Approximate Effective Interaction for Nuclear Matter and Finite Nuclei

Isaiah Ochala; Joseph Fiase; John Adeyemi; Shuaibu Abubakar

doi:doi:10.11648/j.ijamtp.20241001.12

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Approximate Effective Interaction for Nuclear Matter and Finite Nuclei

Isaiah Ochala^*

, Joseph Fiase, John Adeyemi, Shuaibu Abubakar

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 10, Issue 1)

Received: 13 March 2024 Accepted: 24 May 2024 Published: 30 August 2024

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Abstract

In this paper, an approximate effective nucleon-nucleon interaction for nuclear matter and finite studies has been derived using the lowest order constrained variational (LOCV) approach. The LOCV method, a functional minimization procedure, uses a normalization constraint to keep higher-order terms as small as possible. As a first step, two-body matrix elements based on the Reid93 nucleon-nucleon potential were calculated for the nuclear system A = 16 in a harmonic oscillator basis, with the oscillator size parameter ћω = 14.0 MeV, and separated into the central, spin-orbit and tensor channels in conformity with the potentials for Inelastic scattering. Following this, a least squares fitting of the matrix elements to a sum of Yukawa functions was performed to determine the strengths of the effective interaction in the singlet-even, singlet-odd, triplet-even and triplet-odd (Central); tensor-even and tensor-odd (Tensor); spin-orbit-even and spin-orbit-odd (Spin-orbit) channels. Of all the matrix elements, only the triplet-even and tensor-even components, being attractive, are affected by the tensor correlations (a = 0.05); and are shown to exhibit the same trend of variation in conformity with past work, in terms of magnitude, as one goes from the lower-node quantum numbers (n’, n) = (0, 0) to higher ones (n’, n) = (2, 2). When compared with the G-matrix results of previous researchers, the results obtained herein have been found to be in good agreement. This, therefore, gives hope that the new effective interaction promises to be a reliable tool for nuclear matter and nuclear structure studies.

Published in	International Journal of Applied Mathematics and Theoretical Physics (Volume 10, Issue 1)
DOI	10.11648/j.ijamtp.20241001.12
Page(s)	21-27
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Matrix Elements, Effective Interaction, Nuclear Matter, Finite Nuclei

References

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APA Style

Ochala, I., Fiase, J., Adeyemi, J., Abubakar, S. (2024). Approximate Effective Interaction for Nuclear Matter and Finite Nuclei. International Journal of Applied Mathematics and Theoretical Physics, 10(1), 21-27. https://doi.org/10.11648/j.ijamtp.20241001.12

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ACS Style

Ochala, I.; Fiase, J.; Adeyemi, J.; Abubakar, S. Approximate Effective Interaction for Nuclear Matter and Finite Nuclei. Int. J. Appl. Math. Theor. Phys. 2024, 10(1), 21-27. doi: 10.11648/j.ijamtp.20241001.12

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AMA Style

Ochala I, Fiase J, Adeyemi J, Abubakar S. Approximate Effective Interaction for Nuclear Matter and Finite Nuclei. Int J Appl Math Theor Phys. 2024;10(1):21-27. doi: 10.11648/j.ijamtp.20241001.12

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@article{10.11648/j.ijamtp.20241001.12,
  author = {Isaiah Ochala and Joseph Fiase and John Adeyemi and Shuaibu Abubakar},
  title = {Approximate Effective Interaction for Nuclear Matter and Finite Nuclei
},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {10},
  number = {1},
  pages = {21-27},
  doi = {10.11648/j.ijamtp.20241001.12},
  url = {https://doi.org/10.11648/j.ijamtp.20241001.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20241001.12},
  abstract = {In this paper, an approximate effective nucleon-nucleon interaction for nuclear matter and finite studies has been derived using the lowest order constrained variational (LOCV) approach. The LOCV method, a functional minimization procedure, uses a normalization constraint to keep higher-order terms as small as possible. As a first step, two-body matrix elements based on the Reid93 nucleon-nucleon potential were calculated for the nuclear system A = 16 in a harmonic oscillator basis, with the oscillator size parameter ћω = 14.0 MeV, and separated into the central, spin-orbit and tensor channels in conformity with the potentials for Inelastic scattering. Following this, a least squares fitting of the matrix elements to a sum of Yukawa functions was performed to determine the strengths of the effective interaction in the singlet-even, singlet-odd, triplet-even and triplet-odd (Central); tensor-even and tensor-odd (Tensor); spin-orbit-even and spin-orbit-odd (Spin-orbit) channels. Of all the matrix elements, only the triplet-even and tensor-even components, being attractive, are affected by the tensor correlations (a = 0.05); and are shown to exhibit the same trend of variation in conformity with past work, in terms of magnitude, as one goes from the lower-node quantum numbers (n’, n) = (0, 0) to higher ones (n’, n) = (2, 2). When compared with the G-matrix results of previous researchers, the results obtained herein have been found to be in good agreement. This, therefore, gives hope that the new effective interaction promises to be a reliable tool for nuclear matter and nuclear structure studies.
},
 year = {2024}
}

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TY  - JOUR
T1  - Approximate Effective Interaction for Nuclear Matter and Finite Nuclei

AU  - Isaiah Ochala
AU  - Joseph Fiase
AU  - John Adeyemi
AU  - Shuaibu Abubakar
Y1  - 2024/08/30
PY  - 2024
N1  - https://doi.org/10.11648/j.ijamtp.20241001.12
DO  - 10.11648/j.ijamtp.20241001.12
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 21
EP  - 27
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20241001.12
AB  - In this paper, an approximate effective nucleon-nucleon interaction for nuclear matter and finite studies has been derived using the lowest order constrained variational (LOCV) approach. The LOCV method, a functional minimization procedure, uses a normalization constraint to keep higher-order terms as small as possible. As a first step, two-body matrix elements based on the Reid93 nucleon-nucleon potential were calculated for the nuclear system A = 16 in a harmonic oscillator basis, with the oscillator size parameter ћω = 14.0 MeV, and separated into the central, spin-orbit and tensor channels in conformity with the potentials for Inelastic scattering. Following this, a least squares fitting of the matrix elements to a sum of Yukawa functions was performed to determine the strengths of the effective interaction in the singlet-even, singlet-odd, triplet-even and triplet-odd (Central); tensor-even and tensor-odd (Tensor); spin-orbit-even and spin-orbit-odd (Spin-orbit) channels. Of all the matrix elements, only the triplet-even and tensor-even components, being attractive, are affected by the tensor correlations (a = 0.05); and are shown to exhibit the same trend of variation in conformity with past work, in terms of magnitude, as one goes from the lower-node quantum numbers (n’, n) = (0, 0) to higher ones (n’, n) = (2, 2). When compared with the G-matrix results of previous researchers, the results obtained herein have been found to be in good agreement. This, therefore, gives hope that the new effective interaction promises to be a reliable tool for nuclear matter and nuclear structure studies.

VL  - 10
IS  - 1
ER  -

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Author Information

Isaiah Ochala

Department of Physics, Prince Abubakar Audu University, Anyigba, Nigeria

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http://orcid.org/0000-0002-5546-465X
Joseph Fiase

Department of Physics, Benue State University, Makurdi, Nigeria

Contact Email
John Adeyemi

Department of Physics, Prince Abubakar Audu University, Anyigba, Nigeria

Contact Email
Shuaibu Abubakar

Department of Physics, Prince Abubakar Audu University, Anyigba, Nigeria

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APA Style

Ochala, I., Fiase, J., Adeyemi, J., Abubakar, S. (2024). Approximate Effective Interaction for Nuclear Matter and Finite Nuclei. International Journal of Applied Mathematics and Theoretical Physics, 10(1), 21-27. https://doi.org/10.11648/j.ijamtp.20241001.12

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ACS Style

Ochala, I.; Fiase, J.; Adeyemi, J.; Abubakar, S. Approximate Effective Interaction for Nuclear Matter and Finite Nuclei. Int. J. Appl. Math. Theor. Phys. 2024, 10(1), 21-27. doi: 10.11648/j.ijamtp.20241001.12

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AMA Style

Ochala I, Fiase J, Adeyemi J, Abubakar S. Approximate Effective Interaction for Nuclear Matter and Finite Nuclei. Int J Appl Math Theor Phys. 2024;10(1):21-27. doi: 10.11648/j.ijamtp.20241001.12

Copy | Download

@article{10.11648/j.ijamtp.20241001.12,
  author = {Isaiah Ochala and Joseph Fiase and John Adeyemi and Shuaibu Abubakar},
  title = {Approximate Effective Interaction for Nuclear Matter and Finite Nuclei
},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {10},
  number = {1},
  pages = {21-27},
  doi = {10.11648/j.ijamtp.20241001.12},
  url = {https://doi.org/10.11648/j.ijamtp.20241001.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20241001.12},
  abstract = {In this paper, an approximate effective nucleon-nucleon interaction for nuclear matter and finite studies has been derived using the lowest order constrained variational (LOCV) approach. The LOCV method, a functional minimization procedure, uses a normalization constraint to keep higher-order terms as small as possible. As a first step, two-body matrix elements based on the Reid93 nucleon-nucleon potential were calculated for the nuclear system A = 16 in a harmonic oscillator basis, with the oscillator size parameter ћω = 14.0 MeV, and separated into the central, spin-orbit and tensor channels in conformity with the potentials for Inelastic scattering. Following this, a least squares fitting of the matrix elements to a sum of Yukawa functions was performed to determine the strengths of the effective interaction in the singlet-even, singlet-odd, triplet-even and triplet-odd (Central); tensor-even and tensor-odd (Tensor); spin-orbit-even and spin-orbit-odd (Spin-orbit) channels. Of all the matrix elements, only the triplet-even and tensor-even components, being attractive, are affected by the tensor correlations (a = 0.05); and are shown to exhibit the same trend of variation in conformity with past work, in terms of magnitude, as one goes from the lower-node quantum numbers (n’, n) = (0, 0) to higher ones (n’, n) = (2, 2). When compared with the G-matrix results of previous researchers, the results obtained herein have been found to be in good agreement. This, therefore, gives hope that the new effective interaction promises to be a reliable tool for nuclear matter and nuclear structure studies.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Approximate Effective Interaction for Nuclear Matter and Finite Nuclei

AU  - Isaiah Ochala
AU  - Joseph Fiase
AU  - John Adeyemi
AU  - Shuaibu Abubakar
Y1  - 2024/08/30
PY  - 2024
N1  - https://doi.org/10.11648/j.ijamtp.20241001.12
DO  - 10.11648/j.ijamtp.20241001.12
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 21
EP  - 27
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20241001.12
AB  - In this paper, an approximate effective nucleon-nucleon interaction for nuclear matter and finite studies has been derived using the lowest order constrained variational (LOCV) approach. The LOCV method, a functional minimization procedure, uses a normalization constraint to keep higher-order terms as small as possible. As a first step, two-body matrix elements based on the Reid93 nucleon-nucleon potential were calculated for the nuclear system A = 16 in a harmonic oscillator basis, with the oscillator size parameter ћω = 14.0 MeV, and separated into the central, spin-orbit and tensor channels in conformity with the potentials for Inelastic scattering. Following this, a least squares fitting of the matrix elements to a sum of Yukawa functions was performed to determine the strengths of the effective interaction in the singlet-even, singlet-odd, triplet-even and triplet-odd (Central); tensor-even and tensor-odd (Tensor); spin-orbit-even and spin-orbit-odd (Spin-orbit) channels. Of all the matrix elements, only the triplet-even and tensor-even components, being attractive, are affected by the tensor correlations (a = 0.05); and are shown to exhibit the same trend of variation in conformity with past work, in terms of magnitude, as one goes from the lower-node quantum numbers (n’, n) = (0, 0) to higher ones (n’, n) = (2, 2). When compared with the G-matrix results of previous researchers, the results obtained herein have been found to be in good agreement. This, therefore, gives hope that the new effective interaction promises to be a reliable tool for nuclear matter and nuclear structure studies.

VL  - 10
IS  - 1
ER  -

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