Contribution ofp-wave (3)+1 subamplitudes to4He binding energy and scattering observables below four-body breakup threshold

The four-body equations of Alt, Grassberger and Sandhas, in the form that the (2)+(2) subsystem amplitudes are treated by the convolution method, are solved for separable two-body interactions between nucleon pairs in the channels³S₁-³D₁ (t ₀₀ alone) and¹S₀. AllL=0 andL=1 (3)+1 subamplitudes are represented in a separable form using the energy dependent pole expansion. The contribution ofp-wave (3)+1 subamplitudes to the⁴He binding energy, threshold scattering observables and low energy cross sections forn ³Hn ³H,p ³Hep ³He,dddd andddp ³H reactions is studied for different two-body potentials.     

On the role of theΔ -isobar in deep inelastic scattering on the deuteron

The role of the nuclear structure effects, viz. the boundness of nucleons and-isobar components, in the deep inelastic scattering of leptons on the deuteron is considered. It is shown that small admixture of the-isobar configurations to the deuteron wave function may lead to significant effects in the spin structure functions of the deuteronb ₁ ^D andg ₁ ^D (x): up to 4% in g ₁ ^D (x) dx and up to 10% ing ₁ ^D (x) at smallx.One of the authors (A.U.) thanks Prof. F.C. Khanna for helpful discussions and for kind offering the information used in our calculations.     

Second-order quadrupole splittings of the95Mo NMR signal in Mo(CO)6 and their reduction by sample spinning

The lifetimes of higher lying¹S_0?,¹D_2?, and¹F ₃ ⁰ -levels and of the 5s 7s³S₁- and 5p^{2 3}P₁-state in the Sr I-spectrum have been measured by a time resolved registration of the fluorescent intensity. The¹S_0? and¹D₂-levels were populated selectively by a two step optical excitation using two pulsed dye lasers. In the case of the¹F ₃ ⁰ -levels and of the³S_1?,³P₁-states the first excitation step was performed by a discharge, for the second, selective step a pulsed dye laser was used. The agreement of the experimental results with theoretically obtained lifetimes is satisfactory only in some cases.     

Off-shell effects in nucleon-deuteron polarization observables

A separable representation of theS-wave Paris potential and a phase-shift equivalent Yamaguchi-type potential significantly differing in their off-shell behaviours are used to calculate second-order polarization observables of elastic nucleon-deuteron scattering atE _D=10 and 20MeV. Off-shell effects are found that stem from differences in the nuclear interaction in the inner regionr?1.2 fm. Adding approximate Coulomb-distortion contributions to the purely nuclear Faddeev amplitudes proton-deuteron predictions are obtained. Coulomb effects are not found to be negligible. Comparison with experimental data, in particular, the spin-correlation parameterC _y,y of the reaction \({}^1\vec H(\vec d,d)^1 H\) forE _D=10MeV vector-polarized deuterons and the spin-transfer coefficientsK _y ^y′ ,K _x ^x′ andK _z ^x′ for \({}^2H(\vec p,\vec p)^2 H\) atE _p=10MeV, prefer the interaction model that contains an intermediate-range repulsion.     

Momentum-space calculations for three-nucleon scattering including a three-nucleon force

The formalism to include a three-nucleon force into three-nucleon continuum calculations is presented. First numerical results, obtained in momentum space, are shown. The two- and three-nucleon forces have been restricted to act only in the¹ S ₀ and³ S ₁-³ D ₁ partial-wave states. As two-nucleon interaction the Bonn-B potential and as three-nucleon interaction the Tucson-Melbourne two-pion exchange model has been used.     

Heavy-mesons exchange and the backward deuteron electrodisintegration

Backward electrodisintegration of the deuteron is calculated using an exchange-current operator containing , , , , , , andA ₁ exchanges. The deuteron and¹S₀ np wave functions are derived from the Bonn OBEPs. For completeness, we introduced theA ₁-meson exchange into the OBEP's as well. As a consequence, the value ofD-state probabilityP _D is increased by 0.2%–0.8%. The computed cross sections are compared with new data.Partially supported by the Deutsche Forschungsgemeinschaft (SFB 201)     

Picosecond phase-conjugation by degenerate four-wave mixing in sodium vapour

Phase-conjugated waves (PCW), via degenerate four-wave mixing (DFWM) with picosecond laser pulses having a FWHM of 80 ps have been obtained in sodium vapour on both sides of theD ₂(3² S _1/23² P _3/2) transition at 589 nm. The maximum reflectivity of the PCW signals was 60%. The reflectivity of the PCW has been measured as a function of the temperature, the detuning and the pump and probe intensities. Because of the very strong nonlinear behaviour of theD ₂ transition the appearance of the PCW is accompanied by strong self-focusing and defocusing of the beams, which give a rather complicated line-shape of the detuning curve of the PCW. By varying the delay between the beams, the lifetime of the transient volume grating has been, measured to be 7.4 ns. The results are in qualitative agreement with the theoretical model of Abrams and Lind.     

Reaction matrix for nonlocal potentials. I. Magic nuclei

The binding energies of⁴He,¹⁶O, and⁴⁰Ca are computed applying the Brueckner theory of the reaction matrix for the Tabakin and the Mongan nonlocal separable potentials. Binding energies (10 MeV/nucleon) obtained are substantially greater than similar values for the local Hamada-Johnston potential (approx. 4÷5 MeV/nucleon). Detailed comparison of reference and exact reaction matrices for both types of potentials (local and nonlocal) in the coupled³ S-³ D channel confirms the existence of a strong correlation between the magnitude of the matrix elements of the reaction matrix and the intensity of a tensor force. A similar correlation also exists in the¹ S ₀ channel between the magnitude of matrix elements of the reaction matrix and the singlet scattering length. A different off-shell behaviour of individual potentials plays also a certain role.     

Transition Moments betweenΔg,Πg, andΠuStates of the H2Molecule

Electronic transition moments are computed for dipole transitions between theCandD¹Π_u,IandR¹Π_gandJandS¹Δ_gstates of the hydrogen molecule for internuclear distancesR∈ [1, 15] bohr. The character of the wavefunctions at large internuclear distances is investigated. It is shown that in theDandRstates the asymptotic configurations are strongly mixed forR≤ 15 bohrs. TheSstate has mixed character even atR= 40 bohr.     

Strong coupling in the quantum field theory with nonlocal nonpolynomial interaction

In the relativistic quantum field theory the representation for theS-matrix elements is obtained for any coupling constantsg in the case of a one component scalar field (x) with nonlocal nonpolynomial interaction _I ()=gU() when the causal function is bounded in the Euclidean region 0D _c (x _E ² D _c (0)< and the function |U(u)|1 for realu. It is proved that the two point Green function is bounded in the physical region of momenta variablep ².     

The quark configurationsS 6 andS 4 P 2 in the bag model

The spectrum and eigenfunctions of deuteronlike states in the quark bag for the configurationsS ⁶ andS ⁴ P ² have been studied. The complete tables of the fractional parentage coefficients (f.p.c.) for these configurations in thej-j andL-S coupling schemes are presented. The universal method of calculation of the f.p.c. which is based on the complementarity of the unitary and permutation group, is considered. The method enable one to calculate the Clebsh-Gordon coefficients and the invariant symbols of the noted groups. It is shown that the lowest energy state of the configurationS ₁ ^2/4 P ₃ ^2/2 resembles the partial wave³ D ₁ and can, therefore, be coupled to it in a deuteron. On the contrary, the lowest states in the configurationsS ₁ ^2/6 andS ₁ ^2/4 P ₁ ^2/2 resemble the³ S ₁-wave.     

Einfluß der Pion-Pion-Wechselwirkung auf Pion-Nukleon-Streuphasen

The isospin dependent part of theS-wave pion-nucleon amplitude is calculated according to the CGLN approach, but recoil and projection on the partial waves are treated exactly. Then the difference against the experimental data is approximately a constant up to 100 MeV and amounts to 1/3 of the total value. It is shown, that at low energies the main corrections of the CGLN equations are taken into account by a subtraction of theπ+π→?+\(\overline \Re \),J=I=1 amplitudesf _± ¹ (t) as proposed byMandelstam andFrazer. Calculations have been done forS, P andD pion-nucleon amplitudes. The main result is a prediction of theS-wave amplitude obtained without adjusting free parameters up to 100 MeV. The relations of this method to the equations derived byBowcock, Cottingham andLurié according to the Cini-Fubini approach are discussed.     

Production rate and decay lifetime measurements ofBs0 mesons at LEP usingDs and? mesons

The study of the properties of inclusive production ofD _s mesons and of events in which a and a muon are present in the same jet provides two independent measurements of the probability,f _s ^w , for a heavy quark to hadronize into a strangeB orD meson. The data sample analysed corresponds to 243,000 hadronicZ ⁰ decays. The combined value of these measurements isf _s ^w =0.19±0.06±0.08. From the flight distance distributions ofD _s and of (-lepton) secondary vertices, with the lepton emitted at high transverse momentum relative to the jet axis, two values are obtained for theB _s ⁰ meson lifetime. Combining these measurements with a previous result based on the study ofD _s- events, theB _s ⁰ meson lifetime is measured to be: 0.96±0.37 ps.     

X-Band Pulsed ENDOR Study ofFe-Substituted Sodalite— The Effect of the Zero-Field Splitting

X-band (∼9.3 GHz) pulsed ENDOR measurements were carried out on⁵⁷Fe-substituted sodalite (FeSOD) which contains only one type of Fe(III) (S=) located at a framework site. The ENDOR spectrum recorded atg= 2 shows three doublets corresponding to the sixM_Smanifolds. The assignment of these signals was confirmed by hyperfine-selective and triple ENDOR experiments. The components of each of the doublets had different intensities, reflecting the different populations of the EPR energy levels at the measurement temperature, 1.8 K. ENDOR spectra were recorded at magnetic fields within the EPR powder pattern, and the field dependence observed showed an anisotropic behavior, unexpected from the isotropic character of the⁵⁷Fe(III) hyperfine coupling. This dependence was attributed to the high-order effects of the zero-field splitting (ZFS) interaction on the ENDOR frequencies. Three different theoretical approaches were used to account for the dependence of the ENDOR spectrum on the ZFS interaction. The first involves the exact diagonalization of the total spin Hamiltonian, the second uses third-order perturbation approximations, and the third employs an effective nuclear Hamiltonian for each of theM_Smanifolds. The simulations showed that the ENDOR signals of theM_S= ±5/2 (ν_±5/2) manifold are the least sensitive to the magnitude of the ZFS parameterDand are therefore the most appropriate for the determination ofa_iso. It is shown that at X band anda_isovalues of about 30 MHz, the perturbation approach is valid up toDvalues of 500 MHz if all three doublets are concerned. However, if only the ν_±5/2doublet is considered, then this approach is valid forD< 1000 MHz. The third approach was found inappropriate fora_isovalues of ∼30 MHz. Using the method of exact diagonalization together with orientation selectivity, the trends observed in the experimental spectra could be reproduced. The ENDOR spectra of the⁵⁷Fe-substituted zeolites ZSM5, L, and mazzite showed broad and ill-defined peaks since the ZFS of Fe(III) in these zeolites is significantly larger than that of FeSOD. Because this broadening is a high-order effect, it can be significantly reduced at higher spectrometer frequencies.     

I=0 toI=1 transition form factors

A method is proposed to extend the hard scattering picture of Brodsky and Lepage to transitions between hadrons with orbital angular momentuml=0 andl=1. The use of covariant spin wave functions turns out to be very helpful in formulating that method. As a first application we construct a light-cone wave function of the nucleon resonance N^*(1535) in the quark-diquark picture. Using this wave function and the extended hard scattering picture, theN-N ^* transition form factors are calculated at large momentum transfer and the results compared to experimental data. As a further application of our method we briefly discuss the- a₁ form factors in an appendix.Supported by the Deutsche Forschungsgemeinschaft.     

Neutron scattering study of the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr2CuO2Cl2

We have carried out a neutron scattering investigation of the static structure factorS(q _2D ) (q _2D is the in-plane wave vector) in the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr₂CuO₂Cl₂. For the spin correlation length we find quantitative agreement with Monte Carlo results over a wide range of temperature. The combined Sr₂CuO₂Cl₂-Monte Carlo data, which cover the length scale from 1 to 200 lattice constants, are predicted without adjustable parameteres by renormalized classical theory for the quantum nonlinear sigma model. For the structure factor peakS(0), on the other hand, we findS(0) ² for the reduced temperature range 0.16<T/2 _s <0.36, whereas current theories predict that at low temperaturesS(0)T ^{2 2}. This discrepancy has important implications for the interpretation of many derivative quantities such as NMR relaxation rates. In the ordered phase, we have measured the temperature dependence of the out-of-plane spin-wave gap. Its low-temperature value of 5.0 meV corresponds to an XY anisotropyJ _XY /J=1.4×10^–4. From measurements of the sublattice mangetization we obtain =0.22±0.01 for the order parameter exponent. This may either reflect tricricality as in La₂CuO₄, or it may indicate finite-size two-dimensional XY behavior as suggested by Bramwell and Holdsworth. As in theS=1 system K₂NiF₄, the gap energy in Sr₂CuO₂Cl₂ scales linearly with the order parameter up to the Néel temperature. We also reanalyze static structure factor data for K₂NiF₄ using the exact low temperature result for the correlation length of Hasenfratz and Niedermayer and including the Ising anisotropy explicitly. Excellent agreement between experiment and theory is obtained for the correlation length, albeit with the spin-stiffness _s reduced by 20% from the spin-wave value. As in Sr₂CuO₂Cl₂ we find thatS(0) ² for the reduced temperature range 0.22<T/2 _s <0.47.     

Reduction of constrained mechanical systems and stability of relative equilibria

A mechanical system with perfect constraints can be described, under some mild assumptions, as a constrained Hamiltonian system(M, , H, D, W): (M, ) (thephase space) is a symplectic manifold,H (theHamiltonian) a smooth function onM, D (theconstraint submanifold) a submanifold ofM, andW (theprojection bundle) a vector sub-bundle ofT _D M, the reduced tangent bundle alongD. We prove that when these data satisfy some suitable conditions, the time evolution of the system is governed by a well defined differential equation onD. We define constrained Hamiltonian systems with symmetry, and prove a reduction theorem. Application of that theorem is illustrated on the example of a convex heavy body rolling without slipping on a horizontal plane. Two other simple examples show that constrained mechanical systems with symmetry may have an attractive (or repulsive) set of relative equilibria.     

Measurement of a complete set of analyzing powers of the fusion reactions D(\vec d,p)3He atE d=28 keV

Angular distributions of the four analyzing powers of the mirror fusion reactions D( ,p)³H and D( ,n)³He have been measured at the very low energy of 28±3 keV. Differences between both reactions are visible. The data are compared with anR-matrix parametrization and used as input to a comprehensive reaction-matrix fit.D-wave contributions are strongly suppressed in contrast toP- andS-waves. However, entrance-channel quintetS-waves are not suppressed. The possibility of a neutron-lean fusion reactor is therefore excluded.     

Distribution of Particles Which Produces a “Smart” Material

If A _q(β, α, k) is the scattering amplitude, corresponding to a potential , where D⊂ℝ³ is a bounded domain, and is the incident plane wave, then we call the radiation pattern the function , where the unit vector α, the incident direction, is fixed, β is the unit vector in the direction of the scattered wave, and k>0, the wavenumber, is fixed. It is shown that any function , where S ² is the unit sphere in ℝ³, can be approximated with any desired accuracy by a radiation pattern: , where ∊ >0 is an arbitrary small fixed number. The potential q, corresponding to A(β), depends on f and ∊, and can be calculated analytically. There is a one-to-one correspondence between the above potential and the density of the number of small acoustically soft particles D _m⊂ D, 1≤ m≤ M, distributed in an a priori given bounded domain D⊂ℝ³. The geometrical shape of a small particle D _m is arbitrary, the boundary S _m of D _m is Lipschitz uniformly with respect to m. The wave number k and the direction α of the incident upon D plane wave are fixed. It is shown that a suitable distribution of the above particles in D can produce the scattering amplitude , at a fixed k>0, arbitrarily close in the norm of L ²(S ²× S ²) to an arbitrary given scattering amplitude f(α ', α), corresponding to a real-valued potential q∊ L ²(D), i.e., corresponding to an arbitrary refraction coefficient in D. MSC: 35J05, 35J10, 70F10, 74J25, 81U40, 81V05, 35R30. PACS: 03.04.Kf.     

Superradiating 4P-4S-3P cascade of sodium vapour arising on the leading edge of the exciting laser pulse

Investigations of the superradiating cascade of sodium vapour 4P-4S-3P ₁ = 2.21 µm and ₂=1.14 µm) arising on the leading edge of the exciting laser pulse were carried out. The dependences of the actual delay time _D of the ₁ pulse on the population rise time of the laser-excited 4P state were measured and compared with those calculated following the existing theoretical model. The dependence of the actual delay time _D on the inverse density of excited atoms 1/N* is also presented. Analysis of this dependence revealed the influence of the Doppler dephasing and of the second, ₂, transition on the formation of the ₁ superradiance.