Mixed spin-singlet and spin-triplet cooper pairing caused by inhomogeneous magnetism

With an attractive electron-electron interaction only for spin-singlet Cooper pairing and in the presence of inhomogeneous magnetism, spin-singlet and spin-triplet pair amplitudes both occur when only a spin-singlet pair potential occurs. Pair amplitudes in $\text{k}$-space and $\text{r}$-space and the spin susceptibility show that superconductivity in the presence of inhomogeneous magnetism cannot be either purely spin-singlet or purely spin-triplet pairing.     

Energies and electromagnetic moments of deformed nuclei in the rare-earth region

Strutinsky-type cranking calculations with inclusion of pairing correlations have been performed for the rare-earth nuclei ^{156, 158, 164}Dy and ¹⁶⁴Er. The pairing effects contribute significantly and with their inclusion the calculated yrast spectra agree very well with experiments. Using Hartree-Fock-Bogouliubov cranking wave functions we have calculated the magnetic moments and quadrupole moments for states up to spin $\text{I = 20}\text{h}\text{?}$. The quadrupole moments are found to be constant over the whole spin range. The gyromagnetic factors g(I) show a strong I-dependence for ^{156, l58}Dy, a weaker one for ¹⁶⁴Er and none for ¹⁶⁴Dy. The sensitivity of this spin dependence on the single-particle occupation and the pairing degrees of freedom is studied. It is found that the spin variation of the gyrofactors is a rotational alignment effect.     

On the classical limit of relativistic quantum theories with arbitrary spin

Using the general theory of classical limit developed by the author, we show the existence of classical limit for positive energy representations of the Poincaré group $\text{B}$ of arbitrary spin. The resulting classical phase space is an orbit of $\text{B}$ in the dual of its Lie algebra corresponding to given mass and spin.     

Lowest energy Cooper pairing in the presence of antiferromagnetism

Cooper pairing of electron eigenstates of an antiferromagnet involves considerable complexity in spin space and in phases of the order parameters. With a BCS interaction the pairing scheme with lowest free energy has anisotropic spin-matrix order parameter $\textcolor{red}{}\text{(}\text{k}\text{); however}\textcolor{red}{}{}^{\mathrm{+}}\text{(}\text{k}\text{)}\textcolor{red}{}\text{(}\text{k}\text{)=|△|}{}^2\textcolor{red}{}$. Magnitude of the anisotropic order parameter satisfies the simple BCS gap equation but with electron energies of the antiferromagnet eigenstates appearing instead of Bloch state energies of the nonmagnetic crystal.     

High-spin structure in 169W and 170W

High-spin states in ^{169, 170}W have been populated in ${}^{154}\text{Gd}\text{(}{}^{20}\text{Ne}\text{, x}\text{n}\text{)}$ reactions. In-beam γ-ray spectroscopic techniques with multi-detector set-ups, multiplicity filters and an anti-Compton shield have been used. Levels up to about spin 30 (tentatively up to 36) in ¹⁷⁰W and up to $\text{57}\text{2}$ (tentatively up to $\text{61}\text{2}$) in ¹⁶⁹W have been identified. The data are interpreted within the framework of a pairing-selfconsistent cranking model. The nuclear shape evolution with increasing spin is studied theoretically within a configuration-controlled shell correction approach and also pairing effects are studied. The behaviour of the yrast states around 28⁺ in ¹⁷⁰W can be related in a model-dependent way to a reduction of the neutron-pairing correlations.     

Self-consistent field description of high spin states in rare earth nuclei

The Hartree-Fock-Begoliubov cranking equations are solved for ^{168, 170}Yb and ¹⁷⁴Hf. Deformation and pairing properties are both obtained with a G-matrix derived from the Reid soft-core potential. The high spin anomalies are attributed to the disappearance of the neutron pair gap in ¹⁶⁸Yb, the realignment of an $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$. neutron pair in ¹⁷⁰Yb, and a combination of these two mechanisms in ¹⁷⁴Hf. Two bands intersecting at high spin are found for ¹⁷⁴Hf.     

Implications of the τ and b spins for theories of quarks and leptons

We argue that the present evidence that the spin of the τ is $\text{1}\text{2}$ is circumstantial, and that a spin of $\text{3}\text{2}$ is not excluded. If the τ spin were $\text{3}\text{2}$, it would have important implications for the idea that leptons and quarks were composite states, perhaps allowing an explanation of the existence of three generations. Supergravity ideas could also be affected. Similar ideas suggest the b-quark could have spin-$\text{3}\text{2}$; we give several ways to test this.     

Spin anisotropy effects on the dimerization of the magnetostrictive quasi-one-dimensional XY model

The one-dimensional first-neighbour spin - $\text{1}\text{2}$ magnetostrictive XY model (with crystalline degrees of freedom assumed three- dimensional) with $\text{different}$ X and Y spin coupling constants presents a quite rich spin-Peierls dimerization phase diagram. In the (low anisotropy) - (low temperature) region we recover previous results (in particular the possibility for a first-order phase transition in the absence of external magnetic field); in the other three regions of the temperature-anisotropy space interesting branches of the phase diagram (including the tricritical line) are exhibited (for the first time as far as we know).     

Dirac dynamics on stochastic phase spaces for spin 1/2 particles

The Foldy-Wouthuysen representation of the dynamics of a free spin $\text{1}\text{2}$ particle is formulated in a Hilbert space $\text{H}$(Γ) of spinor-valued functions over Γ-space. $\text{H}$(Γ) carries a reducible Wigner-type representation of the Poincaré group. The transition to the Dirac representation in a new bispinor Hilbert space $\text{K}$(Γ) is effected by means of a generalized inverse Foldy-Wouthuysen transformation. Explicit expressions are derived for the resolution generators η of invariant subspaces $\text{K}$±(Γ_η) carrying irreducible representations of the resulting representations of the Poincaré group. The formalism is recast in a manifestly covariant form and the Dirac equation on $\text{H}$(Γ_s) with minimal coupling to a four-potential is examined. It is shown that the resulting external field theory is gauge-invariant and relativistically covariant.     

Spin alternation in one-dimensional exchange-coupled systems: Magnetic behaviour of the (12−1)N chain

We report on the magnetic behaviour of exchange-coupled closed chains (rings) of increasing length made of two alternating spin sublattices $\text{S}{}_{\mathrm{<mtext>a</mtext>}}\text{=}\text{1}\text{2}\text{, S}{}_{\mathrm{<mtext>b</mtext>}}\text{= 1}$. Taking into account the geometrical and spin space symmetries of such syste the problem is shown to be tractable up to 10 spins for distinct values of the g_a/g_b ratio between Landé factors; the results are discussed for an antiferromagnetic coupling. The limiting behaviour for the infinite chain is determined by extrapolation of the data obtained for finite rings. At very low temperatures, the analogy with the regular $\text{S =}\text{1}\text{2}$ ferromagnetic chain is underlined.     

Is there neutron-proton pairing in medium heavy nuclei?

Present knowledge of the proton and neutron pairing energies Δ_p and Δ_n, deduced from nuclear masses, is reviewed and an attempt is made to find general trends in the data. The analysis shows that, besides the well-known smooth slow decrease with A, the pairing energies also contain a symmetry energy-like dependence on the neutron excess $\text{(N?Z)}\text{A}$. The trends is most pronounced in the shell 50<Z<82, 82<N<126 where both pairing energies decrease by a factor of almost two between the most neutron deficient and the most neutron rich nuclei. The same tendency persists in other mass regions, but is not a universal one. An empirical expression for Δ, that is more accurate than the value $\text{12A}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{MeV}$ usually assumed, is proposed.     

The zero field Kondo susceptibility at lower temperatures

The zero field impurity spin susceptibility is calculated for spin $\text{1}\text{2}$ Kondo systems. By taking into account the self energy of the transverse impurity spin excitations the previous selfconsistent approximation is modified such that the unitarity bound for spin wave scattering is taken care of. For lower temperatures an improvement for the static susceptibility is achieved.     

Pairing and quarteting correlations in nuclei

The Gorkov approach to the pairing problem has been generalized in order to take into account pairing and quarteting correlations with a model Hamiltonian including a charge independent pairing interaction and a n-p isopairing term. The single quasi-particle and quasi-hole energies calculated for all the doubly even nuclei of the $\text{7}\text{2}$^? shell show the importance of quarteting correlations in nuclei.     

Production and decay properties of possible spin 32 leptons

A systematic study of production and decay properties of hypothetical charged spin $\text{3}\text{2}$ leptons is presented. These particles are assumed to occur in each lepton family. The simplest V ± A currents constructed with these particle fields and the corresponding spin $\text{1}\text{2}$ neutrinos are assumed to be coupled to the familiar V ? A lepton charged weak currents. Our results are independent from structure models and indicate ways for an experimental search for these particles.     

Usefulness of spin dependent electromagnetic hadronic inteference experiments

For the collision of a beam of neutral spin $\text{1}\text{2}$ particles A with a polarized target of spin $\text{1}\text{2}$charged particles B, it is shown that many spin dependent observables display a simple and characteristic structure in t which can be utilized to measure directly the magnitude and phase of the hadronic amplitudes, both helicity-flip and non flip, in the forward direction.     

On a possible test of massive high spin wave equations in heavy-ion scattering

Cross sections and polarization functions for elastic scattering of identical particles with spin 1 are compared in the relativistic $\text{(s,0)+(s?}\text{1}\text{2}\text{,}\text{1}\text{2}\text{)}$ invariant theory, for arbitrary spin, and the $\text{(}\text{1}\text{2}\text{,}\text{1}\text{2}\text{)}$ invariant Proca theory. Heavy-ion scattering is suggested to test high spin theories.     

Gauge invariance versus masslessness in de Sitter spaces

The connection between gauge invariance, masslessness and null cone propagation is a flat space property which does not persist even in constant curvature geometries. In particular, we show that both the gauge invariant spin $\text{3}\text{2}$ and 2 fields in anti-de Sitter space have support inside the cone, whereas where are conformally invariant, but gauge variant, models which do propagate on the light cone. The Maxwell field in constant curvature spaces of dimension other than four also does not have null cone propagation; again there is a conformally invariant model which does.     

Consistent supergravity

A combined spin 2 - spin $\text{3}\text{2}$ extension of general relativity is given which is both free of the usual higher spin inconsistencies and invariant under local supersymmetry transformations.     

Higher spin vierbein gauge fermions and hypergravities

The actions describing any massless fermion of spin $\text{?}\text{5}\text{2}$ are given uniformly in terms of non-symmetric vierbein-like fields ψ_μã…ãs. Hamiltonian analysis of their dynamical content is performed explicitly for $\text{s =}\text{5}\text{2}\text{7}\text{2}$, and indicated for the general case. The consistency problems in gravitational coupling are discussed. For spin $\text{5}\text{2}$, they are equivalent to those in symmetric tensor-spinor formulation. The general spin case has the same structure: in Minkowski signature, the consistency requirements are too restrictive (vanishing Weyl tensor); their euclidean counterparts require self-duality in both gravity and matter.