The Direct Nuclear Charge Radii Measurement from Potential Wavefunction

Authors

Keywords:

Finite-size nucleus, Nuclear potential charge, Constant nuclear parameter, Z-dependence

Abstract

The charge distribution is a fundamental property of atomic nuclei that affects many of their static characteristics, such as spin, parity, binding energy and effective interaction. Accurately measuring the nuclear charge distribution is of immense importance, as it represents the overall characteristics of the entire nucleus. In this study, we aimed to model a simple and effective formula that could best describe the size of nuclei using the wavefunctions of potential fields originating from positively charged protons. We analyzed finite-size nuclear potential to derive a simple and effective Z-dependent formula. This formula was then applied to calculate the size of various nuclei, and the results were compared with the experimentally measured R and Rrms, showing agreement with a deviation of δ2 = 0.0041. In contrast to the commonly used A1/3-dependent formula, our Z1/3-dependent formula keeps the radius parameter rZ almost constant within 4 < Z < 104. The potential radii of nuclei are reflective of their charge distributions, coulomb energy and lepton energy levels. Additionally, while the A1/3-dependent radius measures the matter radius of nuclei, the Z1/3-dependent radius, RZ and RZ,N, measures the proton wavefunctions beyond the nucleons boundary. Thus, our study provides a simple and effective Z-dependent formula for describing the size of nuclei that can be used to improve our understanding of nuclear physics and the behavior of atomic nuclei. It also provides another dimension for nuclear size measurements and the range of nuclear-lepton interactions.

Dimensions

Adamu A, Ngadda Y H (2017) Determination of Nuclear Potential Radii and Its Parameter from Finite – Size Nuclear Model. International Journal of Theoretical and Mathematical Physics, 7(1): 9 – 13.

Adamu, A (2021) A New Measurement of Nuclear Radius from the study of β+–Decay Energy of Finite-Sized Nuclei. Journal of Radiation and Nuclear Applications, 6(1): 45-49.

Akkoyun S, Bayram T, Kara S O, Sinan, A (2013) An artificial neural network application on nuclear charge radii. Journal of Physics G: Nuclear and Particle Physics, 40: 055106, 1 – 7. doi:10.1088/0954-3899/40/5/055106.

An R, Dong X X, Zhang F S (2021a) Systematic study of nuclear charge radii along Z = 98-120 isotopic chains. arXiv preprint arXiv:2112.03829.

An R, Jiang X, Cao L G, Zhang F S (2021b) Odd-even staggering and shell effects in nuclear charge radii. arXiv preprint arXiv:2108.00278.

Angeli I (2004) A consistent set of nuclear rms charge radii: properties of the radius surface (R, N)*. Atomic Data and Nuclear Data Tables, 87: 185–206.

Angeli I, Marinova K P (2013) Table of experimental nuclear ground state charge radii: An update. Atomic Data and Nuclear Data Tables, 99: 69–95.

Antonov A N, Kadrev D N, Gaidarov M K, de Guerra E M, Sarriguren P, Udias J M, Lukyanov V K, Zemlyanaya E V, Krumova G Z (2005) Charge and Matter Distributions and Form Factors of Light, Medium and Heavy Neutron-Rich Nuclei. Physical Review C, 72: 044307.

Bao M, Zong Y Y, Zhao Y M, Arima A (2020) Local Relations of Nuclear Charge Radii. Physical Review C, 102: 014306.

Basdevant J L, Rich J, Spiro M (2005) Fundamentals in nuclear physics: from nuclear structure to cosmology. Springer Science and Business Media, Inc., New York, USA, page 11.

Bayram T, Akkoyun S, Kara S O, Sinan A (2013) New parameters for nuclear charge radius formulas. Acta Physica Polonica B, 44(8): 1791 – 1799.

Bethe H A (1936) Nuclear Radius and Many- Body Problem. Physical Review, 50: 977.

Bohr, A. and Mottelson, B. R. (1975). Nuclear tructure, Vol. II, Benjamin, MA.

Deck R T, Amar J G, Fralick G (2005) Nuclear Size Corrections to the Energy Levels of Single-electron and -Muon Atoms. Journal of Physics B: Atomic Molecular and Optical Physics, 38: 2173 – 2186.

Ghoshal S N (2007) Nuclear Physics, (S Chand and company limited, Ram Nagar, New Delhi, page 406 – 407, 424.

Kumar A, Das H C, Kaur M, Bhuyan M, Patra S K (2021) Nuclear Matter Parameters for Finite Nuclei Using Relativistic Mean Field Formalism within Coherent Density Fluctuation Model. Physical Review C, 103: 024305.

Ma J-Q, Zhang Z-H (2022) Improved phenomenological nuclear charge radius formulae with kernel ridge regression. Chinese Physics C 46(7): 074105.

Marinova K. (2015) Nuclear Charge Radii Systematics. Journal of Physical and Chemical Reference Data, 44(3); 031214 – 5. http://dx.doi.org/10.1063/1.4921236.

Merino C, Novikov I S, Shabelski Y (2009) Nuclear radii calculations in various theoretical approaches for nucleus-nucleus interactions. Physical Review C, 80(6), 064616.

Michel N, Oreshkina N S (2021) Access to the Kaon Radius with Kaonic Atoms. Annals of Physics (Berlin), 2100150, 1 – 6. DOI:10.1002/andp.202100150.

Mohr P J, Newell D B, Taylor B N (2016) CODATA Recommended Values of the Fundamental Physical Constants: 2014. Review of Modern Physics, 88:(3).

Myers W D, Swiatecki W J (1998) Nuclear Diffuseness as a Degree of Freedom, Physical Review C, 58: 3368.

Nerlo-Pomorska B, Pomorski K (1993) Isospin dependence of nuclear radius. Zeitschrift für Physik A Hadrons and Nuclei, 344(4): 359-361.

Nerlo-Pomorska B, Pomorski K (1994) Simple formula for nuclear charge radius. Z. Phys. A, 348: 169 – 172.

Neznamov V P, Safronov I I (2004) A New Method for Solving the Z > 137 Problem and for Determination of Energy Levels of Hydrogen-Like Atoms, World Scientific, 100: 167 - 180.

Nickel B (2013) Nuclear Size Effects on Hydrogenic Atom Energies: A Semi-Analytic Formulation. Journal of Physics B: Atomic, Molecular and Optical Physics, 46: 015001, 1 – 15. doi:10.1088/0953-4075/46/1/015001.

Niri B N, Anjami A (2018) Nuclear Size Corrections to the Energy Levels of Single-Electron Atoms. Nuclear Science, 3(1): 1 – 8.

Oreshkina N S: Self-energy correction to the energy levels of heavy muonic atoms. arXiv:2206.01006v1 [physics.atom-ph] 2 Jun 2022. https://doi.org/10.48550/arXiv.2206.01006.

Ozawa T, Tanihata S I (2001) Nuclear size and related topics. Nuclear Physics A, 693: 32–62.

Patoary A M, Oreshkina N S (2017) Finite nuclear size effect to the fine structure of heavy muonic atoms. The European Physical Journal D, 72: 54. DOI: 10.1140/epjd/e2018-80545-9.

Rahaman U, Ikram M, Imran M, Usmani A A (2020) A study of nuclear radii and neutron skin thickness of neutron-rich nuclei near the neutron drip line. International Journal of Modern Physics E, 29(09): 2050076.

Reinhard P G, Nazarewicz W (2022) Statistical correlations of nuclear quadrupole deformations and charge radii. Physical Review C, 106(1): 014303.

Reinhard P-G and Nazarewicz W (2021). Nuclear charge densities in spherical and deformed nuclei: towards precise calculations of charge radii. arXiv:2101.00320v2 [nucl-th] 8 May 2021.

Royer G (2008) On the coefficients of the liquid drop model mass formulae and nuclear radii. Nuclear Physics A, 807: 105.

Royer G, Gautier, C (2006) On the coefficients and terms of the liquid drop model and mass formula. Physical Review C, American Physical Society, 73: 067302.

Royer G, Rousseau R (2019) On the Liquid Drop Model Mass Formulae and Charge Radii. The European Physical Journal A, 52: 501.

Shahaev V M (1993) Finite Nuclear Size Corrections to the Energy Levels of the Multicharged Ions. Journal of Physics B: Atomic Molecular and Optical Physics, 26: 1103 – 1108. Printed in the UK.

Sheng Z, Fan G, Qian J, Hu J (2015) An effective formula for nuclear charge radii. The European Physical Journal A, 51: 40. DOI 10.1140/epja/i2015-15040-1.

Sun H, Lu Y, Peng J P, Liu C Y, Zhao Y M: New Charge Radius Relations for Atomic Nuclei. Physical Review C 2015, 9: 019902.

Talmi I (1984) On the Odd-Even Effect in the Charge Radii of Isotopes. Nuclear Physics A, 423: 189-1960. North-Holland Publishing Company.

Tel E, Okuducu S, Tanir G, Akti N N, Bolukdemir M H (2008) Calculation of Radii and Density of 7–19B Isotopes using Effective Skyrme Force. Communication in Theoretical Physics, 49(3): 696 – 702.

Thakur V, Dhiman S K (2019) A Study of Charge Radii and Neutron Skin Thickness near Nuclear Drip Lines. Nuclear Physics A, 992: 121623. https://doi.org/10.1016/j.nuclphysa.2019.121623.

Utama R, Chen W C, Piekarewicz J (2016) Nuclear Charge Radii: Density Functional Theory Meets Bayesian Neural Networks. Journal of Physics G: Nuclear and Particle Physics, 43: 114002.

Wakasa T, Takechi M, Tagami S, Yahiro M (2022) Matter radii and skins of 6,8He from reaction cross section of proton+ 6,8He scattering based on the Love–Franey t-matrix model. Results in Physics, 35: 105329.

Wang N, Li T (2013) Shell and isospin effects in nuclear charge radii. Physical Review C, 88(1): 011301.

Xie L, Yang X F, Wraith C, Babcock C, Bieron J, Billowes J, Bissell M L, Blaum K, Cheal B, Filippin L, Flanagan K T, Garcia Ruiz R F, Gins W, Gaigalas G, Godefroid M, Gorges C, Grob L K, Heylen H, Jönsson P, Kaufmann S, Kowalska M, Krämer J, Malbrunot-Ettenauer S, Neugart R, Neyens G, Nörtershäuser W, Otsuka T, Papuga J, Sánchez R, Tsunoda Y, Yordano D T (2019) Nuclear charge radii of 62−80Zn and their dependence on cross-shell proton excitations. Physics Letters B, 797: 134805. https://doi.org/10.1016/j.physletb.2019.134805.

Yi-An L, Zhen-Hua Z, Jin-Yan Z (2009) Improved Z1/3 Law of Nuclear Charge Radius. Communication in Theoretical Physics (Beijing, China), 51: 123–125.

Published

2023-07-03

How to Cite

Adamu, A., Ngadda, Y. H., & Hassan, M. (2023). The Direct Nuclear Charge Radii Measurement from Potential Wavefunction. Nigerian Journal of Physics, 32(1), 67-75. https://njp.nipngr.org/index.php/njp/article/view/31

Issue

Vol. 32 No. 1 (2023): Nigerian Journal of Physics - Vol. 32 No. 1

Section

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How to Cite

Adamu, A., Ngadda, Y. H., & Hassan, M. (2023). The Direct Nuclear Charge Radii Measurement from Potential Wavefunction. Nigerian Journal of Physics, 32(1), 67-75. https://njp.nipngr.org/index.php/njp/article/view/31

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