Reworking the Tucson-Melbourne Three-Nucleon Potential

 We introduce new values of the strength constants (i.e., a, b, c, and d coefficients) of the Tucson-Melbourne (TM) 2π-exchange three-nucleon potential. The new values come from contemporary dispersion-relation analyses of meson-factory πN-scattering data. We make variational Monte-Carlo calculations of the triton with the original and updated three-body forces to study the effects of this update. We remove a short-range–π-range part of the potential due to the c coefficient and discuss the effect on the triton binding energy. Received September 11, 1999; revised November 2, 1999; accepted February 23,     

Proton-Induced Deuteron Breakup Reaction at 65 MeV: Unspecific Configurations

 Cross sections and vector-analyzing powers for four unspecific configurations of the ²H(p,pp)n breakup reaction at E ^lab _p  = 65MeV were measured in a kinematically complete experiment. Measured observables are compared with rigorous Faddeev calculations using four realistic charge-dependent interaction models, the CD Bonn, Argonne v ₁₈, Nijmegen I, and Nijmegen II potentials with or without inclusion of the Tucson-Melbourne three-nucleon force. Coulomb effects are completely omitted. A satisfactory agreement between theory and experiment has been found. There exist, however, some discrepancies between measured and calculated analyzing-power distributions in certain kinematical regions. The effects of the Tucson-Melbourne three-body force are either negligible or slightly increasing the disagreement. Received May 12, 1999; revised March 3, 2000; accepted for publication April 26, 2000     

S-ware πN scattering effects in the nuclear three-body force

We examine the contributions of the off-mass-shell,s-wave N scattering amplitude terms in the Tucson-Melbourne two-pion-exchange three-body force to the trion binding energy. While thea andc terms are not as important as thep-wave terms, they comprise a nonnegligible part of the three-nucleon force which produces nonperturbative effects in the triton wave function.     

<Superscript>1</Superscript>H Spin–Lattice Relaxation Study of Dynamical Inequivalence of Methyl Groups in Solid 1,2-<Emphasis Type="Italic">O</Emphasis>-(1-Ethylpropylidene)-α-<Emphasis Type="SmallCaps">d</Emphasis>-Glucofuranose

We investigated the dynamics of methyl groups in organic polycrystalline 1,2-O-(1-ethylpropylidene)-α-d-glucofuranose by the proton spin–lattice relaxation method. The temperature and nuclear magnetic resonance Larmor frequency dependence of relaxation time is presented and interpreted in terms of simple possible dynamical model for the reorientation of methyl groups: the random hopping for methyl groups, which are in a, b, and c sites in the crystal. The energy E _a of 13.5 kJ mol⁻¹ for the a-type methyl groups is typical for methyl groups in ethyl groups. In contrast, the b- and c-methyl groups characterized by the lower E _a values of 9.5 and 6.5 kJ mol⁻¹ are located in the crystal structure where the intermolecular interactions significantly influence the potential, leading to a decrease in the total energy.     

Polarization-Transfer Coefficients in and Reactions at MeV: Experiment Compared to Calculations with Recent Nuclear-Interaction Models

The polarization-transfer coefficients K , K and K , K have been measured in the elastic scattering reactions D(, )p and D(, )d at MeV, respectively. They are compared to solutions of the three-nucleon Faddeev equations obtained with the recent nucleon-nucleon interactions AV18, CD Bonn, NijmI and II. Effects of the Tucson-Melbourne three-nucleon force, adjusted separately to reproduce the triton binding energy for each of these potentials, are studied. Both and exhibit a scaling behaviour with the triton binding energy. For and the various predictions with two-nucleon forces only agree practically with each other but spread after inclusion of the three-nucleon force. The agreement of theory and data is fair but the neglect of the proton-proton Coulomb force precludes a final conclusion. Received July 28, 1997; revised February 3, 1998; accepted for publication March 11, 1998     

A two-pion exchange three-nucleon force based on a realistic πN interaction

The contribution of a ππ-exchange three-body force to the three-nucleon binding energy is calculated in terms of a πN amplitude. The latter is based on a meson-theoretical model of πN interaction developed by the Jülich group. Similar to a previous study based on simple phenomenological πN potentials a very small effect of the resulting three-body force is found. Possible origins of the two-orders-of-magnitude discrepancy between the present result and the values obtained for the Tucson-Melbourne three-body force are investigated. Evidence is provided that this discrepancy is most likely due to strikingly different off-shell properties of the πN amplitudes underlying the two approaches. Received: 9 February 2000     

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.     

Compact and accurate variational wave functions of three-electron atomic systems constructed from semi-exponential radial basis functions

The semi-exponential basis set of radial functions [A.M. Frolov, Phys. Lett. A 374, 2361 (2010)] is used for variational computations of bound states in three-electron atomic systems. It appears that the semi-exponential basis set has a substantially greater potential for accurate variational computations of bound states in three-electron atomic systems than was originally anticipated. In particular, the 40-term Larson’s wave function improved with the use of semi-exponential radial basis functions now produces the total energy –7.4780581457 a.u. for the ground 1²S-state in the ^￥Li^\infty{\rm Li} atom (only one spin function c₁\chi_1 = aba\alpha\beta\alpha - baa\beta\alpha\alpha was used in these calculations). This variational energy is very close to the exact ground state energy of the ^￥Li^\infty{\rm Li} atom and is substantially lower than the total energy obtained with the original Larson’s 40-term wave function (–7.477944869 a.u.).     

Pion-mass dependence of three-nucleon observables

We use an effective field theory (EFT) which contains only short-range interactions to study the dependence of a variety of three-nucleon observables on the pion mass. The pion-mass dependence of input quantities in our “pionless” EFT is obtained from a recent chiral EFT calculation. To the order we work at, these quantities are the ¹ S ₀ scattering length and effective range, the deuteron binding energy, the ³ S ₁ effective range, and the binding energy of one three-nucleon bound state. The chiral EFT input we use has the inverse ³ S ₁ and ¹ S ₀ scattering lengths vanishing at m _π ^crit = 197.8577 MeV. At this “critical” pion mass, the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. We compute the binding energies of these states up to next-to-next-to-leading order in the pionless EFT and study the convergence pattern of the EFT in the vicinity of the critical pion mass. Furthermore, we use the pionless EFT to predict how doublet and quartet nd scattering lengths depend on m _π in the region between the physical pion mass and m _π = m _π ^crit .     

Search for narrow dibaryon resonances in neutral pion photoproduction from the deuteron

The reaction γd↦π⁰ X has been measured with TAPS at MAMI in the energy range E _γ = 140-300 MeV. Using the Glasgow tagging spectrometer a photon energy resolution of 0.8 MeV was achieved. The energy excitation functions of integral and differential total cross-sections show no structures of statistical significance > 2σ. Upper limits for the production of narrow isoscalar or isovector dibaryons with masses m? 2100 MeV/c² were deduced. They are in the range 2-5 μb averaged over the 0.8 MeV energy resolution. Received: 25 October 2000 / Accepted: 24 November 2000     

Evolution of the structure of Rb2ZnCl4 over the temperature range 4.2–310 K

X-ray diffraction is used to study the temperature dependence of the lattice parameters and the sequence of structural realignments in crystalline Rb₂ZnCl₄ over temperatures of 4.2–310 K. The appearance of and changes in the system of satellite reflexes indicative of structural ordering are studied. Below 74 K, on going into the monoclinic phase (space group A11a), anomalies are observed in the behavior of the lattice parameters, and superstructural reflexes develop with wave vectors q=a ^*/3+b ^*/2+c ^*/2 corresponding to an increase by a large factor in initial parameters a, b, and c of the Pnma-phase. Fiz. Tverd. Tela (St. Petersburg) 41, 1084–1090 (June 1999)     

Onset of local ordering in some copper-based alloys: critical solute concentration vis-a-vis various solutionhardening parameters

The mode of planar distribution of solute atoms in Cu single crystals alloyed with 0.5 to 8.0 at.%Ge has been investigated via the temperature dependence of the critical resolved shear stress of these alloys. It is found that there exists a critical solute concentration c _m ≈ 5 at.%Ge below which the distribution of solute atoms in the crystal is random, and above which some local ordering occurs. This together with such data available in the literature for Cu-Zn, Cu-Al and Cu-Mn alloys, i.e. c _m ≈7 at. %Zn, 7 at.%Al and 1 at.%Mn, when examined as a function of the size-misfit factor δ = (1/b)(db/dc)of a given binary alloy system, shows that the value of c _m strongly depends on δ; the smaller the magnitude of δ, the greater the value of c _m and vice versa. Also, the value of c _m is found to correlate well with the electron-to-atom ratio (e/a)of the Cu-Zn, Cu-Al, Cu-Ge and Cu-Mn alloys with the solute concentration c = c _m . However, no systematic correlation exists between the critical solute concentration c _m for the onset of local ordering and the modulus-mismatch parameter η = (1/G)(dG/dc).      

Black holes with metric and fields of the same form

We present two rotating black hole solutions with axion ξ, dilaton f{\phi} and two U(1) vector fields. Starting from a non-rotating metric with three arbitrary parameters, which we have found previously, and applying the “Newman–Janis complex coordinate trick” we get a rotating metric g _μν with four arbitrary parameters namely the mass M, the rotation parameter a and the charges electric Q _E and magnetic Q _M . Then we find a solution of the equations of motion having this g _μν as metric. Our solution is asymptotically flat and has angular momentum J = M a, gyromagnetic ratio g = 2, two horizons, the singularities of the solution of Kerr, axion and dilaton singular only when r = a cos θ = 0 etc. By applying to our solution the S-duality transformation we get a new solution, whose axion, dilaton and vector fields have one more parameter. The metrics, the vector fields and the quantity l = x+ie^-2f{\lambda=\xi+ie^{-2\phi}} of our solutions and the solution of: Sen for Q _E , Sen for Q _E and Q _M , Kerr–Newman for Q _E and Q _M , Kerr, Reference Kyriakopoulos [Class. Quantum Grav. 23:7591, 2006, Eqs. (54–57)], Shapere, Trivedi and Wilczek, Gibbons–Maeda–Garfinkle–Horowitz–Strominger, Reissner–Nordstr?m, Schwarzschild are the same function of a, and two functions ρ ² = r(r + b) + a ² cos² θ and Δ = r(r + b) − 2Mr + a ² + c, of a, b and two functions for each vector field, and of a, b and d respectively, where a, b, c and d are constants. From our solutions several known solutions can be obtained for certain values of their parameters. It is shown that our two solutions satisfy the weak the dominant and the strong energy conditions outside and on the outer horizon and that all solutions with a metric of our form, whose parameters satisfy some relations satisfy also these energy conditions outside and on the outer horizon. This happens to all solutions given in the “Appendix”. Mass formulae for our solutions and for all solutions which are mentioned in the paper are given. One mass formula for each solution is of Smarr’s type and another a differential mass formula. Many solutions with metric, vector fields and λ of the same functional form, which include most physically interesting and well known solutions, are listed in an “Appendix”.     

On the existence of four-particle Coulomb systems

Whether bound states of Coulomb systems composed of four particles with unit charges (quadrions), a ⁺ b ⁺ c ⁻ d ⁻, exist is demonstrated to be determined by the masses of the constituent particles. Relations that make it possible to establish the existence of a large number quadrions with different masses of the particles are derived. The energies of reference quadrions of different symmetry, a positronium molecule, a ⁺ a ⁺ a ⁻ a ⁻, a ⁺ b ⁺ a ⁻ b ⁻, a ⁺ b ⁺ a ⁻ b ⁻, and a ⁺ a ⁺ b ⁻ c ⁻, are determined and groups of stable asymmetric quadrions corresponding to them are identified. A relationship between the stability of a number of quadrions and three-particle systems (trions) was found. The results shows that, among all the 406 four-particle independent combinations of electrons, muons, pions, kaons, protons, deuterons, and tritium nuclei or their antiparticles, there are 227 bound quadrions.     

Positron scattering from hydrocarbons

The total cross sections for positron impact on hydrocarbons have been calculated using the additivity rule in which the total cross section for a molecule is the sum of the total cross section for the constituent atoms. The energy range considered is from a few eV to several thousand eV. The total cross sections for positron impact on an atom are calculated by employing a complex spherical potential which comprises of a static, polarization and an absorption potential. We have good agreement with the experimental results for hydrocarbons for positron energy ⩾100 eV. Our results also agree with the available calculations for CH₄ and C₂H₂ which employed full molecular wavefunctions beyond 100 eV. Our absorption cross sections also agree with molecular wave-function calculations for C₂H₂ and CH₄ beyond 100 eV. We have shown the Bethe plots fore ⁺−C ande ⁺−H scattering systems and Bethe parameters have been extracted. We have fitted the cross section for positron impact on hydrocarbons in the formσ _t(C _n H _m )=naE ⁻ b+mcE ⁻ d in the energy range 300–5000 eV wherea=195.0543,b=0.7986,c=371.1757 andd=1.1379 withE in eV andσ _t in 10⁻¹⁶ cm².     

Energy Dependence of the πN Amplitude and the Three-Nucleon Interaction

By calculating the contribution of the ππ three-body force to the three-nucleon binding energy in terms of the πN amplitude using perturbation theory, we are able to determine the importance of the energy dependence and the contribution of the different partial waves of the πN amplitude to the three-nucleon force. A separable representation of the non-pole πN amplitude allows us to write the three-nucleon force in terms of the amplitude for NN → NN*, propagation of the NNN* system, and the amplitude for NN* → NN , with N* being the πN quasi-particle amplitude in a given state. The division of the πN amplitude into a pole and non-pole part gives a procedure for the determination of the πNN form factor within the model. The total contribution of the three-body force to the binding energy of the triton for the separable approximation to the Paris nucleon-nucleon potential (PEST) is found to be very small mainly as a result of the energy dependence of the πN amplitude, the cancellation between the S- and P-wave πN amplitudes, and the soft πNN form factor. Received April 12, 1994; revised November 11, 1994; accepted for publication December 1, 1994     

Low-energy ηd-resonance

Elastic ηd-scattering is considered within the Alt-Grassberger-Sandhas (AGS) formalism for various ηN input data. A three-body resonant state is found close to the ηd threshold. This resonance is sustained for different choices of the two-body ηN-scattering length a _ηN. The position of the resonance moves towards the ηd threshold when Rea _ηN is increased, and turns into a quasi-bound state at Rea _ηN∼ 0.7-0.8 fm depending on the choice of Ima _ηN. Received: 12 June 2000 / Accepted: 3 August 2000     

Renormalization group equation and QCD coupling constant in?the?presence of?SU(3) chromo-electric field

We solve the renormalization group equation in QCD in the presence of a SU(3) constant chromo-electric field E ^a with arbitrary color index a=1,2,…,8 and find that the QCD coupling constant α _s depends on two independent Casimir/gauge invariants C ₁=[E ^a E ^a ] and C ₂=[d _abc E ^a E ^b E ^c ]² instead of one gauge invariant C ₁=[E ^a E ^a ]. The β function is derived from the one-loop effective action. This coupling constant may be useful to study hadron formation from color flux tubes/strings at high energy colliders and to study quark–gluon plasma formation at RHIC and LHC.