Is there a formula for the elusive binding energy of heavy nuclei?

In summary, there is no semi-empirical binding energy formula for the heavy nuclear 'island of stability'. The liquid drop model, represented by the surface and density plots in the attachments, does not fully account for stability as it is influenced by microscopic corrections. However, modern models incorporating a micro-macro formula predict the existence of the island. References such as Moller et al. and Lunney et al. provide further information on this topic.
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Binding Energy...

Is there a semi-empirical binding energy formula for the heavy nuclear 'island of stability'?

The attachments are a plot of the nucleotide chart based upon the semi-empirical binding energy formula for the liquid drop model:

'12a' is a surface plot.
'12b' is a density plot.

The axis are:
x - proton number
y - neutron number
z - binding energy per atomic mass unit (Mev*amu^-1)

I am still in the rough with this software, however anyone's critiques, corrections are welcome.

 

Attachments

  • 12a.JPG
    12a.JPG
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  • 12b.JPG
    12b.JPG
    11.8 KB · Views: 420
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Fast answer is no, because stability is always due to the microscopic correction, not to the liquid drop properties. Now, most modern models use a micro-macro formula, so they predict the island.

Check the references of my http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:nucl-th/0312003 especially Moller et al. and Lunney et al.
 
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Related to Is there a formula for the elusive binding energy of heavy nuclei?

1. What is binding energy and why is it important in the study of heavy nuclei?

Binding energy refers to the amount of energy needed to break apart an atomic nucleus into its constituent parts. In the study of heavy nuclei, binding energy is important because it provides insights into the stability and structure of these nuclei. It also plays a crucial role in nuclear reactions and energy production.

2. Is there a specific formula for calculating the binding energy of heavy nuclei?

Yes, there is a formula known as the Weizsäcker formula or the semi-empirical mass formula that is commonly used to calculate the binding energy of heavy nuclei. This formula takes into account the number of protons and neutrons in the nucleus, as well as their arrangement and interactions, to determine the overall binding energy.

3. How accurate is the Weizsäcker formula in predicting the binding energy of heavy nuclei?

The Weizsäcker formula is considered to be a good approximation for calculating the binding energy of heavy nuclei. However, it is not always accurate as it does not account for certain nuclear properties and effects, such as nuclear spin and nuclear deformation. Thus, more sophisticated and comprehensive models are being developed to improve the accuracy of binding energy calculations.

4. Can the binding energy of heavy nuclei be experimentally measured?

Yes, the binding energy of heavy nuclei can be experimentally measured using techniques such as nuclear mass spectrometry. By measuring the masses of different isotopes of a particular element, the binding energy can be determined by comparing it to the mass of the individual protons and neutrons that make up the nucleus.

5. How does the binding energy of heavy nuclei affect nuclear stability?

The binding energy of heavy nuclei is directly related to their stability. Generally, the higher the binding energy, the more stable the nucleus is. This is because a higher binding energy means that it takes more energy to break apart the nucleus, making it less likely to undergo radioactive decay. Thus, the binding energy is an important factor in determining the stability and longevity of heavy nuclei.

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