Calculation of electric multipole transition radial matrix elements, oscillator strengths and Einstein coefficients over nonrelativistic radial wave function using Slater type orbitals

2011 ◽  
Vol 34 (9) ◽  
pp. 649-651 ◽  
Author(s):  
I.I. Guseinov ◽  
B.A. Mamedov
Keyword(s):  
Wave Function ◽  
Radial Wave Function ◽  
Oscillator Strengths ◽  
Slater Type Orbitals ◽  
Matrix Elements ◽  
Slater Type ◽  
Radial Wave

scholarly journals STUDY OF THE η-7Be INTERACTION NEAR THRESHOLD IN p-6Li FUSION

2009 ◽  
Vol 18 (05n06) ◽  
pp. 1383-1388
Author(s):  
N. J. UPADHYAY ◽  
N. G. KELKAR ◽  
K. P. KHEMCHANDANI ◽  
B. K. JAIN
Keyword(s):  
Wave Function ◽  
Final State Interaction ◽  
Radial Wave Function ◽  
State Interaction ◽  
Nuclear Medium ◽  
Final State ◽  
Radial Wave ◽  
Near Threshold

We present a calculation for η production in the p-6Li fusion near threshold including the η-7Be final state interaction (FSI). We consider the 6Li and 7Be nuclei as α-d and α-3He clusters respectively. The calculations are done for the lowest states of 7 Be with [Formula: see text] resulting from the L = 1 radial wave function. The η-7Be interaction is incorporated through the η-7BeT–matrix, constructed from the medium modified matrices for the η-3He and η-α systems. These medium modified matrices are obtained by solving few body equations, where the scattering in nuclear medium is taken into account.

Asymptotic of the deuteron wave function in the coordinate representation and the charge deuteron form factor at large momentums

2021 ◽  
pp. 2150085
Author(s):  
V. I. Zhaba
Keyword(s):  
Wave Function ◽  
Form Factor ◽  
Deuteron Wave Function ◽  
Radial Wave Function ◽  
Nucleon Nucleon ◽  
Radial Wave ◽  
Nucleon Potential ◽  
Coordinate Representation ◽  
Deuteron Form Factor ◽  
The Difference

Numerical modeling of the deuteron wave function in the coordinate representation for the phenomenological nucleon–nucleon potential Argonne v18 has been performed. For this purpose, the asymptotic behavior of the radial wave function has been taken into account near the origin of coordinates and at infinity. The charge deuteron form factor [Formula: see text], depending on the transmitted momentums up to [Formula: see text], has been calculated employing five models for the deuteron wave function. A characteristic difference in calculations of [Formula: see text] is observed near the positions of the first and second zero. The difference between the obtained values for [Formula: see text] form factor has been analyzed using the values of the ratios and differences for the results. Obtained outcomes for charge deuteron form factor at large momentums may be a prediction for future experimental data.

M-SCHEME CLUSTER-ORBITAL SHELL MODEL APPROACH FOR NEUTRON-RICH SYSTEMS

2009 ◽  
Vol 24 (11n13) ◽  
pp. 1009-1012
Author(s):  
HIROSHI MASUI ◽  
KIYOSHI KATŌ ◽  
KIYOMI IKEDA
Keyword(s):  
Wave Function ◽  
Shell Model ◽  
Oxygen Isotopes ◽  
Radial Wave Function ◽  
Radial Wave ◽  
Gaussian Functions ◽  
Model Formalism ◽  
Model Approach

We developed an m-scheme approach of the cluster-orbital shell model formalism. The radial wave function is treated as the super position of the Gaussian functions with different width parameters. Energies and r.m.s. radii of oxygen isotopes are studied.

Atomic wave functions for gold and thallium

1955 ◽  
Vol 51 (3) ◽  
pp. 486-503 ◽  
Author(s):  
A. S. Douglas ◽  
D. R. Hartree ◽  
W. A. Runciman
Keyword(s):  
Wave Function ◽  
Absorption Edge ◽  
Radial Wave Function ◽  
Wave Functions ◽  
Radial Wave ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Independent Variable ◽  
Independent Calculation

Before the war, self-consistent field calculations for the Au+ ion had been carried out by W. Hartree but were left still unpublished at his death (see prefatory note in (5)). These results have been used by Brenner and Brown (1) in a relativistic calculation of the K-absorption edge for gold, and they were also used in obtaining initial estimates for the partial self-consistent field calculations for thallium of which results are given in §§3–5 of the present paper. In the meantime an independent calculation for Au+ has been carried out by Henry (6), and his results agree closely with those of W. Hartree. However, it still seems desirable to publish the latter, since they give directly the radial wave function P(nl; r) at exact values of r, whereas Henry used log r as independent variable, as had been done for similar calculations for Hg(4), and has tabulated r½P(nl; r) which is the natural dependent variable to use with log r as independent variable (2); in some applications it is more convenient to have the radial wave functions themselves.

The interpolation of atomic wave functions

1955 ◽  
Vol 51 (4) ◽  
pp. 684-692 ◽  
Author(s):  
D. R. Hartree
Keyword(s):  
Wave Function ◽  
Atomic Number ◽  
Radial Wave Function ◽  
Point Of View ◽  
Wave Functions ◽  
Radial Wave ◽  
Atomic Wave ◽  
The Mean

ABSTRACTIf r̄nl is the mean radius for the radial wave function of a complete (nl) group in an atom of atomic number N, the variation of 1/r̄nl with N is nearly linear. Further the variation of a given (nl) radial wave function with N is such that for a given value of (r/r̄nl), the variation of the quantity (r̄nl)½P(nl; r) with r̄nl is nearly linear. These relations between the radial wave functions for different atoms are examined from the point of view of using them as a means of interpolating, with respect to atomic number, between results for atoms for which solutions of Fock's equations have been carried out.

Wave equations in conformal gravity

2018 ◽  
Vol 33 (16) ◽  
pp. 1850090
Author(s):  
Juan-Juan Du ◽  
Xue-Jing Wang ◽  
You-Biao He ◽  
Si-Jiang Yang ◽  
Zhong-Heng Li
Keyword(s):  
Wave Function ◽  
Wave Equations ◽  
Radial Wave Function ◽  
Analytic Solutions ◽  
Heun Equation ◽  
Conformal Gravity ◽  
Radial Wave ◽  
Special Cases ◽  
Metric Functions ◽  
Actual Shape

We study the wave equation governing massless fields of all spins (s = 0, [Formula: see text], 1, [Formula: see text] and 2) in the most general spherical symmetric metric of conformal gravity. The equation is separable, the solution of the angular part is a spin-weighted spherical harmonic, and the radial wave function may be expressed in terms of solutions of the Heun equation which has four regular singular points. We also consider various special cases of the metric and find that the angular wave functions are the same for all cases, the actual shape of the metric functions affects only the radial wave function. It is interesting to note that each radial equation can be transformed into a known ordinary differential equation (i.e. Heun equation, or confluent Heun equation, or hypergeometric equation). The results show that there are analytic solutions for all the wave equations of massless spin fields in the spacetimes of conformal gravity. This is amazing because exact solutions are few and far between for other spacetimes.

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