4. Odds, evens, and shells

2015 ◽  
Author(s):  
Frank Close
Keyword(s):  
Stable Isotopes ◽  
Binding Energy ◽  
Total Mass ◽  
Mass Formula ◽  
Fundamental Property ◽  
Alpha Decay ◽  
Magic Numbers ◽  
Particle Cluster ◽  
Semi Empirical ◽  
Uranium Fission

‘Odds, evens, and shells’ considers the fundamental property laws governing nuclear structure. It explains element stability and abundance, as well as the quantum rules, magic numbers, shells, and binding energy that explain atomic and element structure. An effective guide to stability, and the pattern of radioactive decays, is given by the semi-empirical mass formula. As nature seeks stability by minimising energy, a nucleus seeks to lower the total mass or increase the binding energy by emitting an alpha particle cluster, by beta decay, or by splitting in two, as in uranium fission. Alpha decay and technetium, the lightest element that is totally radioactive, and thus without any stable isotopes, are also described.

scholarly journals Modification of the nuclear landscape in the inverse problem framework using the generalized Bethe–Weizsäcker mass formula

2018 ◽  
Vol 27 (02) ◽  
pp. 1850015 ◽  
Author(s):  
S. Cht. Mavrodiev ◽  
M. A. Deliyergiyev
Keyword(s):  
Inverse Problem ◽  
Mass Formula ◽  
Maximum Deviation ◽  
Model Parameters ◽  
Magic Numbers ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Nuclear Mass ◽  
Nuclear Masses ◽  
Semi Empirical

We formalized the nuclear mass problem in the inverse problem framework. This approach allows us to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. The inverse problem was formulated for the numerically generalized semi-empirical mass formula of Bethe and von Weizsäcker. It was solved in a step-by-step way based on the AME2012 nuclear database. The established parametrization describes the measured nuclear masses of 2564 isotopes with a maximum deviation less than 2.6[Formula: see text]MeV, starting from the number of protons and number of neutrons equal to 1.The explicit form of unknown functions in the generalized mass formula was discovered in a step-by-step way using the modified least [Formula: see text] procedure, that realized in the algorithms which were developed by Lubomir Aleksandrov to solve the nonlinear systems of equations via the Gauss–Newton method, lets us to choose the better one between two functions with same [Formula: see text]. In the obtained generalized model, the corrections to the binding energy depend on nine proton (2, 8, 14, 20, 28, 50, 82, 108, 124) and ten neutron (2, 8, 14, 20, 28, 50, 82, 124, 152, 202) magic numbers as well on the asymptotic boundaries of their influence. The obtained results were compared with the predictions of other models.

Nuclear Physics

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Nuclear Physics ◽  
Alpha Decay ◽  
Nuclear Fission ◽  
Nuclear Potential ◽  
Magic Numbers ◽  
Ongoing Research ◽  
Strong Force ◽  
Atomic Nuclei ◽  
Nilsson Model ◽  
Semi Empirical

The chapter gives an overview of nuclear physics from the discovery of the neutron to ongoing research topics. General properties of atomic nuclei are considered: the valley of stability, the nuclear potential, the pairing of nucleons and the strong force. The semi-empirical liquid drop model is presented as a description of relatively large atomic nuclei. The nuclear shell model is described, along with its relationship to magic numbers and beta decay, and is then refined to produce the Nilsson model. Gamow tunnelling is used to explain alpha decay and the Geiger–Nuttall law. It is then applied to nuclear fission and used to calculate rates for thermonuclear fusion in stars. ITER and controlled nuclear fusion are also discussed. Production of superheavy nuclei is detailed and the existence of exotic nuclei, such as halo nuclei, is considered. The Yukawa theory of the strong force is discussed, including its relationship to QCD.

scholarly journals On the Role of Squared Neutron Number in Reducing Nuclear Binding Energy in the Light of Electromagnetic, Weak and Nuclear Gravitational Constants – A Review

2019 ◽  
pp. 1-22
Author(s):  
U. V. S. Seshavatharam ◽  
S. Lakshminarayana
Keyword(s):  
Binding Energy ◽  
Strong Coupling ◽  
Mass Formula ◽  
Neutron Number ◽  
Strong Coupling Constant ◽  
Nuclear Binding Energy ◽  
Coupling Constant ◽  
Nuclear Binding ◽  
Energy Coefficient ◽  
Semi Empirical

With reference to authors recently proposed three virtual atomic gravitational constants and nuclear elementary charge, close to stable mass numbers, it is possible to show that, squared neutron number plays a major role in reducing nuclear binding energy. In this context, Z=30 onwards, ‘inverse of the strong coupling constant’, can be inferred as a representation of the maximum strength of nuclear interaction and 10.09 MeV can be considered as a characteristic nuclear binding energy coefficient. Coulombic energy coefficient being 0.695 MeV, semi empirical mass formula - volume, surface, asymmetric and pairing energy coefficients can be shown to be 15.29 MeV, 15.29 MeV, 23.16 MeV and 10.09 MeV respectively. Volume and Surface energy terms can be represented with (A-A2/3-1)*15.29 MeV. With reference to nuclear potential of 1.162 MeV and coulombic energy coefficient, close to stable mass numbers, nuclear binding energy can be fitted with two simple terms having an effective binding energy coefficient of  [10.09-(1.162+0.695)/2] = 9.16 MeV. Nuclear binding energy can also be fitted with five terms having a single energy coefficient of 10.09 MeV. With further study, semi empirical mass formula can be simplified with respect to strong coupling constant.

A possible correction of the semi-empirical mass formula

1956 ◽  
Vol 6 (2) ◽  
pp. 345-346 ◽  
Author(s):  
G. Szamosi ◽  
M. A. Ziegler
Keyword(s):  
Mass Formula ◽  
Semi Empirical

Universal origin of heavy elements

2021 ◽  
Author(s):  
Jose Orce ◽  
Balaram Dey ◽  
Cebo Ngwetsheni ◽  
Brenden Lesch ◽  
Andile Zulu ◽  
...  
Keyword(s):  
Binding Energy ◽  
Symmetry Energy ◽  
Neutron Capture ◽  
Decay Rates ◽  
Heavy Elements ◽  
Capture Process ◽  
Atomic Nuclei ◽  
Radiative Neutron ◽  
Radiative Neutron Capture ◽  
Semi Empirical

Abstract The abundance of heavy elements above iron through the rapid neutron capture process or r-process is intimately related to the competition between neutron capture and $\beta$ decay rates, which ultimately depends on the binding energy of atomic nuclei. The well-known Bethe-Weizsacker semi-empirical mass formula describes the binding energy of ground states in nuclei with temperatures of T~0 MeV, where the nuclear symmetry energy saturates between 23-26 MeV. Here we find a larger saturation energy of ~30 MeV for nuclei at T~0.7-1.3 MeV, which corresponds to the typical temperatures where seed elements are created during the cooling down of the ejecta following neutron-star mergers and collapsars. This large symmetry energy yields a reduction of the binding energy per nucleon for neutron-rich nuclei; hence, the close in of the neutron dripline, where nuclei become unbound. This finding constrains exotic paths in the nucleosynthesis of heavy elements -- as supported by microscopic calculations of radiative neutron-capture rates -- and further supports the universal origin of heavy elements, as inferred from the abundances in extremely metal-poor stars and meteorites.

Beta-decay half-lives of the extremely neutron-rich nuclei in the closed-shell N = 50, 82, 126 groups

2021 ◽  
Author(s):  
Nguyen Kim Uyen ◽  
Kyung Yuk Chae ◽  
NgocDuy Nguyen ◽  
DuyLy Nguyen
Keyword(s):  
Half Life ◽  
Random Phase ◽  
Closed Shell ◽  
Decay Rates ◽  
Magic Numbers ◽  
Β Decay ◽  
R Process ◽  
Neutron Rich Isotopes ◽  
Semi Empirical ◽  
The Impact

Abstract The β--decay half-lives of extremely neutron-rich nuclei are important for understanding nucleosynthesis in the r-process. However, most of their half-lives are unknown or very uncertain, leading to the need for reliable calculations. In this study, we updated the coefficients in recent semi-empirical formulae using the newly updated mass (AME2020) and half-life (NUBASE2020) databases to improve the accuracy of the half-life prediction. In particular, we developed a new empirical model for better calculations of the β--decay half-lives of isotopes ranging in Z = 10 – 80 and N = 15-130. We examined the β--decay half-lives of the extremely neutron-rich isotopes at and around the neutron magic numbers of N = 50, 82, and 126 using either five different semi-empirical models or finite-range droplet model and quasi-particle random phase approximation (FRDM+QRPA) method. The β--decay rates derived from the estimated half-lives were used in calculations to evaluate the impact of the half-life uncertainties of the investigated nuclei on the abundance of the r-process. The results show that the half-lives mostly range in 0.001 < T1/2 < 100 s for the nuclei with a ratio of N/Z < 1.9; however, they differ significantly for those with the ratio of N/Z > 1.9. The half-life differences among the models were found to range from a few factors (for N/Z < 1.9 nuclei) to four orders of magnitude (for N/Z > 1.9). These discrepancies lead to a large uncertainty, which is up to four orders of magnitude, in the r-process abundance of isotopes. We also found that the multiple-reflection time-of-flight (MR-TOF) technique is preferable for precise mass measurements because its measuring timescale applies to the half-lives of the investigated nuclei. Finally, the results of this study are useful for studies on the β-decay of unstable isotopes and astrophysical simulations.

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