On the Deser,Gilbert, Sudarshan representation for functions Wi(ν, q2)(i = 1, 2) describing the electroproduction process

The Deser, Gilbert, Sudarshan representation (D.G.S.R.) for the functions W_i(ν, q²) (i = 1,2) is considered as equations determining spectral functions h_i(a, α) via the values W_i(ν, q²) in the physical region of the electroproduction channel. It is shown that if W_i(ν, q²) obey the microcausality and spectrality conditions, then the equations for h_i(a, α) have solutions in the class of Schwartz temperated distributions and thereby the D.G.S.R. is proved. Formulae are obtained expressing spectral functions in the D.G.S.R. through the values of functions W_i(ν, q²) in the physical region of the electroproduction channel.     

Lower bounds to the I = 0, I = 2 ππ s-wave scattering lenghts

Roy's exact partial wave equations allow us to find bounds for any linear combination of the isospin I = 0 and s-wave scattering lengths, with positive coefficients. The bound is a function of the quantity a_D = a₂⁽⁰⁾ + a₂⁽²⁾, where a₂^(I) are the D-wave sacttering lengths. Thus, we can draw on the (a₀⁽⁰⁾, a₀⁽²⁾) plane an allowed domain whose boundary is fairly close to the phenomenological region. For a value of a_D = 1.7×10^?3, we find the following particular bounds: a₀⁽⁰⁾??0.49, a₀⁽²⁾??0.29.     

On spectral representations for the functions Wi(v, q2) (i = 1, 2) describing electroproduction process

It is shown that the Deser, Gilbert, Sudarshan representation (DGSR) does not follow from microcausality and spectrality only. Examples of the functions W_i(v, q²) satisfying the microcausality and spectrality conditions are given which cannot be written as the DGSR with spectral function h(a, α) that is a temperature distribution. Instead of the DGSR the spectral representation for W_i(v, q²) has been proved (eq. (3)) which follows only from microcausality and spectrality.     

Measurement of the coherent neutron scattering length of 3He by neutron interferometry

A precise determination of the coherent scattering length of ³He with a neutron interferometer yields a value a_c = 4.29 ± 0.04 fm. A comparison with varoous theoretical perdictions is made and its relation to the few-body problem is discussed. A combination with other experimental results yield as most probable values for the free singlet- and triplet scattering length a_s = 8.0 ± fm and a_t = 3.05 ± 0.07 fm, respectively.     

On the entropy of systems undergoing time evolution

The aim of the present paper is to discuss the behaviour of entropy of physical systems undergoing time evolution. We discuss the case of an infinite-dimensional separable Hilbert space $\text{H}$ where the entropy of a microstate ? is given by the formula s(?) = ?Tr(?ln?). Information about a physical system is given by the mean values Tr(?A_i) = m, i = 1, …, N, of N self-adjoint (not necessarily bounded) operators A_i.     

Dynamical spin system: Exact solution and mean recurrence time

A model involving a chain of N ≥ 2 spins s_i = ±1, i = 1,…,N, evolvi ng syncronously in discrete time t via a nonlinear, autonomous transformation s_i(t+1) = s_i(t)s_i+1(t), i = 1,…,N−1; s_N(t+1) = s_N(t), is presented. The transformation equations are solved explicitly and the detailed decomposition of state space into ergodic sets is found. On the assumption of equally likely initial states, the mean recurrence time is calculated and its variance is discussed. The model displays a strikingly sensitive dependence on the number of spins, and this is reflected in the “staircase” behavior of the mean recurrence time. Remarks are made regarding the connection between the behavior of the model and the ground states of a related two-dimensional Ising model.     

Hyperfine-structure investigation in the 6s5d configuration of135Ba and137Ba

The hyperfine structure of the metastable states of the 6s5d configuration of¹³⁵Ba and¹³⁷Ba has been studied by the atomic-beam magnetic resonance (ABMR) method. The metastable barium states were populated in a plasma-discharge inside the atomic-beam oven. The atoms emerging from the ABMR-apparatus were detected by the use of a dyelaser. Compared to conventional methods this technique has the advantage of being state selective. The following magnetic dipole and electric quadrupole interaction constantsa andb have been obtained:¹³⁷Ba:a(³ D ₁)=?520.536 (3) MHzb(³ D ₁)=17.890 (3) MHza(³D₂=415.928 (3) MHzb(³D₂)=25.899 (13) MHza(³D₃)=456.559 (4) MHzb ³D₃=47.390 (16) MHz¹³⁵Ba:a ³ D ₁=?465.166 (4) MHzb(³D₁)=11.642 (4) MHza(³D₂)=371.736(4) MHzb ³ D ₂=16.745 (14) MHza(³D₃)=408.038 (6) MHzb(³D₃)=30.801 (24) MHz Using these constants and the earlier known ones for the¹ D ₂ state the hyperfine structure for the 6s5d configuration has been analyzed with an effective hyperfine hamiltonian. Hyperfine parameters obtained from the analysis have been compared with theoretical values calculated with relativistic self-consistent-field (SCF) wavefunctions. The quadrupole moments have been evaluated with the following result Q(¹³⁵Ba) =0.20(3)b and Q(¹³⁷Ba) = 0.34(4)b uncorrected for the quadrupole shielding.     

Strong-coupling constant in coordinate space

The coordinate-space behavior of (vector) strong-coupling constant in the background field α_B(r) is compared with that in standard perturbation theory α_v(r). The numerically calculated two-loop coupling constant α_B(r) is shown to exceed α_v(r) by 1–5% at very small distances, r?0.02 fm, and to be in agreement with lattice measurements of the static potential. At large distances, α_B(r) approaches the freezing value at r?0.5 fm. An analytic form of α_B(r) is proposed that approximates α_B(r) with a precision ?2% in the region r?0.5 fm.     

Perturbation allowed transitions in the infrared spectrum of 14ND3: determination of the K-dependent parameters in the ground state

ABSTRACT

Accurate values of the K-dependent constants ^{( i )} C, ^{( i )} D_K and ^{( i )} H_K in the ground state of ¹⁴ND₃, with i = s, a, have been determined for the first time thanks to the detections of ‘perturbation allowed’ transitions in the ν₁, ν₂, ν₃, ν₄ and 2ν₄ infrared bands. The rotation–inversion and inversion transitions from the literature, together with 7289 ground state combination differences from the infrared vibration–rotation–inversion transitions have been simultaneously analysed. The adopted rotation–inversion Hamiltonian includes distortion constants up to the eighth power and the Δk = ±3 and Δk = ±6 interaction terms. Precise values of the diagonal constants and of the Δk = ±3 interaction coefficients have been obtained. Accurate values of the ground state term values have been calculated for both s and a levels up to J = 21.     

Study of cross sections for the loss of outer 1s, 2s, and 2p electrons by fast ions and atoms of light elements

In the case of light-element ions propagating with velocities V = 1.83 and 3.65 au in H₂, He, N₂, Ne, and Ar, the loss cross sections σ_{i, i+m} for m electrons (m = 1, 2, 3) are considered. The partial loss cross sections σ_i(nl) for one of the outer 1s, 2s, or 2p electrons are determined using the obtained data. It is shown that the experimental cross sections for the loss of the 1s and 2s electrons by positive ions qualitatively agree with the theoretical values calculated in the Born approximation. In the case of the ion velocity V = 1.83 au, the cross sections σ_i for 2p electrons are greater than the cross sections σ_i (1s) and σ_i (2s) by a factor of 1.2–3 for the same binding energies of electrons in the ion (I _nl > 20 eV). It is found experimentally that, at V = 1.83 au, the cross sections σ_i (2p) for I _nl ～ 10–20 eV are less than the cross sections σ_i (1s) by a factor of 2–3, which is probably caused by a decrease in the screening parameter (θ_2p < 1) of the outer shell of atoms.     

Mass distribution in n—polymer stochastic aggregation and large—mass behaviour

The exact solutions of the rate equations of the n-polymer stochastic aggregation involving two types of clusters, active and passive for the kernel \dprⁿ_k=1s_(ik)(s_(ik)=i_k) and \dsumⁿ_k=1s_(ik)(s_(ik)=i_k), are obtained. The large-mass behaviours of the final mass distribution of the active and passive clusters have scaling-like forms, although the models exhibit different properties. Respectively, they have different decay exponents γ=\dfrac{2n+1}{2(n-1)} and γ=q+\dfrac{2n+1}{2(n-1)} for \dprⁿ_{k=1}s(ik)(s(ik)=ik) and γ=\dfrac 3{2(n-1)} and γ=q+\dfrac 3{2(n-1)} for \dsumⁿk=1}s(ik)(s(ik)=ik), which include exponents of two-polymer stochastic aggregation. We also find that gelation is suppressed for kernel \dprⁿk=1s(ik)(s(ik)=ik) which is different from the deterministic aggregation.}     

New determination of the neutron-proton scattering amplitude and precise measurements of the scattering amplitudes on carbon,chlorine, fluorine and bromine

After an improvement on the theory of the neutron-gravity-refractometer and after refinements of the experimental procedure we have performed new measurements of the absolute value of the neutron-proton scattering amplitude at low neutron energies. In order to obtain and to confirm a very high accuracy we carried out neutron-reflection experiments on 18 various liquids of 11 different organic substances containing the elements carbon, hydrogen and/or chlorine. Compounds with fluorine and bromine were used to measure the scattering amplitudes of these elements. We found the coherent scattering amplitudes of the bound atoms to be:a _H=?3.7409(1l)fm,a _c=6.6484(13)fm,a _c1=9.5792(8)fm,a _F=5.66(2)fm anda _Br=6.79(2)fm. The low energy (n, p)-parametersa _t anda _s were calculated with the presenta _H and a new value of the (n, p) scattering cross-sectionσ ₀. By comparing the measureda _C with values obtained from precise transmission experiments we could determine the gravitational accelerationg _f of the free neutron in terms of the local value g. We found the two values to be equal:g _f =0.9996(7)g.     

Elastic scattering of 40Ar on 40Ca at Elab = 191, 236 and 272 MeV

Cross sections for elastic scattering of ⁴⁰Ar on ⁴⁰Ca have been measured at energies E_lab = 191, 236 and 272 MeV employing position-sensitive detectors and the method of kinematical coincidences. The experimental data are first compared with the ordinary and the generalized Fresnel models. Only the generalized Fresnel model describes the experimental data well. An optical model analysis with a Woods-Saxon potential yields an energy independent set of parameters (V_R = ?21.76 MeV, r_OR = 1.37 fm, a_R = 0.45 fm; W₁ = ?13.69 MeV, r₀₁ = 1.40 fm, a₁ = 0.36 fm) very similar to the one found in ⁴⁰Ca-⁴⁰Ca scattering at corresponding energies. Values deduced for the total reaction cross sections for the three energies are in good agreement with those predicted by the generalized Fresnel model. The data are also compared with optical model calculations with the real part of the potential replaced by various microscopically determined potentials. The proximity, Fleckner-Mosel and the Krappe-Nix-Sierk potentials like the phenomenological optical model potential reproduce the measured data fairly well over several orders of magnitude.     

On the unitary pole expansion of the potentials I and III of Malfliet and Tjon

The unitary pole expansion for the local soft-core potentials I and III of Malfliet and Tjon is obtained, and the Faddeev-Lovelace equations are solved for the separable potentials. The energyE _T of the triton and the doublet scattering length² a have been obtained. The results are ?8.59 MeV ≦E_T≦ ?8.57 MeV and 0.89 fm≦² a≦0.91 fm. For the quartet scattering length a value₄ a = 6.39 fm has been found.     

Reaction dependence of nuclear decay linewidths

Various light- and heavy-ion reactions, 20 < E < 100 MeV, have been used to study the reaction dependence of α-decay widths for ⁸Be¹(2 ⁺ , 2.9 MeV) and ¹⁶O¹(1^?, 9.6 MeV). Although slight differences (< 20 %) are found for the observed line shapes (Γ), the resonance widths inferred (Γ_R) are self-consistent and indicate little if any reaction dependence (< 10 %). Near a decay threshold one may expect Γ < Γ_R by 20 % or more, however, and thus care must be taken in comparing decay widths inferred from nuclear reactions with those from scattering resonances. Reduced formal α-decay widths of γ_λ² = 680 ± 100 keV (s = 4.8 fm) and γ_λ² = 350 ± 50 keV(s = 5.4 fm), corresponding to θ_λ² = 0.50 and θ_λ² = 0.49 are deduced for ⁸Be¹(2 ⁺ , 2.9 MeV) and ¹⁶O¹(1^?, 9.6 MeV) using the nuclear-reaction Γ_R values and a particular set of α-nucleus potentials.     

Modal content of noise generated by a coaxial jet in a pipe

The problem investigated was that of noise generated by air flow through a coaxial obstruction in a long, straight pipe of inside diameter, D = 97 mm. Downstream modal pressure spectra in the 200–6000 Hz frequency range were measured by a new technique [1] for orifices and nozzles of diameter d where $\text{0·03 ? (}\text{d}\text{D}\text{) ? 0·52}$. The Mach numbers of the flow through the restrictions ranged from 0·15 to choked conditions. The shape of the modal frequency spectrum was found to be determined by the frequency ratio $\text{f}{}_{\mathrm{r}}\text{=}\text{He}\text{St}\text{=}\text{U}{}_{\mathrm{i}}\text{D}\text{a}{}_0\text{d}$, where U_i is the jet velocity and a₀ is the speed of sound in the gas downstream of the restriction. This parameter is the ratio of two non-dimensional frequencies: namely, He, which controls acoustic propagation inside circular ducts, and St, which scales the jet noise spectrum shape. At low f_r(<3) the higher modes dominate the noise spectrum above their cut-off frequencies, while for higher f_r all modes are approximately of equal amplitude. The nature of large scale turbulence structures in the region of the jet near the nozzle exit may be used to explain these phenomena. The measured modal pressure spectra were converted to modal power spectra and integrated over the frequency range 200–6000 Hz. The acoustic efficiency levels (acoustic power normalized by jet kinetic energy flow), when plotted vs. jet Mach number, depend strongly on the ratio of restriction diameter to pipe diameter ($\text{d}\text{D}$). Dividing the efficiency levels by the area ratio, $\text{(}\text{d}\text{D}\text{)}{}^2$, correlated the results over a moderate range of ($\text{d}\text{D}$).     

On the generality of the mass sum rule

The sum rule, Σ_i(?1)^2J_i(2J_i+1)m_i²=2Σ_aD^aTrQ^a, is studied to first order in supersymmetry breaking, treating the other interactions exactly. It is found to hold for spontaneous breaking and many types of explicit breaking.     

A study of the n-n interaction from a complete experiment of the n + d break-up at 14.5 MeV

Results of the analysis of two complete experiments on ²H(n, nnp) at 14.5±0.1 MeV are given. In the first n-n final-state-interaction (f.s.i.) experiment (neutron lab angles θ₁ = θ₂ = +30°, n-n relative energy E_nn measured between 0 and ≈ 800 keV) about 4400 events were recorded. In the second n-p f.s.i. experiment (neutron lab angles θ₁ = +30°, θ₂ = −80°, and E_np ? 500 keV) about 2860 events were recorded. The analysis has been done by exact solutions of the Faddeev equations with separable potentials: the Amado model was extended using the Yamaguchi potential with charge-independent (a_nm = a_np) and with charge-dependent (a_nn = −16 fm, a_np = −23.7 fm) parameters. The results are: (a) the charge-independent (a_nn = −23.7 fm) model seems to give a better fit for the shape of the n-n f.s.i. peak, but (b) the two-nucleon separable potential calculations disagree by a factor ≈ 2 with the absolute cross sections measured for the f.s.i. peaks.     

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 $\text{0.92 <}\text{s}\text{< 2}\text{GeV}$.