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

Mavrodiev Strachimir Chterev; Vol Alexander

doi:doi:10.11648/j.ns.20190402.11

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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

Mavrodiev Strachimir Chterev, Vol Alexander

Published in Nuclear Science (Volume 4, Issue 2)

Received: 5 June 2019 Accepted: 15 July 2019 Published: 26 July 2019

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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.

Published in	Nuclear Science (Volume 4, Issue 2)
DOI	10.11648/j.ns.20190402.11
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), 2019. 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

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[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.
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[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.
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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

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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

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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

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@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://article.sciencepublishinggroup.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}
}

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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  -

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Author Information

Mavrodiev Strachimir Chterev

Department of the Theoretical Physics Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
Vol Alexander

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

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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

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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

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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

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@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://article.sciencepublishinggroup.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  -

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