Resonances and Their Relations to Spectral Densities and Scattering Cross Sections in the Schrödinger Formulation

The concept of resonances for a two-body single and many channel Schrödinger problem is discussed with respect to the Titchmarsh–Weyl theory. It is argued that the contributions from the entire set of resonances together with the free particle spectral density build the entire spectrum. The implication of this statement on the influence of resonances on a two-body scattering cross section is discussed. It is described how the residues of the S-matrix at a complex resonance energy, i.e. two complex numbers, is used to define its contribution to the cross section. The limitations of the Breit–Wigner approximation is discussed.     

Three-alpha force and the 3-α model of12C

We postulate a Gaussian three-body potential amongα particles and adjust its parameters so that, when it is added to the Ali-Bodmerα-α potential, a good fit to experimental energies of low-lying 0⁺ and 2⁺ states of¹²C is achieved. With these potentials we made a linear variational calculation in a basis of harmonic oscillator functions which are translationally invariant, completely symmetric, and have a definite orbital angular momentum. We study the influence of this three-body potential on elastic and inelastic form factors, transition widths, Coulomb energy and charge radius of the 3-α system. The 3-α potential improved results found with the Ali-Bodmer potential alone. We find the 0 ₂ ⁺ state to be a (non-rigid) linear chain and the ground state to be a triangle ofα particles.     

Structure of 12C and the triple-α process

We review experiments at IGISOL and associated work at ISOLDE and KVI on the use of the β-decays of ¹²N and ¹²B for the study of the structure of ¹²C and the consequences for the rate of the triple-α reaction in stars.     

Low-Energy 12C States in Three-α Model

Cross sections for three-α photodisintegration process of the¹²C nucleus are calculated by a Faddeev formalism, from which 0⁺- and 2⁺ low-lying resonant ¹²C states are studied. The triple-alpha reaction rate is evaluated from the calculated cross sections of the disintegration process.     

Response to Disturbance and Abundance of Final State： a Measure for Complexity？

We propose a new definition of complexity. The definition shows that when a system evolves to a final state via a transient state, its complexity depends on the abundance of both the final state and transient state. The abundance of the transient state may be described by the diversity of the response to disturbance. We hope that this definition can describe a clear boundary between simple systems and complex systems by showing that all the simple systems have zero complexity, and all the complex systems have positive complexity. Some examples of the complexity calculations are presented, which supports our hope.     

Cabibbo-Suppressed Non-leptonic Decays of ∧c and Final State Interaction

With the diquark structure of ∧c, we investigate the branching ratio of ∧c→nπ^ and pπ^0. The results show that without considering the finM state interaction (FSI), the branching ratio of ∧c→pπ^0 is only of order 10^-6 whereas this ratio could reach 10^-4 and is at the same order as ∧c→nπ^ if taking into account the FSI effects. Concrete values depend on phenomenologicM parameters adopted in the calculations. These branching ratios can be measured in the experiments to come.     

S-Wave Shape Resonances in the Ps− System

We have investigated the S-wave shape resonance states of the positronium negative ion (Ps^?) system. The resonance poles are traced from H^? system to Ps^? by systematically varying the mass of the positively charged particle from infinitely heavy to one unit of the electron mass. The shape resonances that associated with and lying above the Ps(N = 2, 3, 4 and 5) thresholds are located by employing the complex-coordinate rotation method with highly correlated Hylleraas-type wave functions. It has been shown that the Ps^?(N = 3) shape resonance lies at an energy which is higher than the Ps(N = 4) thresholds and even the Ps^?(N = 4) shape resonance. An explanation was given to shed light on such phenomena.     

���Ѧ� Interaction Leading to N* and ��* Resonances

We have performed a calculation for the three-body ????? system by using the fixed center approximation to Faddeev equations, taking the interaction between ?? and ??, ?? and ??, and ?? and ?? from the chiral unitary approach. We find several peaks in the modulus squared of the three-body scattering amplitude, indicating the existence of resonances, which can be associated to known I?=?1/2, 3/2 and J ^P ?=?1/2⁺, 3/2⁺ and 5/2⁺ baryon states.     

Resonances and near-threshold scattering in 3,4Hedμ

Elastic and inelastic scattering cross-sections in the ^3,4Hedμ systems near the dμ threshold are calculated. The isotopic effect and strong energy dependence in ⁴Hedμ are found. The reason for these peculiarities is the near-threshold pole of the ⁴Hedμ scattering amplitude. This revised version was published online in August 2006 with corrections to the Cover Date.     

Transverse Momentum Distribution of Final State π in Relativistic Heavy Ion Collisions

Using hydrodynamical model of transverse expansion,we investigate the transverse momentum distribution of the final state π on ¹⁶O－Au collisions.When the constituent influence of the gas is taken into account the calculated result fits the NA35 data better than that of D.Knsnezov's.     

Relativistic Effects in Neutron�CDeuteron Elastic Scattering and Breakup

We solved the Faddeev equation in a Poincaré invariant model of the three-nucleon system. Two-body interactions are generated so that when they are added to the two-nucleon invariant mass operator (rest energy) the two-nucleon S matrix is identical to the experimental S matrix modeled with a given nucleon?Cnucleon interaction. Cluster properties of the three-nucleon S-matrix determine how these two-nucleon interactions are embedded in the three-nucleon mass operator. Differences in the predictions of the relativistic and corresponding non-relativistic models for elastic and breakup processes are investigated. Of special interest are effects of relativity on the elastic scattering angular distribution and total cross sections, the lowering of the A _y maximum in elastic nucleon-deuteron (Nd) scattering below ??25?MeV caused by the Wigner spin rotations and the significant changes of the breakup cross sections in certain regions of the phase-space.     

Dipolar Interaction and Magnetic Ordering Ground State in Mn12 Molecular Magnet

Here a direct calculation of the dipolar interaction in a single crystal Mn12, with all of Mn ions summed, shows that a transition between ferromagnetic and antiferromagnetic ground states takes place where the dimension along the α（b） axis versus the dimension along the c axis reaches a certain critical value. It is shown that the w ~ ~ ground state is dependent upon the shape of the specimen. The reason of the shape dependence of ordering is that dipolar interaction is of long-range nature and the sign of dipolar interaction is dependent on the direction.     

Electron scattering with the excitation of the 15.11 MeV state of12C and theπ 12B12C coupling constant

Theπ ¹²B¹²C coupling constant is extracted from the data on theM1 form factor of¹²C using the PCAC and CVC hypotheses. The extrapolation of the form factor to the pion pole using analyticity arguments leads to the value \(f_{\pi ^{12} B^{12} C}^2 = 0.052\) . Our present knowledge of this coupling constant is discussed.     

Cλ-Extended Oscillator Algebras and Some of Their Deformations and Applications to Quantum Mechanics

C-extended oscillator algebras generalizing the Calogero—Vasiliev algebra,where C is the cyclic group of order , are studied both from mathematical andapplied viewpoints. Casimir operators of the algebras are obtained and used toprovide a complete classification of their unitary irreducible representations underthe assumption that the number operator spectrum is nondegenerate. Deformedalgebras admitting Casimir operators analogous to those of their undeformedcounterparts are looked for, yielding three new algebraic structures. One of themincludes the Brzezi´nski et al. deformation of the Calogero—Vasiliev algebra as aspecial case. In its bosonic Fock-space representation, the realization ofC-extended oscillator algebras as generalized deformed oscillator ones is shown toprovide a bosonization of several variants of supersymmetric quantum mechanics:parasupersymmetric quantum mechanics of order p = – 1 for any , as wellas pseudosupersymmetric and orthosupersymmetric quantum mechanics of ordertwo for = 3.     

17O12C17O and 18O12C17O spectroscopy in the 1.6 μm region

Near infrared spectra of a carbon dioxide sample enriched with oxygen-17 have been recorded using a high-resolution continuous scan Fourier transform interferometer fitted with a femto OPO/Idler laser source. Cavity enhanced absorption has been achieved in a static gas cell allowing an optimal rms noise equivalent absorption of 1.2?×?10^?10?cm^?1?Hz^?1/2 per spectral element to be reached, corresponding to α_min?=?10^?8?cm^?1. Spectra were calibrated against acetylene reference line positions. Three bands in the 3ν₁?+?ν₃ tetrad in both ¹²C¹⁷O₂ and ¹²C¹⁷O¹⁸O have been identified and rotationally analyzed, as well as some related hot bands, eight of which are newly reported and three with their analysis updated compared with a preliminary report (X. de Ghellinck d’Elseghem Vaernewijck et al., Chem. Phys. Lett. 514, 29 (2011)).     

Vector and Tensor Analyzing Powers in Deuteron�CProton Breakup

High precision data for vector and tensor analyzing powers of the ${^1{\rm {H}}(\vec{\rm{d}},\rm{{pp}})\rm{n}}$ breakup reaction at 130 and 100?MeV deuteron beam energies have been measured in a large fraction of the phase space. They are compared to the theoretical predictions based on various approaches to describe the three nucleon (3N) system dynamics. Theoretical predictions describe very well the vector analyzing power data, with no need to include any three-nucleon force effects for these observables. Tensor analyzing powers can be also very well reproduced by calculations in most of the studied region, but locally certain discrepancies are observed. At 130?MeV for A _xy such discrepancies usually appear, or are enhanced, when model 3N forces are included. Predicted effects of 3NFs are much lower at 100?MeV and at this energy equally good consistency between the data and the calculations is obtained with or without 3NFs.     

Spontaneous Resonances and the Coherent States of the Queuing Networks

We present an example of a highly connected closed network of servers, where the time correlations do not vanish in the infinite volume limit. The limiting interacting particle system behaves in a periodic manner. This phenomenon is similar to the continuous symmetry breaking at low temperatures in statistical mechanics, with the average load playing the role of the inverse temperature.     

πN Elastic Scattering and Resonances in Quark Potential Model

The quark potential model is used to investigate the low-energy elastic scattering of πN system. The model potential consists of the t-channel and s-channel one-gluon exchange potentials and the harmonic oscillator confining potential. By means of the resonating group method, a nonlocal effective potential for the πN system is derived from the interquark potentials and used to calculate the πN elastic scattering phase shifts. By considering the effect of QCD renormalization, the suppression of the spin-orbital coupling and the contribution of the color octet of the clusters （qq） and （qqq）, the numerical results are in fairly good agreement with the experimental data. The same model and method are employed to investigate the possible πN resonances. For this purpose, the resonating group equation is transformed into a standard Schrodinger equation in which the nonlocal effective πN interaction potential is included. Solving the Schrodinger equation by the variational method, we are able to reproduce the masses of some currently concerned πN resonances.     

Breit–Wigner Approximation and the Distribution¶of Resonances

For operators with a discrete spectrum, {λ _j ²}, the counting function of λ _j 's, N (λ), trivially satisfies N ( λ+δ ) −N ( λ−δ ) =∑ _j δ_{λ j} ((λ−δ,λ+δ]). In scattering situations the natural analogue of the discrete spectrum is given by resonances, λ _j ∈ℂ₊, and of N (λ), by the scattering phase, s(λ). The relation between the two is now non-trivial and we prove that