Editing Semi-empirical mass formula (section)

==Calculating coefficients==
The coefficients are calculated by fitting to experimentally measured masses of nuclei. Their values can vary depending on how they are fitted to the data and which unit is used to express the mass. Several examples are as shown below.

{|class="wikitable sortable"
! 
! Eisberg & Resnick<ref>{{cite book |last1=Eisberg |first1=Robert |last2=Resnick |first2=Robert |author-link2=Robert Resnick |year=1985 |title=Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles |url=https://archive.org/details/quantumphysicsof00eisb |url-access=registration |edition=Second |publisher=John Wiley & Sons |isbn=0-471-87373-X |page=[https://archive.org/details/quantumphysicsof00eisb/page/528 528]}}</ref>
! Least-squares fit (1)
! Least-squares fit (2)<ref>{{cite book |last1=Alonso |first1=Marcelo |url=https://archive.org/details/theatreofmixedme00kost/ |title=Fundamental University Physics. Vol. III. Quantum and Statistical Physics |last2=Finn |first2=Edward J. |publisher=[[Addison-Wesley Publishing Company]] |year=1969 |pages=297}}</ref>
! Rohlf<ref name=Rohlf>{{cite book |last=Rohlf |first=J. W. |year=1994 |title=Modern Physics from &alpha; to Z<sup>0</sup> |publisher=[[John Wiley & Sons]] |isbn=978-0471572701}}</ref>
! Wapstra<ref>{{cite book |last=Wapstra |first=A. H. |title=External Properties of Atomic Nuclei / Äussere Eigenschaften der Atomkerne |year=1958 |chapter=Atomic Masses of Nuclides |editor-last=Flügge |editor-first=S. |series=Encyclopedia of Physics |publisher=[[Springer (publisher)|Springer]] |doi=10.1007/978-3-642-45901-6_1 |isbn=978-3-642-45902-3 |bibcode=1958HDP....38....1W |volume=8 / 38 / 1 |pages=1–37}}</ref>
|-
! unit
| [[Atomic mass unit|u]]
| MeV
| MeV
| MeV
| MeV
|-
! <math>a_{\rm V}</math>
| 0.01691
| 15.8
| 15.76
| 15.75
| 14.1
|-
! <math>a_{\rm S}</math>
| 0.01911
| 18.3
| 17.81
| 17.8
| 13
|-
! <math>a_{\rm C}</math>
| 0.000763{{efn-lg|This model uses <math>Z^2</math> in the numerator of the Coulomb term.}}
| 0.714
| 0.711
| 0.711
| 0.595
|-
! <math>a_{\rm A}</math>
| 0.10175{{efn-lg|This model uses <math>(Z-A/2)^2</math> in the numerator of the Asymmetry term.}}
| 23.2
| 23.702
| 23.7
| 19
|-
! <math>a_{\rm P}</math>
| 0.012
| 12
| 34
| 11.18
| 33.5
|-
!<math>k_{\rm P}</math>
| −1/2
| −1/2
| −3/4
| −1/2
| −3/4
|-
! <math>\delta_0</math> (even-even)
| <math>-0.012 \over A^{1/2}</math>
| <math>+12 \over A^{1/2}</math>
| <math>+34 \over A^{3/4}</math>
| <math>+11.18 \over A^{1/2}</math>
| <math>+33.5 \over A^{3/4}</math>
|-
! <math>\delta_0</math> (odd-odd)
| <math>+0.012 \over A^{1/2}</math>
| <math>-12 \over A^{1/2}</math>
| <math>-34 \over A^{3/4}</math>
| <math>-11.18 \over A^{1/2}</math>
| <math>-33.5 \over A^{3/4}</math>
|-
! <math>\delta_0</math> (even-odd, odd-even)
| 0
| 0
| 0
| 0
| 0
|-
| colspan="6" | {{notelist-lg}}
|}

The formula does not consider the internal [[Nuclear shell model|shell structure]] of the nucleus.

The semi-empirical mass formula therefore provides a good fit to heavier nuclei, and a poor fit to very light nuclei, especially [[helium-4|<sup>4</sup>He]]. For light nuclei, it is usually better to use a model that takes this shell structure into account.