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.     

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.     

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.     

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.     

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.     

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.     

Geometric expansion of the boundary free energy of a dilute gas

We consider a dilute classical gas in a volume ^–1 which tends to ^d by dilation as 0. We prove that the pressurep(^–1) isC ^q in at =0 (thermodynamic limit), for anyq, provided the boundary isC ^q and provided the Ursell functionsu _n (x ₁, ...,x _n) admit moments of degreeq and have nice derivatives.     

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 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 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 .     

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.     

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.     

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.     

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.     

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.     

Decay of Nd140→Pr140→Ce140

An intermediate image magnetic spectrometer was used to study the continuous ⁺-spectrum of Pr¹⁴⁰ and the Auger electrons of the decay chain Nd¹⁴⁰Pr¹⁴⁰Ce¹⁴⁰. The maximum energy of the continuous ⁺-spectrum is 2318±10 keV. The ratio of the intensities of the different Auger groupsK–LLK–LXK–MX=1 (0.58±0.05) (0.09±0.02). The ratio of the number of Auger electrons of the K-series to the electrons of the continuous spectrume _K/ ⁺ is 0.292.

---

Nd¹⁴⁰Pr¹⁴⁰Ce¹⁴⁰

Pr¹⁴⁰ Nd¹⁴⁰ Pr¹⁴⁰¹⁴⁰. ⁺- — 2318±10 keV. -:K–LLK–LXK–MX=1(0,58±0,05) (0,09±0,02). K e _K/ ⁺=0,292.

---

---

We should like to thank Z. Macháek and Z. Dubcová for help in the measurements and J. Vlachý, graduate of the Faculty of Technical and Nuclear Physics, for help in the measurements and elaboration of the experimental results.     

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.     

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.     

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.     

LETTER: On the Minimal Angular Size in Open, ΛCDM, and Scalar Field Cosmologies

We propose a simple method for determining the redshift z _m at which the angular size of an extragalactic source with fixed proper diameter takes its minimal value. A closed analytical expression, which is often convenient for numerical evaluation is derived. The method is exemplified with the following FRW type expanding universes: the open matter dominated models ( = 0), a critical density model with cosmological constant ( 0), and the class of scalar field cosmologies proposed by Ratra and Peebles. The influence of systematic evolutionary effects is briefly discussed.