Spontaneous fission condition of the nucleus

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SUMMARY

The spontaneous fission of an odd nucleus into two odd nuclei occurs with high probability when the ratio (Z^2)/A is greater than or equal to 45. For the fission of an even-even nucleus into two odd-odd nuclei, the Weizsäcker formula introduces a non-linear "delta" term, which is proportional to A^(-3/4). This term complicates the calculation, as it alters the conditions for fission compared to the odd nucleus scenario. A detailed understanding of the Weizsäcker formula and its implications is essential for solving this problem.

PREREQUISITES
  • Understanding of spontaneous fission and nuclear physics concepts
  • Familiarity with the Weizsäcker formula for binding energy
  • Knowledge of nuclear mass number (A) and atomic number (Z)
  • Basic mathematical skills for manipulating non-linear equations
NEXT STEPS
  • Study the Weizsäcker formula in detail, focusing on the "delta" term
  • Research the conditions for fission in even-even and odd-odd nuclei
  • Explore advanced topics in nuclear physics related to binding energy
  • Practice solving equations involving non-linear terms in nuclear fission
USEFUL FOR

Students and researchers in nuclear physics, particularly those preparing for examinations or seeking to understand the complexities of nuclear fission processes.

TheDestroyer
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As we know the spontaneous fission of an odd nucleus to an 2 odd nuclei happens with high probability when (Z^2)/A is greater than or equals 45

The conclusion of this is attached in pdf file with the post using the liquid drop nucleus model to explain the problem

The question is here now, What the condition Will be if the fission is from even-even to 2 nucleus odd-odd?

this is different than the previous situation because here appears the term "delta" in Weizsäcker formula of binding energy (Weizsäcker formula is attached in the pdf), which have a value when the nucleus is even-even or odd-odd... this term isn't linear and is proportional with the term A^(-3/4) where A is the atomic mass...

How can I solve this problem?

Thanks you, If what I've written isn't clear please let me know I've got examination on next sunday and need a solution for this...

thanks
 

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Very funny, Since I entered this forum I wanted to be answered for some real difficult question... but seems all members of this forum is students,

Isn't there PROFESSORS TO ANSWER ME??
 
Why don't you ask your professor? ;)

I would help you if you showed some work so I see were you are stucked. i.e you write down the equation/expression you want to solve.

Your question is "how to do a similar solution including the paring term" right?
 
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Dear please, I wrote the part of the odd equations, and I specified that the difference for even is only when adding the "delta" term, then we'll not be able to solve for Z^2/A as I did in odd part

Thanks
 
TheDestroyer said:
Thanks you, If what I've written isn't clear please let me know I've got examination on next sunday and need a solution for this...
To get to the final expression, it takes a very long time. Why don't you provide us with the exact equation you want to solve?
 
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