Mathematical models for quantum point-contact spectroscopy

We sketch here two mathematical models intended to describe the point-contact spectroscopical experiments. A new item is added to the list of recently discovered applications of the self-adjoint extensions theory.The paper represents an extended version of the lecture given by one of the authors at the 8th Congress of IAMP, Marseille, July 1986.On leave of absence fromNuclear Physics Institute, Czechosl. Acad. Sci., 250 68 e near Prague, Czechoslovakia.On leave of absence fromNuclear Centre, Charles University, V Holeovikách 2, 180 00 Prague, Czechoslovakia.     

ГАММА-СПЕКТР ИЗ РАДИА ЦИОННОГО ЗАХВАТА НА Cs

The measurements of the -ray spectra, following resonance, neutron capture in¹³³Cs, performed with the aid of the Ge(Li) detector of active volume about 12 cm³, are described. The energies and intensities of a number of transitions have been obtained.

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On leave fromFaculty of Mathematics and Physics, Charles University, Behová 7, Praha 1, Czechoslovakia.

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On leave fromNuclear Research Institute, Czechosl. Acad. Sci., e, Czechoslovakia.     

Radiative muon capture on nuclei

Radiative muon capture rates of stopped meons, spectra, circular polarisation, and asymmetries of emitted -quanta in¹⁶O and⁴⁰Ca are analysed using the shell-model nuclear wave functions. Calculated characteristics show considerable sensitivity to the value of induced pseudoscalar coupling constantg _p. Where possible we compare the theoretical results with the preliminary experimental data.Dedicated to the 25th anniversary of the Joint Institute for Nuclear Research.On leave of absence fromthe Institute of Nuclear Physics, Czechosl. Acad. Sci., 250 68 e, Czechoslovakia.     

A simple model of thin-film point contact in two and three dimensions

We treat a free spinless quantum particle moving on a configuration manifold which consists of two identical parts connected in one point. Most attention is paid to the three-dimensional case when these parts are halfspaces with Neumann condition on the boundary; we also discuss briefly a more general boundary conditions. The class of admissible Hamiltonians is constructed by means of the theory of self-adjoint extensions. Among them, particularly important is a two-parameter family whose elements are invariant with respect to exchange of the halfspaces; we compute the transmission coefficient for each of these extensions. We discuss also the motion on two planes considered in our recent paper, obtaining another characterization of the admissible Hamiltonians. In conclusion, the two situations are compared as models for point-contact spectroscopical experiments in thin metal films.On leave of absence fromNuclear Physics Institute, Czechosl. Acad. Sci., 250 68 e near Prague, Czechoslovakia.On leave of absence fromNuclear Centre, Charles University, V Holeovikách 2, 180 00 Prague 8, Czechoslovakia.     

РАСПAД170Lu

The spectrum of -radiation of the radioactive isotope¹⁷⁰Lu was studied by means of two Ge(Li) coaxial semiconductor detectors. Around 150-transitions belonging to the decay of¹⁷⁰Lu were found and their relative intensities were determined. Using the relative intensities of the conversional electrons from other works the internal conversional coefficients and the multipolarities of -ray transitions in the¹⁷⁰Yb nucleus were established. Twenty new excited levels of the¹⁷⁰Yb nucleus were introduced.A comparison of the experimental results with the predictions of the superfluid and Davydov models is made. The possible existence of I=O^– excited states in the level scheme of¹⁷⁰Yb is discussed.

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On leave fromFaculty of Mathematics and Physics, Charles University, Behová 7, Praha, Czechoslovakia.

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On leave fromNuclear Research Institute, Czechosl. Acad, Sci., e, Czechoslovakia.     

The nucleon-nucleon triple scattering parameters for recoil particles

Relativistic formulae are obtained, expressing the polarization of the initially unpolarized particle in the scattering of an unpolarized nucleon on a polarized one, in terms of the polarization transfer tensor and in terms of the scattering matrix elements.On leave of absence from theFaculty of Technical and Nuclear Physics, Czech Technical University, Prague, Czechoslovakia.On leave of absence from theNuclear Research Institute of the Czechoslovak Academy of Sciences, e, Czechoslovakia.In conclusion the authors express their profound gratitude to S. M. Bilenky, L. I. Lapidus, R. M. Ryndin and Ya. A. Smorodinsky for useful discussions and to E. Dudova and J. Fingerova for help in the work.     

Directional correlations of γ-rays in149Gd

The- directional correlations for cascades observed in the 4.1 hour¹⁴⁹Tb decay were measured on the multidetector system consisting of 7 Ge (Li) detectors. The results together with the experimental data on the internal electron conversion allowed a model-independent assignment of the spin values at a confidence level higher than 95% for three levels in¹⁴⁹Gd: 325 keV 3/2^–, 817 keV 3/2^– and 1206 keV 1/2^–. Multipole mixing ratios for six-transitions were also derived.On leave fromInstitute of Nuclear Physics, 250 68 e, Czechoslovakia On leave fromInstitute of Nuclear Energy and Nuclear Research, Bulgarian Acad. Sci., 1184 Sofia, Bulgaria     

One- and two-nucleon emission following the nuclear radiative pion capture

Decay channels in the radiative pion capture reactions are discussed and their respective yields calculated. Specific consequences of a recently suggested quadrupole excitation mode in the ( ^–,) reaction are found and their experimental investigation is urged. A yield of about 19% of the total decay was estimated for the two-nucleon decay channel even for the light nuclei like¹⁶O.On leave of absence fromthe Institute of Nuclear Physics, Czechosl. Acad. Sci., 250 68 e, Czechoslovakia.We a re grateful to the members of Lausanne-Münich-Zürich collaboration, particularly to C.Joseph, G.Strassner and P.Trüol for supplying us with the experimental results prior to publication. M. G. also thanks them and R.Wünsch for interesting discussions. We are grateful to R. A.Sakaev for his help at an early stage of this work.     

Positive parity giant multipole resonances in16O

Distributions of the (J =0⁺, 1⁺, 2⁺, 3⁺, 4⁺) isoscalar and isovector strength in¹⁶O have been calculated in then particle —n hole (n=0, 1, 2) shell model. The isoscalar quadrupole giant resonance comes out fragmentated over eight peaks which exhaust 33% of the EWSR betweenE ^*=17 and 25 MeV. This result agrees nicely with the recent³He and alpha inelastic scattering experiments. Giant monopole isoscalar (isovector) resonance appears to exhaust more than 50% of the EWSR nearE ^*=30 MeV (E ^*=40 MeV). Several collective states of other multipolarities are predicted either near to 30 MeV or between 50 and 60 MeV. The ground state correlations of the 2p2h type give rise to a considerable strength redistributions as compared with the case of the closed shell ground state.On leave fromInstitute of Nuclear Physics, Czechosl. Acad. Sci., 250 68 e, Czechoslovakia.     

Polarization correlation in the scattering of polarized nucleons

Experiments concerning the spin correlation tensorC _pqik in the scattering of polarized nucleons on polarized nucleons are discussed. Relativistic formulae are derived for the experimental quantities. The scattering matrix is directly reconstructed with the help of experimentally measured quantities. The components ofC _pqik are predicted for np-scattering at 630 MeV and are given on graphs.On leave from Faculty of Technical and Nuclear Physics, Czech Technical University, Behová 7, Praha 1, Czechoslovakia.On leave from Nuclear Research Institute, Czechosl. Acad. Sci., e, Czechoslovakia.The authors are indebted to S. M. Bilenskij, J. Bystrický, I. M.Kazarinov, L. I. Lapidus, R. M. Ryndin and Ja. A. Smorodinskij for stimulating discussions and valuable comments and to L. I. Graeva and A. M. Fulkina for their assistance.     

Spark chambers for measurements of elastic backward scattering of positive pions by protons

The paper deals with multiplate spark chambers employed in measurements of elastic ⁺ p backward scattering. The basic characteristics of the spark chambers and their time variation are described and the measured recording efficiencies for one particle against a high background of other particles are given.On leave of absence from the Institute of Physics, Czechosl. Acad. Sci., Lumumbova 1, Praha 8, Czechoslovakia.     

A new class of realizations of the lie algebragl(n + 1, ℓ)

In this paper, we apply the previously published method (J. Phys. A18(1985) 3101) to the construction of boson realizations for Lie algebrasgl(n + 1, ). These realizations are expressed by means of certain recurrent formulae in terms ofr(n + 1 – r) canonical pairs and generators of the subalgebragl(r, ) + gl(n + 1 – r, ), wherer = 1,2,...,n. They are skew-Hermitean and Schurean.Dedicated to the 30th anniversary of the Joint Institute for Nuclear Research.On leave of absence from theNuclear Centre of the Faculty of Mathematics and Physics, V Holeovikách 2, 180 00 Praha 8, Czechoslovakia.The author is grateful to Drs. P. Exner, M. Havliek and O. Navrátil for useful discussions.     

A Metallografic study of the homogeneization quenching of copper

During homogeneization quenching the dislocation density in copper grows up to saturation and the dislocation structure becomes stabilized. This process is realized on quenching into gases and liquids, i.e. at both lower and higher quenching rates. Grain growth is also observed. The dislocation structure formed by cold-working is removed by annealing at temperatures near to the melting point in a time interval shorter than 30 minutes and the dislocation density reaches a stable value, growing with decreasing thickness of the specimen.The authors would like to thank Dr. K. Míek, CSc. (Institute of Solid State Physics, Czechosl. Acad. Sci., Prague) for his comments, Dr. J. Kuera CSc. and Dr. P. Luká, CSc. (Institute of Metallurgy, Czechosl. Acad. Sci., Brno) for critical remarks on the paper and Mrs. J. Zoubková for assistance with the experiments.     

An analysis of dibaryon resonance spectra by GSAP,AUTSPAN and SAMPO-80 codes

Narrow dibaryon resonances observed in elastic and inelastic hadron scattering channels atM _NN ^* =1875–2300 MeV/c² are characterized by the relative resolution (FWHM/M _pp ^* ) 10^–3 comparable to that provided by Ge(Li) detectors in the case of gamma-ray spectroscopy. The gamma-ray spectrum analysis codes GSAP, AUTSPAN and SAMPO-80 have been used to analyse the effective mass distributions of dibaryons from the reactions dp (pn) p, dp (pp) n, np pp^–, and pppp studied at the Dubna synchrophasotron. The produced results suggest these codes to be reliable software tools in the new spectroscopic region of interest.On leave fromNuclear Physics Institute, Czechosl. Acad. Sci., 250 68 e near Prague, Czechoslovakia.     

On existence of a bound state in an L-shaped waveguide

We investigate the Laplace operator in an L-shaped strip of a widthd with Dirichlet boundary conditions. It is shown that it has a unique eigenvalue corresponding to a square-integrable eigenfunction, namely = 0·93 (/d)². This result has implications for the theory of waveguides as well as for electron motion in some microscopic semiconductor devices.Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.On leave of absence from Nuclear Physics Institute, Czechoslovak Academy of Sciences,250 68 e near Prague, Czechoslovakia.On leave of absence fromDepartment of Mathematics, Faculty of Nuclear and Technical Engineering, Czech Technical University, Trojanova 13, 120 00 Prague, Czechoslovakia.     

On fixing the scale in QCD from lattice calculations

Recent results of lattice Monte-Carlo calculations in QCD are used to estimate the value of . Special attention is paid to the role played by the light quarks in the construction of the continuum limit in QCD. The resulting value of turns out to be strongly dependent onn _f , the number of light quarks taken into account.Dedicated to the 30th anniversary of the Joint Institute for Nuclear Research.On leave of absence from theInstitute of Physics, Czechosl. Accd. Sci., Na Slovance 2, 180 40 Praha 8, Czechoslovakia.     

The kinetics of phase transition in systems with nonconservative order parameter

The kinetics of ordering in systems described by the nonconservative order parameter is studied near the second-order transition critical point.On leave fromDepartment of Nuclear Physics and Biophysics, Faculty of Natural Sciences, University of P. J. afárik, Moyzesova 11, 041 67 Koice, Czechoslovakia.     

Levels in165Tm excited by the decay of 9·8 min165Yb

The decay of¹⁶⁵Yb (T _1/2=9·8 min) has been investigated with Ge(Li), Si(Li) and NaI(Tl) detectors, a toroidal -spectrometer and magnetic -spectrographs. The isobarically separated samples produced by the YASNAPP facility at the Dubna Institute were used. The single -ray spectrum, the conversion electron spectrum, prompt and delayed - coincidences have been measured. The decay scheme of¹⁶⁵Yb involving 40 excited states in¹⁶⁵Tm has been proposed. The first members of the rotational bands l/2⁺[411], 3/2⁺[411], 5/2⁺[402], 7/2⁺[404], 1/2^–[541], 7/2^–[523] and 9/2^–[514] have been identified.On leave fromthe Nuclear Physics Institute, e near Prague, Czechoslovakia.On leave fromthe Institute for Nuclear Physics, Uzbek Academy of Sciences, Tashkent,USSR.On leave fromthe Technical University, Dresden, GDR.We should like to thank Professor V. P.Dzhelepov for his support. Our thanks are due to M.Jachim for preparing the mass-separated sources. We are indebted to the electronics team of the measuring centre and to the synchrocyclotron staff of the Laboratory of Nuclear Problems.     

Pion form factor and its asymptotic behaviour

A simple phenomenological formula is constructed, consistent with the basic principles, providing a definite freedom in the choice of asymptotic behaviour and reflecting all experimentally known features of the pion form factor. The formula is used to test the asymptotic behaviour of the pion form factor both in spacelike and timelike regions simultaneously. The present experimental data require the fall-off t ^–2, which differs from the quark model prediction.On leave of absence fromInstitute of Physics, Slovak Acad. Sci., 899 30 Bratislava 1, Czechoslovakia.One of the authors (S. D.) would like to thank ProfessorAbdus Salam, the International Atomic Energy Agency and UNESCO for hospitality at the International Centre for Theoretical Physics, Trieste, where the final part of this work was done.     

Iodine photodissociation laser system Perun II

A construction and exploitation of a medium size iodine photodissociation laser system Perun II is reported. This laser produced pulses of infrared light (=1.315m) up to 50 J in energy and 300 ps in duration. The diameter of the beam is 82 mm. The beam divergence is about 4×10^–4 rad. The laser beam can be focused in a focal spot of a power density exceeding 10¹⁴ W/cm². The resuls of measurements of basic plasma parameters on an Al foil target are also presented. A recent improvement of the system includes a conversion to the second harmonic by a DKDP crystal.Presented at bilateral international seminar of High Temperature Laser Plasma and High Gain Iodine Lasers held on 4 July 1991 in the Inst. of Physics, Czechosl. Acad. Sci., in Prague (organized by Division of Optics of the Inst. of Physics, Czechosl. Acad. Sci., and Physical Section (Plasma Division) of the Union of Czech Mathematicians and Physicists.