Pion-exchange contributions to the nuclear charge,current, and Hamiltonian operators

Using a Foldy-Wouthuysen reduction procedure and the time-dependent perturbation theory, we have calculated the one-pion-exchange contribution to the nuclear charge and current densities to order $\text{(}\text{v}\text{c}\text{)}{}^2$. At the same time a renormalization scheme defines the pion-exchange potential including nonstatic and three-body correction terms of order $\text{(}\text{v}\text{c}\text{)}{}^2$. The requirements of relativity are investigated, and it is found that the retardation effect in the potential and charge density plays a critical role. The covariance conditions for the potential, charge, and current densities are shown to be satisfied to the order we have calculated. Finally, the deuteron case is discussed in detail. Throughout the calculation the role of the equivalence theorem is stressed.     

On the relativistic Thomas-Fermi model

The relativistic generalization of the Thomas-Fermi model of the atom is derived. It approaches the usual nonrelativistic equation in the limit Z ? Z_crit, where Z is the total number of electrons of the atom and $\text{Z}{}_{\mathrm{<mtext>crit</mtext>}}\text{=(}\text{3π}\text{4}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{α}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ and α is the fine structure constant. The new equation leads to the breakdown of scaling laws and to the appearance of a critical charge, purely as a consequence of relativistic effects. These results are compared and contrasted with those corresponding to N self-gravitating degenerate relativistic fermions, which for $\text{N ≈ N}{}_{\mathrm{<mtext>crit</mtext>}}\text{=(}\text{3π}\text{4}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(m/m}{}_{\mathrm{<mtext>p</mtext>}}\text{)}{}^3$ give rise to the concept of a critical mass against gravitational collapse. Here m is the mass of the fermion and $\text{m}{}_{\mathrm{<mtext>p</mtext>}}\text{=(?c/G)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is the Planck mass.     

Perhaps scalar neutrinos are the lightest supersymmetric partners

We consider the possibility that the scalar partners of the neutrinos $\text{(}\text{v}\text{)}$ are the least massive supersymmetric partners, and show that this alternative is compatible with cosmological constraints, which put a significant lower bound on photino masses but not on $\text{v}$ masses. Various consequences are examined: the photon counting rate for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{-}}\text{→γ}\text{v}$$\text{v}\text{?}\text{?}$ may be large; the rate for $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{-}}\text{→}\text{W}{}^{\mathrm{+}}\text{a}\text{W}{}^{\mathrm{-}}$ by $\text{v}$ exchange is enhaced; Z⁰→ increases Γ(Z⁰) by about 0.25 GeV; $\text{W}{}^{\mathrm{\pm }}\text{→}\text{?}{}^{\mathrm{+-}}\text{v}$ may be enhanced; the decay $\text{τ→}\text{v}{}_{\mathrm{\tau }}\text{?}{}_{\mathrm{?}}$$\text{v}\text{?}\text{?}$ may be detectable; there can be additional contributions to the rare decay $\text{K}{}^{\mathrm{+}}\text{→π}{}^{\mathrm{+}}\text{v}$$\text{v}\text{?}\text{?}$; restrictions on gluino masses, which depend on photinos interacting before they decay, have to be re-examined; scalar neutrinos have suitable characteristics as candidates for dark matter in the universe. We discuss one currently fashionable class of models that can predicr a light $\text{v}$.     

Space-time symmetries and the gravitational-neutrino field equations in general relativity

We consider a neutrino field with geodesic rays in interaction with a gravitational field admitting a Killing vector field n^μ. It is found that for solutions of the Einstein-Weyl field equations the neutrino field ξ^A and the neutrino flux vector l^μ are restricted by the equations: $\text{L}{}_{\mathrm{n}}\text{ξ}{}^{\mathrm{<mtext>A\; =\; ?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{is}\text{ξ}{}^{\mathrm{A}}$ and $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= 0}$, whereas s is a real constant. In the case of pure radiation neutrino fields these equations become: $\text{L}\text{ξ}{}^{\mathrm{A}}\text{=}\text{case1}\text{2}\text{(p ? is)ξ}{}^{\mathrm{A}}$, $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= pl}{}^{\mathrm{\mu }}$, where p and s are in general real functions of the coordinates.     

Quantum theory of a free electron in a tapered wiggler field

It is pointed out that a slight modification of the relativistic quantum theory of a free electron in a uniform wiggler field enables the study of motion in a tapered wiggler field of the form $\text{k}{}_{\mathrm{w}}{}^1\text{= k}{}_{\mathrm{w}}\text{?}\text{b}\text{z}$ which merits attention. The lower limit of z is 800 cm. The exact relativistic quantum mechanical calculation shows an enhancement in the gain for single pass. The frequencies are up-shifted by amounts depending on the parameter b.     

Mobility edge shift in external magnetic field

It is shown that magnetoconductivity in the critical region near the metal-insulator transition is equal to $\text{A}{}_{\mathrm{l}}\text{H}$ and the coefficient A_l does not depend on the proximity to the mobility edge. The magnetic field leads to the mobility edge shift, which is proportional to $\text{H}{}^{\mathrm{<mtext>1</mtext><mtext>(2v</mtext><mtext>)</mtext>}}$, where v is the conductivity critical index.     

Poincaré gauge invariance and the dynamical role of spin in gravitational theory

We classify, according to the number of independent gauge fields, Poincaré gauge invariant theoretical frameworks of describing gravity into three categories. One of them may provide the dynamical definition of the spin tensor S and that of the energy-momentum tensor T, resulting in the response equation of matter to gravity with the gravitational field strengths, D′ and F, coupled to the former tensors

$\text{T}{}_{\mathrm{\nu }}{}^{\mathrm{\mu }}\text{;}{}_{\mathrm{\mu }}\text{=D′}{}_{\mathrm{\mu \lambda \nu }}\text{T}{}^{\mathrm{\mu \lambda }}\text{+F}{}_{\mathrm{\mu \lambda \nu \rho }}\text{S}{}^{\mathrm{\rho \mu \lambda }}$

, where the right-hand side represents spin force densities. In the absence of spin the response reduces to the conventional one of general relativity, i.e., without the spin forces. For the electromagnetic field the phase-gauge invariance requires the same conclusion as for a scalar field. For a spin $\text{1}\text{2}$ particle there is torsion, which deflects its trajectory from geodesic; an explicit expression for torsion takes a simple form of the axial vector current $\text{ψ}\text{γ}{}_5\text{γ}{}_{\mathrm{k}}\text{ψ}$.     

Nuclear polarization and signs of quadrupole moments of high-spin Gd isomers

Time-differential perturbed-angular-distribution (TDPAD) experiments have been performed on polarized intermediate- and high-spin isomers ${}^{144}\text{Gd}\text{(10}{}^{\mathrm{+}}\text{)}\text{and}{}^{147}\text{Gd}\text{(}\text{13}\text{2}{}^{\mathrm{+}}\text{,}\text{27}\text{2}{}^{\mathrm{?}}\text{,}\text{49}\text{2}{}^{\mathrm{+}}\text{)}$. Excited Gd nuclei populated by $\text{(}{}^{28}\text{Si}\text{, x}\text{n}\text{)}$ reactions were polarized by the tilted-multifoil technique and implanted in a Gd single-crystal host. Observation of the subsequent electric quadrupole interaction with the known electric field gradient yielded negative values of the sign of the deformation for all isomers studied. The magnitude of the induced nuclear polarization P_I was also determined from the TDPAD data and compared to model calculations in order to deduce the average atomic angular momentum and polarization of Gd ions at v/c ～ 0.018.     

Edge emission of CdS crystals stimulated by infrared

Excitation in the band edge region of CdS (wave numbers $\text{v}\text{≈ 20,000}\text{cm}{}^{\mathrm{?1}}$) sensitizes the crystals in the far infrared range ($\text{v}\text{≈ 200}\text{cm}{}^{\mathrm{?1}}$). The resulting characteristic sensitized i.r. absorptions (SIRA) are used at T ≈ 5 K as a measuring probe for the degree of population of donors. These donors can be emptied by irradiation with red or near infrared light ($\text{v}\text{? 2000}\text{cm}{}^{\mathrm{?1}}$). At this stimulation process, the low energy series of the green edge luminescence is emitted.     

Electron localisation in systems with purely off-diagonal randomness

A probability distribution for the off-diagonal matrix elements v_nm of the tight binding Hamiltonian is assumed to be $\text{P(v}{}_{\mathrm{nm}}\text{) =}\text{1}\text{Wv}{}_{\mathrm{nm}}$ for $\text{e}{}^{\mathrm{<mtext>?</mtext><mtext>W</mtext><mtext>2</mtext>}}\text{≤ v}{}_{\mathrm{nm}}\text{/v}{}_0\text{≤ e}{}^{\mathrm{<mtext>?</mtext><mtext>W</mtext><mtext>2</mtext>}}$ and P(v_nm = 0 otherwise. A homomorphic cluster CPA with the L(E) criterion is used to study localisation in a simple cubic lattice and a computer simulation is used to study a square lattice with the participation-ratio criterion. It is found, in both cases, that Anderson's transition takes place for a critical degree of disorder.     

Dirac equation with cylinder-symmetrical potential

For a potential V(?), $\text{?=(x}{}^2\text{+y}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, the Dirac equation is reduced to a pair of first-order differential equations in ?. The fine structure of relativistic “channeling” electrons bound to a crystal axis is calculated.     

Nuclear magnetic moment of the 9.7 h 12− isomer 196mAu

The magnetic hyperfine splitting v_M=|gμ_NB_HF/h| of ^196mAu (j^π=12^?; configuration ¦(π$\text{11}\text{2}$($\text{v}\text{13}\text{2}{}^{\mathrm{+}}\text{)〉}{}_{12}{}^{\mathrm{?}}$; $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 9.7}\text{h}\text{)}$ as dilute impurity in Ni has been determined with nuclear magnetic resonance on oriented nuclei as 96.0(2) MHz. With the known hyperfine field B_HF = ?264.4(3.9) kG corrected for hyperfine anomalies the g-factor and magnetic moment of ^196mAu are deduced to be |g| = 0.476(7) and |μ| = 5.72(8) μ_N. Taking into account the known magnetic properties of $\text{π}\text{1}\text{2}{}^{\mathrm{?}}$ and $\text{v}\text{13}\text{2}{}^{\mathrm{+}}$ isomeric states in the neighbouring odd Pt, Au and Hg nuclei the structure of the 12^? state is discussed.     

Phase transition in strongly inhomogeneous ferromagnets

A field theoretical model is proposed to describe the critical behaviour of a strongly inhomogeneous spin system with a position dependent concentration of magnetic atoms C(R) and magnetisation M(R). Assuming a finite number of $\text{n}$ Fouriermodes $\text{C}{}_{\mathrm{<mtext>Q</mtext>}}{}_{\mathrm{<mtext>v</mtext>}}\text{v}\text{= 1}$,..., $\text{n}$, to express C(R), the quenched randomness requires to interpret {$\text{Q}{}_{\mathrm{<mtext>v</mtext>}}\text{|}\text{Q}{}_{\mathrm{<mtext>v</mtext>}}\text{|}{}^2$} on a set of invariant or marginal lengths. As consequence, M(R) can be described by n Fourier-modes M_Qv, where $\text{n ?}\text{n}$. For short range spin-spin interaction, we find for strong inhomogeneity, i.e. large n, the critical exponent between those of the related homogeneous system and those of the spherical model.     

The equivalent potential for relativistic confined systems

In previous papers a method of obtaining bound states and wavefunctions for confined relativistic systems was presented. The input is the asymptotic expansion of the two-point functions. Confinement is imposed by systematic removal of the two-particle cut. We extend this method by developing an equivalent (angular momentum dependent) potential, which gives the correct wavefunction to a given order of R, the infrared scale parameter. We prove the uniqueness of the wavefunction by requiring that there are no CDD poles and by the connection of our moment conditions to the requirement that the residues of the bound-state poles must be positive. Finally we test the bound-state approximation for a system defined by an equivalent potential $\text{V(r) = λ}{}^2\text{tanh}{}^2\text{(}\text{g}{}^2\text{r}\text{λ}\text{)}$. Although in this case there is a threshold we still find excellent results when $\text{λ}{}^2\text{g}{}^2$ is large, i.c., when there are many bound states.     

Assignment of continuous spectra by photofragment spectroscopy: C state of I2

Photofragment spectroscopy has been used to probe the C state of iodine by determining its symmetry and dissociation products. By crossing a molecular beam with a powerful pulsed laser beam in high vacuum and monitoring the arrival times of the recoiling photofragments with a mass spectrometer detector, the translational energy distribution of the photodis-sociation products is measured. From energy balance the fragment internal energy is then calculated. Our peak indicates that the C state dissociates to one excited and one ground state atom. The symmetry of the transition is determined by rotating the plane of polarization of the laser light and measuring a fragment angular distribution. The transition was found to be 1 ← 0. The results are consistent with Mulliken's assignment of the C state as 1441 $\text{1}{}_{\mathrm{u}}\text{(}{}^3\text{Σ}{}^{\mathrm{+}}\text{)}$, but inconsistent with the earlier assignment of 2332 $\text{0}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{(}{}^3\text{Σ}{}^{\mathrm{+}}\text{)}$ by Mathieson and Rees.     

Graphite indium chloride studied by time-differential perturbed angular correlations of γ-rays

The technique of time-differential perturbed angular correlations of γ-rays (TDPAC) has been applied to the study of graphite indium chloride using ¹¹¹In as a probe. The results indicate the presence in the intercalated sample of two static quadrupole interactions with frequencies v⁽¹⁾_Q = 55.83±0.04 MHz and v⁽²⁾_Q = 270.44±0.05 MHz, plus a time-dependent interaction with decay constant $\text{1}\text{τ}\text{= (3.288±0.002) × 10}{}^{-2}\text{ns}{}^{-1}$. The electric field gradient components for the static interactions were determined together with corresponding asymmetry and width parameters.     

Determination of the isotopic shift of the first resonance line in Cs(I) spectrum for the isotopes 131Cs, 132Cs,and 136Cs

The isotope shifts of the resonance line $\text{λ = 8521}\text{A}\text{?}$ of ¹³¹Cs, ¹³²Cs, and ¹³⁶Cs with respect to ¹³³Cs were determined by a new scanning technique to be $\text{v}\text{?}\text{(}{}^{133}\text{Cs}\text{)-}\text{v}\text{?}\text{(}{}^{131}\text{Cs}\text{) = +1.70(40)}\text{mK}$, $\text{v}\text{?}\text{(}{}^{133}\text{Cs}\text{)-}\text{v}\text{?}\text{(}{}^{132}\text{Cs}\text{) = ?0.95(80)}\text{mK}$, $\text{v}\text{?}\text{(}{}^{136}\text{Cs}\text{)-}\text{v}\text{?}\text{(}{}^{133}\text{Cs}\text{) = ?4.0(3.0)}\text{mK}$. In accordance with results from other Cs isotopes and neighbouring elements they show the change 〈δr²〉 in the second radial moment of the nuclear charge distribution to be a factor of 5 to 10 smaller than expected from the model of uniform charge distribution. Integral isotope shifts over the isotopic chains of Xe, Cs, and Ba were analyzed in terms of collective models. Assuming an isotopic shift discrepancy of 0.5 for the nuclear volume shift it was possible to derive deformation parameters $\text{〈β}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ in quantitative agreement with those from B(E2) measurements.     

The absorption spectrum of CuH in the 2350- to 1890-Å region

The high-dispersion absorption spectrum of the CuH molecule has been photographed in the ～2500- to 1750-Å region. Observations include the previously reported $\text{D}{}^1\text{Π}\text{-X}{}^1\text{Σ}{}^{\mathrm{+}}$ and $\text{E}{}^1\text{Σ}{}^{\mathrm{+}}\text{-X}{}^1\text{Σ}{}^{\mathrm{+}}$ transitions and four new transitions which occur between 2100 and 1890 Å: $\text{F 1}{}^{\mathrm{\pm }}\text{-X}{}^1\text{Σ}{}^{\mathrm{+}}$, $\text{G 0}{}^{\mathrm{+}}\text{-X}{}^1\text{Σ}{}^{\mathrm{+}}$, $\text{H 1}{}^{\mathrm{\pm }}\text{-X}{}^1\text{Σ}{}^{\mathrm{+}}$, and $\text{I 1}{}^{\mathrm{\pm }}\text{-X}{}^1\text{Σ}{}^{\mathrm{+}}$. The $\text{D}{}^1\text{Π}$ state has been characterized through v = 2 while the new observations on $\text{E}{}^1\text{Σ}{}^{\mathrm{+}}$ include v = 11 through 16. The F, H, and I states are characterized through v = 1. All of the upper states exhibit perturbations. In addition the H 1^± and I 1^± states show signs of predissociation.     

Relation between classical and quantum formulations of the Franck-Condon principle: The generalized r-centroid approximation

The classical transition point $\text{r}{}_{\mathrm{v\prime v″}}{}^1$ for the (v′, v″) band is introduced as the point where the kinetic energy does not change during the transition (classical statement of the Franck-Condon principle). It is shown that when the r-centroid approximation is valid, it implies that the r centroid $\text{r}{}_{\mathrm{v\prime v″}}$ equals $\text{r}{}_{\mathrm{v\prime v″}}{}^1$, allowing a new connection to be made between the classical and quantum statements of the Franck-Condon principle. The r-centroid approximation fails for some classically allowed bands having large Franck-Condon factors. This occurs when the (v′, v″) band has more than one classical transition point. A generalization of the r-centroid approximation permits such bands to be used in determining the variation of the electronic transition moment with internuclear distance.     

Charm production by weak neutral currents

We discuss quantitatively the production of charm in $\text{v}\text{N and}\text{v}\text{N}$ neutral current interactions, and the anomalous lepton events that follow from semi-leptonic charm decay. Diagonal neutral currents, in the Weinberg-Salam model and similar models, predict associated charm production with small cross sections: e.g. $\text{σ(v}\text{N}\text{→ vcc}{}^{\mathrm{?}}\text{X}\text{)/σ(v}\text{N}\text{→ μ}{}^{\mathrm{?}}\text{X}\text{) ? 10}{}^{\mathrm{?2}}$ at high energy. The meagre data on vN → ve⁺X are consistent with a rate of this order. Non-diagonal neutral currents, if present, could give larger cross sections via valence p → c transitions. It should be possible to distinguish diagonal from non-diagonal contributions by their x- or u-dependences, where u = x(1 ? y). We calculate the expected energy distributions of the leptons in characteristic vN → v?⁺X and vN → v?⁺?^?X charm decay events using simple models, and discuss some practical problems in neutral current measurements.