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.     

Uniqueness of gibbs fields via cluster expansions

For the unbounded spin systems one cannot get cluster expansion if there exist large enough boundary values. A simple idea to avoid these difficulties is to prove that with probabilityp 1 when ^v there is a large subvolume of such that on all spin values do not exceed some fixed number. This gives a new method to prove uniqueness results for the unbounded spin systems generalizing some results of Refs. 1 and 2. The formulations of these results are in Section 1; the proofs are in Section 2.     

The charge fluctuations in classical Coulomb systems

We study the asymptotic behavior of the charge fluctuations (Q – (Q )² in infinite classical systems of charged particles, and show, under certain clustering assumptions, that if the charge fluctuations are not extensive, then they are necessarily of the order of the surface ¦¦. Moreover, when the canonical sum rules that are typical for equilibrium states of particles interacting with long-range forces hold true, we prove a central limit theorem for the normalized charge variable ¦¦^–1/2((Q – (Q )) in two and three dimensions. In one dimension, the probability distribution of the charge itself converges. The latter case is illustrated by the example of the one-dimensional Coulomb gas.     

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.     

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.     

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.     

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\,.     

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.     

The λN interaction and structures of the16–18O hypernuclei

The shell model without the nuclear centre-of-mass spuriosity is applied to ^16,17,18O isotopes, predicting the bunched and dense hypernuclear energy levels. The (K^–, ^–) reaction cross sections are calculated at several angles with the =0° ones being in good agreement with the experimental data on ¹⁶O and ¹⁸O. The realistic N effective interaction derived on the basis of the Nijmegen Model-D is employed and the N J=0⁺ pairing correlation is found to be repulsive, which is reflected in the¹⁸O(K^–,^–) ¹⁸O excitation function.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.The author is thankful to Professor H. Bando. Professor Y. Yamamoto and Professor H. Ikeda for collaboration and useful discussion.     

A mean spherical model with coulomb interactions

We consider simple cubic lattice systems ind dimensions with a continuous real charge variableq(n) at each lattice siten. These variables are subject t'o a mean spherical constraint forcing _n q ²(n)=Q ², where is the number of lattice sites in andQ is an elementary charge. The energy of the charges comes from interactions with an electrostatic potential, which is the solution of a symmetric second-difference Poisson equation on the lattice. Two cases are considered, both of which allow the inclusion of the effects of a fixed, constant, external electric field. On the lattice ₁=[1,N]^d , a Neumann condition is imposed at the surface of the lattice. The lattice ₂=[1,N] [–M,M]^(d–1) is periodic in each direction ranging over [–M, M] and has a Dirichlet condition imposed at the other two surfaces. On ₂ a finite electric field may be applied, while on ₂ a finite potential difference may be applied across the lattice. The models are exactly solvable. We study the distribution functions on each system and show that they satisfy appropriate forms of the first two Stillinger-Lovett moment conditions. The two charge distribution functions show screening behavior at high temperature and extreme short range at an intermediate temperatureT ₀(d), and oscillate as they decay to zero forT<T ₀(d). Because of the continuous nature of the charge variables, there is no Kosterlitz-Thouless transition in two dimensions. In three dimensions the change in the decay behavior of the distribution functions atT<T ₀(d) is precursor to a phase transition to a charge ordered state.     

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.     

p-adic Heisenberg group and Maslov index

A system of coordinates on a set of selfdual lattices in a two-dimensionalp-adic symplectic space (V,) is suggested. A unitary irreducible representation of the Heisenberg group of the space (V,) depending on a lattice (an analogue of the Cartier representation) is constructed and its properties are investigated. By the use of such representations for three different lattices one defines the Maslov index =(₁,₂,₃) of a triple of lattices. Properties of the index are investigated and values of in coordinates for different triples of lattices are calculated.     

P-wave charmonium decays into baryon and antibaryon pairs in quark pair creation model

A simple quark pair creation model is introduced to study exclusive decays of _{{c_J}} into baryon-antibaryon pairs. With this simple model, some exclusive decay processes, for example, _{c0} B¯ (B = ,⁰,^-) are investigated and their decay widths are evaluated by inclusion of the properties of outgoing baryons, and the results show that the strengthened decay channels _{{c_J}} ¯(J = 0, 2) are easily understood by considering only the color singlet contribution of P-wave charmonium.     

Local fluctuation of the spectrum of a multidimensional Anderson tight binding model

We consider the Anderson tight binding modelH=–+V acting inl ²(Z ^d ) and its restrictionH to finite hypercubes Z ^d . HereV={V _x ;xZ ^d } is a random potential consisting of independent identically distributed random variables. Let {E _j ()} _j be the eigenvalues ofH , and let _j (,E)=||(E _j ()–E),j1, be its rescaled eigenvalues. Then assuming that the exponential decay of the fractional moment of the Green function holds for complex energies nearE and that the density of statesn(E) exists atE, we shall prove that the random sequence { _j (,E)} _j , considered as a point process onR ¹, converges weakly to the stationary Poisson point process with intensity measuren(E)dx as gets large, thus extending the result of Molchanov proved for a one-dimensional continuum random Schrödinger operator. On the other hand, the exponential decay of the fractional moment of the Green function was established recently by Aizenman, Molchanov and Graf as a technical lemma for proving Anderson localization at large disorder or at extreme energy. Thus our result in this paper can be summarized as follows: near the energyE where Anderson localization is expected, there is no correlation between eigenvalues ofH if is large.     

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.     

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.     

Nontrivial extensions of a massless representation with definite helicity of the Poincaré group in 3+1 dimensions by the tensor product of two other massless representations with definite helicity

Let U _n (a, ) be a massless, helicity n/2, representation of the Poincaré group in 3+1 dimensions. U _n (a, ) is realized in an adapted nuclear space D _n. We explicitly determine the various classes of cohomology for the extension of U _n (a, ) by U _n1 (a, ) U _n2 (a, ).     

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.     

On the equivalence of boundary conditions

We show that ifb andb are two boundary conditions (b.c.) for general spin systems on ^d such that the difference in the energies of a spin configuration in ^d is uniformly bounded, |H _,b ()–H _,b()|C < , then any infinite-volume Gibbs states and obtained with these b.c. have the same measure-zero sets. This implies that the decompositions of and into extremal Gibbs states are equivalent (mutually absolutely continuous). In particular, if is extremal,=. Application of this observation yields in an easy way (among other things) (a) the uniqueness of the Gibbs states for one-dimensional systems with forces that are not too long-range; (b) the fact that various b.c. that are natural candidates for producing non-translation-invariant Gibbs states cannot lead to such an extremal Gibbs state in two dimensions.Supported in part by NSF Grant PHY 78–15920 and by the Swiss National Foundation For Scientific Research.     

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.