Nuclear Shape Model#
Legendre polynomials expand the nuclear surface equation in spherical harmonics, allowing the modeling of nuclear shapes and deformations by quantifying deviations from spherical symmetry in nuclear physics and structure studies. The plots below show the effect the \(\beta\) parameter has on the surface of our nucleus.
Nuclear Structure \(Y_{0}^{0}\) and \(Y_{1}^{0}\)#
x y z c l m Level R
0 0.000000 0.000000e+00 0.531126 1.0 0 0 Y(l=0,m=0) 0.282095
1 0.042738 0.000000e+00 0.529404 1.0 0 0 Y(l=0,m=0) 0.282095
2 0.085199 0.000000e+00 0.524248 1.0 0 0 Y(l=0,m=0) 0.282095
3 0.127107 0.000000e+00 0.515692 1.0 0 0 Y(l=0,m=0) 0.282095
4 0.168191 0.000000e+00 0.503792 1.0 0 0 Y(l=0,m=0) 0.282095
... ... ... ... ... .. .. ... ...
1595 0.062324 -1.526501e-17 -0.186684 1.0 2 2 Y(l=2,m=2) 0.038735
1596 0.035595 -8.718283e-18 -0.144415 1.0 2 2 Y(l=2,m=2) 0.022123
1597 0.015993 -3.917045e-18 -0.098406 1.0 2 2 Y(l=2,m=2) 0.009940
1598 0.004024 -9.856431e-19 -0.049849 1.0 2 2 Y(l=2,m=2) 0.002501
1599 0.000000 -0.000000e+00 -0.000000 1.0 2 2 Y(l=2,m=2) 0.000000
[4800 rows x 8 columns]