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Open AccessCommunication

Optimal Perturbation Technique within the Asymptotic Iteration Method for Heavy-Light Meson Mass Splittings

by Haifa I. Alrebdi and Thabit Barakat

Universe 2021, 7(6), 180; https://doi.org/10.3390/universe7060180 - 4 Jun 2021

Cited by 2 | Viewed by 1990

For further insight into the perturbation technique within the framework of the asymptotic iteration method (PAIM), we suggest this method to be used as an alternative method to the traditional well-known perturbation techniques. We show by means of very simple algebraic manipulations that PAIM can be directly applied to obtain the symbolic expectation value of any perturbed potential piece without using the eigenfunction of the unperturbed problem. One of the fundamental advantages of PAIM is its ability to extract a reference unperturbed potential piece or pieces from the total Hamiltonian which can be solved exactly within AIM. After all, one can easily compute the symbolic expectation values of the remaining potential pieces. As an example, the present scheme is applied to the semi-relativistic wave equation with the harmonic-oscillator potential implemented with the Fermi–Breit potential terms. In particular, the non-trivial symbolic expectation values of the Dirac delta function, and the momentum-dependent orbit–orbit coupling terms are successfully calculated. Results are then used, as an illustration, to compute the semi-relativistic s-wave heavy-light meson masses. We obtain good agreement with experimental data for the meson mass splittings

c \bar{u}

c \bar{d}

c \bar{s}

b \bar{u}

b \bar{d}

b \bar{s}

. Full article

(This article belongs to the Section High Energy Nuclear and Particle Physics)

5 pages, 224 KB

Open AccessArticle

Expectation Values of the Neutral Chromium Radius

by Nafeesah Abdul Rahim Yaqub, Rabia Qindeel, Norah Alonizan and Nabil Ben Nessib

Atoms 2018, 6(3), 51; https://doi.org/10.3390/atoms6030051 - 12 Sep 2018

Cited by 3 | Viewed by 3013

Abstract

Neutral Chromium (Cr I) is an important element in many laboratory plasma applications. In this work, expectation values of the radius for Cr I are calculated. These atomic data are calculated with three different atomic codes: Cowan code using the Hartree–Fock Relativistic approximation, SUPERSTRUCTURE and AUTOSTRUCTURE codes using scaled Thomas–Fermi–Dirac–Amaldi potential. Relativistic corrections are introduced according to the Breit–Pauli approach. The

3 d^{5} 4 s

3 d^{4} 4 s^{2},

3 d^{5} 4 d, 3 d^{5} 4 p

and

3 d^{4} 4 s 4 p

configurations are included to obtain the expectation values of radius of Cr I and compared with available data. The novelty of our work is to obtain new values of

< \frac{1}{r} >, < r >,

and

< r^{2} >

for the configuration of

4 p

and

4 d

and the values of

< r^{3} >

for all orbitals configurations considered in this work. Full article

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