scholarly journals Calculation of asymptotic normalization coefficients in the complex-ranged Gaussian basis

2020 ◽  
Author(s):  
Dinmukhamed Sailaubek ◽  
Olga Rubtsova
Keyword(s):  
Bound States ◽  
Bound State ◽  
Hamiltonian Matrix ◽  
Asymptotic Normalization ◽  
Bound State Wave Function ◽  
Non Local ◽  
Asymptotic Normalization Coefficients ◽  
A New Technique ◽  
The Given ◽  
Non Locality

A new technique towards finding asymptotic normalization coefficients in the complex-ranged Gaussian basis is presented. It is shown that a diagonalisation procedure for the total Hamiltonian matrix in the given basis results in approximation for a radial part of the bound state wave function from the origin up to the far asymptotic distances, which allows to extract ANCs rather accurately. The method is illustrated by calculations of single-particle ANCs for nuclei bound states in cases of non-local nucleon-nucleus interactions, in particular, phenomenological global potentials with the Perey-Buck’s non-locality.

RETARDATION EFFECTS IN COVARIANT THREE-DIMENSIONAL BOUND STATE WAVE FUNCTIONS

2005 ◽  
Vol 14 (06) ◽  
pp. 931-947 ◽  
Author(s):  
F. PILOTTO ◽  
M. DILLIG
Keyword(s):  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Relative Energy ◽  
Wave Functions ◽  
Three Dimensions ◽  
State Wave ◽  
Scalar Diquark ◽  
Bound State Wave Function ◽  
Retardation Effects

We investigate the influence of retardation effects on covariant 3-dimensional wave functions for bound hadrons. Within a quark-(scalar) diquark representation of a baryon, the four-dimensional Bethe–Salpeter equation is solved for a 1-rank separable kernel which simulates Coulombic attraction and confinement. We project the manifestly covariant bound state wave function into three dimensions upon integrating out the non-static energy dependence and compare it with solutions of three-dimensional quasi-potential equations obtained from different kinematical projections on the relative energy variable. We find that for long-range interactions, as characteristic in QCD, retardation effects in bound states are of crucial importance.

scholarly journals Closed form bound-state perturbation theory

1980 ◽  
Vol 3 (2) ◽  
pp. 351-368 ◽  
Author(s):  
Ollie J. Rose ◽  
Carl G. Adler
Keyword(s):  
Perturbation Theory ◽  
Eigenvalue Problem ◽  
Closed Form ◽  
Bound States ◽  
Integral Form ◽  
Approximate Solutions ◽  
Perturbation Parameter ◽  
Bound State ◽  
The Given ◽  
Natural Way

The perturbed Schrödinger eigenvalue problem for bound states is cast into integral form using Green's Functions. A systematic algorithm is developed and applied to the resulting equation giving rise to approximate solutions expressed as functions of the given perturbation parameter. As a by-product, convergence radii for the traditional Rayleigh-Schrödinger and Brillouin-Wigner perturbation theories emerge in a natural way.

S-MATRIX AND WAVE FUNCTION METHODS FOR THE CALCULATION OF SMALL DECAY WIDTHS

2010 ◽  
Vol 25 (07) ◽  
pp. 535-547 ◽  
Author(s):  
BASUDEB SAHU ◽  
Y. K. GAMBHIR ◽  
C. S. SHASTRY
Keyword(s):  
Wave Function ◽  
Bound States ◽  
Spherical Wave ◽  
Bound State ◽  
Experimental Results ◽  
Q Value ◽  
Α Decay ◽  
State Wave ◽  
Bound State Wave Function ◽  
S Matrix

Most of the decaying systems namely α-decay and proton radio activity have extremely narrow widths and hence are termed as quasi-bound states. There are three methods available for the computation of very narrow widths. First, the analytic S-matrix method which treats resonance as a pole in complex energy plane with its real part representing resonance energy and the imaginary part the half width. Another two methods namely (i) direct (D) method and (ii) distorted wave (DW) method are based on the property of the quasi-bound state wave function which is quite similar to a bound state wave function in the interior region and is matched with an outgoing spherical wave representing decaying behavior. We make a comparative study of these methods by applying them to the α-decay systems whose experimental results of Q-value and decay half-lives are known recently. It is observed that all the three methods give practically the same results for widths calculated at the same Q-value and explain the experimental results of Q-values and half-lives in several α-decaying nuclei quite well with a proper Coulomb nuclear interaction potential for the α+daughter nucleus system.

FOCK EXPANSION FOR QED BOUND STATES

1989 ◽  
Vol 04 (17) ◽  
pp. 4535-4550 ◽  
Author(s):  
PAUL HOYER
Keyword(s):  
Wave Function ◽  
Bound States ◽  
Bound State ◽  
State Equation ◽  
Positive Energy ◽  
Bound State Wave Function ◽  
Fock State ◽  
Intermediate States ◽  
Schrödinger Picture ◽  
State Content

Using the path integral formulation of QED in the Schrödinger picture, we explicitly show the completeness of photon and electron states at equal (discrete) time. We then formulate an approximation of the bound state wave function, based on its maximal Fock state content, by restricting the intermediate states at all times in the bound state propagator. The approximation becomes (formally) exact as the restriction on the intermediate states is lifted. Hence the Fock expansion provides an alternative to bound state calculations based on the Bethe-Salpeter equation. As an example, we study the bound states formed by a fermion f is an external potential, and by a fermion-antifermion pair [Formula: see text]. At the valence level of the Fock expansion, where the wave function is at all times restricted to f (or [Formula: see text]), we show that only instantaneous Coulomb exchange occurs between the fermions. The resulting bound state equation is similar to the Salpeter equation, but has only positive energy projectors.

scholarly journals Scattering description of Andreev molecules

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Jean-Damien Pillet ◽  
Vincent Benzoni ◽  
Joël Griesmar ◽  
Jean-Loup Smirr ◽  
Çağlar Girit
Keyword(s):  
Bound States ◽  
State Energy ◽  
Bound State ◽  
Transport Processes ◽  
Weak Links ◽  
Bound State Energy ◽  
One Dimensional ◽  
Conduction Channel ◽  
Non Local ◽  
Local Transport

An Andreev molecule is a system of closely spaced superconducting weak links accommodating overlapping Andreev Bound States. Recent theoretical proposals have considered one-dimensional Andreev molecules with a single conduction channel. Here we apply the scattering formalism and extend the analysis to multiple conduction channels, a situation encountered in epitaxial superconductor/semiconductor weak links. We obtain the multi-channel bound state energy spectrum and quantify the contribution of the microscopic non-local transport processes leading to the formation of Andreev molecules.

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