The structure of single vortices in type II superconductors

This paper reports the first results of a program for the investigation of the detailed electronic and magnetic structure of type II superconductors. The structure of a single flux bundle or vortex in an infinite superconducting specimen is investigated, assuming weak coupling and a spherical Fermi surface of the material. The equations governing the gap parameterΔ(r) and the vector potentialA(r) are suitably scaled and simplified using the symmetry of the system. These equations can be solved numerically only; for their solution the asymptotics ofΔ(r) andA(r) far from the center of the vortex are required. These asymptotics are derived here by properly linearising the equations; they are found to be of the typer ^?1/2 exp (?r/rin0) wherer ₀ is determined by temperature and material parameters. Implicit equations forr ₀ are derived and discussed. We find that for materials withκ-values less than 1.7 (e.g. pure niobium)r ₀ becomes complex at low temperatures; i.e. the deviation ofΔ(r) andA(r) from their values at infinity is a damped oscillation as function ofr.     

Phase transitions in a ferromagnetic semiconductor. III

We investigate the ferromagnetic phase transition in a heavily doped semiconductor or semimetal containing magnetic ions. The coupling between conduction electrons and magnetic ions is treated in the molecular field approximation. We show that the system undergoes a transition to an ordered state for arbitrarily small concentrations of the magnetic ions and the conduction electrons. In the limitJ/? _F?1 we obtain the Ruderman-Kittel result for the Curie temperature, and forJ/? _F?1 a generalization of Thompson’s strong coupling result. (J is the exchange coupling constant between conduction electrons and magnetic ions and? _F is the kinetic Fermi energy at absolute zero.) The intermediate range is evaluated numerically.     

Nuclear hyperfine structure in the XΣ state of ZrC

Electronic band systems of zirconium monocarbide, ZrC, in the 16 000-19 000 cm⁻¹ region have been observed following the reaction of laser-ablated Zr atoms with methane under supersonic free-jet conditions. Rotational analyses of high-resolution spectra have shown that the ground state of ZrC is a ³Σ state, with r₀=1.8066 Å and an unexpectedly small spin-spin parameter, λ=0.5139 cm⁻¹. The spectra are dense because of the five naturally occurring isotopes of Zr. Four of these, with mass numbers 90, 92, 94, and 96, have I=0, but the fifth, ⁹¹Zr, present in 11.22% abundance, has I=5/2. Lines of ⁹¹ZrC can be assigned in some of the strongest bands, and are found to display sizeable hyperfine splittings, with widths of up to 0.2 cm⁻¹. Analysis shows that the largest hyperfine effects are in the ground state, where b=−0.03133±0.00015 cm⁻¹ and c=−0.00123±0.00037 cm⁻¹ (3σ error limits). The large Fermi contact parameter, b, indicates that an unpaired Zr 5sσ electron is present, which, taken together with the small value of λ, means that the ground state must be a ³Σ⁺ state, from the electron configuration (Zr 5sσ)¹ (C 2pσ)¹. Internal hyperfine perturbations occur between the F₁ and F₃ electron spin components of the ground state in the range N=2-4, producing extra lines in some of the branches; the perturbations are of the type ΔN=0, ΔJ=±2, and are a second-order effect arising because the F₁ (J=N+1) and F₃ (J=N−1) spin components both interact with the F₂ (J=N) component through ΔN=0, ΔJ=±1 matrix elements of the Fermi contact operator. Second-order perturbations of this type can only occur in states that are very close to case (b) coupling.     

Multicomponent dense electron gas as a model of Si MOSFET

We solve a 2D model of N-component dense electron gas in the limit N→∞ and in the range of the Coulomb interaction parameter N ^?3/2?r _s ?1. The quasiparticle interaction on the Fermi circle vanishes as ?²/Nm. The ground-state energy and the effective mass are found as series in powers of r _s ^2/3 . In the quantum Hall state on the lowest Landau level at integer filling 1?ν<N, the charge-activation-energy gap and the exchange constant are Δ=log(r _s N^3/2)?ω_H/ν and J=0.66?ω_H/ν.     

Mass spectrum ofP-wave mesons

Mass splittings of mesons withL≧1 are discussed on the basis of a general spin-dependent potential consisting of a vector (V(r)) and a scalar (S(r)) part. For arbitraryV(r) andS(r), the four masses, for the three³ L _J and the one¹ L _J=L levels, are given in terms of only three unknown expectation values 〈(1/r)(dV/dr)〉, 〈d ² V/dr ²〉 and 〈(1/r)(dS/dr)〉. These expectations values are extracted for theP-wave \(u\bar s\) (or \(d\bar s\) ) mesons which are discussed in detail. It is argued that the 0⁺⁺ mass should be around 1150 to 1230 MeV, rather than at 1350 MeV. On comparing the expectation values for the \(u\bar s\) , \(c\bar c\) , \(b\bar b\) and the \(I = 1u\bar u\) systems, we find that they all scale asa+bμ, wherea andb are constants and μ is the reduced mass. Remarkably enough, we also find that theP-wave meson masses for these systems satisfy mass formulae of the formA+B(m₁+m₂), with constantA andB. It is shown that similar linear mass formulae also work forS-wave mesons. These facts seem to reveal a rather general property of \(q\bar q\) states.     

The convergence behaviour of expansions in the classical collision theory

In the classical collision theory the scattering angle? depends on the impact parameterb and on the kinetic energyE _r of the relative motion. This angle?(b, E _r ) is expanded for two limiting cases: 1. Expansion in powers of the potentialV(r)/E _r (momentum approximation). 2. Expansion in powers of the impact parameterb (central collision approximation). The radius of convergence of the series depends onb andE _r . It will be given for the following potentialsV(r):

$$A\left( {\frac{a}{r}} \right)^\mu ;Ae^{ - \frac{r}{a}} ;A\frac{a}{r}e^{ - \frac{r}{a}} ;A\left( {\frac{a}{r}} \right)^2 e^{ - \left( {\frac{r}{a}} \right)^2 } .$$     

Disordered magnet near the percolation threshold

A disordered Potts magnet containing a random mixture of ferromagnetic exchange constants J_a and J_b (J_a?J_b) near the percolation threshold is considered. The scaling form for the free energy contains two crossover exponents. Duality arguments in two dimensions show that these exponents are equal. They are also shown to be equal to unity in d = 6 ? ? dimensions to order ?.     

Klein paradox in the Breit equation

We demonstrate that in the Breit equation with a central potentialV(r) having the propertyV(r ₀)=E there appears a Klein paradox atr=r ₀. This phenomenon, besides the previously found Klein paradox arr→∞ appearing ifV(r)→∞ atr→∞, seems to indicate that in the Breit equation valid in the singleparticle theory the sea of particle-antiparticle pairs is not well separated from the considered two-body configuration. We conjecture that both phenomena should be absent from the Salpeter equation which is consistent with the hole theory. We prove this conjecture in the limit ofm ⁽¹⁾→∞ andm ⁽²⁾→∞, where we neglect the terms ～1/m ⁽¹⁾ and 1/m ⁽²⁾. In Appendix I we show that in the Breit equation the oscillations accumulating atr=r ₀ in the case ofm ⁽¹⁾≠m ⁽²⁾ are normalizable to the Dirac δ-function. In Appendix II the analogical statement is justified for the nonoscillating singular behaviour appearing atr=r ₀ in the case ofm ⁽¹⁾=m ⁽²⁾.     

The discrete Gaussian chain with 1/r n interactions: Exact results

We show that the discrete Gaussian chain with interactionV(r) = 1/(r ²–1/4) is self-dual. At the dual temperaturek _B T = 1 we calculate the height-height correlation function and find that the system is rough. A duality relation is established for the temperature-dependent correlation function exponent. We also consider interactionsV(r)–1/r ⁿ and show that absence of a phase transition for 2 <n < 3 implies absence of a phase transition for 1 <n < 2. All these results have their counterparts in a linear system of charges interacting through a potential which is asymptotically logarithmic (forn = 2) or power-law-like (forn 2.On leave of absence from Chemistry Laboratory III, Universitetsparken 5, 2100 ©, Copenhagen, Denmark.     

Rotational spectra of quinoline and of isoquinoline: spectroscopic constants and electric dipole moments

Rotational spectra of quinoline and of isoquinoline have been observed in the centimeter- and millimeter-wave regions. The spectra were assigned on the basis of bands formed by high-J transitions, which were measured up to J″?128 and ν?234 GHz. Complementary measurements were also made on low-J, centimeter-wave spectra observed in supersonic expansion and with fully resolved nuclear quadrupole hyperfine structure. Accurate rotational, centrifugal distortion and hyperfine splitting constants for the ground states of both molecules are reported. The electric dipole moments for the two molecules were also determined from Stark effect measurements and are μ_a=0.14355(19), μ_b=2.0146(17), μ_tot=2.0197(17) D for quinoline, and μ_a=2.3602(21), μ_b=0.9051(14), μ_tot=2.5278(20) D for isoquinoline. The experimental observables were found to be rather accurately predicted by MP2/6-31G** ab initio calculations, and corresponding molecular geometries are also reported.     

Molecular transient effects in K-band spectroscopy

The time dependence of microwave transient absorption and emission was measured forJ=2←1 of the OCS molecule under on- and off-resonant conditions by the technique of Stark switching. The results are analyzed with the theory of a coherent electromagnetic wave interacting with a two-level quantum system through the electric dipole interaction to obtain the pressure dependence of the relaxation timesT ₂ and in consequence the pressure broadening parameterC _w=26.7±0.9 (μs·mTorr)^?1 has been obtained.     

The alpha-branching ratios of the188,190,192Pb isotopes

Theα-branching ratios (b _α ) of^192,190,188Pb are measured using mass-separated sources. Different experimental set-ups are used — one detector as well as two detector set-ups — thereby detecting theα particles from the parent and/or viaα decay formed daughter nuclei, theβ-delayed gamma radiation from the parent and/or viaβ decay formed daughter nuclei and the Tl KX rays from electron capture decay. Values forb _α of 6.2(6) 10^?5 and 4.0(4) 10^-3 were found for^192,190Pb respectively. For¹⁸⁸Pb, limits on theb _α values were obtained: 0.03<b _α <0.10. A careful analysis of the previously reportedb _α values showed that the discrepancies in theb _α values were not due to inadequate correction procedures, as was suggested, but to experimental uncertainties in the efficiency determination of the different detection set-ups and to an unreliableβ-decay scheme for¹⁸⁸Pb. Theb _α obtained in this work show that the leadα decay is not faster than the Hgα decay and that there is no need to assume a disappearance of theZ=82 shell closure halfway betweenN=82 andN=126.     

Frei zerfallende Magnetfelder von Kugelschalen

The decay constants of free decaying magnetic fields of sphere shells are calculated. In the regionr ₁<r<r ₀ the electrical conductivity isσ. For different values of the parameterγ=r ₀/(r ₀-r ₁) the following models are considered: The conductivity is zero forr>r ₀ andr<r ₁ (model 1). The conductivity is zero forr>r ₀, and forr<r ₁ the magnetic field is excluded by infinite conductivity (model 2). The magnetic field is excluded forr>r ₀ andr<r ₁ (model 3).     

Determination of the constantg ωρπ from QCD sum rules

The ωρπ coupling constant is calculated using a modified form of sum rules for the vertex function 〈0|T(J _μ(x),J _ν(0))|π〉 accounting for the axial anomaly. The resultg _ωρπ=16 GeV^?1 is in good agreement with the estimates of the Vector Meson Dominance model. We show that the standard procedure gives forg _ωρπ a considerably smaller value compared to the experimental number.     

Ab initio SCF-Cl studies on the large amplitude bending motion of the water molecule: Rigid,semirigid, and nonrigid bender models for the Hamiltonian

Self-Consistent Field (SCF) and Configuration Interaction (CI) studies are performed on the bending mode of the water molecule using a double zeta plus polarization basis set. The ab initio points are fitted to a three-parameter double minimum potential consisting of a quadratic plus Lorentzian terms. The vibration-rotation energies are then evaluated using the large amplitude Hamiltonian developed by P. R. Bunker and co-workers at various levels of approximations. It is found that the calculated frequencies improve significantly as one proceeds from approximate H_b⁰⁰(ρ) to rigid bender H_b⁰(ρ) [P. R. Bunker and J. M. R. Stone, J. Mol. Spectrosc.41, 310–332 (1972)] to semirigid bender H_b⁰(r, ρ) [P. R. Bunker and P. M. Landsberg, J. Mol. Spectrosc.67, 374–385 (1977)] Hamiltonian. With H_b⁰(r, ρ), the ab initio calculated bending frequency ν₂ differs from the observed value (1595 cm^?1) by 30 cm^?1 and the barrier height is 12 229 cm^?1. It is also shown that ν₂ and its first four overtones are better calculated by 45–98 cm^?1 when the ab initio potential is used directly instead of the three-parameter analytic potential fitted to ab initio data. Finally, rotation bending energy levels are calculated for v₂ ≤ 3 and J ≤ 10 on the basis of a nonrigid bender Hamiltonian of A. R. Hoy and P. R. Bunker [J. Mol. Spectrosc.74, 1–8 (1979)], using the ab initio quadratic force field of P. Hennig, W. P. Kraemer, G. H. F. Diercksen, and G. Strey, [Theor. Chim. Acta47, 233–248 (1978)]. These results show that the accuracy of calculated force constants and frequencies is critically dependent not only on the size of the basis set but also on the number and spacing of the ab initio points used to derive the force field.     

Zur Rumpfpolarisation des Rb-Atoms: Hyperfeinstruktur des 72 P 1/2-Terms von Rb85

The hyperfine structure splitting of the 7² P _1/2 state of Rb⁸⁵ has been investigated with optical double resonance spectroscopy. The results are:v _F=3?F=2=52.95(6) Mc/s,A _J=1/2=17.65(2) Mc/s,g _J (7² P _1/2, Rb)=0.6668(1). From the hfs interaction constants of the 7² P multiplett a 12% core polarization contribution to the magnetic hfs of the 7² P _3/2 state can be deduced. Comparison is made between the values of 〈r ^?3〉 calculated from either the magnetic hfs or the² P fine structure separation.     

Isomeric yield ratio of fission product148Pr in235U(n th,f)

The independent isomeric yield ratio of¹⁴⁸Pr in thermal neutron induced fission of²³⁵U has been determined experimentally. The fission product¹⁴⁸Pr isomers, extracted directly by on-line mass separation technique, have high-spin (J=4) to low-spin (J=1) isomer ratio of 0.14±0.04 using growth and decay analysis. Statistical model calculation of isomeric yeild ratio using constant initial r.m.s. angular momentumJ _rms can not reproduce either present results or other recent measurements of isomer ratios. TheJ _rms derived from isomer ratio data in all thermal fissioning systems indicate a wide spread ranging from 2? to 13?. No clear correlation betweenJ _rms and isomeric spins or number of neutrons of isomers is found, thus, more model refinements and experimental works should be done in order to evaluate independent isomeric yields correctly.     

A Laser-Induced Fluorescence Study of the Visible Spectrum of Rhodium Monoxide

A first analysis of an electronic spectrum of RhO is presented. The molecular species has been produced in a jet-cooled molecular beam following reaction in a laser ablation plasma. Laser excitation spectra have been recorded between 600 and 640 nm at 200 MHz resolution. Two transitions have been identified of ²Π_r(a)-X⁴Σ⁻(b) type and six subbands have been rotationally analyzed, four being (0,0) components. Molecular parameters for the X⁴Σ ⁻ state are B₀=0.41320 cm⁻¹, λ₀=−0.5733 cm⁻¹, γ₀=−0.10276 cm⁻¹, and r₀=0.1717 nm. An analysis of the hyperfine structure involving the ¹⁰³Rh nucleus has been made. It shows that the ground state of RhO conforms to Hund's coupling case b_βJ with b=− 0.0203 cm⁻¹. Hyperfine effects in the excited states are negligible.