Neutron-emission mechanisms in the <Superscript>115</Superscript>In(<Emphasis Type="Italic">α, xn</Emphasis>) reactions

Spectra and angular distributions of neutrons from the ¹¹⁵In(α, xn) reactions were measured at α-particle energies of 16, 18, 27, and 45 MeV. The measurements were performed with time-of-flight neutron spectrometers at pulsed accelerators of charged particles. The data obtained in this way were analyzed within the models of equilibrium, preequilibrium, and direct reaction mechanisms. The exact formalism of Hauser-Feshbach statistical theory was used in the calculations, level densities in residual nuclei excited in the reactions under consideration being found from the neutron evaporation spectra in the (p, n) reactions on tin isotopes. Contributions from equilibrium, preequilibrium, and direct neutron emission were studied in a wide range of α-particle energies.     

A statistical model for simulating the emission of light particles from excited nuclei

The algorithms and basic equations of a novel evaporation model that have been implemented in the program package EVAP15 are detailed. The level density of an excited nucleus is described by the composite Gilbert–Cameron formula with parameter values as suggested by the IAEA working group RIPL-3. Special attention is paid to the cross sections of inverse reactions and, in particular, to those for the interactions of low-energy neutrons with nuclei and for crossing of the Coulomb barrier by low-energy charged particles. The model predictions are compared with a large volume of experimental data on the spectra of particles emitted in the reactions (n, xn), (n, xp), and (n, xα) induced by neutrons with energy near 14 MeV and on the four spectra for the reaction (p, xp) induced by 62-MeV protons.     

Coordinate asymptotic behavior of the radial three-particle wave function for a bound state involving two charged particles

The asymptotic expression for the radial component of the wave function for a three-particle bound state involving two charged particles is derived in an explicit form. This expression contains a three-particle asymptotic normalization factor C(φ), where φ is a hyperangle in the six-dimensional space of intrinsic coordinates of the three-particle system. The resulting expressions are used to analyze the asymptotic behavior of the wave functions for the ⁹Be nucleus that were calculated within the α + α + n three-particle model for various forms of the an potential. A comparison of the asymptotic expression derived here and the asymptotic expressions for model wave functions makes it possible to extract C(φ) values, which turned out to be sensitive to the form of αn interaction. This permits deducing information about two-particle interaction from a comparison of the theoretical values of C(α) with their phenomenological counterparts found from an analysis of experimental differential cross sections for relevant nuclear reactions.     

<Emphasis Type="Italic">T</Emphasis>-odd angular asymmetry in nuclear reactions involving sequential particle emission

A triple T-odd angular correlation is considered in the kinematically similar reactions ¹⁰B(n, αγ) and ²³³U(n, αf) induced by cold polarized neutrons. It is shown that, in the former reaction, this correlation is suppressed by the double parity-conservation selection rule due to the two-step character of the process; however, T invariance does not impose any specific constraints on this correlation. The mechanism through which the T-odd correlation found in ternary-fission reactions is formed seems to be closely related to a nearly simultaneous disintegration of the nucleus involved into two fission fragments and an alpha particle.     

Influence of high-spin states on isomeric ratios of nuclear reaction products

The isomeric ratios of some nuclear products of (p, n), (d, 2n), (α, p3n) reactions were analyzed. A comparison of calculation data obtained by using TALYS 1.4 software package with experimental ones shows that the observed significant discrepancies for definite nuclei may be accounted for by the influence of high-spin states on the values of isomeric ratios.     

Progress of Jinping Underground laboratory for Nuclear Astrophysics (JUNA)

Jinping Underground laboratory for Nuclear Astrophysics(JUNA) will take the advantage of the ultra-low background of CJPL lab and high current accelerator based on an ECR source and a highly sensitive detector to directly study for the first time a number of crucial reactions occurring at their relevant stellar energies during the evolution of hydrostatic stars. In its first phase, JUNA aims at the direct measurements of~(25)Mg(p,γ)~(26)Al,~(19)F(p,α)~(16)O,~(13)C(α,n)~(16)O and ~(12)C(α,γ)~(16)O reactions. The experimental setup,which includes an accelerator system with high stability and high intensity, a detector system, and a shielding material with low background, will be established during the above research. The current progress of JUNA will be given.     

Phase Diagram of a Generalized ABC Model on the Interval

We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site i=1,…,N is occupied by a particle of type α=A,B,C, with the average density of each particle species N _α /N=r _α fixed. These particles interact via a mean field nonreflection-symmetric pair interaction. The interaction need not be invariant under cyclic permutation of the particle species as in the standard ABC model studied earlier. We prove in some cases and conjecture in others that the scaled infinite system N→∞, i/N→x∈[0,1] has a unique density profile ρ _α (x) except for some special values of the r _α for which the system undergoes a second order phase transition from a uniform to a nonuniform periodic profile at a critical temperature \(T_{c}=3\sqrt{r_{A} r_{B} r_{C}}/2\pi\).     

Global geometric entanglement and quantum phase transition in three-leg spin-3/2 Heisenberg tubes

Based on the tensor network representations, we have developed an efficient scheme to calculate the global geometric entanglement as a multipartite entanglement measure for the three-leg spin tubes. From the geometric entanglement, the phase diagram of a spin-3 / 2 isosceles triangle spin tube has been investigated varying the base interaction α. Two Berezinsky-Kosterlitz-Thouless phase transitions are estimated to be α_c1 ? 0.68 and α_c2 ? 3.85, respectively. Then, even though the spin tube is in gapless spin liquid phases for α<α_c1 and α >α_c2, the geometrical structure difference between the groundstate wavefunctions for the two regions is found to reflect the global geometric entanglement that contains bipartite and multipartite contributions. Further, the phase transition points from the von Neumann entropies and fidelity are consistent with that from the geometric entanglement. As a result, the global geometric entanglement can be used to explore a geometrical nature of quantum phases as well as an indicator for quantum phase transitions in many-body lattice systems.     

Isomeric ratios of (γ,p) and (γ,α) reactions on <Superscript>117<Emphasis Type="Italic">m,g</Emphasis></Superscript>In

The isomeric ratios of the (γ,p) and (γ,α) reactions on ^117m,g In have been measured. The ratios Y _m /Y _g was found to be 1.18(9) and 0.23(9), respectively, at a boundary energy of 22 MeV. The statistical character of the reactions under such conditions is shown.     

Investigation of the reaction mechanism for the four-particle photodisintegration of a carbon nucleus

The four-particle photodisintegration of a carbon nucleus in the reactions ¹²C(γ, p)³H2α and ¹²C(γ, n)³H2α is investigated by a method that employs a diffusion chamber in a magnetic field. It is shown that these reactions proceed according a sequential-type scheme: excited states of ¹¹B and ¹¹C nuclei decay to weakly excited states of ⁸Be, ⁷Li, and ⁷Be nuclei. It is concluded that nucleons are knocked out from the s shell. In the excitation curve for the 2α system in the reaction ¹²C(γ, p)³H2α, a resonance is found between the maxima corresponding to the ground and the first excited state of the ⁸Be nucleus, and this resonance is identified as a ghost anomaly. The branching fractions of the decay modes are determined. The angular distributions of nucleons in the reaction c.m. frame are measured. The energy dependence of the asymmetry coefficient for the angular distributions is obtained. A fast increase in this coefficient is observed in the energy range 38–40 MeV. It is concluded that the asymmetry coefficient depends on the excitation energy of the final nucleus in the region of intermediate photon energies.     

Description of cross sections for photonuclear reactions in the energy range between 7 and 140 MeV

A combination of the exciton and evaporation models is used to describe photonuclear reactions induced in light, medium-mass, and heavy nuclei by photons of energy in the range 7 ≤ E _γ ≤ 140 MeV. Two mechanisms of the photoexcitation of nuclei are considered. These are the formation of a giant dipole resonance at energies in the range E _γ ? 30 MeV and quasideuteron photoabsorption, which is dominant at energies in the region E _γ ? 40 MeV. The density of particle-hole states, which appears in the exciton model, is calculated on the basis of the Fermi gas model. The emission of two preequilibrium particles is taken into account in describing the quasideuteron reaction channel. The effect of isospin conservation on giant-dipole-resonance decay accompanied by photonucleon emission is examined. The model in question is used to describe cross sections for photon-induced reactions on ²⁶Mg, ⁵⁴Fe, ^{112,118,119,124}Sn, and ¹⁸¹Ta nuclei.     

Solutions of a Particle with Fractional <Emphasis Type="Italic">δ</Emphasis>-Potential in a Fractional Dimensional Space

A Fourier transformation in a fractional dimensional space of order λ (0<λ≤1) is defined to solve the Schrödinger equation with Riesz fractional derivatives of order α. This new method is applied for a particle in a fractional δ-potential well defined by V(x)=?γ δ ^λ (x), where γ>0  and δ ^λ (x) is the fractional Dirac delta function. A complete solutions for the energy values and the wave functions are obtained in terms of the Fox H-functions. It is demonstrated that the eigen solutions are exist if 0<λ<α. The results for λ=1 and α=2 are in exact agreement with those presented in the standard quantum mechanics.     

Studying the ejection of light charged particles induced by 50 MeV <Superscript>3</Superscript>He ions upon interacting with a <Superscript>112</Superscript>Sn nucleus

Experimental double-differential and integral spectra of (³He, xp), (³He, xd), (³He, xt), (³He, x³He) and (³He, xα) reactions on ¹¹²Sn nuclei induced by 50 MeV 3He ions are presented. Theoretical calculations of the experimental inclusive spectra of the reactions are performed using the exciton model of preequilibrium decay. The corresponding mechanisms of reactions are determined. The experimental results can be used to develop new approaches in the theory of nuclear reactions, and to design safe and wasteless hybrid nuclear power plants.     

On the Negative Spectrum of the Two-Dimensional Schrödinger Operator with Radial Potential

For a two-dimensional Schrödinger operator H _{α V}  = ?Δ ?αV with the radial potential V(x) = F(|x|), F(r) ≥ 0, we study the behavior of the number N _?(H _{α V} ) of its negative eigenvalues, as the coupling parameter α tends to infinity. We obtain the necessary and sufficient conditions for the semi-classical growth N _?(H _{α V} ) = O(α) and for the validity of the Weyl asymptotic law.     

Parametric study of radiofrequency helium discharge under atmospheric pressure

The parameters of radiofrequency helium discharge under atmospheric pressure were studied by electrical and optical measurements using high voltage probe, current probe and optical emission spectroscopy. Two discharge modes α and γ were observed within certain limits. During α to γ mode transition, a decrease in voltage (280–168 V), current (2.05–1.61 A) and phase angle (76^°–56^°) occurred. The discharge parameters such as resistance, reactance, sheath thickness, electron density, excitation temperature and gas temperature were assessed by electrical measurements using equivalent circuit model and optical emission spectroscopy. In α mode, the discharge current increased from 1.17 to 2.05 A, electron density increased from 0.19 × 10¹² to 0.47 × 10¹² cm^?3 while sheath thickness decreased from 0.40 to 0.25 mm. The excitation temperatures in the α and γ modes were 3266 and 4500 K respectively, evaluated by Boltzmann’s plot method. The estimated gas temperature increased from 335 K in the α mode to 485 K in the γ mode, suggesting that the radiofrequency atmospheric pressure helium discharge can be used for surface treatment applications.     

A study of fractional Schrödinger equation composed of Jumarie fractional derivative

In this paper we have derived the fractional-order Schrödinger equation composed of Jumarie fractional derivative. The solution of this fractional-order Schrödinger equation is obtained in terms of Mittag–Leffler function with complex arguments, and fractional trigonometric functions. A few important properties of the fractional Schrödinger equation are then described for the case of particles in one-dimensional infinite potential well. One of the motivations for using fractional calculus in physical systems is that the space and time variables, which we often deal with, exhibit coarse-grained phenomena. This means infinitesimal quantities cannot be arbitrarily taken to zero – rather they are non-zero with a minimum spread. This type of non-zero spread arises in the microscopic to mesoscopic levels of system dynamics, which means that, if we denote x as the point in space and t as the point in time, then limit of the differentials dx (and dt) cannot be taken as zero. To take the concept of coarse graining into account, use the infinitesimal quantities as (Δx) ^α (and (Δt) ^α ) with 0 < α < 1; called as ‘fractional differentials’. For arbitrarily small Δx and Δt (tending towards zero), these ‘fractional’ differentials are greater than Δx (and Δt), i.e. (Δx) ^α > Δx and (Δt) ^α > Δt. This way of defining the fractional differentials helps us to use fractional derivatives in the study of dynamic systems.     

Renormalons and analytic properties of the β function

The presence or absence of renormalon singularities in the Borel plane is shown to be determined by the analytic properties of the Gell-Mann-Low function β(g) and some other functions. A constructive criterion for the absence of singularities consists in the proper behavior of the β function and its Borel image at infinity, β(g) ∝ g^α and B(z) ∝ z^α with α ≤ 1. This criterion is probably fulfilled for the ?⁴ theory, quantum electrodynamics, and quantum chromodynamics, but is violated in the O(n)-symmetric sigma model with n → ∞.     

The structure of a vortex line and the lower critical field in superconducting alloys

The structure of an isolated vortex line, and the lower critical fieldH _c 1, is calculated by means of the generalized Ginzburg-Landau (GL) theory for arbitrary values of the GL-parameterk(≧1/√2) and the mean free pathl at temperaturesT in the vicinity ofT _c . The free energy functional including the corrections of order [1?(T/T _c )] to the GL-functional is derived exactly. The corresponding Euler-Lagrange equations determining the zero-order (GL) contributions and the corrections of order [1?(T/T _c )] to the order parameter,f(r), and the superfluid velocity,v(r), have been solved numerically. The shapes of the first-order corrections off(r), v(r), and the magnetic field,h(r) are found to depend markedly, for a given value ofκ, on a second parameter,α=0.882(ξ ₀ /l) (whereξ ₀ is theBCS-coherence-distance). The deviations from the GL-solutions become largest forh(r) at parameter valuesk≈ 1 andα ≈ 0(the deviation ofh(0) is about 6% atT=0.9T _c forκ=1 andα=0). The ratioH _c1/H _c (where the thermodynamic criticalH _c has the BCS-temperature-dependence) is found to increase slightly in the “clean” limit (α=0), and to decrease slightly in the “dirty” limit (α=∞) asT decreases (the variation ofH _c 1/H _c is always less than 3% for arbitrary values ofκ andα asT decreases fromT _c to 0.9T _c ).     

Reaction dynamics at the barrier for heavy compound systems

To investigate basic properties of the fusion reaction dynamics for heavy compound systems, the partial wave distribution σ _l extracted from measured γ multiplicities can be employed as an alternative to the classically used fusion/fission excitation functions. A variety of reactions leading to compound nuclei in the Pb region can be used to investigate features like the fusion-fission competition, the role of deformation in the fusion of heavy systems, and a possible effect of the Z=82 shell on the enhancement of evaporation residue production. The measured spin distribution can provide information on the single partial wave cross sections, which is hidden in the integral fusion cross section. Moreover, it can reveal signatures in the high-spin region, which could be an indication of a stabilization due to an increase in the potential hole by shell correction energies E_shell in the vicinity of a closed shell. The systematic investigation and understanding of the fusion-fission reaction dynamics, together with the understanding of the structure of transfermium nuclei, which are stabilized only via shell effects, are essential for a successful program aiming at the synthesis of new elements at GSI, Dubna, or elsewhere. We started a series of experiments to measure those properties for the reactions at the Laboratori Nazionali di Legnaro, Italy. In order to extract the compound nucleus spin distribution, γ multiplicities are measured using the γ-detector array GASP and its inner ball in the multiplicity filter mode.     

Quantifying Correlations via the Wigner-Yanase-Dyson Skew Information

In this paper, based on a discussion about the Wigner-Yanase-Dyson (WYD) skew information, the measure F_a,α(ρ_ab) for correlations in terms of the WYD skew information is introduced and discussed. The following conclusions are obtained. For a classical-quantum state ρ_ab, F_a,α(ρ_ab)=0 if and only if ρ_ab is a product state; F_a,α(ρ_ab) is locally unitary invariant and convex on the set of states with the fixed marginal ρ_a; F_a,α(ρ_ab) decreases under local random unitary operation on H_b; For a quantum-classical state ρ_ab, F_a,α(ρ_ab) decreases under local operation on H_b; Lastly, F_a,α(ρ_ab) is computed for the pure states and the Bell-diagonal states, respectively.