Q_ef, Q_fe, and P_ee. From their analysis the rotational constants in the various vibrational levels of the three electronic states have been determined. While no spin splitting in the B²Σ⁺ state has been found the ground state X²Σ shows a very large spin splitting and the $\text{A}{}_2{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ state a very large $\text{Ω-type}$ doubling. The vibrational numberings in all these states were established by the study of the spectrum of ³HeNe⁺. At the same time the hyperfine structure observed in all lines of ³HeNe⁺ confirmed the nature of the upper state B²Σ⁺ as resulting from He⁺ + Ne, i.e., by charge exchange from the ground state. The ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ component of the ²Π state has not been observed, presumably because of low intensity.     

Structure of positive parity states in 29P and two-step processes in (p,t) reactions

From a study of (p,t) reactions on ³¹P and ³⁰Si it is suggested that in ²⁹P the states with $\text{J}{}^{\mathrm{\pi }}\text{=}\text{1}\text{2}{}_1{}^{\mathrm{+}}$ and $\text{1}\text{2}{}_2{}^{\mathrm{+}}$, the pair $\text{3}\text{2}{}_2{}^{\mathrm{+}}$, $\text{5}\text{2}{}_1{}^{\mathrm{+}}$, and the pair $\text{7}\text{2}{}_3{}^{\mathrm{+}}$, $\text{9}\text{2}{}_1{}^{\mathrm{+}}$ are related by weak coupling of a s${}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ proton with the states 0₁⁺, 0₂⁺, 2₁⁺ and 4₁⁺ respectively of ²⁸Si. Completely atypical L = 2 angular distributions have been obtained for the $\text{3}\text{2}{}_1{}^{\mathrm{+}}$ and $\text{5}\text{2}{}_2{}^{\mathrm{+}}$ states in ²⁹P and it is suggested that this is due to contribution by two-step processes.     

νW2 at small ω′ and resonance form factors in a quark model with broken SU(6)

The small ω′ behaviour of F₂^en/F₂^ep and the apparent difference in the q² dependences of the magnetic form factor of the proton and of the transition to Δ⁺(1236) are quantitatively correlated in a model where nucleon consistes of a quarks and a scalar or vector core. The proton and Δ transition form factors suggest that only the scalar core contributes at large q² and small ω′. As a result the ω′ dependence of $\text{F}{}_2{}^{\mathrm{<mtext>en</mtext>}}\text{F}{}_2{}^{\mathrm{<mtext>ep</mtext>}}$ is obtained for ω′ < 3 and predictions for the weak structure functions and polarisation asymmetries at smallω′ are presented. We predict $\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>p</mtext>}}\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>n</mtext><mtext>\omega \prime \to 1</mtext><mtext>0</mtext>}}$ asymmetries $\text{ω′→1}\text{1}$ and also expect that $\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>n</mtext>}}\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>p</mtext>}}\text{→}\text{?1}\text{2}$ as q²→∞.     

Ni2+ emission in MgO,KMgF3, KZnF3 and MgF2

The emission of Ni²⁺ ions in MgO, KMgF₃, KZnF₃ and MgF₂ crystals has been investigated. The fine structure on the bands at about 20 000 cm^-1 and 13 000 cm^-1 has been studied in detail and from this and the excitation spectra these bands are assigned to ${}^1\text{T}{}_{\mathrm{2g}}\text{→}{}^3\text{A}{}_{\mathrm{2g}}$ and ${}^1\text{T}{}_{\mathrm{2g}}\text{→}{}^3\text{T}{}_{\mathrm{2g}}$ transitions respectively.     

Spectral and temperature characteristics of Cs2Na(Er,Yb, Y)Cl6 upconverters

Spectral luminescence characteristics of the Cs₂Na(Er, Yb, Y)Cl₆ type upconverter have been measured in the range 300–650 K. A nearly sixfold decrease of the emission intensity of an upconverter was observed in the green area. This emission corresponds to two luminescence transition of Er³⁺ ions: ${}^2\text{H}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{→}{}^4\text{I}{}_{\mathrm{<mtext>15</mtext><mtext>2</mtext>}}$ and ${}^4\text{S}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{→}{}^4\text{I}{}_{\mathrm{<mtext>15</mtext><mtext>2</mtext>}}$. A mechanism of the luminescence intensity decrease has been proposed, in which deexcitation of the ${}^4\text{S}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ level to the ${}^4\text{I}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ level is caused by a neighbouring Er³⁺ ion being excited to the ${}^4\text{I}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ level.     

Electric dipole transition cross sections and effective site symmetry of Eu3+ in pseudocentric K5Eu(MoO4)4

The fluorescence and absorption spectra of Eu³⁺ in K₅Eu(MoO₄)₄ have been measured at 300 K and 77 K. The fluorescence lifetime of the ⁵D₀ state is 1.4 ms at 300 K. The largest cross section $\text{σ(}{}^5\text{D}{}_0\text{→}{}^7\text{F}{}_2\text{(4)) = 1.3 × 10}{}^{\mathrm{?21}}\text{cm}{}^2$ and the removal of degeneracies require to replace the nearest neighbour D_3d symmetry of Eu³⁺ by the effective symmetries C₁, C₂ and C_s of the whole unit cell. It is shown that C₁ dominates because of the statistical distribution of K⁺ and Eu³⁺. The corresponding inhomogeneous broadening is observed at 77 K.     

Fine and hyperfine structure spectra of the ultra-violet 2 3S → 5 3P transition in 4He and 3He with a frequency doubled CW ring laser,detected via associative ionization

High resolution laser spectroscopy coupled to a sensitive method of detection via mass analysis of He⁺₂ ions produced in $\text{He(5}{}^3\text{P) + He(1}{}^1\text{S)}$ collisions, is used to obtain the fine and hyperfine spectra of the ultra-violet He 2 ³S → 5 ³P transition. A cw tunable UV radiation around 294.5 nm is generated by intracavity frequency doubling a Rhodamine 6G single mode ring dye laser using an ADA crystal. Both spectra enable fine and hyperfine structures to be determined within a few MHz. The magnetic dipole coupling constant A of the 5 ³P term of ³He is found to be -4326 ± 9 MHz (-0.1443 ± 0.0003 cm^-1).     

N2+ bound quartet and sextet state potential energy curves

Potential energy curves for the ${}^4\text{Σ}{}^{\mathrm{+}}{}_{\mathrm{u}}$, ${}^4\text{Π}{}_{\mathrm{g}}$ and ${}^6\text{Σ}{}^{\mathrm{+}}{}_{\mathrm{g}}$ states of N⁺₂ that dissociate to N (${}^4\text{S}{}^0$) and $\text{N}{}^{\mathrm{+}}\text{(}{}^3\text{P)}$, have been determined from a complete active space self-consistent field calculation. The ${}^6\text{Σ}{}^{\mathrm{+}}{}_{\mathrm{g}}$ state is found to be significantly bound (D_e = 2.68 eV) with a minimum at 1.72 Å.     

Nuclear matrix elements from L/K electron capture ratios in 59Ni decay

Using a recent theoretical method, the ratio of nuclear matrix elements $\text{R = (}{}^{\mathrm{v}}\text{F}{}^0{}_{220}\text{?√}\text{3}\text{2}{}^{\mathrm{A}}\text{F}{}^0{}_{221}\text{/}{}^{\mathrm{v}}\text{F}{}^0{}_{211}\text{)}$ was determined to be either 20.50^+0.35_?0.55 or 25.22^+0.28_?0.17 in the second-forbidden nonunique decay of 8 × 10⁴ y ⁵⁹Ni. These values of R were obtained from a value of L₃/K = 0.008 ± 0.002 found by subtracting the theoretical ratio $\text{(L}{}_1\text{+ L}{}_2\text{)}\text{K}$ = 0.113 (based on Q_PEC = 1070 ± 8 keV) from the total ratio L/K = 0.121 ± 0.002, which was measured with a reactor-produced, doubly-mass-separated ⁵⁹Ni source introduced as gaseous nickel-ocene, (C₅H₅)₂, into a wall-less, anticoincidence, multiwire proportional counter. The 854–1008 eV L and the 8.33 keV K peaks were measured simultaneously.     

The spectrum and structure of the He2 molecule: Multichannel quantum defect analyses of the triplet levels associated with (1σg)2(1σu)npλ

Emission spectra for the electronic transitions $\text{6–17pπ}{}^3\text{Π}{}_{\mathrm{g}}\text{-2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and $\text{7–16pσ}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{-2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ of He₂ are reported and the electronic structures of $\text{npπ}{}^3\text{Π}{}_{\mathrm{g}}{}^{\mathrm{?}}$ and $\text{np(}{}^2\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{)}$ characterized. The energy levels associated with $\text{(1σ}{}_{\mathrm{g}}\text{)}{}^2\text{(1σ}{}_{\mathrm{u}}\text{)np(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{)}$ exhibit extensive channel mixing, which leads to a breakdown of conventional band models for the higher n¹-members of these Rydberg “series.” However, a model based on multichannel quantum defect theory quantitatively correlates the observed level structures. The higher-energy ($\text{n}{}^1\text{> ～5}$) portions of the $\text{np(}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{)}$ channels can be represented by two eigen-quantum defects μ₁ = 0.225 and μ₂ = 0.930 and the close- to loose-coupling matrix elements $\text{U}{}_{11}\text{= U}{}_{22}\text{= [N(2N + 1)}{}^{\mathrm{?1}}\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{U}{}_{12}\text{= ?U}{}_{21}\text{= [(N + 1)(2N + 1)}{}^{\mathrm{?1}}\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. The inclusion of energy dependence in the μ_α's leads to quantitative correlations for all n¹-values.     

Etude d'un groupement (Ru3O12)13− en presence de degenerescence orbitale et de couplage spin-orbite

A trinuclear cluster (Ru₃O₁₂)^13? occurs in the Ba₄NbRu₃O₁₂, and Ba₄TaRu₃O₁₂ compounds where the oxydation states of ruthénium are +III and +IV. The exchange interaction between magnetic sites is described by a Hamiltonian, which takes account of the orbital degeneracy of the ${}^2\text{T}{}_{\mathrm{<mtext>2</mtext><mtext>g</mtext>}}\text{(}\text{Ru}{}^{\mathrm{3+}}\text{)}\text{and}{}^3\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>g</mtext>}}\text{(}\text{Ru}{}^{\mathrm{4+}}\text{)}$ terms. For these ions, the spin-orbit coupling is the dominant effect and it appears that the low temperature magnetic susceptibility depends essentially on the orbital reduction factor and the distortion of the coordination octahedra. There is apparently no first order perturbation of the ground state due to the interaction between magnetic ions.     

EPR of V2+ in SrCl2

The X-band EPR spectrum of SrCl₂:V has been measured at liquid nitrogen temperature. A signal associated with V²⁺ in a site of trigonal symmetry is observed. The EPR data have been explained using the spin hamiltonian $\textcolor{red}{}\text{= μ}{}_{\mathrm{\beta }}\text{H}\text{g}\text{?}\text{S}\text{+ D[S}{}^2{}_{\mathrm{z}}\text{?}\text{1}\text{3}\text{S(SH)] +}\text{S}\text{A}\text{?}\text{I}$, with D ? hv, g_∥ = 1.957 ± 0.004, g₆ = 1.954 ± 0.004, A_∥ = 230 ± 5 MHz, A₆ = 235 ± 5 MHz. This V²⁺ defect is similar to those previously reported in fluoride crystals with the fluorite structure.