Nucleon-nucleon potential for isotopic triplet state

The nucleon-nucleon potential for the isotopic triplet state is computed as a superposition of Yukawa-type potentials. It contains the central, spin, spin-orbit, quadratic spin-orbit and tensor term and is dependent on the total angular momentumJ. The parameters of the individual terms are fitted to the experimental data.The computing was performed on the Elliot 4130 computer in Prague. The authors are indebted to Z. Janout for valuable discussions on phase shift analysis.The authors would like to express their gratitude to Prof. G. Alaga and Prof. M. K. Pal for arranging a special seminar on this topic at the International Course on Nuclear Theory (Trieste 1969).Dedicated to Professor V. Votruba on his sixtieth birthday.     

Glauber model and time reversal invariance

The Glauber model is discussed from the point of view of time reversal invariance. It is shown that the model slightly violates the T-invariance conditions unless the longitudinal momentum transfers are not negligible relative to a nucleon mass.On leave of absence fromCharles University, Prague, Czechoslovakia.The author would like to thank Professor Abdus Salam, the International Atomic Energy Agency and UNESCO for hospitality at the International Centre for Theoretical Physics, Trieste.     

Impact parameter study in multiparticle production at 70 GeV/c

This paper presents a study of the experimental lower boundb _L, on the root-mean-squared impact parameter of the multiparticle production in 70 GeV/c p-nucleon interaction. It has been observed that theb _L decreases with increasing final state multiplicity (n) at this fixed energy. The results are in good agreement with those of other authors.The authors would like to thank Prof. K. D. Tolostov of Dubna, U.S.S.R. for kindly supplying the exposed emulsion plates.     

The renormalizability and the asymptotically behaviour of the extended Wess-Zumino models

By using the path integral method for superfields the Ward identities and the Callan-Symanzik equations for the extended Wess-Zumino models are derived. From these the renormalizability and the asymptotic behaviour of all the extended Wess-Zumino models ind=2,4 (mod 8)-dimensional space-time are studied. In particular, we come to the conclusion that the supersymmetric Ward identities together with the broken chiral Ward identities imply that a single wave function renormalization is sufficient to renormalize the theory, and the theory is not asymptotically free.We would like to thank Professor Dao Vong Duc for putting forward the problem and for his helpful discussions. One of us (H. N. L) would like to thank Professor Abdus Salam, the International Atomic Energy and UNESCO for hospitality at the International Centre for Theoretical Physics, Trieste.     

Canonical realizations of classical lie algebras

We construct sets of canonical realizations for all classical Lie algebras (A _n ,B _n ,C _n ,D _n ). These realizations depend ond parameters,d=1, 2, 3,...,n; all Casimir operators are realized by multiples of identity. For most of the real forms of these algebras we give sets of realizations which are, moreover, in well-defined sense skew-Hermitian. Further we study extremal cases of the presented realizations. The realizations with minimal numbers of canonical pairs are discussed from the point of view of general results concerning minimal realizations. On the other hand, a connection is found between our maximal realizations ofA _n and the Gel'fand-Kirillov Conjecture.The authors would like to thank Prof. A.Uhlmann for his kind interest in this work. They are very grateful to Prof. A. A.Kirillov and Prof. D. P.Zhelobenko for helpful discussions and to Prof. J.Dixmier for his informative letter concerning the problem mentioned in Sect. 5.One of the authors (W. L.) thanks Prof. I.Úlehla for the hospitality at the Nuclear Center of the Charles University, Praha.     

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.     

Highest-weight representations ofsl(2, ℂ) andsl(3, ℂ) via canonical realizations

The infinite-dimensional representations of thesl(n+1, ) Lie algebras (maximal representations) constructed in our previous paper are studied on the two simplest examplesn = 1,2. The sufficient condition for irreducibility of the maximal representations is proved to be also necessary in these cases. It is further shown, that our method allows us to construct other set of infinite-dimensional highest-weight representations ofsl(3, ), so calledmixed representations which are irreducible in some cases when the maximal as well as the standard highest-weight representations (Verma modules) are reducible.Dedicated to the 25th anniversary of the Joint Institute for Nuclear Research.The authors are grateful to Prof. A. A. Kirillov, Dr. A. U. Klimyk, Dr. W. Lassner and Prof. D. P. Zhelobenko for stimulating discussions.     

Coherent memory functions for finite systems: Hexagonal photosynthetic unit

Coherent memory functions entering the Generalized Master Equation are presented for a hexagonal model of a photosynthetic unit. Influence of an energy heterogeneity and possible superstructure on an exciton transfer in an antenna system as well as to a reaction center is investigated.One of us (I.B.) would like to thank Professor Abdus Salam, the International Atomic Energy Agency, and Unesco, for hospitality at the International Centre for Theoretical Physics,Trieste.     

AnomalousE1 conversion in octupole-deformed nuclei and muon shake-off in prompt fission

It has been shown that the coexistence of octupole and quadrupole deformation in nuclei gives rise to strong penetration effects in internal conversion for theE1 transitions. This idea has been applied for evaluating the muon shake-off probabilityW _sh. The value obtained,W _sh/–0.5% per prompt fission, is in good agreement with the experimental result. Possibilities for further experimental studies of this effect are discussed.The author would like to acknowledge fruitful discussions of the problem together with Prof. Yu.P. Gangrsky, Dr. V. Yu. Denisov and Prof. D.F. Zaretsky. He is also grateful to Prof. G.Ye. Belovitsky, Prof. P. David and Dr. Ch. Rösel for discussions of the experimental situation. This work was completed at the University of Bonn in the frame of a fellowship from the Heinrich Hertz Foundation.     

Energy dependence of the fast fragment of the target nucleus in high energy hadron-nucleus interaction

This paper presents an extensive study on the dependence of the mean number of the fast fragment of the target nucleus n _g on the incident beam energy in proton-nucleus interaction in emulsion in the range 6·2E ₀400 GeV/c. It has been observed that n _g decreases in the range 6·2E ₀200 GeV/c, then increases and attains an approximately steady value up to 400 GeV/c. It is very difficult to explain this behaviour with the help of the existing nuclear production models.The author would like to thank Prof A. J. Herz (CERN), Prof. K. D. Tolostov (Dubna, U.S.S.R.), Prof. P. L. Jain (State University of New York, U.S.A.), Prof. G. Giacomelly (Italy) for kindly supplying the exposed emulsion plates.     

Low-energy effects in brane worlds: Liennard–Wiechert potentials and Hydrogen Lamb shift

Testing extra dimensions at low-energies may lead to interesting effects. In this work a test point charge is taken to move uniformly in the 3D subspace of a (3 + n)-brane embedded in a (3 + n + 1)-space with n compact and one warped infinite spatial extra dimensions. We found that the electromagnetic potentials of the point charge match standard Liennard–Wiechert’s at large distances but differ from them close to it. These are finite at the position of the charge and produce finite self-energies. We also studied a localized Hydrogen atom and take the deviation from the standard Coulomb potential as a perturbation. This produces a Lamb shift that is compared with known experimental data to set bounds for the parameter of the model. This work provides details and extends results reported in a previous Letter. We are pleased to dedicate this work to Professor Octavio Obregón on occasion of his 60th birthday. H. A. Morales-Técotl is an associate member of the Abdus Salam ICTP, Trieste Italy.     

Fluctuations and the magnetic equation of state

The influence of inhomogeneity of magnetization on the equation of state for a magnetic system has been considered in the approximation of homogeneous fluctuations of magnetic moment. The fluctuations have been described in the molecular field approximation. It has been shown that taking into account the fluctuations of magnetic moment at the derivation of the equation of state changes the relation among the variablesM, H andT, the temperature dependence of the spontaneous magnetization near the critical point, and shifts the critical temperature.The author would like to thank Prof. J.Kocinski and Prof. L.Wojtczak for their interest in the subject of the paper and for numerous elucidating discussions. The author is indebted to Prof. L.Valenta for his helpful remarks concerning this paper.     

Use of some fermion field identities for bosonisation of U(n) thirring and Schwinger models

A set of identities involving triple products of free fermion fields belonging to the fundamental representation of U(n) is established. These would give a direct bosonised form of U(n) massless as well as massive Thirring model for \(g_\upsilon = - \frac{{4\pi }}{{n + 1}}\) . The identities are also shown to exist for fields whose leading operator product expansion is same as that of free fermion fields. This would then give us an exactly solvable bosonised form of U(n) Schwinger model.     

Inner shell structure of heavy atoms

The inner-shell structure of some heavy atoms is examined using a self-consistent relativistic local density method. Ar(K), Kr(K) and Xe (K,L ₁,L ₂ andL ₃) binding energies and {ie863-1} (hyper-satellite) energies of Tl, Hg and Tm are calculated. The results are compared with available experimental data. A part of this work was presented byMPD at the Trieste International Symposium on “Core level excitations in atoms, molecules and solids,” 22–26 June 1981, Extended Abstracts (ed.) E Tosatti, ICTP Report No. 89/81 p. 11.     

Cross-sections of the 238U (n, γ) 239U reaction in the 3.0–7.0 MeV energy region measured by relative activation method

The reaction cross-sections of ²³⁸U (n, γ)²³⁹U have been experimentally determined at neutron energies of 6.117 ± 0.119 MeV, 4.626 ± 0.086 MeV, and 3.622 ± 0.348 MeV employing the relative activation approach along with the off-line γ-ray spectroscopy method. The D (d, n)³He reaction was utilized to obtain monoenergetic neutrons of the required energy, and the ¹⁹⁷Au (n, γ)¹⁹⁸Au reaction cross-sections were adopted as the referential standard to ascertain the neutron capture cross-sections of ²³⁸U. Furthermore, the effects of low-energy scattered neutrons, neutron fluence fluctuations, counting of geometric corrections when measuring γ-rays, and neutron and γ-ray self-absorption caused by the sample thickness have been considered and revised in the present work. For a comparison with experimental results, the cross-sections of the ²³⁸U (n, γ)²³⁹U reaction were calculated theoretically with the original parametric TALYS-1.9 program. The experimental measurements were in contrast to previous experimental results and the evaluation data available for ROSFOND-2010, CENDL-3.2 and ENDF/B-VIII.0.     

Sensitivity of cross section andT 20 to secondary interactions in the reaction indp → ppn at medium energies

Secondary effects in deuteron breakup reactions are reexamined for the process¹ H(d, p) pn with a proton detected at 0° and for the process¹ H (d, pp)n with two fast forward moving protons fixed at the beam line. Sensitivity of the cross section and the tensor asymmetryT ₂₀ to the double-scattering and final-state-interaction corrections is demonstrated. The nonrelativistic method used here incorporates both the energy-conserving and the principal-value part of the free nucleon propagator. The calculations are compared with the inclusive experimental data¹ H(d, p)X at the 1.25 and 2.1 GeV deuteron kinetic energy.The author would like to express his thanks to Prof. B. Tecoult for valuable ideas stimulating this work and Yu.Panebratsev and A. Litvinenko for many helpful discussions. For ideas and advice concerning Sect. 4, I thank to G. Lykasov and S. Shimansky.     

The n = 0 replica limit of U(n) and models

Recently the replica limit n = 0 of the U(n) and models have attracted interest since they describe the Anderson localization behaviour in the band-centre of a two-sublattice model. For n ≠ 0 the theories can be decomposed into one with symmetry U(1) and one for SU(n) and . This does not no longer hold for n = 0. We show how the beta-functions and zeta-functions for operators without derivatives can be obtained in this limit from those of SU(n) and and draw consequences for these functions in this limit.     

Cumulative fission yield measurements with 14.7 MeV neutrons on 238U

The fission yield data in the 14 MeV energy neutron induced fission of ²³⁸U play an important role in decay heat calculations and generation-IV reactor designs. In order to accurately measure fission product yields (FPYs) of ²³⁸U induced by 14 MeV neutrons, the cumulative yields of fission products ranging from ⁹²Sr to ¹⁴⁷Nd in the ²³⁸U(n, f) reaction with a 14.7 MeV neutron were determined using an off-line γ-ray spectrometric technique. The 14.7 MeV quasi-monoenergetic neutron beam was provided by the K-400 D-T neutron generator at China Academy of Engineering Physics (CAEP). Fission products were measured by a low background high purity germanium gamma spectrometer. The neutron flux was obtained from the ⁹³Nb (n, 2n)^92mNb reaction, and the mean neutron energy was calculated using the cross-section ratios for the ⁹⁰Zr(n, 2n)⁸⁹Zr and ⁹³Nb(n, 2n)^92mNb reactions. With a series of corrections, high precision cumulative yields of 20 fission products were obtained. Our FPYs for the ²³⁸U(n, f) reaction at 14.7 MeV were compared with the existing experimental nuclear reaction data and evaluated nuclear data, respectively. The results will be helpful in the design of a generation-IV reactor and the construction of evaluated fission yield databases.     

Microscopic study of the low-energy3H(d,n)4He reaction

We have studied the³H(d, n)⁴He reaction at low energies within a multi-channel resonating-group calculation based on many-bodyn+ andd+³H configurations and pseudo-states as well as on an effective nucleonnucleon interaction containing central, spin-orbit, and tensor components. The low-energy fusion cross section is excellently reproduced within our approach.Dedicated to Prof. Erich Schmid on the occasion of his 60th birthday     

Interpolation of entire functions,product formula for basic sine function

Abstract

We solve the problem of constructing entire functions where ln M (r; f) grows like ln² r from their values at q^?n, for 0 < q < 1. As application we give a product formula for the basic sine function.