Model of scalar mesons

A model containing a nonet of scalar mesonsS, a nonet of pseudoscalar mesonsP, and a nonet of baryons is constructed where the mesons enter in the form of the matrixM=e^i(S+iP), Several Lagrangians are introduced such that the mesons get their physical masses, and the decay widths of the scalar mesons are calculated. The model satisfies generalized PCAC. It is found that the coupling constants of the mesonsε(700) andε′(1060) to pions and nucleons satisfy the relations: $$\frac{{|G_{\varepsilon NN} |}}{{|G_{\varepsilon \pi \pi } |}} = 1 \cdot 4,\frac{{|G_{\varepsilon 'NN} |}}{{|G_{\varepsilon '\pi \pi } |}} = 0 \cdot 89,\frac{{|G_{\varepsilon \pi \pi } G_{\varepsilon NN} |}}{{4\pi }} = 4 \cdot 9,{\text{and}}\frac{{|G_{\varepsilon '\pi \pi } G_{\varepsilon 'NN} |}}{{4\pi }} = 0 \cdot 34.$$      

Measurement of the\sum {^ - \to ne^ - \bar v} rate and search for ΔQ=−ΔS transitions in Σ+→ne + ν decay

In a bubble chamber experiment about 2×10⁶ Σ ^±-decays have been measured to separateΣ ^±→ne^±¯ν events from the two-body modes. NoΣ ⁺ →ne ⁺ ν event was found whereas 607Σ ^?→ne^?¯ν decays could be identified. The data yield for the ΔQ=?ΔS decay an upper limit: $$\frac{{\Gamma \left( {\sum {^ + } \to ne^ + v} \right)}}{{\Gamma \left( {\sum {^ - } \to ne^ - v} \right)}}< 1.9 x 10^{ - 2} (90\% confidence level)$$ and the branching ratio: $$\frac{{\Gamma \left( {\sum {^ - } \to ne^ - v} \right)}}{{\Gamma \left( {\sum {^ - } \to n\pi ^ - } \right)}} = (1.09 \pm 0.06) x 10^{ - 3} .$$      

Magnetisches Moment und Quadrupolmoment des 8,42 keV-Zustandes von Tm169 aus der Hyperfeinstrukturaufspaltung in Tm-Metall

The hyperfine transition from the 8·42 kev level to the groundstate of Tm¹⁶⁹ was investigated using the Mössbauer-Effect in Tm-metal in the temperature range between 5° K and 60° K. Well resolved hyperfine spectra were found between 5° K and 25° K indicating an internal magnetic field of about 7×10⁶ Oe and a large electric fieldgradient. The ratio of the magnetic moments of the 8·42 keV rotational state to the groundstateμ _a /μ _g =?2·33±0·04 was deduced from these measurements. The magnetic moment of the groundstate and the quadrupole moment of the 8·42 kev level were deduced from calculated internal fields. These data were analyzed in terms of the “Unified Nuclear Model” and the results compared with other known magnetic moments andM-1-transition probabilities in theK=1/2 rotational band of Tm¹⁶⁹. The complicated hyperfine spectra obtained above 25° K reveal the influence of complex magnetic ordering on the internal fields in Tm-metal.     

Antiproton-proton annihilation at rest intoπ + π − η ′ andπ + π − η from atomicS andP states

We have measured the branching ratios for \(\bar pp\) annihilation at rest intoπ ⁺ π ^? η andπ ⁺ π ^? η′ in hydrogen gas in two data samples that have different fractions ofS-wave andP-wave initial states. The branching ratios are derived from a comparison with the topological branching ratio for \(\bar pp\) annihilations into four charged pions of (49±4)% and the branching ratio intoπ ⁺ π ^? π ⁺ π ^? π ⁰ of (18.7±1.6)%. We find a significant reduction of the branching ratios fromP-states for \(\bar pp \to \pi ^ + \pi ^ - \eta \) andπ ⁺ π ^? η′ in comparison toS-state annihilation. $$\begin{gathered} BR(S - wave \to \pi ^ + \pi ^ - \eta ) = (13.7 \pm 1.46) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta ) = (3.35 \pm 0.84) \cdot 10^{ - 3} \hfill \\ BR(S - wave \to \pi ^ + \pi ^ - \eta ') = (3.46 \pm 0.67) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta ') = (0.61 \pm 0.33) \cdot 10^{ - 3} . \hfill \\ \end{gathered} $$ In a partial wave analysis of theπ ⁺ π ^? η Dalitz plot we find the following contributions: Phase space, \(a_2^ + (1320)\pi ^ \mp \) ,ηρ⁰ andf ₂(1270)η: $$\begin{gathered} BR(S - wave \to \pi ^ + \pi ^ - \eta PS) = (6.31 \pm 1.22) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to \pi ^ + \pi ^ - \eta PS) = (0.47 \pm 0.26) \cdot 10^{ - 3} \hfill \\ BR(^1 S_0 \to a_2^ \pm (1320)\pi ^ \mp ) = (2.59 \pm 0.73) \cdot 10^{ - 3} \hfill \\ BR(^3 S_1 \to a_2^ \pm (1320)\pi ^ \mp ) = (1.31 \pm 0.48) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to a_2^ \pm (1320)\pi ^ \mp ) = (1.31 \pm 0.69) \cdot 10^{ - 3} \hfill \\ BR(^3 S_1 \to \rho \eta ) = (3.29 \pm 0.90) \cdot 10^{ - 3} \hfill \\ BR(^1 P_1 \to \rho \eta ) = (0.94 \pm 0.53) \cdot 10^{ - 3} \hfill \\ BR(^1 S_0 \to f_2 (1270)\eta ) = (0.083 \pm 0.086) \cdot 10^{ - 3} \hfill \\ BR(P - wave \to f_2 (1270)\eta ) = (0.64 \pm 0.26) \cdot 10^{ - 3} . \hfill \\ \end{gathered} $$ We find a 2 σ effect for the reaction \(\bar pp \to a_0^ \pm (980)\pi ^ \mp \) , \(a_0^ \pm \to \eta \pi ^ \pm \) , with a branching ratio of (0.13±0.07)·10^?3. For η' production we give a branching ratio of \(\bar pp \to \rho \eta '\) of (1.81±0.44)·10^?3 from³ S ₁. We estmate a contribution of about 0.3·10^?3 for ρη' fromP-states. The ratio of ρη and ρη' rpoduction is used to test the validity of the quark line rule. In theπ ⁺ π ^? π ⁺ π ^? γ final state we do not observe the reaction \(\bar pp \to \pi ^ + \pi ^ - \omega \) , ω→π ⁺ π ^? λ and derive an upper limit of 3·10^?3 for decay modeω→π ⁺ π ^? λ.     

Measurement of charged kaon semileptonic decay branching fraction K^ - \to e^ - \bar \nu _e \pi ^0 using ISTRA+ detector

The ratio of branching fractions for \(K^ - \to e^ - \bar \nu _e \pi ^0\) andK ^? → π^?π⁰ decays has been measured using the ISTRA+ spectrometer. The result of our measurement is the following: $$\mathcal{R}_{Ke_3 /K_{2\pi } } = 0.2423 \pm 0.0015(stat.) \pm 0.0037(syst.).$$ Using the current PDG value for the K _2π branching fraction, this result leads to the measured K _e3 branching fraction of Br(K _e3) = 0.0501 ± 0.0009 and to the value of |V _us |f ₊(0) = 0.2115 ± 0.0021.     

Radiative Σ± decays and search for neutral currents

The decay modesΣ ^±→nπ ^± γ, Σ ⁺→pγ,Σ ⁺ →pe ⁺ e ^}- were studied in the 81 cm Saclay hydrogen bubble chamber. In the radiative decayΣ ^±→nπ ^± γ only low momentum pions which stop in the chamber were accepted. We obtain the following branching ratios: (1) $$\frac{{\Gamma {\text{(}}\sum ^{\text{ + }} \to n\pi ^ + \gamma , p_{\pi + }^*< 110{\text{ MeV/c)}}}}{{\Gamma {\text{(}}\sum ^{\text{ + }} \to n\pi ^ + )}} = (2.7 \pm 0.5) \times 10^{ - 4} ,$$ (2) $$\frac{{\Gamma {\text{(}}\sum ^ - \to n\pi ^ - \gamma , p_{\pi - }^*< 110{\text{ MeV/c)}}}}{{\Gamma {\text{(}}\sum ^ - \to n\pi ^ - )}} = (1.0 \pm 0.2) \times 10^{ - 4} ,$$ (3) $$\frac{{\Gamma {\text{(}}\sum ^ + \to p\gamma {\text{)}}}}{{\Gamma {\text{(}}\sum ^ + \to p\pi ^0 )}} = (2.1 \pm 0.3) \times 10^{ - 3} ,$$ (4) $$\frac{{\Gamma {\text{(}}\sum ^ + \to pe^ + e^ - {\text{)}}}}{{\Gamma {\text{(}}\sum ^ + \to p\pi ^0 )}} = (1.5 \pm 0.9) \times 10^{ - 5} .$$ The radiative branching ratios (1) and (2) agree well with theoretical calculations and confirm very strongly the assignmentS wave toΣ ^? →nπ ^? andP wave toΣ ⁺→nπ ⁺ decay. The branching ratio (4) is based on 3 events with very low invariant masses of the electron-positron pair, being most probably radiative decays with internal conversion of theγ-ray. Combining (3) and (4) we obtain for the conversion coefficientρ: in agreement with predictions from electrodynamics.     

Eine neue Methode zur Berechnung der elektrischen Leitfähigkeit von Halbleitern in starken homogenen elektrischen Feldern

The Boltzmann equation for electrons in a semiconductor is assumed to be of the form $$\frac{{\partial f}}{{\partial t}} + F \cdot \frac{{\partial f}}{{\partial k}} = \frac{{h - f}}{{\tau _0 }} + \frac{1}{{\tau \left( k \right)}} \cdot \frac{1}{{4\pi }}\int {d\Omega 'w\left( \theta \right)\left( {f\left( {k,\vartheta '} \right) - f\left( {k,\vartheta '} \right)} \right)} $$ whereh is the Maxwell-Boltzmann distribution. The energy surface structure of the lattice electronsE(k) is assumed to be spheric. The stationary solutions for strong electric fields show a concentration of electrons into the field direction (field orientation), if the elastic collision frequency is not too large. This means, at least for large energies, that nearly all electrons are in a cone with small aperture around the field direction. Every transport problem whose collision operator can be reduced to the upper form at least for large energies, can be solved by a perturbation method whose zeroth order is the ideal field orientation. The conditions for a field orientation of the electron distribution to exist will be investigated.     

Widths of the 7.74 MeV analogue state in39K

The³⁸Ar(p, p)³⁸Ar and³⁸Ar(p, γ)³⁹K reactions have been investigated in the analogue resonance region at E_p=1.39 MeV. For the 7.74 MeV state of³⁹K branching ratios, unique spin and parity, \(J^\pi = \tfrac{3}{2} - \) , proton and total width, Γ_p=Γ=1.1±0.2 keV, have been determined.     

Optical spectroscopy of Dysprosium Aluminum Garnet (DAG)

The absorption spectrum of antiferromagnetic dysprosium aluminium garnet (DAG) (T _N =2.50 °K) has been investigated at low temperatures. The groundstate splitting due to all interactions in the antiferromagnetic state is (5.27±0.10) cm^?1 extrapolated to 0 °K. The temperature dependence of the lineshift of the absorption lines is measured. Zeeman effect studies give theg-tensor of the groundstate asg _z =18.4±0.5,g _x =g _y =0.5±0.2. The studies also allow the determination of the critical fields asH _c ^[100] =(5.0±0.1) koe,H _c ^[111] =(3.9±0.2) koe andH _c ^[110] =(4.9±0.6) koe. In addition an investigation of a number of satellite lines is performed. Some of them can be interpreted as spin wave sidebands (Stokes and anti-Stokes); others obviously come from dysprosium ions which have impurity ions on regular lattice sites as neighbours.     

Optical investigation of metamagnetic DyAlO3

We have investigated the optical absorption spectra of metamagnetic DyAlO₃ (T _N =3.4 °K) above and below the Néel temperature. We find that the magnetic interactions are predominantly between the ions along the crystallographicc-axis; the interaction energy between two ions isW _C =? (2.9±0.6) cm^?1. Additional line-shifts below 3.4 °K yield the Néel temperature. Zeeman effect studies give the magnetic moment of the groundstate as μ=(9.2 ± 0.9)μ _B . The direction of the magnetic moments is in thea-b plane, with angles of ± 33.5° and ± 146.5° from theb-axis. The Zeeman effect studies reveal two metamagnetic transitions (forH _ext∥μ) at 7.0 and 7.3 kOe respectively. Additional susceptibility and Mössbauer measurements confirm the Néel temperature and the magnetic moment.     

Exact solution of the Boltzmann equation in the relaxation approximation,existence of negative differential conductivity for certain types of energy bands and its implication for the fluctuation spectrum and the noise temperature

The Boltzmann equation for the distributionf _k of a system of charged particles obeying classical statistics in a uniform fieldF, $$\frac{{\partial f_k }}{{\partial t}} + F\frac{{\partial f_k }}{{\partial k}} = \smallint d^3 k'(W_{kk'} f_{k'} - W_{k'k} f_k ),$$ will be solved analytically for a special class of transition ratesW _kk′=const·h _k ·ν _k ·ν _k′ for any initial distribution.h _k is the Maxwell distribution andν _k >0 can be interpreted as ak-dependent relaxation frequency. The constant relaxation approximation (ν _k =ν) will be used to discuss the drift velocitiesu for all the fields and temperaturesT for certain types of band structuresE(k). Bands with lineark-dependence for largek give rise to drift velocities saturating for large fields. For bands with the periodicity of the reciprocal lattice, the zero drift-theorem has been proved. It states that $$\mathop {\lim }\limits_{F \to \infty } u (F,T) = \mathop {\lim }\limits_{T \to \infty } u (F,T) = 0$$ for all the periodic band structures. This theorem is even correct for a generalW _kk′ if certain restrictions are made. Finally, making use of the Markov character of the conditional probability (Green's function) solution of the Boltzmann equation, the velocity fluctuation spectrumS is calculated forE(k)=A(1?cosa k). It will be shown thatS(F, T, 0) remains positive for the critical field and all temperatures, and therefore the noise temperature diverges on approaching the critical field.     

A determination of the leptonic neutral current couplings

An analysis is presented of the recent data which are sensitive to thee, μ and τ neutral current couplings. A fit combining all results (e ⁺ e ^?, μC,ve, eD, atoms) selects a unique solution in agreement with the standard-model expectation. Assuming lepton universality, the vector and axial-vector couplings are determined to bev=?0.013±0.048 anda=?0.520±0.014. Similarly we find (sin² θ=0.213±0.012,ρ=0.015±0.038) or (sin² θ=0.211α0.012, ρ≡1 which, combined with all other values, gives an average of sin² θ=0.216±0.006.     

Asymptotic inverse spectral problem for anharmonic oscillators

We study perturbationsL=A+B of the harmonic oscillatorA=1/2(??²+x ²?1) on ?, when potentialB(x) has a prescribed asymptotics at ∞,B(x)～|x|^?α V(x) with a trigonometric even functionV(x)=Σa _mcosω _m x. The eigenvalues ofL are shown to be λ _k =k+μ _k with small μ _k =O(k ^?γ), γ=1/2+1/4. The main result of the paper is an asymptotic formula for spectral fluctuations {μ _k }, $$\mu _k \sim k^{ - \gamma } \tilde V(\sqrt {2k} ) + c/\sqrt {2k} ask \to \infty ,$$ whose leading term \(\tilde V\) represents the so-called “Radon transform” ofV, $$\tilde V(x) = const\sum {\frac{{a_m }}{{\sqrt {\omega _m } }}\cos (\omega _m x - \pi /4)} .$$ as a consequence we are able to solve explicitly the inverse spectral problem, i.e., recover asymptotic part |x ^?α|V(x) ofB from asymptotics of {µ _k }. ₁ ^∞      

Boundedness of total cross-sections in potential scattering. II

If, in addition to the condition $$\frac{1}{{(4\pi )^2 }}\int {d^3 xd^3 x'} \frac{{|V(x)||V(x')|}}{{|x - x'|^2 }}< 1$$ in units where 2M/?² = 1, which guarantees that the total cross-section averaged over incident directions is finite, we have also $$\frac{1}{{(4\pi )}}\int {d^3 xd^3 x'} \frac{{|V(x)||V(x')|}}{{|x - x'|}}$$ finite, the total cross-section is finite for all energies and all directions of the incident beam.     

On Lévy (or stable) distributions and the Williams-Watts model of dielectric relaxation

This paper is concerned with the Lévy, or stable distribution function defined by the Fourier transform $$Q_\alpha \left( z \right) = \frac{1}{{2\pi }}\int {_{ - \infty }^\infty \exp \left( { - izu - \left| u \right|^\alpha } \right)du} with 0< \alpha \leqslant 2$$ Whenα=2 it becomes the Gauss distribution function and whenα=1, the Cauchy distribution. Whenα≠2 the distribution has a long inverse power tail $$Q_\alpha \left( z \right) \sim \frac{{\Gamma \left( {1 + \alpha } \right)\sin \tfrac{1}{2}\pi \alpha }}{{\pi \left| z \right|^{1 + \alpha } }}$$ In the regime of smallα, ifα¦logz¦?1, the distribution is mimicked by a log normal distribution. We have derived rapidly converging algorithms for the numerical calculation ofQ _α (z) for variousα in the range 0<α<1. The functionQ _α (z) appears naturally in the Williams-Watts model of dielectric relaxation. In that model one expresses the normalized dielectric parameter as $$ \in _n \left( \omega \right) \equiv \in '_n \left( \omega \right) - i \in ''_n \left( \omega \right) = - \int {_0^\infty e^{ - i\omega t} \left[ {{{d\phi \left( t \right)} \mathord{\left/ {\vphantom {{d\phi \left( t \right)} {dt}}} \right. \kern-\nulldelimiterspace} {dt}}} \right]} dt$$ with $$\phi \left( t \right) = \exp - \left( {{t \mathord{\left/ {\vphantom {t \tau }} \right. \kern-\nulldelimiterspace} \tau }} \right)^\alpha $$ It has been found empirically by various authors that observed dielectric parameters of a wide variety of materials of a broad range of frequencies are fitted remarkably accurately by using this form ofφ(t).ε″ _n (ω) is shown to be directly related toQ _α (z). It is also shown that if the Williams-Watts exponential is expressed as a weighted average of exponential relaxation functions $$\exp - \left( {{t \mathord{\left/ {\vphantom {t \tau }} \right. \kern-\nulldelimiterspace} \tau }} \right)^\alpha = \int {_0^\infty } g\left( {\lambda , \alpha } \right)e^{ - \lambda t} dt$$ the weight functiong(λ, α) is expressible as a stable distribution. Some suggestions are made about physical models that might lead to the Williams-Watts form ofφ(t).     

Optical investigation of DyFeO3

Optical absorption spectra of DyFeO₃ have been investigated at 1.2≦T≦4.2 °K, andT=77 °K From the temperature dependent lineshift a Néel temperature ofT _N=(3.8±0.5) °K is deduced for the dysprosium sublattices. The groundstate splitting due to the iron-dysprosium interactions is about 1.5 cm^?1 and due to the dysprosiumdysprosium interactions (5.0±1.4) cm^?1. Zeeman studies give the magnetic moment of the dysprosium ions asμ=(9.2±1.0)μ _B.     

Level spacing distributions and the Bessel kernel

Scaling models of randomN×N hermitian matrices and passing to the limitN→∞ leads to integral operators whose Fredholm determinants describe the statistics of the spacing of the eigenvalues of hermitian matrices of large order. For the Gaussian Unitary Ensemble, and for many others'as well, the kernel one obtains by scaling in the “bulk” of the spectrum is the “sine kernel” $\frac{{\sin \pi (x - y)}}{{\pi (x - y)}}$ . Rescaling the GUE at the “edge” of the spectrum leads to the kernel $\frac{{Ai(x)Ai'(y) - Ai'(x)Ai(y)}}{{x - y}}$ , where Ai is the Airy function. In previous work we found several analogies between properties of this “Airy kernel” and known properties of the sine kernel: a system of partial differential equations associated with the logarithmic differential of the Fredholm determinant when the underlying domain is a union of intervals; a representation of the Fredholm determinant in terms of a Painlevé transcendent in the case of a single interval; and, also in this case, asymptotic expansions for these determinants and related quantities, achieved with the help of a differential operator which commutes with the integral operator. In this paper we show that there are completely analogous properties for a class of kernels which arise when one rescales the Laguerre or Jacobi ensembles at the edge of the spectrum, namely $$\frac{{J_\alpha (\sqrt x )\sqrt y J'_\alpha (\sqrt y ) - \sqrt x J'_\alpha (\sqrt x )J_\alpha (\sqrt y )}}{{2(x - y)}},$$ , whereJ _α(z) is the Bessel function of order α. In the cases α=?1/2 these become, after a variable change, the kernels which arise when taking scaling limits in the bulk of the spectrum for the Gaussian orthogonal and symplectic ensembles. In particular, an asymptotic expansion we derive will generalize ones found by Dyson for the Fredholm determinants of these kernels.     

Electron-electron interaction and instabilities in one-dimensional metals

The possible instabilities of a 1-dimensional itinerant electron gas are discussed, assuming electron-electron interaction to play the dominant role. As is well known, in the RPA, a 1-dimensional metal is prone to spin density wave (SDW), charge density wave (CDW) and Cooper pair (CP) instabilities. The spin channel decomposition of the irreducible scattering amplitude I is made and the spin channel projections are evaluated in terms of the matrix elements of bare electron-electron interactionV(x) for momenta of interest. It is found that if the bare electron interactionV(x) is repulsive and decreases monotonically with separation, only the SDW instability will occur. If the small separation (x?(2k _F )^?1) part of the interaction is greatly reduced or is made attractive,V(x) is non-monotonic,V _q (q?2k _F ) is negative, and a CDW instability is preferred. A CP instability is possible if the electron interaction is attractive,i.e., if [V _q (0<q<k _F )+V _q (q?2k _F )]<0. The above RPA results serve only as rough indicators, since in general there are important two-electron configurations with two-electron momentum close to zero and with electron hole momentum close to 2k _F , an example being the near Fermi energy configurationk ₁?k _F ,k ₂??k _F ,k ₃??k _F k ₄?k _F . Therefore as pointed out first by Bychkov, Gorkov and Dzhyaloshinskii (BGD), cross channel coupling is especially significant. It is shown that the cross channel coupling is constructive is some cases,eg., exchange of CD fluctuations leads to an effective electron-electron spin singlet attraction and vice-versa. A formalism for studying such effects is set up, and the particular example mentioned above is discussed. An RPA-like approximation is made for the form of the reducible singlet electron hole scattering amplitudeγ _s ^d and the resulting induced Cooper pair attraction is calculated to be $$\begin{gathered} [I_s ^e ]_{ind.} \rho _{{}^\varepsilon F} = [ln(\lambda \beta \omega _c )]^{ - 1} ln\{ [1 + 2\pi ^{ - 1} ln(\lambda \beta \omega _c )^2 ]/ \hfill \\ 1 + [8\pi ^{ - 1} \gamma _s ^d (q = 2k_F )^{ - 1} )^2 ]\} \hfill \\ \end{gathered} $$ where λ=1.14,β=(k _B T)^?1 andω ₀ is an electronic energy cut-off ～ε _F . The induced electron hole attraction due to the exchange of virtual Cooper pairs has a similar expression, but with a factor of (1/4) and withγ _s ^e (q=0) replacingγ _s ^d (q=2k _F ). The induced Cooper pair attraction is seen to be quite large over a broad range of temperatures close to but aboveT _CDW [i.e., aboveT such thatγ _s ^d (q=2k _F )^?1=0]. There is no requirement thatγ _s ^d (q=2k _F ) andγ _s ^e (q=0) become singular at the same temperature, as found by BGD. The BGD prediction is seen to arise from the neglect of real particle hole and particle-particle excitations while calculatingγ _s ^d andγ _s ^e . The effect of impurities, of electron-phonon coupling, of interchain coupling and of interaction between thermal order parameter fluctuations is discussed. The results are then applied to a discussion of the properties of TTF-TCNQ, where it is suggested that a CDW instability occurs becauseV _q (q=2k _F )<0,i.e., because the small separation electron repulsion is strongly reduced by the highly polarizable TTF. Because of substantial interchain coupling, the bulk CDW instability occurs close to the RPA instability temperature. The giant conductivity observed by Colemanet al is attributed to superconductive fluctuations in a 1-dimensional system with large mean field superconductive transition temperatureT _CP ^MF of order 300°K. Such a largeT _CP ^MF is shown to result from the induced Cooper pair attraction due to CD fluctuation exchange.     

Test of 600 and 750 MeV NN matrix on elastic scattering Glauber model calculations

The 600 and 750 MeV proton nucleus elastic scattering cross section and polarization calculations have been performed in the framework of the Glauber model to test the pp and pn scattering amplitudes deduced from a phase shift analysis by Bystricky, Lechanoine and Lehar. It is well known that up to now we do not possess a non-phenomenological NN scattering matrix at intermediate energies. However proton-nucleus scattering analyses are used to extract information about short range correlations¹), Δ resonance²) or pion condensation presences)... etc. Most scattering calculations made at these energies have been done with phenomenological NN amplitudes having a gaussian q-dependence $$A(q) = \frac{{k\sigma }}{{4\pi }}(\alpha + i) e^{ - \beta ^2 q^2 /2} $$ and $$C(q) = \frac{{k\sigma }}{{4\pi }}iq(\alpha + i) D_e - \beta ^2 q^2 /2$$ K andσ being respectively the projectile momentum and the total pN total cross section. The parameters α, β and D are badly known and are adjusted by fitting some specific reactions as p+⁴He elastic scattering⁴). Even when these amplitudes provide good fits to the data, our understanding of the dynamics of the scattering remains obscure.