Nuclear Science

| Peer-Reviewed |

Improved Numerical Generalization of the Bethe-Weizsäcker Mass Formula for Prediction the Isotope Nuclear Mass, the Mass Excess Including of Artificial Elements 119 and 120

Received: Jun. 05, 2019    Accepted: Jul. 15, 2019    Published: Jul. 26, 2019
Views:       Downloads:

Share This Article

Abstract

George Gamow’s liquid drop model of the nucleus can account for most of the terms in the formula and gives rough estimates for the values of the coefficients. Its semi-numerical equation was first formulated in 1935 by Weizsäcker and in 1936 Bethe [1, 2], and although refinements have been made to the coefficients over the years, the structure of the formula remains the same today. Their formula gives a good approximation for atomic masses and several other effects, but does not explain the appearance of magic numbers of protons and neutrons, and the extra binding-energy and measure of stability that are associated with these numbers of nucleons. Mavrodiev and Deliyergiyev [3] formalized the nuclear mass problem in the inverse problem framework. This approach allowed them to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. They formulated the inverse problem for the numerically generalized semi-empirical mass formula of Bethe and von Weizsäcker going step-by-step through the AME2012 [4] nuclear database. The resulting parameterization described the measured nuclear masses of 2564 isotopes with a maximal deviation of less than 2.6 MeV, starting from the number of protons and number of neutrons equal to 1. The unknown functions in the generalized mass formula was discovered in a step-by-step way using the modified procedure realized in the algorithms developed by Aleksandrov [5-7] to solve nonlinear systems of equations via the Gauss-Newton method. In the presented herein article we describe a further development of the obtained by [3] formula by including additional factors,- magic numbers of protons, neutrons and electrons. This inclusion is based the well-known experimental data on the chemically induced polarization of nuclei and the effect of such this polarization on the rate of isotope decay. It allowed taking into account resonant interaction of the spins of nuclei and electron shells. As a result the maximal deviation from the measured nuclear masses of less than 1.9 MeV was reached. This improvement allowed prediction of the nuclear characteristics of the artificial elements 119 and 120.

DOI 10.11648/j.ns.20190402.11
Published in Nuclear Science ( Volume 4, Issue 2, June 2019 )
Page(s) 11-22
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

Bethe-Weizsäcker Mass Formula, Magic Numbers, Binding Energy, Wigner Term, Inverse Problem, Electrons-Nucleus Interaction, Chemical Polarization, Isotopes

References
[1] Weizsäcker, C. F. von. Z. Phys. 96 (1935) 431.
[2] Bethe, H. A. and Bacher, R. F. Rev. Mod. Phys. 8 (1936) 82.
[3] S. C. Mavrodiev and M. A. Deliyergiyev, Modification of the Nuclear Landscape in the Inverse Problem Framework using the Generalized Bethe-Weizsäcker Mass Formula (2016), [arXiv: nucl-th/1602. 06777].
[4] W. J. Huang et al., The AME2016 atomic mass evaluation (I). Evaluation of input data; And adjustment procedures, Chin. Phys. C41 (3) (2017) 030002.
[5] L. Aleksandrov, Program AFXY (Analyze FX=Y) for Investigation of Nonlinear Systems, Private communications.
[6] L. Aleksandrov, On Numerical Solution on Computer of the Nonlinear Ill-posed Problems, Comm. JINR P5-10366 (Dubna, 1977), [in Russian].
[7] L. Aleksandrov, M. Drenska, D. Karadjov, Program code REGN (Code System for Solving Nonlinear Systems of Equations via the Gauss-Newton Method), RSIC-PSR-165, JINR 61-11-82-767 (Dubna, 1982). URL: https: //rsicc. ornl. gov/codes/psr/psr1/psr-165. html
[8] G. T. Emery, Perturbation of Nuclear Decay Rates, Annual Review of Nuclear Science 22, pg 165 (1972).
[9] D. Atanasov et al. Studies at the border between nuclear and atomic physics: Weak decays of highly charged ions. IOP Conf. Series: Journal of Physics: Conf. Series 875 (2017) 012008 doi: 10.1088/1742-6596/875/2/012008.
[10] M. Jung, F. Bosch, K. Beckert, H. Eickhoff, H. Folger, B. Franzke, A. Gruber, P. Kienle, O. Klepper, W. Koenig, C. Kozhuharov, R. Mann, R. Moshammer, F. Nolden, U. Schaaf, G. Soff, P. Spädtke, M. Steck, Th. Stöhlker, and K. Sümmerer. (1992) First observation of bound-state β− decay. Phys. Rev. Lett. 69, 2164 – Published 12 October 1992.
[11] F. Bosch, T. Faestermann, J. Friese, F. Heine, P. Kienle, E. Wefers, K. Zeitelhack, K. Beckert, B. Franzke, O. Klepper, C. Kozhuharov, G. Menzel, R. Moshammer, F. Nolden, H. Reich, B. Schlitt, M. Steck, T. Stöhlker, T. Winkler, and K. Takahashi. (1996), Observation of Bound-State β− Decay of Fully Ionized 187Re: 187Re−187Os Cosmochronometry, Phys. Rev. Lett. 77, 5190 – Published 23 December 1996.
[12] Yu. A Litvinov (Darmstadt, GSI & Giessen U. ), F. Bosch (Darmstadt, GSI), N. Winckler (Darmstadt, GSI & Giessen U. ), D. Boutin (Giessen U. ), H. G. Essel (Darmstadt, GSI), T. Faestermann (Stefan Meyer Inst. Subatomare Phys. ), H. Geissel (Darmstadt, GSI & Giessen U. ), S. Hess (Giessen U. ), P. Kienle (Stefan Meyer Inst. Subatomare Phys. & Michigan State U.), R. Knobel (Darmstadt, GSI & Giessen U. ) et al. 2008, Observation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like 140Pr and 142Pm Ions. Phys. Lett. B664 (2008).
[13] Karpeshin F. F., Trzhaskovskaya M. B. Triggering the 178mHf isomer and resonance conversion: contemporary problems. www. kinr. kiev. ua/NPAE_Kyiv2008/proceedings//Karpeshin_289-292. pdf162-168 DOI: 10. 1016/j.physletb.2008.04.062.
[14] Karpeshin F. F., Trzhaskovskaya M. B. Impact of the ionization of the atomic shell on the lifetime of the 229mTh isomer. J. Nuclear Physics A 969 (2018) 173–183. https://doi.org/10.1016/j. nuclphysa.2017. 0.0030375-9474.
[15] Vol A. A. (2018) The Role of the Chemically Induced Polarization of Nuclei in Biology SPG, DOI: 10. 32392/biomed. 26.
[16] M. A. Deliyergiyev, D. S. Vlasenko, Quantization in Classical Mechanics and Diffusion Mechanism of Alpha Decay, Proton and Cluster Radioactivity, Spontaneous Fission, Proceedings of the 4th Gamow International Conference on Astrophysics and Cosmology after Gamow and The 9th Gamow Summer School, Odessa, Ukraine, 17-23 August 2009, AIP Melville, New York, AIP Conf. Proc. 1206 (2009) 208-218; V. D. Rusov, S. Cht. Mavrodiev, M. A. Deliyergiyev, D. A. Vlasenko, In: “Quantum theory. Reconsideration of foundations” (New York, 2010) Vol. 1232, pp. 213-221.
[17] S. Cht. Mavrodiev, and M. A. Deliyergiyev. 2017, Computation of the Binding Energies in the Inverse Problem Framework, DOI: 10. 1142/9789813226548_0050, Conference: C16-09-04. 6 (Exotic Nuclei, p. 330-337 (2017)), p. 330-337 Proceedings, https://arxiv.org/pdf/1708.07966. pdf
[18] S. Cht. Mavrodiev1, M. A. Deliyergiyev, Decay Half-Life of Nuclei-Proton, Alpha, Cluster Decays and Spontaneous Fissions, NUCLEAR THEORY, Vol. 36 (2017) eds. M. Gaidarov, N. Minkov, Heron Press, Sofia.
[19] Cht. Mavrodiev, Numerical Generalization of Bethe- Weizsäcker Mass Formula, Proceedings of the 35-th International Workshop on Nuclear Theory (IWNT-35), Rila Mountains, 2016, Editors: M. Gaidarov and N. Minkov, Nuclear Theory, Vol. 35 (2016), ISSN 1313-2822.
[20] S. Cht. Mavrodiev, Improved generalization of Bethe-Weizsäcker mass formula, Probl. Nonlin. An. Eng. Syst, Vol. 23 (2 (48)) (2017) 46–69 PNAES ISSN 1727-687 X.
[21] Audi et al., The AME2012 atomic mass evaluation, Chin. Phys. C36 (2012) 1287.
[22] Audi et al., The NUBASE2012 evaluation of nuclear properties, Chin. Phys. C36 (2012) 1157.
[23] O.  B. Tarasov, Discovery of 60Ca and Implications for the Stability of 70Ca, Phys. Rev. Lett. 121, 022501 – Published 11 July 2018.
[24] M. Gryzinski, Phys. Rev. 115 (1959) 374-383; Phys. Rev. 138 (1965) A322-A335; Chem. Phys. 62 (1975) 2610, 2620, 2629; Int. J. Theor. Phys. 26 (1987) 967980; http: //dx. doi. org/10. 1007/BF00670821; “On atom exactly: Seven lectures on the atomic physics”, ed. by M. M. Lavrentiev (Novosibirsk: IM SF RAS, (Ser. Conferences Library, No 1, 2004); http://www.gryzinski.com
[25] N. G. Chetaev, Educational notes of Kazan University 91 book 4, Mathematics, N1, (1931) 3; Sci. Proc. Kazan Aircraft Inst. 1 (1936) 3; “The Stability of Motion” (Permagon, 1961); “Motion stability. Researches on the analytical mechanics” (Nauka, Moscow, 1962) (in Russian); Sov. Appl. Math. Mech. 24 (1960) 33; Sov. Appl. Math. Mech. 20 (1956) 309; Sov. Appl. Math. Mech. 23 (1959) 425.
Cite This Article
  • APA Style

    Mavrodiev Strachimir Chterev, Vol Alexander. (2019). Improved Numerical Generalization of the Bethe-Weizsäcker Mass Formula for Prediction the Isotope Nuclear Mass, the Mass Excess Including of Artificial Elements 119 and 120. Nuclear Science, 4(2), 11-22. https://doi.org/10.11648/j.ns.20190402.11

    Copy | Download

    ACS Style

    Mavrodiev Strachimir Chterev; Vol Alexander. Improved Numerical Generalization of the Bethe-Weizsäcker Mass Formula for Prediction the Isotope Nuclear Mass, the Mass Excess Including of Artificial Elements 119 and 120. Nucl. Sci. 2019, 4(2), 11-22. doi: 10.11648/j.ns.20190402.11

    Copy | Download

    AMA Style

    Mavrodiev Strachimir Chterev, Vol Alexander. Improved Numerical Generalization of the Bethe-Weizsäcker Mass Formula for Prediction the Isotope Nuclear Mass, the Mass Excess Including of Artificial Elements 119 and 120. Nucl Sci. 2019;4(2):11-22. doi: 10.11648/j.ns.20190402.11

    Copy | Download

  • @article{10.11648/j.ns.20190402.11,
      author = {Mavrodiev Strachimir Chterev and Vol Alexander},
      title = {Improved Numerical Generalization of the Bethe-Weizsäcker Mass Formula for Prediction the Isotope Nuclear Mass, the Mass Excess Including of Artificial Elements 119 and 120},
      journal = {Nuclear Science},
      volume = {4},
      number = {2},
      pages = {11-22},
      doi = {10.11648/j.ns.20190402.11},
      url = {https://doi.org/10.11648/j.ns.20190402.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ns.20190402.11},
      abstract = {George Gamow’s liquid drop model of the nucleus can account for most of the terms in the formula and gives rough estimates for the values of the coefficients. Its semi-numerical equation was first formulated in 1935 by Weizsäcker and in 1936 Bethe [1, 2], and although refinements have been made to the coefficients over the years, the structure of the formula remains the same today. Their formula gives a good approximation for atomic masses and several other effects, but does not explain the appearance of magic numbers of protons and neutrons, and the extra binding-energy and measure of stability that are associated with these numbers of nucleons. Mavrodiev and Deliyergiyev [3] formalized the nuclear mass problem in the inverse problem framework. This approach allowed them to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. They formulated the inverse problem for the numerically generalized semi-empirical mass formula of Bethe and von Weizsäcker going step-by-step through the AME2012 [4] nuclear database. The resulting parameterization described the measured nuclear masses of 2564 isotopes with a maximal deviation of less than 2.6 MeV, starting from the number of protons and number of neutrons equal to 1. The unknown functions in the generalized mass formula was discovered in a step-by-step way using the modified procedure realized in the algorithms developed by Aleksandrov [5-7] to solve nonlinear systems of equations via the Gauss-Newton method. In the presented herein article we describe a further development of the obtained by [3] formula by including additional factors,- magic numbers of protons, neutrons and electrons. This inclusion is based the well-known experimental data on the chemically induced polarization of nuclei and the effect of such this polarization on the rate of isotope decay. It allowed taking into account resonant interaction of the spins of nuclei and electron shells. As a result the maximal deviation from the measured nuclear masses of less than 1.9 MeV was reached. This improvement allowed prediction of the nuclear characteristics of the artificial elements 119 and 120.},
     year = {2019}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Improved Numerical Generalization of the Bethe-Weizsäcker Mass Formula for Prediction the Isotope Nuclear Mass, the Mass Excess Including of Artificial Elements 119 and 120
    AU  - Mavrodiev Strachimir Chterev
    AU  - Vol Alexander
    Y1  - 2019/07/26
    PY  - 2019
    N1  - https://doi.org/10.11648/j.ns.20190402.11
    DO  - 10.11648/j.ns.20190402.11
    T2  - Nuclear Science
    JF  - Nuclear Science
    JO  - Nuclear Science
    SP  - 11
    EP  - 22
    PB  - Science Publishing Group
    SN  - 2640-4346
    UR  - https://doi.org/10.11648/j.ns.20190402.11
    AB  - George Gamow’s liquid drop model of the nucleus can account for most of the terms in the formula and gives rough estimates for the values of the coefficients. Its semi-numerical equation was first formulated in 1935 by Weizsäcker and in 1936 Bethe [1, 2], and although refinements have been made to the coefficients over the years, the structure of the formula remains the same today. Their formula gives a good approximation for atomic masses and several other effects, but does not explain the appearance of magic numbers of protons and neutrons, and the extra binding-energy and measure of stability that are associated with these numbers of nucleons. Mavrodiev and Deliyergiyev [3] formalized the nuclear mass problem in the inverse problem framework. This approach allowed them to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. They formulated the inverse problem for the numerically generalized semi-empirical mass formula of Bethe and von Weizsäcker going step-by-step through the AME2012 [4] nuclear database. The resulting parameterization described the measured nuclear masses of 2564 isotopes with a maximal deviation of less than 2.6 MeV, starting from the number of protons and number of neutrons equal to 1. The unknown functions in the generalized mass formula was discovered in a step-by-step way using the modified procedure realized in the algorithms developed by Aleksandrov [5-7] to solve nonlinear systems of equations via the Gauss-Newton method. In the presented herein article we describe a further development of the obtained by [3] formula by including additional factors,- magic numbers of protons, neutrons and electrons. This inclusion is based the well-known experimental data on the chemically induced polarization of nuclei and the effect of such this polarization on the rate of isotope decay. It allowed taking into account resonant interaction of the spins of nuclei and electron shells. As a result the maximal deviation from the measured nuclear masses of less than 1.9 MeV was reached. This improvement allowed prediction of the nuclear characteristics of the artificial elements 119 and 120.
    VL  - 4
    IS  - 2
    ER  - 

    Copy | Download

Author Information
  • Department of the Theoretical Physics Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria

  • Department of the Applied Physics, Hebrew University of Jerusalem, Jerusalem, Israel

  • Section