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Home  >  Volume 28. No.1 (Nov. 2014)

47. The Effect of 1st Order Time Independent Perturbation on the Finite Size of the Nuclei of Atoms by Adamu, A. andNgadda, Y.H - Volume28, No. 1, (November, 2014), pp333 – 338
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In solving Schrödinger’s equation for the hydrogen  atom, one assumes the nucleus to be a point charge. The nucleus has a finite-size with some shape over 

which the proton charge is distributed. In this work, we first showed that the nucleus of atoms have finite size, and then examined the potential energy for 

both the point-like and the finite-size nucleus of  hydrogen atom. The results obtained revealed the finite size charge distribution of nucleus which is not only spherical but also assumes a cigar-like or oblate (discuss) shape. The point-like and the finite-size nucleus of hydrogen atom potentials are plotted against the radius of the nucleus. The time-independent perturbation method was applied to 

calculate energy shift due to finite-size nature ofthe nucleus of hydrogen atom. 

The relative energy change calculated from the 1

st order correction in the ground state of hydrogen atom was extended for light, medium and large nuclei and the results were plotted graphically as function of radius. The plots have shown that, due to the finite-size nature, the energy level of a nucleus is shifted upwards and its magnitude depends on the size (nucleon distribution) of the nucleus. Thus, for 

isotopes of a given element where the proton numberis the same but the mass number and therefore the nuclear radii are different, the energy correction will 

be different and due to this the spectral lines will not coincide completely.This correction is one of many corrections that need to be added to the atomic model. 

Keywords:Schrödinger’s equation, hydrogen atom, point nucleus, finite size nucleus, potential energy, Hamiltonian, perturbation, relative energy change, nuclear radius