Transverse spin correlation function of the one-dimensional spin-12 XY model

The transverse spin pair correlation function p^x_n=<S^x_mS^x_m+n>=<S^x_mS^x_m+n> is calculated exactly in the thermodynamic limit of the system described by the one-dimensional, isotropic, spin-$\text{1}\text{2}$, XY Hamiltonian

$\text{H=?2J}\text{∑}\text{l=1}\text{N}\text{(S}{}^{\mathrm{x}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{x}}{}_{\mathrm{l+1}}\text{+S}{}^{\mathrm{y}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{y}}{}_{\mathrm{l+1}}\text{)}$

. It is found that at absolute zero temperature (T = 0), the correlation function ρ^x_n for n ≥ 0 is given by

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p}}\text{=}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p}}\text{Π}\text{j=1}\text{p?1}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p?2j}}\text{if}\text{n=2p}$

,

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p+1}}\text{=±}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p+1}}\text{Π}\text{j=1}\text{p}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p+2j}}\text{if}\text{n=2p+1}$

, where the plus sign applies when J is positive and the minus sign applies when J is negative. From these the asymptotic behavior as n → ∞ of |?^x_n| at T = 0 is derived to be $\text{|ρ}{}^{\mathrm{x}}{}_{\mathrm{n}}\text{| ～}\text{a}\text{n}$ with a = 0.147088?. For finite temperatures, ρ^x_n is calculated numerically. By using the results for ?^x_n, the transverse inverse correlation length and the wavenumber dependent transverse spin pair correlation function are also calculated exactly.     

Nuclear magnetic moment of the 9.7 h 12− isomer 196mAu

The magnetic hyperfine splitting v_M=|gμ_NB_HF/h| of ^196mAu (j^π=12^?; configuration ¦(π$\text{11}\text{2}$($\text{v}\text{13}\text{2}{}^{\mathrm{+}}\text{)〉}{}_{12}{}^{\mathrm{?}}$; $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 9.7}\text{h}\text{)}$ as dilute impurity in Ni has been determined with nuclear magnetic resonance on oriented nuclei as 96.0(2) MHz. With the known hyperfine field B_HF = ?264.4(3.9) kG corrected for hyperfine anomalies the g-factor and magnetic moment of ^196mAu are deduced to be |g| = 0.476(7) and |μ| = 5.72(8) μ_N. Taking into account the known magnetic properties of $\text{π}\text{1}\text{2}{}^{\mathrm{?}}$ and $\text{v}\text{13}\text{2}{}^{\mathrm{+}}$ isomeric states in the neighbouring odd Pt, Au and Hg nuclei the structure of the 12^? state is discussed.     

Two theorems on the level order in potential models

We study the potentials of the form U(r)=?r^?1+λV(r), $\text{(}\text{d}\text{d}\text{r}\text{)(}\text{r}{}^2\text{d}\text{V}\text{d}\text{r}\text{)?0}$, and show that the energy levels satisfy the inequalities $\text{E(N}{}_{\mathrm{c}}\text{, l)?E(N}{}_{\mathrm{c}}\text{, l+1)}$ to first order in λ, where N_c denotes the coulombic principal quantum number and l the angular momentum. Similarly for potentials $\text{U(r)=r}{}^2\text{+λV(r), (}\text{d}\text{d}\text{r}{}^2\text{)}{}^2\text{V(r)?0}$, we prove to first order in λ that $\text{E}\text{?}\text{(N}{}_{\mathrm{H}}\text{,}\text{l}\text{)?}\text{E}\text{?}\text{(N}{}_{\mathrm{H}}\text{,}\text{l}\text{+2)}$, where NH denotes the harmonic oscillator quantum number. In the latter case, we give also quantitative restrictions on the relative positions at the lth and (l+1)th states.     

Lorentz contracted geometrical model

The model assumes that when two high energy particles collide each behaves as a geometrical object which has a Gaussian density and is spherically symmetric except for the Lorentz-contraction in the incident direction. Folding the two spatial distribution together we obtain the slope (b) of the elastic diffraction peak in terms of the c.m. velocities (β_i and β_j) and the sizes (A_i and A_j) of the two incident particles. These sizes are assumed to have the experimental s-dependence of σ_tot ∝ πA² for each reaction. The combined s-dependence of the σ_tot's and the β's gives the s-dependence of the elastic slope $\text{b}{}_{\mathrm{ij}}\text{(s) =}\text{1}\text{2}\text{(A}{}_{\mathrm{i}}{}^2\text{β}{}_{\mathrm{i}}{}^2\text{+ A}{}_{\mathrm{j}}{}^2\text{β}{}_{\mathrm{j}}{}^2\text{)}\text{σ}{}^{\mathrm{ij}}{}_{\mathrm{<mtext>tot</mtext>}}\text{(s)}\text{σ}{}^{\mathrm{ij}}{}_{\mathrm{<mtext>tot</mtext>}}\text{(∞)}$. This formula agrees with the experimental slope for p-p, $\text{p}$-p, K⁺-p, K^?-p and π^±-p elastic scattering from 3 to 1500 GeV/c, with only 3 parameters: A_π² = 6.1, A_K² = 3.3 and A_p² = 10.5 (GeV/c)^?2.     

The 85Rb(p,d)84Rb reaction

The spectrum seen in single neutron pickup leading to the doubly odd nucleus ⁸⁴Rb is remarkably clean, with only five levels populated by l = 4 and six by l = 1 transitions. A simple 2J+1 weighting for the l = 4 data, combined with previous information on ⁸⁴Rb, allowed the J^π = 2^?–7^? states of the ($\text{v}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}{}^{\mathrm{?3}}\text{? π}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}{}^{\mathrm{?3}}$) multiplet to be identified. These data are used to determine the two-hole $\text{π}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{-v}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}{}^{\mathrm{?}}$ interaction matrix elements.     

Satellite electron-diffraction in NbSe3 below T = 59 K

At temperatures below 59 K, coexistence of two types of satellite was observed in reciprocal lattice plane of b¹?c¹ as expressed by $\text{q}{}_1\text{= 0.24}\text{b}{}^1$ and $\text{q}{}_2\text{= 0.26}\text{b}{}^1\text{+0.50}\text{c}{}^1$. On the basis of nesting conditions by these q₁ and q₂, a feature of the Fermi surface for NbSe₃ is discussed.     

Influence of self-fields on the Vlasov equilibrium and stability properties of relativistic electron beam-plasma systems

The influence of self-fields on the equilibrium and stability properties of relativistic beam-plasma systems is studied within the framework of the Vlasov-Maxwell equations. The analysis is carried out in linear geometry, where the relativistic electron beam propagates through a background plasma (assumed nonrelativistic) along a uniform guide field $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$, It is assumed that $\text{ν}\text{γ}{}_0\text{? 1}$ for the beam electrons (ν is Budker's parameter, and γ₀mc² is the electron energy), but no a priori assumption is made that the beam density is small (or large) in comparison with the plasma density, or that conditions of charge neutrality or current neutrality prevail in equilibrium. It is shown that the equilibrium self-electric and self-magnetic fields, $\text{E}{}_{\mathrm{r}}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{r}}$ and $\text{B}{}_{\mathrm{\theta }}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{\theta }}$, can have a large effect on equilibrium and stability behavior. Equilibrium properties are calculated for beam (j = b) and plasma (j = e, i) distribution functions of the form f_b⁰(H, P_θ, P_z) = F(H ? ω_rbP_θ) × δ(P_z ? P₀)(j = b), and $\text{f}{}_{\mathrm{j}}{}^0\text{(H, P}{}_{\mathrm{\theta }}\text{, P}{}_{\mathrm{z}}\text{) = f}{}_{\mathrm{j}}{}^0\text{(H ? ω}{}_{\mathrm{rj}}\text{P}{}_{\mathrm{\theta }}\text{? V}{}_{\mathrm{j}}\text{P}{}_{\mathrm{z}}\text{?}\text{m}{}_{\mathrm{i}}\text{V}{}_{\mathrm{j}}{}^2\text{2}\text{)}$ (j = e, i), where H is the energy, P_θ is the canonical angular momentum, P_z is the axial canonical momentum, and ω_rj (the angular velocity of mean rotation for j = b, e, i), V_j (the mean axial velocity for j = e, i), and P₀ are constants. The linearized Vlasov-Maxwell equations are then used to investigate stability properties in circumstances where the equilibrium densities of the various components (j = b, e, i) are approximately constant. The corresponding electrostatic dispersion relation and ordinary-mode electromagnetic dispersion relation are derived (including self-field effects) for body-wave perturbations localized to the beam interior (r <R_b). These dispersion relations are analyzed in the limit of a cold beam and cold plasma background, to illustrate the basic effect that lack of charge neutrality and/or current neutrality can have on the two-stream and filamentation instabilities. It is shown that relative rotation (induced by self-fields) between the various components (j = b, e, i) can (a) result in modified two-stream instability for propagation nearly perpendicular to $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$, and (b) significantly extend the band of unstable k_z-values for axial two-stream instability. Moreover, in circumstances where the beam-plasma system is charge-neutralized but not current-neutralized, it is shown that the azimuthal self-magnetic field $\text{B}{}_{\mathrm{\theta }}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{\theta }}$ has a stabilizing influence on the filamentation instability for ordinary-mode propagation perpendicular to $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$.     

Lepton mixing and neutrino oscillations

The present article is a review of phenomena connected with neutrino oscillations. Mixing of two neutrinos (Majorana as well as Dirac) with masses m₁ and m₂ is considered in detail. It is shown that the hypothesis of lepton mixing is not in contradiction with the existing data if |m₁²?m₂²| ? 1 (eV)². Possible experiments designed to reveal neutrino oscillations at reactor, meson factory and high energy accelerator facilities are considered. In such experiments oscillation might be found if $\text{|m}{}_1{}^2\text{?m}{}_2{}^2\text{| ? 0.01}\text{(eV)}{}^2$. The possibilities of searching for oscillations by experiments on cosmic ray neutrinos and especially on solar neutrinos are discussed in detail. The last experiments have an incredible high sensitivity from the point of view of testing the lepton mixing hypothesis (oscillation effects might be observable if $\text{|m}{}_1{}^2\text{?m}{}_2{}^2\text{| ? 10}{}^{\mathrm{?12}}\text{(eV)}{}^2$). The “solar neutrino puzzle” is also discussed from the point of view of lepton mixing. Neutrino oscillations are considered then in the case where in nature there exist N ? 2 neutrino types.In conclusion the case of heavy lepton mixing is considered. It is shown that in a concrete scheme with right-handed currents, the probabilities of such processes as μ → eγ, μ → 3e etc. can be close to existing experimental upper limits, provided the heavy lepton masses are of an order of a few GeV, whereas the probabilities of the above processes are entirely negligible if only neutrinos are mixed.     

Coriolis intensity perturbations in the SO2 molecule: Experimental determination of the relative signs of (∂μ∂Qi)

The Coriolis interactions between ν₁ and ν₃, and between ν₂ and ν₃ in SO₂ have been analyzed to obtain the signs of the products $\text{ζ}{}_{3.1}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_1\text{)}$ and $\text{ζ}{}_{3.2}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_2\text{)}$. It has been found that both of the signs of these products are positive. Then, relative signs of ($\text{?μ}\text{?Q}{}_1$) have been determined using the calculated values of the Coriolis zeta constants for the present definition of the normal coordinates. The obtained sign combination of ($\text{?μ}\text{?Q}{}_{\mathrm{i}}$) is ±(+?+), which agrees with the one predicted by the molecular orbital calculations. Using the sign combination (+?+), the polar tensors of S and O atoms were also calculated.     

Conductivity of a quasi-one-dimensional metal at finite temperatures

The longitudinal conductivity of a quasi-one-dimensional metal is calculated for the case T?ω_D (ω_D being the limiting phonon frequency) and ω_Dl¹/v?1 where l¹ is the effective mean free path determined by impurity and phonon scattering: $\text{l}{}^1\text{= (l}{}^{\mathrm{?1}}{}_{\mathrm{ph}}\text{+ l}{}^{\mathrm{?1}}{}_{\mathrm{i}}\text{)}{}^{\mathrm{?1}}\text{, l}{}_{\mathrm{ph}}\text{= v/λT, l}{}_{\mathrm{i}}$ is the impurity mean free path. The conductivity is σ = (c₁e²/πS)l³_iv^?2ω_DλT for l_i?l_ph, σ = (c₂e²/πS)vω_D(λT)^?2 for l_i?l_ph, λ being the dimensionless electron-phonon interaction constant, c₁, c₂ ～ 1, S = a_xa_y is the (xy) area per one chain.     

Nonorthogonality corrections in the method of correlated basis functions

A set of normalized linearly independent basis functions φ₁, φ₂, …, φ_j, … generates matrix representatives $\text{H}$ and $\text{N}$ of the Hamiltonian operator and the identity. An orthonormal basis $\text{φ}{}_1$, $\text{φ}{}_2$, …, $\text{φ}{}_{\mathrm{j}}$, … generated by a Löwdin transformation is characterized by the distance in Hilbert space between $\text{φ}{}_{\mathrm{j}}$ and φ_j. The choice of positive definite $\text{N}$${}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ minimizes these distances and maximizes the diagonal elements of $\text{N}$${}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. Again for positive definite $\text{N}$${}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and a finite basis, 1 ? j ? p, the analysis yields a general theorem on Trace $\text{N}$${}^{\mathrm{<mtext>?n</mtext><mtext>2</mtext>}}$ (? p for all positive and negative integral values of n except n = ?1 and ? p for n = ?1).Sufficient conditions are determined which permit the application of the binomial theorem to the evaluation of the transform of $\text{H}$. Approximate formulas for the energy eigenvalues through third order in nondiagonal matrix elements are presented in a compact form containing characteristic nonorthogonality corrections depending on the exterior or interior location of the matrix element in the perturbation formulas.     

Rotationally resolved spectra of two van der Waals states of I + Cl

Three-step optical resonance is used to execute state-selected transitions from the ground state of ICl to two van der Waals states, $\text{b(}\text{Ω}\text{= 1)}$ and $\text{b′(}\text{Ω}\text{= 2)}$, both of which correlate with the second dissociation limit, $\text{I}\text{(}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{) +}\text{Cl}\text{(}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$, of ICl. Since the B(0⁺) state also belongs to this limit, three out of five states converging to I + Cl¹ are now accounted for. Principal constants of these states are: b′(2): T_e = 18275.84, ω_e = 31.093, ω_ex_e = 1.672, ω_ey_e = 0.0070, B_e = 0.034834, α_e = .001587, and D_e = 164.09 cm^?1; b(1): T_e = 18273.30, ω_e = 26.75, ω_ex_e = 0.882, B_e = 0.03579, q = 0.00084, and D_e = 166.63 cm^?1. In both states the equilibrium distance is near 4.2 Å, slightly greater than the sum of van der Waals contact radii, $\text{r}{}_{\mathrm{<mtext>I</mtext>}}\text{+ r}{}_{\mathrm{<mtext>Cl</mtext>}}\text{= 3.95}\text{A}\text{?}$. The large value of q in the b(1) state indicates that, in the basis set $\text{|j}{}_{\mathrm{a}}\text{j}{}_{\mathrm{b}}\text{j}\text{Ω}\text{〉}$ (a = I, b = Cl, j = j_a + j_b) the b(1) and b′(2) states belong to j = 1 and j = 2 “complexes,” respectively.     

Nuclear magnetic moment of the 3.9 s112− isomer 193mAu

The magnetic hyperfine splitting ν_M = |gμ_NB_HF/h| of ${}^{\mathrm{<mtext>193</mtext><mtext>m</mtext>}}\text{Au}\text{(j}{}^{\mathrm{\pi }}\text{=}\text{11}\text{2}{}^{\mathrm{?}}\text{, E = 290}\text{keV}$; $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 3.9}\text{s}\text{)}$ as a dilute impurity in Ni has been measured with nuclear magnetic resonance on oriented nuclei as 226.4(2) MHz. With the known hyperfine field B_HF = ?264.4(3.9) kG corrected for hyperfine anomalies the g-factor and magnetic moment of ^193mAu are deduced to be |g| = 1.123(17) and |μ| = 6.18(9) μ_N.     

Octet dominance in nonleptonic decays

The question of octet enhancement for the nonleptonic decays is studied within the framework of a current-algebra approach. By writing an unsubtracted dispersion relation for the matrix elements 〈B_k|H_w|B_j〉 and 〈M_k|H_w|M_j〉 (B denoting a $\text{1}\text{2}{}^{\mathrm{+}}$ baryon and M a 0^? meson) in the momentum transfer squared variable t and using the assumption of threshold dominance, namely that two pseudoscalar meson states dominate the absorptive parts of the above matrix elements and that in the chiral limit the meson-baryon and meson-meson scattering amplitudes which enter in the absorptive parts are exactly given by current algebra low energy theorems, it is shown that the above matrix elements are octet enhanced without assuming the octet transformation property for H_w. Further it is shown that the $\text{d′}\text{f′}$ ratio for the octet enhanced matrix elements 〈B_k|H_w|B_j〉 satisfies the relation , where $\text{(}\text{f}\text{d}\text{)}{}_{\mathrm{A}}$ denotes the $\text{f}\text{d}$ ratio of the axial vector current baryon couplings. The implications of this result for the s- and p-wave hyperon non-leptonic decays are discussed.     

Elastoresistivity of TTF-TCNQ and related compounds

Elastoresistances of TCNQ high conducting salts have been measured at room temperature by an original strain gauge technique. The effects, on the longitudinal and transverse resistivities ?, of an elementary uniaxial strain ? applied along one of the three axes, a, b or c¹ respectively, have been estimated.For TTF-TCNQ, they are:

$\text{K}{}^{\mathrm{b}}{}_{\mathrm{a}}\text{=? ln ?}{}^{\mathrm{b}}\text{/??}{}_{\mathrm{a}}\text{= 16±3}$

;

$\text{K}{}^{\mathrm{b}}{}_{\mathrm{b}}\text{= ? ln α}{}^{\mathrm{b}}\text{/??}{}_{\mathrm{b}}\text{= 34±4}$

;

(5% risk).So, in an hydrostatic pressure experiment, the fraction of piezoresistivity attributable to transverse effects is 43± 10% of the total value χ^b (K^b_a and K^b_c effects accumulated).Low values have been found for the anisotropy (?^a/?^b) variations due to strains. So one may write:

$\text{K}{}^{\mathrm{a}}{}_{\mathrm{a}}\text{= ? ln ?}{}^{\mathrm{a}}\text{/??}{}_{\mathrm{a}}\text{≌K}{}^{\mathrm{a}}{}_{\mathrm{b}}$

;

$\text{K}{}^{\mathrm{a}}{}_{\mathrm{b}}\text{= ? ln ?}{}^{\mathrm{a}}\text{/??}{}_{\mathrm{b}}\text{≌ K}{}^{\mathrm{b}}{}_{\mathrm{b}}$

;

.The TTF-, HMTTF-, TSF-, HMTSF-TCNQ elastoresistance values are coherent with the previously measured hydrostatic pressure piezoresistivity values.All these experimental results are in good agreement with a model where the longitudinal but also the transverse elastoresistivities are essentially due to variations with strains of the longitudinal scattering time τ_ν defined by σ^b = ne²τ_ν/m¹.     

Spectroscopy of 62Ni with the 61Ni(d, p) reaction

Differential cross sections, vector and tensor analysing powers have been measured for the ⁶¹Ni(d, p) reaction at a deuteron energy of 12.3 MeV. Most of the 30 transitions observed below 8.5 MeV excitation are dominated by a single j-value, which was determined from behaviour of the analysing power data. For a number of transitions it was possible to make unambiguous j-assignment relying on the established j-dependence of the T₂₂ tensor analysing power. The deduced spectroscopic factors indicate that the full strength of neutron transfer to the ($\text{2p, 1f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$) and $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ orbits was found and seven $\text{5}\text{2}{}^{\mathrm{+}}$ transitions were located above 5.3 MeV. The separated strengths of the $\text{3}\text{2}{}^{\mathrm{?}}\text{,}\text{1}\text{2}{}^{\mathrm{?}}\text{and}\text{5}\text{2}{}^{\mathrm{?}}$ transitions are compared with shell-model calculations for the low-lying states of ⁶²Ni.     

Predissociation and Λ-doubling in the even-parity Rydberg states of the nitrogen molecule

Predissociations in the y¹Π_g and $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ Rydberg states of N₂ (configurations $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{4pσ}$ and $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{3pπ}$, respectively) and their likely causes, are discussed. Peaking of rotational intensity at unusually low J values, without sharp breaking off, is interpreted as due to case c^? or case cⁱ predissociation. Λ doubling in the y state, attributed to interactions with the $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state and with another, ¹Σ⁺, state of the same electron configuration as x, is analyzed. From this analysis the location of the (unobserved) ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ state, here labeled x′, is obtained. It is concluded that the predissociation in the Π⁺ levels of the y state is an indirect one mediated by the interaction with x′ coupled with predissociation of x′ by a ${}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state dissociating to ${}^4\text{S +}{}^2\text{P}$ atoms: combined, however, with perturbation of the y state by the k¹Π_g Rydberg state (configuration $\text{3σ}{}_{\mathrm{g}}{}^{\mathrm{?1}}\text{4dπ}$), whose Π⁺ levels are completely predissociated.     

Problems of a perpetually oscillating universe

A model is constructed where a Friedmann universe, when collapsing, passes the region of Planek's dimensions near the classical singularity in the De Sitter state. The model assumes that the condition of the one-loop approximation $\text{R}{}_{\mathrm{\mu \nu \lambda \delta }}\text{· R}{}^{\mathrm{\mu \nu \lambda \delta }}\text{≤}\text{1}\text{l}{}_{\mathrm{<mtext>P1</mtext>}}{}^4$ is a universal law of nature. In the case of a dust-like matter the law restricts the mass density (?) to Planck's density $\text{?}{}_{\mathrm{<mtext>P1</mtext>}}\text{=}\text{c}{}^5\text{khx}{}^2$; $\text{?}{}^2\text{?}{}_{\mathrm{<mtext>P1</mtext>}}{}^2\text{≤ 1}$. In the dust-like model it is assumed that the gravitation constant χ depends on the density as $\text{χ = χ}{}_0\text{φ(}\text{?}{}^2\text{?}{}_{\mathrm{<mtext>P1</mtext>}}\text{?1)}$, the function φ vanishes at ? = ?_P1 so that the matter tensor in the right-hand side of the Einstein equation χT_μ^ν disappears in this limit, and the Friedmann universe becomes a De Sitter universe whose Λ¹ term is written in the form $\text{Λ}{}^1\text{θ(}\text{?}{}^2\text{?}{}_{\mathrm{<mtext>P1</mtext>}}{}^2\text{)}$ and at ? → ?_P1, θ → 1. As kh → 0, the theory becomes classical. Some difficulties of a perpetually oscillating model, namely, entropy increase, mass increase due to particle production, and increase of metric perturbations (appearance of gravitational waves) in the process of collapse, are considered in the framework of the model. Various possibilities of the mathematical apparatus of the theory that naturally involve limitations on the curvature value and, in particular, nonlinear Born-type lagrangians are discussed.     

Multiplicity distributions and double-scattering effects in π−d interactions at 360 GeV/c

Double-scattering effects are studied in π^?d interactions at 360 GeV/c. The partial cross sections $\text{σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(π}{}^{\mathrm{?}}\text{d}\text{), σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(“π}{}^{\mathrm{?}}\text{p}\text{”)}\text{and}\text{σ}{}_{\mathrm{<mtext>N</mtext>}}\text{(“π}{}^{\mathrm{?}}\text{n}\text{”)}$ are presented. The double-scattering probability per πd collision is found to be $\text{? = 0.15 ± 0.02}$. We have extracted the partial cross section X_N of the double-scattering plus interference contributions, and find that X_N obeys KNO scaling. The data are compared with various theoretical predictions.     

Particle-hole multiplets in 40Ca observed in the 41Ca(τ, α) reaction

Energy levels in ⁴⁰Ca up to 10.2 MeV have been studied in the neutron pickup reaction ⁴¹Ca(τ, α)⁴⁰Ca with 20 MeV bombarding energy. Thirty excited states have been identified and angular distributions have been measured in the interval from 5° to 40° by means of a split-pole magnetic spectrometer. The angular distributions together with DW calculations have been used to extract l_n values and spectroscopic factors. The l_n = 2 strength distribution for the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ particle-hole levels is compared to the l_p = 3 strength distribution from pr stripping data.