Perturbation theory for the effective interaction in nuclei

Starting from a decomposition of the Hamiltonian H(x) of the nuclear many-body problem in the form H(x) = H₀ + xV, where H₀ is a shell-model Hamiltonian, V the residual interaction, and x a strength parameter, we introduce a general effective interaction W(x) describing the interaction of nucleons within a shell, and the associated effective operators $\text{A}\text{?}\text{(x)}$. We display some properties of these operators. From a particular choice of W(x) we obtain the expressions introduced earlier by several authors. The convergence of the expansions for W(x) and $\text{A}\text{?}\text{(x)}$ in powers of x is investigated. It is shown that W(x) and $\text{A}\text{?}\text{(x)}$ are holomorphic in a domain of the complex x-plane including the point x = 0. With the help of a generalization of the von Neumann-Wigner noncrossing rule, we exhibit the nature of the common singularity of W(x) and $\text{A}\text{?}\text{(x)}$ which is closest to the origin and thus defines the radius r₀ of convergence of the expansions of W and $\text{A}\text{?}$. It is shown that r₀ is unaffected by the cancellation of unlinked diagrams. A criterion of consistency is established, which shows that most of the practical calculations of W lead to results which are inconsistent with the definition of W.     

Nonexponential decay law

The decay of a nonstationary state usually starts as a quadratic function of time and ends as an inverse power law (possibly with oscillations). Between these two extremes, the familiar exponential decay law may be approximately valid. The main purpose of this paper is to find the conditions which must be satisfied by the Hamiltonian and by the initial state, for the exponential law to have a significant domain of validity. It is shown that the evolution of a nonstationary state is governed by a nonnegative function W(E), having the dimensions of an energy. Among its properties are: the energy uncertainty is given by $\text{(ΔH)}{}^2\text{= ?W(E)dE}$, and the inverse lifetime by Γ = 2πW(E₀), where E₀ is the expectation value of H. The detailed shape of W(E) defines two characteristic times between which the exponential decay law is a good approximation: roughly speaking, the smoother W(E), the larger the domain of validity of the exponential law. For instance, if W(E) is very smooth ($\text{|}\text{dW}\text{dE}\text{| ? 1}$) except for a sharp threshold at E = E_thr, the transition from quadratic to exponential decay occurs for $\text{t ?}\text{1}\text{(E}{}_0\text{? E}{}_{\mathrm{<mtext>thr</mtext>}}\text{)}$, and the transition from exponential to inverse power law when $\text{Γt ?}\text{log}\text{[}\text{(E}{}_0\text{? E}{}_{\mathrm{<mtext>thr</mtext>}}\text{)}\text{Γ}\text{]}$.     

Can the optical excitations of surface plasmons be used to study (liquid) metal surfaces?

The surface plasmon dispersion relation is obtained for a metal with a free electron density given by N(z) = N_b + (N_s ? N_b) exp $\text{(}\text{?z}\text{a}\text{)}$ for z ? 0 and N = 0 for z < 0. We have used a local theory which includes the effects of retarded fields and found the dispersion relation to be sensitive to the parameters $\text{(N}{}_{\mathrm{s}}\text{? N}{}_{\mathrm{b}}\text{)}\text{N}{}_{\mathrm{b}}$ and a, which characterize our density profile.     

Phenomenological consequences of N = 1 supergravity theories with non-minimal kinetic energy terms for vector superfields

It is shown that N=1 supergravity theories can have a GUT scale as large as the Planck scale if the kinetic energy terms for vector superfields are non-minimal. The canonical values for sin²θ_W (M_W), α₃ (M_W) and $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}\text{(M}{}_{\mathrm{<mtext>W</mtext>}}\text{)}$ are respected. In those theories masses of SU(3), SU(2) and U(1) gauginos may be different at the unification scale. Consequences for the low-energy particle spectrum are discussed in the extreme case where one of the gaugino masses is large while the other two vanish.     

Photoelectron spectra of pyromellitic dianhydride,dithioanhydride and diimide and of trimellitic anhydride

The photoelectron (He(I)) spectra of the tricyclic tetracarbonyl compounds pyromellitic dianhydride, dithioanhydride and diimide and of the tetracyclic hexacarbonyl compound trimellitic anhydride have been investigated. To aid the interpretation of the main features of the spectra, i.e. the ordering and splitting of the ⁿCO ionisations and the behaviour of the ‘benzenic’ and heteroatom π ionisations, MO calculations based on a ZDO pragmatic model and semiempirical SCF-PP calculations have been carried out. The evolution of the ⁿCO and π_X ionisations upon progressive fusion of anhydride moieties with a benzene nucleus is analysed in detail. The proposed orbital sequences for the n orbitals are: a_g(S⁺) $\text{\$}\text{?}$b_1u(AS⁺) $\text{\$}\text{?}$b_2u(S^?) $\text{\$}\text{?}$b_3g(AS^?) for the tetracarbonyls and a′₁(S⁺) $\text{\$}\text{?}$e′(AS⁺) $\text{\$}\text{?}$a′₂ (AS^?) ≈ e′(S^?) for the hexacarbonyl.     

Continuum limit of QED2 on a lattice

A path integral is defined for the vacuum expectation values of Euclidean QED₂ on a periodic lattice. Wilson's expression is used for the coupling between fermion and gauge fields. The action for the gauge field by itself is assumed to be a quadratic in place of Wilson's periodic action. The integral over the fermion field is carried out explicitly to obtain a Matthews-Salam formula for vacuum expectation values. For a combination of gauge and fermion fields $\text{G}$ on a lattice with spacing proportional to N^?1, N?Z⁺, the Matthews-Salam formula for the vacuum expectation 〈G〉_N has the form ($\text{G}$)_N=∫d_nu;W_N($\text{G}$,f), where dμ is an N-independent measure on a random electromagnetic field ? and $\text{W}{}_{\mathrm{N}}\text{(G, ?)}$ is an N-dependent function of ? determined by $\text{G}$. For a class of $\text{G}$ we prove that as N → ∞, $\text{W}{}_{\mathrm{N}}\text{(C, ?)}$ has a limit $\text{W(G, ?)}$ except possibly for a set of ? of measure zero. In subsequent articles it will be shown that ∫d_nu;W_N($\text{G}$,f) exists and lim_N→∞∫d_nu;W_N($\text{G}$,f).     

Irreducible gauge theory of a consolidated Salam-Weinberg model

We derive the Salam-Weinberg model by gauging an internal simple supergroup $\text{SU}\text{(}\text{2}\text{1}\text{)}$. The theory uniquely assigns the correct SU(2)_L ? U(1) eigenvalues for all leptons, fixes θ_W = 30°, generates the W^±_σ, Z⁰_σ and A_σ together with the Higgs-Goldstone $\text{I}{}_{\mathrm{<mtext>L</mtext>}}\text{=}\text{1}\text{2}$ scalar multiplets as gauge fields, and imposes the standard spontaneous breakdown of SU(2)_L ? U(1). The masses of intermediate bosons and fermions are directly generated by $\text{SU}\text{(}\text{2}\text{1}\text{)}$ universality, which also fixes the Higgs field coupling.     

The velocity distribution and the density near a particle of an equilibrium two component plasma

The electronic and ionic velocity distributions and densities of an equilibrium two component plasma at distances from a test particle (electron or ion) smaller than the interparticle distance, are derived using a technique developed recently by the author. In the case of particles repelled by the test particle the results agree with the results obtained by integrating the Gibbs distribution. In the case of particles attracted by the test particle however, the velocity distribution has the form of a translated maxwellian with an empty sphere in the middle and the asymptotic form of the density as r → 0 is given by n_a(r) ～r^{$\text{-1}\text{2}$}. By the latter formula the classical problem of stability of matter is locally resolved without using short distance repulsive potentials.     

A new electronic band system of PbO

The chemiluminescence spectrum of atomic Pb reacting with O₃ under single-collision conditions includes a series of 55 bands in the regions 450–850 nm. A vibrational analysis is obtained which shows emission is to the ground state of PbO from excited electronic states not previously analyzed. Forty-nine of the bands are assigned to the a(1)-X(0⁺) transition and the remaining six are tentatively identified as the forbidden b(0^?)-X(0⁺) transition. Both the a and b states are believed to be Hund's case (c) components of the ³Σ⁺ states arising from the configuration $\text{σ}{}^2\text{π}{}^3\text{π}{}^1$. The vibrational parameters of the a state are ν₄ = 16 029 ± 8, ω_e′ = 478.7 ± 1.9, and ω_ex_e′ = 2.292 ± 0.128 cm^?1, where the uncertainties represent two standard deviations of the least-squares fit. Emission is also observed from the PbO B state produced in the reaction of metastable Pb atoms with O₃. Using pulsed laser excitation, an attempt is made to determine radiative lifetimes. We find for the PbO A(0⁺) state τ = 3.74 ± 0.3 μsec, and for the PbO B(1) state τ = 2.58 ± 0.3 μsec, while for the a(1) state τ is estimated to be greater than 10 μsec. From the vibrational analysis, energy conservation arguments place a lower limits to the ground state dissociation energy of $\text{D}{}_0{}^0\text{(}\text{PbO}\text{) ≥ 3.74 ± 0.03}\text{eV}$ (86.2 ± 0.7 kcal/mole). For the Pb + O₃ reaction we find less than 1% of the products are PbO¹ molecules that emit in the visible. Correlations are made with the low-lying states of other Group IV chalconides based on the assignment of the PbO $\text{a}{}^3\text{Σ}{}^{\mathrm{+}}\text{(1)}$ state and the correspondence between the low-lying triplet states of PbO and CO.     

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.     

Petrov classification of supergravity

N = 1 supergravity is analyzed in light of the Petrov classification scheme. It is found that the ($\text{2,}\text{3}\text{2}$) chiral multiplet obtained must be recognized as the Weyl submultiplet, W_abα, where only $\text{(}\text{3}\text{2}\text{, 0) + (0,}\text{3}\text{2}\text{)}$ components contribute. Due to the SUSY transformation laws the classes of solutions allowed for various Petrov types are shown to be restrictive — indeed, in certain instances there can be no consistent solution. The freedom left in the solutions and their possible interpretation are discussed. One-loop invariants are also considered by resorting to non-covariant forms.     

Electronic emission spectrum attributed to the arsenic monoselenide radical

Six red degraded bands in the region 5300–5700 Å have been observed and attributed to the radical AsSe. Arguments are presented to suggest that the bands arise from two subsystems of a²Π_r(a)-X²Π_r(a) transition and that the value of $\text{Δ}\text{G}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{″}$ is approximately 281 cm^?1.     

The Kosterlitz-Thouless transitions by the mayer expansion finiteness of the perturbations

The Kosterlitz-Thouless transitions in 2D XY and Coulomb gas models are discussed by the Mayer expansion. After transforming the 2D XY model into a (generalzed) 2D Coulomb gas model by the duality transformation, it is shown that the free energy (pressure) and the two point correlation function 〈cos(θ₀?θ_ζ)〉 are expressed as Σa_N(β) and $\text{exp}\text{[(}\text{2}\text{β}\text{) C}{}_0\text{(ζ) + Σb}{}_{\mathrm{N}}\text{(β:ζ)]}$, respectively, for large inverse temperature β > β_c, where {a_N(β)} are the usual virial coefficients and {a_N, b_N} are the contributions from N-electron system. Moreover C₀(ζ) ? ? (2π)^?1 log(|ζ| + 1), |a_N(β)| ≤ C₁(N) exp[?βK₃N] and |b_N(β:N) ≤ C₂(N) exp[?βK₄N] |C₀(ζ)| (K_i > 0). By comparing this system with the dipole gas system in which these series converge absolutely, it is conjectured that these series converge absolutely for large β.     

Thickness dependence of the surface-polariton relaxation rates in a crystal slab

A few useful formulas are derived concerning the damping properties of long-wavelength surface polaritons (SP) in a crystal slab. For example, it is shown that the SP propagation length in a metal slab with thickness 2a satisfying $\text{ω}{}_{\mathrm{p}}\text{a}\text{c}\text{< 1}$ (c is the velocity of light and ω_p the electronic plasma frequency) is increased by the factor $\text{3}\text{2}\text{(}\text{c}\text{ω}{}_{\mathrm{p}}\text{a}\text{)}{}^4$ in comparison with the corresponding value for SP in a semi-infinite metal.     

New evaluation of muon (g − 2) hadronic anomaly

The hadronic part a_H of the muon g-factor anomaly $\text{a ≡}\text{(g ? 2)}\text{2}$ is evaluated from latest data on σ(e⁺e^? → hadrons). For a p-wave ππ scattering length of a₁ = 0.04±0.005 we calculate a_H = (66±10) × 10^?9, compared to a(experiment) ? a(QED) = (60±29) × 10^?9. Half of the uncertainty on a_H is associated with the energy interval $\text{0.92 <}\text{s}\text{< 2}\text{GeV}$.     

Operator formulation of Regge asymptotic behavior

If the appropriate high-energy limits of the amplitudes $\text{W ≡ ?}\text{d}\text{x}\text{e}{}^{\mathrm{<mtext>i</mtext><mtext>q\; ·\; x</mtext>}}\text{<b|j(x)j′(0)|b′ >}$ are Regge pole dominated, then the large distance (x₀ → ∞, x²fixed) behavior of the current product is completely characterized by an operator expression $\text{R}\text{(x : 0)}$, involving only local operators at 0, which is such that $\text{R ≡ ?}\text{d}\text{x}\text{e}{}^{\mathrm{<mtext>i</mtext><mtext>q\; ·\; x</mtext>}}\text{<b|}\text{R}\text{|b′ >}$ and W have the same high-energy behavior. In the only case (|b> a single particle stateand |b′> the vacuum) where W is not Regge behaved, it is shown that R is identical to W, and so the relation $\text{jj′ →}\text{R}$ is established as a large distance operator expansion, valid between all states. $\text{R}$ is expressed as a differential operation B(□_x, ?_x · ?₀, □₀) on the light-cone expansion and some of its properties are deduced by carrying out the differentiations. A second form of $\text{R}$ is given in terms of non-local “reggeon” field operators R_αm(0) (α is a (fixed) spin index and m is a (variable) helicity index) which might be useful coordinate in reggeon field theories. These operators can be used to define reggeon-particle amplitudes and if conventional double-Regge and triple-Regge behaviors are further assumed, the large distance behaviors of the current-reggeon and reggeon-reggeon field products are specified in terms of other reggeon fields.     

Electrical charging of non-conductors in a photoelectron spectrometer; effect of X-ray source voltage

The electrical charging on samples of gadolinium trifluoride, sodium fluoride and fused silica, has been investigated as a function of the voltage in the X-ray source of a photoelectron spectrometer. The results can be expressed in the form,E_c = d + c(V – V₀) + a(1 - e^{?b(V – V₀)}) an equation which expresses the linear dependence of the intensity of the photoelectrons on X-ray intensity and the dependence of the low energy electrons as that corresponding to the equivalent electrical circuit consisting of an emf, a capacitor, and a resistor. With gadolinium trifluoride and sodium fluoride, both of which have a relatively high photoconversion, the electrical potential is positive for all voltages. With fused silica, which has a relatively low photoemission, the electrical potential is negative for the lower voltages. Relative to an assumed value of 83.8 eV for the binding energy for Au(4f_{$\text{7}\text{2}$}) of gold deposited on NaF and GdF₃, the charge corrected values for F(1s) and the Gd(4f_{$\text{sol7}\text{2}$}) orbital binding energies are determined to be 684.57 ± .07 and 10.1 eV, respectively.     

The analyzing power for neutron scattering from 9Be at 9 to 17 MeV

Time-of-flight techniques were used to measure the analyzing power for the scattering of neutrons from ⁹Be at energies from 9 to 17 MeV. Because of the high nuclear density of beryllium, particular attention was paid to finite-geometry and multiple-scattering effects. For representing the data, an unusual method of Legendre-coefficient analysis was used to establish the smooth energy dependence of both the cross section σ(θ) and the analyzing power A_y(θ). Spherical optical-model calculations were able to describe the σ(θ) and A_y(θ) data simultaneously, but only after the introduction of an imaginary spin-orbit potential W_s.o.(r). The geometry of the W_s.o.(r) term was found to be the same as that of the surface-peaked imaginary central potential. Coupledchannels calculations using a quadrupole-deformed rotational model built on the $\text{3}\text{2}{}^{\mathrm{?}}$ ground state were able to describe inelastic scattering to the $\text{5}\text{2}{}^{\mathrm{?}}$ and $\text{7}\text{2}{}^{\mathrm{?}}$ excited states, but also required a W_s.o.r potential.     

Quantizing a classically ergodic system: Sinai's billiard and the KKR method

Sinai's “billiards on a torus,” i.e., free motion of a particle in a plane amongst reflecting discs of radius R centred on points of the unit square lattice, is a classically ergodic system with two freedoms, parametrized by R. Quantal energy levels E_n are given by the vanishing of the Korringa-Kohn-Rostoker (KKR) determinant of solid state theory. This gives a rapid computational scheme for computing E_n as functions of R. Except for the integrable case R = 0, no degeneracies are found, illustrating the theorem that two parameters, not one, are required to make levels cross in a generic system. The same theorem leads to the prediction that the probability distribution of the spacings S of neighbouring levels is $\text{O}$(S) as S → 0, in good agreement with computation. The KKR determinant is transformed analytically to give the level density d(E) semiclassically (i.e., as ? → 0) as the sum of a steady contribution $\text{d}\text{?}\text{(E)}$ and an oscillatory contribution d_osc(E). $\text{d}\text{?}$ is $\text{O}$(?^?2) and is given by the Weyl “area” formula plus “edge,” “corner” and “curvature” corrections, in excellent agreement with computation. d_osc is given by a sum over classical closed orbits (all unstable). Nonisolated closed orbits (not hitting discs) contribute terms with $\text{O}$$\text{(?}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext><mtext>)</mtext>}}$ to d_osc, while isolated closed orbits (bouncing between discs) contribute terms with $\text{O}$(?^?1) to d_osc. The isolated orbits are vastly more numerous than the nonisolated orbits and their contributions cannot be neglected. As a means of calculating the individual E_n (rather than the smoothed spectrum), the KKR method is much more efficient than the classical path sum.