Energy levels of nuclei 40Sc and 40K as a function of semi-classical coupling angle θ1,2 within the modified surface delta-interaction

Abstract

In this work, nuclear shell model was applied using modified surface delta-interaction to calculate, in particle-hole state, the energy levels of isobar nuclei 40 Sc and 40 K. Particles are in the model space (1f 7/2 ) while the holes are found in the model space (1d 3/2 , 1s 1/2 , 1d 5/2 ). The total angular momentum and parity are identified for possible particles and holes in nuclei above. Thus, we have used a theoretical study to find relationship between energy levels and the semiclassical coupling angle θ 1 , 2 at different orbitals within particle-hole configuration. We notice the energy levels seem to follow two universal functions which depend on the semi-classical coupling angles θ 1,2 . We found the theoretical data agree to the experimental data.

Level Structure of 58Cu Within Modified Surface Delta-Interaction

“…V is the matrix element [ 11,12,14] If the 2 particles occupy the same level, the energy relative to the closed shell is: then their energies with respect to the core are given by [11,13,15] 11…”

“…where b a ,  is the angle between the vectors a j and b j . Since the length of vector j is given by ) 1 (  j j one obtains from eq (10 ) in a classical picture [6,8,13,16]…”

“…The I-dependence of the matrix element  .The radial overlaps of the particle orbits for light nuclei differ from those for heavy nuclei. The proton -neutron configurations correspond to nucleon pair having mixed isospin and one find [13,16]     1 0 ( , ) 0.5…”

“…In the mass range A =50 to 102, J. Kostensalo and J. Suhonen [9] calculated the characteristics pairing interaction for even-even) reference nuclei. We used modified surface delta interaction and surface delta interaction to investigate the excitation energies for states two-hole and twoparticle [10,11,12], one particle -one hole [13,14]. In conclusion, investigations accept the new study's purpose, primarily by the use of MSDI, which predicts low-lying levels structure of 58 Cu nuclei.…”