San José State University

applet-magic.com
Thayer Watkins
Silicon Valley
& Tornado Alley
USA

The Division of the Binding Energy of the
Triteron Between That Due to the Strong Force
and That Due to Nucleon Spin Pair Formation

The triteron, sometimes called tritium, is the Hydrogen 3 nuclide. As the name indicates, the triteron contains three nucleons, two neutrons and one proton.

The conventionally accepted figure for the binding energy of the triteron is 8.48182 MeV. Because this is computed using a mass for the neutron that is too low by 0.98638 MeV the binding energy of the triteron is 8.481821+2(0.98638)=10.4546 MeV.

According to the article, "Precise Radii of Light Nuclei from Electron Scattering," by I. Sick published in Precision Physics of Simple Atoms and Molecules (edited by Savely G. Karshenboin), the root-mean-square (rms) charge radius of the triteron is 1.755 fermi; and that of a proton is 0.895 fermi. Thus the distance from the centroid of the triangle to the center of the proton is 0.860 fermi.

For an equilateral triangle the distance between adjacent vertices is √3*(0.86)=1.49 fermi. Relative to the scale parameter of 1.522 fermi for nuclei this is 0.98. The value of W(0.98) is 0.37357.

Thus the equation to be sastified for the triteron if its spatial arrangement is that of an equilateral triangle is

2Pnp + Pnn + (4/3−4/9)(H/s0)(0.37357) = 8.481821 + 2(0.98638)
or, upon substitution of known values
2(1.98671) + Pnn + (8/9)(18.3636)(0.37357) = 10.4546
which evaluates to
3.9734 + Pnn + 6.0979 = 10.4546
and hence
Pnn = 0.3847 MeV

This figure for the binding energy for the formation of a neutron spin pair is within the realm of plausibility but it is at variance with the order of magnitude for the enhancement of binding energy associated with the incremental binding energy associated with additional neutrons. For example, consider the case of Tin.

Here the effect of an added neutron that could form a neutron pair appears to be on the order of 2 MeV. There is however a transition at nuclear magic number 82 and the enhancement is clearly smaller beyond 82. The enhance due to the formation ofa neutron-neutron is seen more precisely in the following graph.

The spike in the values near 82 neutrons is due soley to the transition. The average of the values for the 51 to 82 shell is 2.63211 MeV.

(To be continued.)


HOME PAGE OF applet-magic
HOME PAGE OF Thayer Watkins