Four-parameter potential and its bound-state matrix elements

1990 ◽  
Vol 23 (15) ◽  
pp. 2521-2529 ◽  
Author(s):  
Wei Hua
Keyword(s):  
Bound State ◽  
Matrix Elements ◽  
State Matrix

Stationary and Quasistationary Bounds on Arbitrary Bound-State Matrix Elements

1973 ◽  
Vol 8 (1) ◽  
pp. 131-137 ◽  
Author(s):  
Robert Blau ◽  
A. R. P. Rau ◽  
Larry Spruch
Keyword(s):  
Bound State ◽  
Matrix Elements ◽  
State Matrix

scholarly journals BARYONS AS THREE-FLAVOR SOLITONS

1996 ◽  
Vol 11 (14) ◽  
pp. 2419-2544 ◽  
Author(s):  
HERBERT WEIGEL
Keyword(s):  
Symmetry Breaking ◽  
Vector Meson ◽  
Degrees Of Freedom ◽  
Magnetic Moments ◽  
Axial Vector ◽  
Vector Current ◽  
Bound State ◽  
Axial Vector Current ◽  
Flavor Symmetry ◽  
Matrix Elements

The description of baryons as soliton solutions of effective meson theories for three-flavor (up, down and strange) degrees of freedom is reviewed and the phenomenological implications are illuminated. In the collective approach the soliton configuration is equipped with baryon quantum numbers by canonical quantization of the coordinates describing the flavor orientation. The baryon spectrum resulting from exact diagonalization of the collective Hamiltonian is discussed. The prediction of static properties, such as the baryon magnetic moments and the Cabibbo matrix elements for semileptonic hyperon decays, are explored with regard to the influence of flavor symmetry breaking. In particular, the role of strange degrees of freedom in the nucleon is investigated for both the vector and axial vector current matrix elements. The latter are discussed extensively within the context of the proton spin puzzle. The influence of flavor symmetry breaking on the shape of the soliton is examined, and observed to cause significant deviations from flavor-covariant predictions on the baryon magnetic moments. Short range effects are incorporated by a chirally invariant inclusion of vector meson fields. These extensions are necessary for properly describing the singlet axial vector current and the neutron–proton mass difference. The effects of the vector meson excitations on baryon properties are also considered. The bound state description of hyperons and its generalization to baryons containing a heavy quark are illustrated. In the case of the Skyrme model a comparison is made between the collective quantization scheme and the bound state approach. Finally, the Nambu–Jona-Lasinio model is employed to demonstrate that hyperons can be described as solitons in a microscopic theory of the quark flavor dynamics. This is explained for both the collective and the bound state approaches to strangeness.

scholarly journals TOWARDS A THREE-DIMENSIONAL SOLUTION FOR 3N BOUND STATES WITH 3NFs

2009 ◽  
Vol 24 (11n13) ◽  
pp. 816-822 ◽  
Author(s):  
M. R. HADIZADEH ◽  
S. BAYEGAN
Keyword(s):  
Partial Wave ◽  
Integral Equations ◽  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Matrix Elements ◽  
Dimensional Solution ◽  
Dimensional Integral

After a brief discussion about the necessity of using the 3D approach, we present the non partial wave (PW) formalism for 3N bound state with the inclusion of 3N force (3NF). As an example the evaluation of 3NF matrix elements, which appear in the obtained coupled three-dimensional integral equations, for 2π-exchange Tucson–Melbourne 3NF show how would be this formalism efficient and less cumbersome in comparison with the PW formalism.

scholarly journals Quarkonium Production: Velocity-Scaling Rules and Long-Distance Matrix Elements

1997 ◽  
Vol 12 (22) ◽  
pp. 3951-3963 ◽  
Author(s):  
Gerhard A. Schuler
Keyword(s):  
Heavy Quark ◽  
Bound States ◽  
Potential Model ◽  
Distance Matrix ◽  
Bound State ◽  
Matrix Elements ◽  
Long Distance ◽  
Quarkonium Production ◽  
Quark Potential ◽  
Colour Octet

The hierarchy of long-distance matrix elements (MEs) for quarkonium production depends on their scaling with the velocity v of the heavy quark in the bound state. Ranges for the velocities in various bound states and uncertainties of colour-singlet MEs are estimated in a quark-potential model. Different possibilities for the scaling with v of the MEs are discussed; they depend on the actual values of v and the QCD scale. As an application, J/ψ polarization in e+e- annihilation is discussed. The first non-perturbative estimates of colour-octet MEs are presented and compared with phenomenological determinations. Finally, various predictions of prompt quarkonium production at LEP are compared.

scholarly journals Excited states in nucleon structure calculations

2021 ◽  
Vol 57 (2) ◽  
Author(s):  
Konstantin Ottnad
Keyword(s):  
Excited State ◽  
Excited States ◽  
Current Status ◽  
Nucleon Structure ◽  
Matrix Elements ◽  
Hadron Structure ◽  
State Matrix ◽  
Physical Systems ◽  
Formidable Challenge ◽  
Structure Calculations

AbstractExcited state contributions represent a formidable challenge for hadron structure calculations in lattice QCD. For physical systems that exhibit an exponential signal-to-noise problem they often hinder the extraction of ground state matrix elements, introducing a major source of systematic error in lattice calculations of such quantities. The development of methods to treat the contribution of excited states and the current status of related lattice studies are reviewed with focus on nucleon structure calculations that are notoriously affected by excited state contamination.

scholarly journals Energy levels in muonic helium

2019 ◽  
Vol 222 ◽  
pp. 03009
Author(s):  
A.V. Eskin ◽  
V.I. Korobov ◽  
A.P. Martynenko ◽  
V.V. Sorokin
Keyword(s):  
Hyperfine Structure ◽  
Bound States ◽  
Energy Levels ◽  
Computer Code ◽  
Bound State ◽  
Relativistic Correction ◽  
Matrix Elements ◽  
Gaussian Form ◽  
Stochastic Variational Method ◽  
The Matrix

The energy spectrum of bound states and hyperfine structure of muonic helium is calculated on the basis of stochastic variational method. The basis wave functions of muonic helium are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. For numerical calculation a computer code is written in the MATLAB system. As a result, numerical values of bound state energies and hyperfine structure are obtained. We calculate also correction to the structure of the nucleus, vacuum polarization and relativistic correction.

Form Factors and Correlation Functions

2020 ◽  
pp. 744-788
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Correlation Functions ◽  
Form Factors ◽  
Vacuum Expectation ◽  
Bound State ◽  
Kernel Functions ◽  
Energy Tensor ◽  
Matrix Elements ◽  
Stress Energy ◽  
The Matrix ◽  
Recursive Equations

At the heart of a quantum field theory are the correlation functions of the various fields. In the case of integrable models, the correlators can be expressed in terms of the spectral series based on the matrix elements on the asymptotic states. These matrix elements, also known as form factors, satisfy a set of functional and recursive equations that can exactly solved in many cases of physical interest. Chapter 19 covers general properties of form factors, Faddeev–Zamolodchikov algebra, symmetric polynomials, kinematical and bound state poles, the operator space and kernel functions, the stress-energy tensor and vacuum expectation values and the Ising model in a magnetic field.

Generation of harmonics treated by a new integral equation method

1993 ◽  
Vol 71 (7-8) ◽  
pp. 340-346 ◽  
Author(s):  
S Varró ◽  
F. Ehlotzky
Keyword(s):  
Integral Equation ◽  
Laser Field ◽  
Integral Equation Method ◽  
Bound State ◽  
Multiphoton Processes ◽  
Matrix Elements ◽  
Short Range Potential ◽  
High Laser ◽  
Transition Matrix Elements ◽  
Generation Of Harmonics

We derive a new integral equation for the nonperturbative evaluation of transition matrix elements of multiphoton processes at high laser field intensities. Our approach to the problem is partly based on the use of the Kramers–Henneberger transformation. As a specific example, we apply our method to the generation of harmonics by an electron in a short range potential, supporting a single bound state. We evaluate the rates R2m+1 for the odd harmonics created in this process for a set of specifically chosen parameters and we compare our results with presently available experimental data.

Mikroskopische Theorie der Kernreaktionen für einen Mehrteilchen-Aufbruch / Microscopic Theory of Nuclear Reactions for a Multi-particle-break-up

1974 ◽  
Vol 29 (6) ◽  
pp. 859-866 ◽  
Author(s):  
A. Grauel
Keyword(s):  
Nuclear Reactions ◽  
Microscopic Theory ◽  
Bound State ◽  
Wave Functions ◽  
Matrix Elements ◽  
S Matrix ◽  
The Matrix ◽  
Nucleon Emission ◽  
The Continuum ◽  
Continuum Wave

Introducing correlated continuum wave functions for the two- and re-particle-continuum a microscopic theory of nuclear reactions based on a method of Fano is developed. The S-matrix-elements are given by the matrix-elements between correlated continuum wave functions and bound state wave functions. The antisymmetrization of the continuum wave functions with more than one particle in the continuum is included. The theory can be straightforwardly applied on the n-nucleon-emission process following photo- and particle excitations.

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