Accurate Three-Nucleon Bound-State Calculation with an Extended Separable Expansion of the Two-Body T-Matrix

An accurate solution for the three-nucleon bound state is obtained within 1 keV in the binding energy and, on the whole, better than 1% in the wave function, using a new systematic and efficient method. The method is based on a recently developed separable expansion for any finite-range interaction, in which a rigorous separable series for the two-body t-matrix is obtained by expanding the wave function in terms of a complete set of basis functions inside the range of the potential. In order to treat a potential with a strong repulsive core, as in the case of the Argonne potential, we develop a two-potential formalism. The expansion starts with a few EST (Ernst, Shakin, and Thaler) terms in order to accelerate the convergence and continues with an orthogonal set of polynomials, avoiding the known difficulties of a pure EST expansion. Thus, several techniques are combined in the present extended separable expansion (ESE). In this way, the method opens a new systematic treatment for accurate few-body calculations resulting in a dramatic reduction in the CPU time required to solve few-body equations. Received November 6, 1996; revised April 14, 1997; accepted for publication April 30, 1997     

Along the Lines of Nonadditive Entropies: q-Prime Numbers and q-Zeta Functions

The rich history of prime numbers includes great names such as Euclid, who first analytically studied the prime numbers and proved that there is an infinite number of them, Euler, who introduced the function ζ(s)≡∑n=1∞n−s=∏pprime11−p−s, Gauss, who estimated the rate at which prime numbers increase, and Riemann, who extended ζ(s) to the complex plane z and conjectured that all nontrivial zeros are in the R(z)=1/2 axis. The nonadditive entropy Sq=k∑ipilnq(1/pi)(q∈R;S1=SBG≡−k∑ipilnpi, where BG stands for Boltzmann-Gibbs) on which nonextensive statistical mechanics is based, involves the function lnqz≡z1−q−11−q(ln1z=lnz). It is already known that this function paves the way for the emergence of a q-generalized algebra, using q-numbers defined as 〈x〉q≡elnqx, which recover the number x for q=1. The q-prime numbers are then defined as the q-natural numbers 〈n〉q≡elnqn(n=1,2,3,⋯), where n is a prime number p=2,3,5,7,⋯ We show that, for any value of q, infinitely many q-prime numbers exist; for q≤1 they diverge for increasing prime number, whereas they converge for q>1; the standard prime numbers are recovered for q=1. For q≤1, we generalize the ζ(s) function as follows: ζq(s)≡〈ζ(s)〉q (s∈R). We show that this function appears to diverge at s=1+0, ∀q. Also, we alternatively define, for q≤1, ζq∑(s)≡∑n=1∞1〈n〉qs=1+1〈2〉qs+⋯ and ζq∏(s)≡∏pprime11−〈p〉q−s=11−〈2〉q−s11−〈3〉q−s11−〈5〉q−s⋯, which, for q<1, generically satisfy ζq∑(s)<ζq∏(s), in variance with the q=1 case, where of course ζ1∑(s)=ζ1∏(s).     

NMR and DFT studies on persistent carbocations derived from benzo[kl]xanthene,dibenzo[d,d′]benzo[1,2‐b:4,3‐b′]difuran,and dibenzo[d,d′]benzo[1,2‐b:4,5‐b′]difuran in superacidic media

Persistent carbocations generated by the protonation of hetero‐polycyclic aromatic compounds with oxygen atom(s) were studied by experimental NMR and density function theory calculations. Benzo[kl]xanthene ( 1 ), dibenzo[d,d′]benzo[1,2‐b:4,3‐b′]difuran ( 2 ), and dibenzo[d,d′]benzo[1,2‐b:4,5‐b′]difuran ( 3 ) were synthesized by the annulation of arenediazonium salts. Compound 1 in FSO₃H‐SbF₅ (4:1)/SO₂ClF and 3 in FSO₃H‐SbF₅ (1:1)/SO₂ClF ionized to 1aH⁺ with protonation at C(4) and to 3aH⁺ with protonation at C(6), and these cations were successfully observed by NMR at low temperatures. The density function theory calculations indicated that 1aH⁺ and 3aH⁺ were the most stable protonated carbocations and that 2 should ionize to 2aH⁺ with protonation at C(6). According to the changes in ¹³C chemical shifts (Δδ¹³C), the positive charge was delocalized into the naphthalene unit for 1aH⁺ , into one benzo[b,d]furan unit for 2aH⁺ , and into one benzo[b,d]furan unit for 3aH⁺ . Copyright © 2015 John Wiley & Sons, Ltd.     

Computer-generated holograms for 3D display（ Invited Paper）

We have been studying various types of computer-generated holograms for three-dimensional （3D） displays both for a real-time holographic video display and a hard copy, or a printed hologram. For the hard copy output, we have developed a direct fringe printer, which is achieved to print over 100 gigapixels computer-generated hologram with 0.44μm pitch. In this paper, we introduce our recent progresses on the rainbow hologram, the cylindrical holograms, and the disk hologram for 3D display.     

The ̅K N → π Σ decay threshold effect in 3He(in-flight K –, n) reaction spectrum

The formation of a deeply-bound K?? ^–? pp state by the ³He(in-flight K? ^–, n) reaction is investigated theoretically in a distorted-wave impulse approximation using the Green’s function method. The expected inclusive and semi-exclusive spectra at $p_{K^-} = 1.0$ GeV/c and $\theta_n = 0^{\circ}$ are calculated for the forthcoming J-PARC E15 experiment. We discuss these spectra with some K? ^–-“pp” optical potentials, taking into account the energy-dependence of the imaginary part of the potentials by a phase space suppression factor.     

Light Diffraction of Aligned Polymer Fibers Periodically Dispersed by Phase Separation of Liquid Crystal and Polymer

We have confirmed light diffraction of aligned polymer fibers obtained by a phase separation of an anisotropic-phase solution of liquid crystal and polymer. He—Ne laser light passing through the polymer fibers was scattered in the axis vertical to the fibers, and had two peaks of light intensity symmetrical to the center of the transmitting laser spot. The two peaks were found to be caused by light diffraction due to the periodic polymer-fiber dispersion because the peaks corresponded to values calculated by intervals between the fibers. The periodical fiber networks are considered to be formed by anisotropic spinodal decomposition. This effect can be used to measure the dispersion order of the polymer fibers. © 2004 The Optical Society of Japan     

Preparation of Cu2ZnSnS4 thin films by hybrid sputtering

In order to fabricate Cu₂ZnSnS₄ thin films, hybrid sputtering system with two sputter sources and two effusion cells is used. The Cu₂ZnSnS₄ films are fabricated by the sequential deposition of metal elements and annealing in S flux, varying the substrate temperature. The Cu₂ZnSnS₄ films with stoichiometric composition are obtained at the substrate temperature up to 400 °C, whereas the film composition becomes quite Zn-pool at the substrate temperature above 450 °C. The Cu₂ZnSnS₄ film shows p-type conductivity, and the optical absorption coefficient and the band gap of the Cu₂ZnSnS₄ film prepared in this experiment are suitable for fabricating a thin film solar cell.     

Evidence for two energy scales in the superconducting state of optimally doped (Bi,Pb)2(Sr,La)2CuO6+delta

We use angle-resolved photoemission spectroscopy to investigate the energy gap(s) in (Bi,Pb)2(Sr,La)2CuO6+delta. We find that the spectral gap has two components in the superconducting state: a superconducting gap and pseudogap. Differences in their momentum and temperature dependence suggest that they represent two separate energy scales. Spectra near the node reveal a sharp peak with a small gap below T(c) that closes at T(c). Near the antinode, spectra are broad with a large energy gap of approximately 40 meV above and below T(c). The latter spectral shape and gap magnitude are almost constant across T(c), indicating that the pseudogap state coexists with the superconducting state below T(c), and it dominates spectra around the antinode. We speculate that the pseudogap state competes with the superconductivity by diminishing spectral weight in antinodal regions, where the superconducting gap is largest.     

Unequally spaced multiple mid-infrared wavelength generation using an engineered quasi-phase-matching device

We propose a novel quasi-phase-matched (QPM) device that can generate unequally spaced multiple wavelengths. Unequally spaced multiple QPM peaks can be obtained by employing the optimized phase modulation of a periodic domain structure. We fabricated a LiNbO3 waveguide device for 3.2-3.4 microm band difference frequency generation based on the design. Using the multiple mid-infrared outputs, we demonstrate the detection of multiple hydrocarbon gases, namely, methane, ethylene, and ethane.     

Atomic and molecular spectroscopy with a continuous-wave, doubly resonant, monolithic optical parametric oscillator

Doppler-broadened atomic and molecular spectra were observed with a one octave tunable, continuous-wave, doubly resonant, monolithic optical parametric oscillator (OPO) using 5% MgO-doped LiNbO₃ as a non-linear crystal with a birefringent phase-matching configuration. By tuning the frequency of a pump laser, longitudinal mode selection over 20 successive modes, corresponding to a 60 GHz span, was possible, owing to the simple structure of the monolithic OPO. Continuous frequency tuning was achieved using an external waveguide-type electrooptic phase modulator (EOM). By changing the modulation frequency of the EOM, frequency tuning of the optical sidebands over 12 GHz was possible, which is larger than the one free spectral range of the monolithic cavity of 3 GHz. We could observe the Cs-D₁ (894 nm), Cs-D₂ (852 nm), Rb-D₁ (795 nm), acetylene R9 (1520 nm) and P9 (1530 nm) transitions with the single monolithic OPO.