LOCV calculation of nuclear matter with relativistic Hamiltonian

The equation of state of symmetric nuclear matter is calculated using the relativistic Hamiltonian (H_R) with potentials which have been fitted with the N -N scattering data using the relativistic two-body Hamiltonian ( [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} and the non-relativistic two-body Hamiltonian, i.e. the Argonne V₁₄ interaction. The boost interaction corrections as well as the relativistic one-body and two-body kinetic energy corrections in cluster expansion energy within the lowest-order-constrained variational method are calculated. It is shown that the relativistic corrections reduce the binding energy by 1.5MeV for [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} and AV₁₄ interactions. The symmetric nuclear-matter saturation energy is about -16.43 MeV at r \rho = 0.253 (fm^-3) with [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} interaction plus relativistic corrections. Finally, various properties of the symmetric nuclear matter are given and a comparison is made with the other many-body calculations.     

Some results for SU(N) gauge-fields on the Hypertorus

We show how to prove and to understand the formula for the “Pontryagin” indexP for SU(N) gauge fields on the HypertorusT ⁴, seen as a four-dimensional euclidean box with twisted boundary conditions. These twists are defined as gauge invariant integers moduloN and labelled byN _μv (=?N _μv ). In terms of these we can write (ν∈#x2124;) $$P = \frac{1}{{16\pi ^2 }}\int {Tr(G_{\mu v} \tilde G_{\mu v} )d_4 x = v + \left( {\frac{{N - 1}}{N}} \right) \cdot \frac{{n_{\mu v} \tilde n_{\mu v} }}{4}} $$ . Furthermore we settle the last link in the proof of the existence of zero action solutions with all possible twists satisfying \(\frac{{n_{\mu v} \tilde n_{\mu v} }}{4} = \kappa (n) = 0(\bmod N)\) for arbitraryN.     

Production of colored scalar particles in <Emphasis Type="Italic">pp</Emphasis> collisions and masses of scalar gluons from future LHC data

The production of pairs of scalar particles belonging to an arbitrary color multiplet of the SU _c (3) group in proton-proton collisions is considered, and the differential and total cross sections for the corresponding partonic processes are obtained. The total cross section for the production of octets of scalar gluons F ₁ and F ₂ at LHC is calculated versus their mass, and their dominant decays, which are necessary for their searches, are discussed. It is shown that, for mF ₁ ≲ 1000 GeV, the number of signal $ t\tilde tb\tilde b $ t\tilde tb\tilde b events fromthe decays of the scalar gluon F ₁ may exceed substantially (by not less than three standard deviations) the Standart Model background and that the cross section for the production of scalar gluons F ₁ and F ₂ having masses in the region m _F1,m _F2 ≲ 1300 GeV may be sufficient for the efficient (N _events ≲ 100–1000 at L = 10–100 fb⁻¹) production of these particles at LHC.     

Relativistically invariant analysis of -isobar production in deuteron electrodisintegration: : General analysis of polarization effects

The differential cross-section and the polarization observables for Δ-isobar production in the deuteron electrodisintegration process, e^-+d→e^-+Δ+N, are calculated in a general formalism based on structure functions. The obtained expressions have a general nature, hold for one-photon-exchange, assuming P-invariance of the electromagnetic interaction and the conservation of the hadron electromagnetic current. The dependence of the differential cross-section of the e^-+d→e^-+Δ+N reaction on the vector and tensor polarizations of the deuteron target with unpolarized and longitudinally polarized electrons is considered. The general dependence of the asymmetries on two of five kinematic variables, the azimuthal angle φ and (linear polarization of the virtual photon) is calculated. A similar analysis is performed for the polarization of the nucleon produced in γ^*d→ΔN reaction provided the electron beam is unpolarized or longitudinally polarized. Polarization effects, which are due to the strong ΔN-interaction in the final state are calculated. The photoproduction of the Δ-isobar on the deuteron target has been considered in detail, as a particular case. The differential cross-section and various polarization observables have been derived in terms of the reaction amplitudes. The polarization observables due to the linear and circular polarizations of the photon, when the deuteron target is arbitrarily polarized have been derived in terms of the reaction amplitudes. The polarization of the final nucleon is also considered.     

Pion production by protons on nuclei near the threshold

We propose including in the calculation of the cross section of the process p + N → N + N + π the process of pion production and absorption that proceeds through creation of a Δ-resonance. By taking into account the energy dependence of Δ-resonance width, the contribution of deuteron channel is included in the cross section of π⁰-, π⁺-meson production.     

The concept of a powerful antineutrino source

A powerful antineutrino source with a hard [(n)\tilde] _e\tilde \nu _e spectrum obtained upon the (n, γ) activation of the ⁷Li isotope and the subsequent β⁻ decay (T _1/2 = 0.84 s) of the ⁸Li isotope with the emission of high-energy [(n)\tilde] _e\tilde \nu _e with E _v of up to 13 MeV was discussed. The source can be constructed both in the static regime (by covering the active reactor zone with highly purified ⁷Li) and in the dynamic regime of operation. In the dynamic regime, lithium is pumped over in a closed cycle through a converter (i.e., a volumetric reservoir) close to the active reactor zone and further to a remote detector. The source can be constructed on the basis of both highly purified ⁷Li isotope in the metal state and chemical compounds of the ⁷Li isotope. The setup can be developed on the basis of an intensive neutron source or an accelerator with a neutron-producing target. In the dynamic regime, the proposed lithium antineutrino source enables us to increase the cross-section of the ([(n)\tilde] _e\tilde \nu _e , d) reaction by two orders of magnitude over a purely reactor spectrum.     

Dynamics in molecular crystals: An application of proton NMR to selectively protonated biphenyl. Do the rings flip together or independently?

The synthesis of a specific isotopomer, C₆D₄H(ortho)-H(ortho)D₄C₆ of biphenyl is reported. The intramolecular dipolar coupling of the protons leads to a well-resolved single-crystal proton nuclear magnetic resonance (NMR) spectrum and allows one to study the dynamics of the phenyl rings in a unique way. At room temperature and above, the most conspicuous dynamical mode consists of 180° ring flips. The present data together with previous measurements of the total flip rate allow us to conclude that the rings flip almost exclusively independently of each other. Between the incommensurate (IC) phase transition of biphenyl at 38 K andT=250 K, the prominent namical mode consists of oscillatory twists ϕ(t) of the two rings. The data allow us to infer the mean square, (φ²), of these twists. (φ²) is found to grow linearly withT for 50<T<200 K. From the slope of (φ²) vs.T the frequency (the wave number[(v)\tilde]\tilde v) is derived. The result is[(v)\tilde] = 20\tilde v = 20 cm⁻¹. ForT<38 K, the spectra give direct evidence of the IC phase transition and its nature (stripelike rather than quiltlike). The temperature dependence of the magnitude of the order parameter of the IC phase is obtained.     

On the correlation between the deuteron quadrupole moment,the deuteron asymptotic <Emphasis Type="Italic">D/S</Emphasis> ratio,and the <Emphasis Type="Italic">S</Emphasis>-wave normalization constant

The correlation between the deuteron quadrupole moment Q, the deuteron asymptotic D/S ratio η, and the deuteron asymptotic normalization constant AS is studied. For local nucleon-nucleon potentials, it was found that the quantities Q/η and A _S ² are related by a linear equation. Owing to this, the deuteron quadrupole moment Q can be determined from known values of AS and η with an absolute precision of about 0.0003 fm². The inclusion of the correction for meson-exchange currents and the use of the experimental neutron-proton phase shifts from the GWU partial-wave analysis made it possible to estimate the deuteron quadrupole moment at Q = 0.2852 fm², which is in good agreement with experimental data.     

Double polarization experiments at MAMI

A broad experimental program is being carried in Mainz for the experimental verification of the fundamental Gerasimov-Drell-Hearn sum rule on the neutron and to measure the helicity dependence of the γn → Nπ(π) channels. In this review, the results obtained up to now using both polarized deuteron and ³He targets are shown.     

Fine and hyperfine structure of the muonic <Superscript>3</Superscript>He ion

On the basis of quasipotential approach to the bound state problem in QED we calculate the vacuum polarization, relativistic, recoil, structure corrections of orders α ⁵ and α ⁶ to the fine structure interval ΔE ^fs = E(2P _3/2) − E(2P _1/2) and to the hyperfine structure of the energy levels 2P _1/2 and 2P _3/2 in muonic ₂³He ion. The resulting values ΔE ^fs = 144 803.15 μeV, Δ$ \tilde E $ \tilde E ^hfs(2P _1/2) = −58 712.90 μeV, Δ$ \tilde E $ \tilde E ^hfs(2P _3/2) = −24 290.69 μeV provide reliable guidelines in performing a comparison with the relevant experimental data.     

The deuteron D-state probability

A method of direct determination of the deuteron D-state probability from the experiment, based on thed ↑p →ppn reaction analyzis is suggested. Using the known results on the vector analyzing power in elasticN N-scattering, the values of the overall nucleon polarization and the deuteron vector polarization have been obtained. The probability of the deuteron D-state is estimated to beW _D =0.078±0.046.     

Dielectron widths of the <Emphasis Type="Italic">S</Emphasis>-, <Emphasis Type="Italic">D</Emphasis>-vector bottomonium states

The dielectron widths of Y(nS)(n = 1, …, 7) and vector decay constants are calculated using the relativistic string Hamiltonian with a universal interaction. For Y(nS) (n = 1, 2, 3) the dielectron widths and their ratios are obtained in full agreement with the latest CLEO data. For Y(10580) and Y(11020) a good agreement with experiment is reached only if the 4S-3D mixing (with a mixing angle θ = 27°± 4°) and 6S-5D mixing (with θ = 40°±5°) are taken into account. The possibility to observe higher “mixed D-wave” resonances, $ \tilde \Upsilon $ \tilde \Upsilon (n ³ D ₁) with n = 3, 4, 5 is discussed. In particular, $ \tilde \Upsilon $ \tilde \Upsilon (≈11120), originating from the pure 5³ D ₁ state, can acquire a rather large dielectron width, ∼130 eV, so that this resonance may become manifest in the e ⁺ e ⁻ experiments. On the contrary, the widths of pure D-wave states are very small, Γ _ee (n ³ D ₁)≤ 2 eV.     

Search for chargino/neutralino pairs inpp-collisions in theSU(2) L ×SU(2) R ×U(1) B−L supersymmetric model

An extension of the supersymmetric standard model to the supersymmetricSU(2) _L ×SU(2) _R ×U(1) _B–L model with Higgs triplets is considered. We study in detail production of chargino and neutralino pairs at the LHCpp-collider of centre of mass energy TeV. A numerical analysis for different sets of mass values of charginos and neutralinos is considered. The analysis shows that the signatures are an increase of the total cross sections \sigma _T (pp \to \tilde \chi _2^ + \tilde \chi _1^ - ,\tilde \chi _2^0 \tilde \chi _1^0 + X) > \sigma _T (pp \to \tilde \chi _2^ + \tilde \chi _2^ - ,\tilde \chi _2^0 \tilde \chi _2^0 + X)$$ " align="middle" border="0"> , in the region of the transverse momentum,k _t . The analysis also shows that the experimental signatures depend essentially on the mixing matrix parameters of theL–R SUSY model.     

Production of a0-mesons in the reactions πN↦a0N and pp↦da0 + at GeV energies

We investigate the reactions πN↦a ₀ N and pp↦da ₀ ⁺ near threshold and at medium energies. An effective Lagragian approach and the Regge pole model are applied to analyze different contributions to the cross-section of the reaction πN↦a ₀ N. These results are used to calculate the differential and total cross-sections of the reaction pp↦da ₀ ⁺ within the framework of the two-step model in which two nucleons produce an a₀-meson via π-meson exchange and fuse to a deuteron. The necessity of new measurements on a₀ production and branching fractions (of its decay to the K and πη channels) is emphasized for clarifying the a₀ structure. Detailed predictions for the reaction pp→da ₀ ⁺ are presented for the energy regime of the proton synchrotron COSY-Jülich. Received: 4 August 2000 / Accepted: 17 September 2000     

Deuteron size effects on its elastic scattering from1H and4He

The effect of change in deuteron size on its elastic scattering from protons and alphas is investigated by varying the Hulthen parameters of the deuteron wave function in the scattering process. The cross sections forp-d scattering, calculated in the Born approximation, are found to increase substantially at backward angles even when the deuteron size is reduced by a small amount, whereas the shape of the angular distribution does not change significantly. For theα-d elastic scattering, interaction potential is obtained by folding the deuteron wave function and the optical potential for nucleon-scattering. The cross sections calculated atE _d = 13·7 MeV, shows that the first minimum around Θ_cm = 60° is deepend as the deuteron size is reduced, while at 52 MeV bombarding energy, the size effects are not very distinct. These observations are useful in the interpretation of deuteron cluster knockout reactions.     

A Note on Classical Ground State Energies

The pair-specific ground state energy ε _g (N):=ℰ _g (N)/(N(N−1)) of Newtonian N body systems grows monotonically in N. This furnishes a whole family of simple new tests for minimality of putative ground state energies ℰ _g ^x (N) obtained through computer experiments. Inspection of several publicly available lists of such computer-experimentally obtained putative ground state energies ℰ _g ^x (N) has yielded several dozen instances of ℰ _g ^x (N) which failed one of these tests; i.e., for those N one concludes that ℰ _g ^x (N)>ℰ _g (N) strictly. Although the correct ℰ _g (N) is not revealed by this method, it does yield a better upper bound on ℰ _g (N) than ℰ _g ^x (N) whenever ℰ _g ^x (N) fails a monotonicity test. The surveyed N-body systems include in particular N point charges with 2- or 3-dimensional Coulomb pair interactions, placed either on the unit 2-sphere or on a 2-torus (a.k.a. Thomson, Fekete, or Riesz problems).     

An DWBA Analysis of the Angular Distribution and Polarization of Neutrons from the Reaction 12C(d,n0)13N in the Deuteron Energy Range 1.7–2.8 MeV

The angular distribution and the polarization of neutrons from the reaction ¹²C(d, n₀)¹³N in the deuteron energy range 1.7–2.8 MeV have been analyzed in terms of the DWBA theory.     

Solid-state NMR investigations of Si-29 and N-15 enriched silicon nitride

We compare ²⁹Si magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectra from the two modifications of silicon nitride, α-Si₃N₄ and β-Si₃N₄, with that of a fully (²⁹Si, ¹⁵N)-enriched sample ²⁹Si₃¹⁵N₄, as well as ¹⁵N NMR spectra of Si₃¹⁵N₄ (having ²⁹Si at natural abundance) and ²⁹Si₃¹⁵N₄. We show that the ¹⁵N NMR peak-widths from the latter are dominated by J(²⁹Si–¹⁵N) through-bond interactions, leading to significantly broader NMR signals compared to those of Si₃¹⁵N₄. By fitting calculated ²⁹Si NMR spectra to experimental ones, we obtained an estimated coupling constant J(²⁹Si–¹⁵N) of 20 Hz. We provide ²⁹Si spin-lattice (T₁) relaxation data for the ²⁹Si₃¹⁵N₄ sample and chemical shift anisotropy results for the ²⁹Si site of β-Si₃N₄. Various factors potentially contributing to the ²⁹Si and ¹⁵N NMR peak-widths of the various silicon nitride specimens are discussed. We also provide powder X-ray diffraction (XRD) and mass spectrometry data of the samples.     

Dirac Operators on Quantum Projective Spaces

We construct a family of self-adjoint operators D _N , ${N\in{\mathbb Z}}We construct a family of self-adjoint operators D _N , N ? \mathbb Z{N\in{\mathbb Z}} , which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space \mathbb CP^l_q{{\mathbb C}{\rm P}^{\ell}_q} , for any ℓ ≥ 2 and 0 < q < 1. They provide 0⁺-dimensional equivariant even spectral triples. If ℓ is odd and N=\frac12(l+1){N=\frac{1}{2}(\ell+1)} , the spectral triple is real with KO-dimension 2ℓ mod 8.