ENERGY SPECTRA OF GLUINONIUM

2011 ◽  
Vol 20 (supp02) ◽  
pp. 200-209
Author(s):  
CÉSAR A. Z. VASCONCELLOS ◽  
DIMITER HADJIMICHEF ◽  
MÁRIO L. L. DA SILVA ◽  
MOISÉS RAZEIRA ◽  
ALEXANDRE MESQUITA ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Excited States ◽  
Bound States ◽  
Bound State ◽  
State Equation ◽  
Relativistic Case ◽  
Light Scalar ◽  
Pseudo Scalar ◽  
Relativistic Bound States

We investigate relativistic bound states for a hypothetical light scalar gluino pair (gluinonium), in the framework of the covariant Bethe-Salpeter equation (BSE). In this paper, we derive, from the covariant BSE for a fermion-anti-fermion system, using charge conjugation, the corresponding bound-state equation for a gluino pair and we then formulate, for a static harmonic kernel, the coupled differential equations for the corresponding static Bethe-Salpeter amplitude. The steps of our approach then include a numerical solution of the Bethe-Salpeter amplitude for a two-body interaction consisting of scalar, pseudo-scalar, and four-vector components and the determination of the energy spectrum for the ground and the radially excited states of massive gluinonium. We found the energy spectrum and radial distributions of fundamental and excited states of gluinonium. The comparison of the values obtained in the extreme relativistic case with the corresponding values predicted by a harmonic oscillator potential model shows that there is good agreement between the two formulations. The predictions of the binding energy of glunionium in the non-relativistic model are however systematically higher.

scholarly journals Partial Photoionization Cross Sections of Chromium from the Ground and Excited States

Atoms ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 51
Author(s):  
Oleg Zatsarinny ◽  
Swaraj Tayal
Keyword(s):  
Excited States ◽  
Cross Sections ◽  
Bound States ◽  
Close Coupling ◽  
R Matrix ◽  
Hartree Fock ◽  
Nonresonant Background ◽  
Ionic States ◽  
Matrix Calculation

Partial and total photoionization cross sections of iron-peak elements are important for the determination of abundances in late-type stars and nebular objects. We have investigated photoionization of neutral chromium from the ground and excited states in the low energy region from the first ionization threshold at 6.77 eV to 30 eV. Accurate descriptions of the initial bound states of Cr I and the final residual Cr II ionic states have been obtained in the multiconfiguration Hartree-Fock method together with adjustable configuration expansions and term-dependent non-orthogonal orbitals. The B-spline R-matrix method has been used for the calculation of photoionization cross sections. The 194 LS final ionic states of Cr II 3d44s, 3d34s2, 3d5, 3d44p, and 3d34s4p principal configurations have been included in the close-coupling expansion. The inclusion of all terms of these configurations has significant impact on the near-threshold resonance structures as well as on the nonresonant background cross sections. Total photoionization cross sections from the ground 3d54sa7S and excited 3d54sa5S, 3d44s2a5D, 3d54pz5P, and 3d44s4py5P states of Cr I have been compared with other available R-matrix calculation to estimate the likely uncertainties in photoionization cross sections. We analyzed the partial photoionization cross sections for leaving the residual ion in various states to identify the important scattering channels, and noted that 3d electron ionization channel becomes dominant at higher energies.

scholarly journals EXACT-PROPAGATOR INSTANTANEOUS BETHE–SALPETER EQUATION FOR QUARK–ANTIQUARK BOUND STATES

2006 ◽  
Vol 21 (21) ◽  
pp. 1657-1673 ◽  
Author(s):  
ZHI-FENG LI ◽  
WOLFGANG LUCHA ◽  
FRANZ F. SCHÖBERL
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Bound States ◽  
Lattice Gauge Theory ◽  
Bound State ◽  
State Equation ◽  
Wave Functions ◽  
Quantum Field ◽  
Lattice Gauge ◽  
Instantaneous Approximation

Recently an instantaneous approximation to the Bethe–Salpeter formalism for the analysis of bound states in quantum field theory has been proposed which retains, in contrast to the Salpeter equation, as far as possible the exact propagators of the bound-state constituents, extracted nonperturbatively from Dyson–Schwinger equations or lattice gauge theory. The implications of this improvement for the solutions of this bound-state equation, i.e. the spectrum of the mass eigenvalues of its bound states and the corresponding wave functions, when considering the quark propagators arising in quantum chromodynamics are explored.

Threshold conditions and bound states for locally periodic delta potentials

Open Physics ◽  
2014 ◽  
Vol 12 (10) ◽  
Author(s):  
Marappan Dharani ◽  
Basudeb Sahu ◽  
Chakrakodi Shastry
Keyword(s):  
Energy Spectrum ◽  
Bound States ◽  
Threshold Energy ◽  
Bound State ◽  
Separation Distance ◽  
Recursive Procedure ◽  
Threshold Conditions ◽  
Repulsive Potentials ◽  
Energy Bound ◽  
Pattern Of Variation

AbstractWe present a systematic study of the conditions for the generation of threshold energy eigen states and also the energy spectrum generated by two types of locally periodic delta potentials each having the same strength λV and separation distance parameter a: (a) sum of N attractive potentials and (b) sum of pairs of attractive and repulsive potentials. Using the dimensionless parameter g = λV a in case (a) the values of g = g n, n = 1, 2, …, N at which threshold energy bound state gets generated are shown to be the roots of Nth order polynomial D 1(N, g) in g. We present an algebraic recursive procedure to evaluate the polynomial D 1(N, g) for any given N. This method obviates the need for the tedious mathematical analysis described in our earlier work to generate D 1(N, g). A similar study is presented for case (b). Using the properties of D 1(N, g) we establish that in case (a) the critical minimum value of g which guarantees the generation of the maximum possible number of bound states is g = 4. The corresponding result for case (b) is g = 2. A typical set of numerical results showing the pattern of variation of g n as a function of n and several interesting features of the energy spectrum for different values of g and N are also described.

scholarly journals CLASSIFICATION OF THE SCALAR MESONS: A STRANGE POLE EXPEDITION INTO CHARM AND BEAUTY TERRITORY

2004 ◽  
Vol 19 (26) ◽  
pp. 1949-1967 ◽  
Author(s):  
EEF VAN BEVEREN ◽  
GEORGE RUPP
Keyword(s):  
Cross Sections ◽  
Bound States ◽  
Bound State ◽  
S Wave ◽  
Exotic Meson ◽  
Scalar Mesons ◽  
S Matrix ◽  
Light Scalar ◽  
Scalar Sector

The classification of scalar and vector mesons is reviewed within the framework of the Resonance-Spectrum Expansion (RSE). This method allows a simple and straightforward description of non-exotic meson–meson scattering, incorporating the effects of quark confinement and OZI-allowed decay in a fully nonperturbative way. Results for resonances and bound states are compared to experiment, on the basis of computed pole positions and cross-sections. New predictions for open-charm and -bottom scalar mesons are presented.Concretely, observed vector states for [Formula: see text] and [Formula: see text] are reproduced, and others are predicted. In the light scalar sector, the now established two nonets, one below 1 GeV and one in the region 1.3–1.5 GeV, are easily described, through the appearance of extra poles in the S-matrix. The recently found [Formula: see text](2317) meson is accurately reproduced by the same mechanism, as a quasi-bound state in the coupled [Formula: see text] system.In S-wave Dπ and Bπ scattering, new resonances are foreseen close to threshold, i.e. a [Formula: see text] at 2.16±0.05 GeV some 250 MeV wide, and a [Formula: see text] at 5.47±0.05 GeV with a width of about 50 MeV. Additional predictions concern the existence of [Formula: see text] and [Formula: see text] scalar mesons, stable with respect to OZI-allowed decay to BK and BD, respectively, namely at 5.61±0.05 GeV resp. 6.64±0.05 GeV.

Quantum field theory of bound states IV. Relativistic theory of the excited states of hydrogen

1953 ◽  
Vol 219 (1139) ◽  
pp. 516-526 ◽  
Keyword(s):  
Excited States ◽  
Lamb Shift ◽  
Bound States ◽  
Bound State ◽  
Crossing Over ◽  
Quantum Field ◽  
Coupled Equations ◽  
First Approximation ◽  
Single Integral ◽  
The Difference

When allowance is made for the instability of the excited states of hydrogen it is necessary to replace the equation of Salpeter & Bethe (1951) by a set of coupled integral equations for representatives of the state vector. These representatives correspond to an electron-proton bound state and also to the electron and proton with any number of photons present. The coupled equations can be reduced to a single integral equation, which gives the electronproton bound state as an eigenstate of a modified propagator. The modified propagator is related to the two-body propagator of Salpeter & Bethe. The difference between the first approximation to the modified propagator and the first approximation to the two-body compound propagator (Eden 1952, 1953) can be represented by a displacement of its singularity in total energy-momentum space. This displacement gives in a relativistic form all the relevant contributions to the Lamb shift to this order; these include the contribution from low-energy transverse photons crossing over an arbitrary number of longitudinal photons; previously this term has always been deduced by physical arguments and obtained by non-relativistic methods (Bethe 1947; Salpeter 1952). The displacement of the singularity also gives decay coefficients to this order in the charge. The method can readily be extended to higher approximations.

scholarly journals Tetraquark state X(6900) and the interaction between diquark and antidiquark

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Hong-Wei Ke ◽  
Xin Han ◽  
Xiao-Hai Liu ◽  
Yan-Liang Shi
Keyword(s):  
Excited States ◽  
Bound States ◽  
Effective Interaction ◽  
Axial Vector ◽  
Bound State ◽  
Tetraquark State ◽  
Effective Coupling ◽  
Final State ◽  
Interaction Kernel ◽  
Quantum Numbers

AbstractRecently LHCb declared a new structure X(6900) in the final state di-$$J/\psi $$ J / ψ which is popularly regarded as a cc-$$\bar{c}\bar{c}$$ c ¯ c ¯ tetraquark state. Within the Bethe–Salpeter (B–S) framework we study the possible cc-$$\bar{c}\bar{c}$$ c ¯ c ¯ bound states and the interaction between diquark (cc) and antidiquark ($$\bar{c}\bar{c}$$ c ¯ c ¯ ). In this work cc ($$\bar{c}\bar{c}$$ c ¯ c ¯ ) is treated as a color anti-triplet (triplet) axial-vector so the quantum numbers of cc-$$\bar{c}\bar{c}$$ c ¯ c ¯ bound state are $$0^+$$ 0 + , $$1^+$$ 1 + and $$2^+$$ 2 + . Learning from the interaction in meson case and using the effective coupling we suggest the interaction kernel for the diquark and antidiquark system. Then we deduce the B–S equations for different quantum numbers. Solving these equations numerically we find the spectra of some excited states can be close to the mass of X(6900) when we assign appropriate values for parameter $$\kappa $$ κ introduced in the interaction (kernel). We also briefly calculate the spectra of bb-$$\bar{b}\bar{b}$$ b ¯ b ¯ bound states. Future measurement of bb-$$\bar{b}\bar{b}$$ b ¯ b ¯ state will help us to determine the exact form of effective interaction.

Elektronenstoßspektrometrische Bestimmung von Besetzungsdichten in einem Heliumplasma / Determination of Population Densities in a Helium Plasma by Electron Impact Spectroscopy

1971 ◽  
Vol 26 (2) ◽  
pp. 198-203 ◽  
Author(s):  
H. Boersch ◽  
J. Geiger ◽  
M. Topschowsky
Keyword(s):  
Energy Spectrum ◽  
Excited States ◽  
Electron Energy ◽  
Low Voltage ◽  
Transition Probabilities ◽  
Primary Energy ◽  
Electron Energy Spectrum ◽  
Population Densities ◽  
Excitation Processes

AbstractDetermination The energy spectrum of a narrow electron beam (primary energy 25 keV, energetic width 0,08 eV) has been measured after having passed a low voltage helium discharge constricted by a metal capillary. Besides the resonance series, which is characteristic for the helium atoms in the ground state, electron energy losses are found due to transitions from excited states. In addition superelastic collisions occur which are caused by de-excitation processes. Population densities of the atoms in excited states are derived from the intensities in the electron energy spectrum using the wellknown transition probabilities. The result is compared with population densities obtained by means of Saha's equation as well as with those in both cases.

scholarly journals Bound states of Newton’s equivalent finite square well

2018 ◽  
Vol 33 (33) ◽  
pp. 1850195
Author(s):  
Amornthep Tita ◽  
Pichet Vanichchapongjaroen
Keyword(s):  
Energy Spectrum ◽  
Bound States ◽  
Infinite Order ◽  
State Energy ◽  
Order Differential Equation ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Standard Quantum ◽  
Square Well

In this paper, a one-parameter family of Newton’s equivalent Hamiltonians (NEH) for finite square well potential is analyzed in order to obtain bound state energy spectrum and wave functions. For a generic potential, each of the NEH is classically equivalent to one another and to the standard Hamiltonian yielding Newton’s equations. Quantum mechanically, however, they are expected to be different from each other. The Schrödinger’s equation coming from each NEH with finite square well potential is an infinite order differential equation. The matching conditions, therefore, demand the wave functions to be infinitely differentiable at the well boundaries. To handle this, we provide a way to consistently truncate these conditions. It turns out as expected that bound state energy spectrum and wave functions are dependent on the parameter [Formula: see text] which is used to characterize different NEH. As [Formula: see text], the energy spectrum coincides with that from the standard quantum finite square well.

Infinite bound states and $1/n$ energy spectrum induced by a Coulomb-like potential of type III in a flat band system

2021 ◽  
Author(s):  
Yi-Cai Zhang
Keyword(s):  
Energy Spectrum ◽  
Continuous Spectrum ◽  
Bound States ◽  
State Energy ◽  
Band System ◽  
Bound State ◽  
Flat Band ◽  
Bound State Energy ◽  
Type Iii ◽  
Potential Strength

Abstract In this work, we investigate the bound states in a one-dimensional spin-1 flat band system with a Coulomb-like potential of type III, which has a unique non-vanishing matrix element in basis $|1\rangle$. It is found that, for such a kind of potential, there exists infinite bound states. Near the threshold of continuous spectrum, the bound state energy is consistent with the ordinary hydrogen-like atom energy level with Rydberg correction. In addition, the flat band has significant effects on the bound states. For example, there are infinite bound states which are generated from the flat band. Furthermore, when the potential is weak, the bound state energy is proportional to the potential strength $\alpha$. When the bound state energies are very near the flat band, they are inversely proportional to the natural number $n$ (e.g., $E_n\propto 1/n, n=1,2,3,...$). Further we find that the energy spectrum can be well described by quasi-classical approximation (WKB method). Finally, we give a critical potential strength $\alpha_c$ at which the bound state energy reaches the threshold of continuous spectrum. After crossing the threshold, the bound states in the continuum (BIC) would exist in such a flat band system.

scholarly journals Diphoton decay of the Higgs boson and new bound states of top and antitop quarks

2015 ◽  
Vol 30 (21) ◽  
pp. 1550132 ◽  
Author(s):  
C. D. Froggatt ◽  
C. R. Das ◽  
L. V. Laperashvili ◽  
H. B. Nielsen
Keyword(s):  
Higgs Boson ◽  
Excited States ◽  
Atomic Physics ◽  
Bound States ◽  
Gluon Fusion ◽  
Top Quarks ◽  
Bound State ◽  
Sigma Level ◽  
Gluon Production ◽  
State Formula

We consider the constraints, provided by the LHC results on Higgs boson decay into 2 photons and its production via gluon fusion, on the previously proposed Standard Model (SM) strongly bound state S of six top quarks and six antitop quarks. A correlation is predicted between the ratios [Formula: see text] and [Formula: see text] of the Higgs diphoton decay and gluon production amplitudes, respectively to their SM values. We estimate the contribution to these amplitudes from one-loop diagrams involving the 12 quark bound state S and related excited states using an atomic physics based model. We find two regions of parameter space consistent with the ATLAS and CMS data on [Formula: see text] at the three sigma level: a region close to the SM values [Formula: see text] with the mass of the bound state [Formula: see text][Formula: see text]GeV and a region with [Formula: see text] corresponding to a bound state mass of [Formula: see text][Formula: see text]GeV.

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