Double hypernuclei and the Λ-Λ interaction

The binding energy of the double hypernucleus Be¹⁰ analyzed using an -particle model. A relationship is found between B, the binding energy of two -particlcs, and ¯V, the - potential integral. For the experimental value B = 17.5 Me V ¯V varies from 250 to 850 MeV-F³ according to the form of the - potential used.In conclusion, I wish to thank S. N. Kryuchkova for carrying out these calculations on a Minsk-2 electronic computer. I also wish to thank my senior colleague, V. A. Filimonov, for his support in the completion of the present work.     

Neutron stars in a Skyrme model with hyperons

Available Skyrme parametrizations with hyperons are examined from the point of view of their suitability for applications to neutron stars. It is shown that the hyperons can attenuate or even remove the problem of ferromagnetic instability common to (nearly) all Skyrme parametrizations of the nucleon-nucleon interaction. At high density the results are very sensitive to the choice of the interaction. The selected parameter sets are then used to obtain the resulting properties of both cold neutron stars and hot protoneutron stars. The general features known from other models are recovered.     

Weakly Bound States in Light Hypernuclei

From the viewpoint of critical stability, we discuss the three- and four-body structure of ⁶He, ⁷He, ⁴He, and ⁴H. With the + + N three-body model, ⁶He is found to have a three-layer structure of the matter distribution: core, a skin and neutron halo. Also the level structure of ⁷He with the three-body model of ⁵He + n + n is predicted. This stimulates a new study of neutron-rich and proton-rich hypernuclei. By performing a four-body calculation with both NNN and NNN channels and with both NN and NNN channels, we show that the N-N and -N couplings are very important in critical stability of few-body hypernuclear systems.     

Meyer's concept of quasicrystal and quasiregular sets

This paper relates two mathematical concepts of long-range order of a set of atoms , each of which is based on restrictions on the set of interatomic distances –. A set in ⁿ is aMeyer set if is a Delone set and there is a finite setF such that . Meyer proposed that such sets include the possible structures of quasicrystals. He obtained a structure theory for such sets, which reformulates results that he obtained in harmonic analysis around 1970, and which relates these sets to cut-and-project sets. In geometric crystallography V.I. Galiulin introduced the concept ofquasiregular set, which is a set such that both and – are Delone sets. This paper shows that these two concepts are identical.     

Λ-d Scattering

A three-particle variational calculation of the cross sections and phases of elastic -d scattering in the doublet and quartet states with zero orbital angular momentum is carried out in the energy range from 0 to 20 MeV (laboratory system of coordinates). The calculation is carried out with semirealistic N-N Afnan-Tang potentials and -N potent: —N, which describe -p scattering correctly, as well as the binding energy of the hyperfragments ⁵ He, ¹³ C (within the scope of the + core model), and ³ H (considered as a three-body system).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 114–118, 1981.     

On the Surface Pressure for the Edwards-Anderson Model

For the Edwards-Anderson model we introduce an integral representation for the surface pressure (per unit surface) in terms of a quenched moment of the bond-overlap on the surface. We consider free , periodic and antiperiodic ^* boundary conditions (by symmetry ⁽⁾=^(*)), and prove the bounds We show moreover that at high temperatures ⁽⁾ is close to ^2/4 and ⁽⁾ is close to ^2/4 uniformly in the volume .     

Lattice dynamics of sapphire (Al2O3)

Using inelastic neutron scattering we have determined all the dispersion branches of the ₁, ₂ and ₃ representations along the three-fold axis as well as the 2 times 15 branches of ₁ and ₂ symmetry along the -A-direction plus some branches along the -D-direction. The experimental data are analyzed using various rigid ion, polarizable ion and shell models. The shell models give a very satisfactory account of the dispersion curves as well as the scattering intensities. Special attention is given to the investigation of dielectric constants and equilibrium conditions.     

Bound on the mass gap for finite volume stochastic ising models at low temperature

We consider a sequence of finite volume Z ^d ,d2, reversible stochastic Ising models in the low temperature regime and having invariant measures satisfying free boundary conditions. We show that associated with the models are random hitting times whose expectations, regarded as a function of , grow exponentially in ||( ^d-1)/d ; moreover, the mass gaps for the models shrink exponentially fast in ||( ^d-1)/d . A geometrical lemma is employed in the analysis which states that if a Peierls' contour is sufficiently small relative to the faces of , then the fraction of the contour tangent to the faces is less than a constant smaller than one.     

Nontrivial extensions of a representation of the Poincaré group with mass and helicity zero by its tensorial product

Let U(a, ) be a representation of the Poincaré group with mass and helicity zero, realized in the space of C -functions with compact support on ³, without the origin. Let U ⁽²⁾(a, ) denote the tensorial product of U(a, ) by itself. We explicitly determine the cocycles of extension of U(a, ) by U ⁽²⁾(a, ) and we prove that the nontrivial cohomology is indexed by (u(),),u()D ¹ _]0,3\,.     

Charge Fluctuations in the Two-Dimensional One-Component Plasma

We study, via computer simulations, the fluctuations in the net electric charge in a two-dimensional, one component plasma (OCP) with uniform background charge density –e in a region inside a much larger overall neutral system. Setting e=1, this is the same as the fluctuations in N , the number of mobile particles of charge e. As expected, the distribution of N has, for large , a Gaussian form with a variance which grows only as ^||, where || is the length of the perimeter of . The properties of this system depend only on the coupling parameter =kT, which is the same as the reciprocal temperature in our units. Our simulations show that when the coupling parameter increases, ^() decreases to an asymptotic value ^()^(2)/2 which is equal (or very close) to that obtained for the corresponding variance of particles on a rigid triangular lattice. Thus, for large , the characteristic length _L=2^/ associated with charge fluctuations behaves very differently from that of the Debye length, _D1/ , which it approaches as 0. The pair correlation function of the OCP is also studied.     

Meson decays of hypertritium

Using ³ H and³He wave functions found by multiparameter variation calculations with N-potentials consistent with fundamental hypernuclear data and Afnan-Tang and Malfiet-Tjon type NN-potentials, the fraction of two particle ^–-decays in the total number of ^–-decays in ³ H is calculated and the ³ H lifetime is estimated. The results obtained are compared with experimental data on decay and binding energy of ³ H.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 44–48, March, 1988.     

Debye screening for two-dimensional Coulomb systems at high temperatures

The grand canonical ensemble of a two-dimensional Coulomb system with±1 charges is proved to have screening phenomena in its high-temperature region. The Coulomb potential in a finite region is assumed to be (–)^–1, where is the Laplacian with zero boundary conditions on. The hard-core condition is not assumed. The model is set up by separating (–)^–1 into a shortrange part and a long-range part depending on a parameter. The self-energies are subtracted only for the short-range part and therefore a choice of is a choice of subtraction of self-energies. The method of proof is in general the same as that of Brydges-Federbush Debye screening, except that here a modification for the short-range part of the potentials is needed.     

Stability domain of coherent laser waves

The constant-amplitude solutions with wavelength of a semiclassical laser model exhibit three different instabilities in the (, )-plane for pumpparameters above threshold.     

Hypernuclear spectroscopy

Conclusions The main difference between the- nucleus and the nucleon-nucleus interaction is in the spin dependence. The spin-spin and spin-orbit interaction is an order of magnitude weaker for the-nucleus than for the nucleon-nucleus system. If we want to emphasize the difference between hypernuclei and nuclei in an oversimplifying manner, we may say that the particle in the nucleus behaves like a spinless neutron.This radical difference in the behaviour of particles and nucleons in nuclear matter presents a sensitive test for the models of nuclear matter. Hypernuclear spectroscopy if studied in detail, a program just begun, promises to give valuable information on the effective properties of the quasiparticles in the nucleus and their interactions, both basic ingredients of nuclear models.Rather surprisingly, hypernuclei live long enough to observe individual states, as can be deduced from the berylium results. These results should be verified as soon as possible. If they are confirmed, this will challenge experimentalists to determine the -nucleus interaction in the same way as done for particles and the theorists to explain why the strong decay of particles in the nucleus is hindered.Invited talk at the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

Widths in the conversion of Σ and Ξ hyperons in nuclear matter

The widths of the conversion processes N, N in nuclear mattter were calculated based on the model of single-boson exchange. It was established that the conversion width for is significantly reduced by the interference of the contributions of separate mesons to the conversion amplitude. The conversion width obtained for in nuclear matter turned out to be less than 1 MeV.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 79–84, March, 1988.     

Mesonless decay of hypernucleiΛH4 andΛHe4 in a model of the direct conversion of Λ to a neutron

The decay probabilities of the hypernuclei H⁴ and He⁴ are calculated within the framework of the mesonless decay model of hypernuclei with direct conversion of to a neutron. All possible channels are considered: H⁴ tn, d2n, p3n and He⁴ He³n, tp, dd, dpn, 2p2n. Interaction in the final state between the decay products was neglected, but Pauli's principle for the final identical particles was taken into account completely. The predominant decay channels are three- and four-particle paths. The results are compared with experimental data.Translated from Izvestiya VUZ. Fizika, No. 1, pp. 86–94, January, 1972.     

Study of the Magnitude-Redshift Relation for Type Ia Supernovae in a Model Resulting from a Ricci-Symmetry

Models with a dynamic cosmological term (t) are becoming popular as they solve the cosmological constant problem in a natural way. Instead of considering any ad-hoc assumption for the variation of , we consider a particular symmetry, the contracted Ricci-collineation along the fluid flow, in Einstein's theory. We show that apart from having interesting properties, this symmetry does demand to be a function of the scale factor of the Robertson-Walker metric. In order to test the consistency of the resulting model with observations, we study the magnitude-redshift relation for the type Ia supernovae data from Perlmutter et al. The data fit the model very well and require a positive non-zero and a negative deceleration parameter. The best-fitting flat model is obtained as ₀ 0.5 with q ₀ –0.2.     

Inertial reference frames in Einstein's theory of gravitation

A physical definition of the inertial reference frame (IRF) is given, and the properties of solutions of the Einstein equation (with cosmological constant), which admit an IRF (IRF solutions) are investigated. Their Petrov type is uniquely determined by the viscous stress tensor. Only the typesI, D or 0 are possible. The unique vacuum IRF solution is the Minkowski space-time. The unique IRF solution belonging to a perfect fluid is the Einstein universe. is of special importance. For=0, the only physically admissible IRF solution is the Minkowski space-time. For0, only interior solutions with strong restrictions for density and pressure are possible.     

On the asymptotics of occurrence times of rare events for stochastic spin systems

We consider translation-invariant attractive spin systems. LetT _,x ^v be the first time that the average spin inside the hypercube reaches the valuex when the process is started from an invariant measure with density smaller thanx. We obtain sufficient conditions for (1) ¦¦^–1 logT _,x ^v (x) in distribution as ¦¦ , and ¦¦^–1 logT _,x ^v (x) as ¦¦ , where (x):= –lim ¦¦^–1 log {(average spin inside ) x. And (2)T _,x ^v /ET _,x ^v converges to a unit mean exponential random variable as ¦¦ . Both (1) and (2) are proven under some type of rapid convergence to equilibrium. (1) is also proven without extra conditions for Ising models with ferromagnetic pair interactions evolving according to an attractive reversible dynamics; in this case is a thermodynamic function. We discuss also the case of finite systems with boundary conditions and what can be said about the state of the system at the timeT _,x ^v .On leave from São Paulo University.     

Particle polarizations in decays of5HeΛ and4HΛhypernuclei

Nucleon polarizations are examined in the hypernucleus decays⁵He, ⁴He + p + _–,⁴H, ³H + p + _–, and⁴H, ³He + n + _–. The effect of the strong interaction in the final state is taken into account. A significant role is predicted for the resonance interaction in the p-⁴He system in the formation of the proton polarization in the⁵He decay. It is also shown that in the⁴H, ³H + p + _– decay the proton-polarization components should attain significant magnitudes, while in the charge-exchange decay⁴H, ³He + n + _–, the neutron polarization is expected to be not too large.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 100–103, October, 1988.