Evaluation of the Gaunt Coefficients by Using Recurrence Relations for Spherical Harmonics

Selda Özay

Makale detayları

Evaluation of the Gaunt Coefficients by Using Recurrence Relations for Spherical Harmonics

Yazarlar:

Selda Özay

Yayıncı:

Süleyman Demirel University

Ana Başlıklar:

Atomic and Molecular Physics

Dergi:

Süleyman Demirel University Faculty of Arts and Science Journal of Science Vol.18 Issue 3, pp.213-222

Belge Tipi:

Makale

Yayın Tarihi:

11/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001304037

pISSN:

1306-7575

Anahtar kelimeler:

Özet:

 The Gaunt coefficient is one of the important coefficients to be known for calculating molecular integrals in quantum theory of coupling of three angular momenta. Generally, these coefficients are calculated analytically by using the properties of the associated Legendre polynomials. In this study, Gaunt coefficients were calculated algebraically by using the recurrence relations and orthogonality conditions of spherical harmonics and different mathematical expressions were obtained from known analytical expressions for Gaunt coefficients in terms of factorial functions or binomial coefficients. By using the program written in the Mathematica programming language, both the analytical expressions and the algebraic expressions were calculated, and the numerical results obtained were compared. Numerical results are in quite agreement with the literature and each other.

 The Gaunt coefficient is one of the important coefficients to be known for calculating molecular integrals in quantum theory of coupling of three angular momenta. Generally, these coefficients are calculated analytically by using the properties of the associated Legendre polynomials. In this study, Gaunt coefficients were calculated algebraically by using the recurrence relations and orthogonality conditions of spherical harmonics and different mathematical expressions were obtained from known analytical expressions for Gaunt coefficients in terms of factorial functions or binomial coefficients. By using the program written in the Mathematica programming language, both the analytical expressions and the algebraic expressions were calculated, and the numerical results obtained were compared. Numerical results are in quite agreement with the literature and each other.

 The Gaunt coefficient is one of the important coefficients to be known for calculating molecular integrals in quantum theory of coupling of three angular momenta. Generally, these coefficients are calculated analytically by using the properties of the associated Legendre polynomials. In this study, Gaunt coefficients were calculated algebraically by using the recurrence relations and orthogonality conditions of spherical harmonics and different mathematical expressions were obtained from known analytical expressions for Gaunt coefficients in terms of factorial functions or binomial coefficients. By using the program written in the Mathematica programming language, both the analytical expressions and the algebraic expressions were calculated, and the numerical results obtained were compared. Numerical results are in quite agreement with the literature and each other.

 The Gaunt coefficient is one of the important coefficients to be known for calculating molecular integrals in quantum theory of coupling of three angular momenta. Generally, these coefficients are calculated analytically by using the properties of the associated Legendre polynomials. In this study, Gaunt coefficients were calculated algebraically by using the recurrence relations and orthogonality conditions of spherical harmonics and different mathematical expressions were obtained from known analytical expressions for Gaunt coefficients in terms of factorial functions or binomial coefficients. By using the program written in the Mathematica programming language, both the analytical expressions and the algebraic expressions were calculated, and the numerical results obtained were compared. Numerical results are in quite agreement with the literature and each other.

Makale detayları

Evaluation of the Gaunt Coefficients by Using Recurrence Relations for Spherical Harmonics

Yazarlar:

Selda Özay

Yayıncı:

Süleyman Demirel University

Ana Başlıklar:

Atomic and Molecular Physics

Dergi:

Süleyman Demirel University Faculty of Arts and Science Journal of Science Vol.18 Issue 3, pp.213-222

Belge Tipi:

Makale

Yayın Tarihi:

11/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001304037

pISSN:

1306-7575

Clebsch – Gordan Coefficients

Vector Coupling Constant

Gaunt Coefficients

Sayı

Makale detayları

Evaluation of the Gaunt Coefficients by Using Recurrence Relations for Spherical Harmonics

Yazarlar: Selda Özay

Yayıncı: Süleyman Demirel University

Ana Başlıklar: Atomic and Molecular Physics

Dergi: Süleyman Demirel University Faculty of Arts and Science Journal of Science Vol.18 Issue 3, pp.213-222

Belge Tipi: Makale

Yayın Tarihi: 11/2023

Belge Dili: İngilizce

Document ID (Org No.): 2001304037

pISSN: 1306-7575

Clebsch – Gordan Coefficients

Vector Coupling Constant

Gaunt Coefficients

Sayı

Yazarlar:

Selda Özay

Yayıncı:

Süleyman Demirel University

Ana Başlıklar:

Atomic and Molecular Physics

Dergi:

Süleyman Demirel University Faculty of Arts and Science Journal of Science Vol.18 Issue 3, pp.213-222

Belge Tipi:

Makale

Yayın Tarihi:

11/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001304037

pISSN:

1306-7575