Study Of Nuclear Structure Properties Based On Skyrme HFB Approach

In this paper,under the theoretical framework of energy density functional theory,we use the Skyrme Hartree-Fock-Bogoliubov?HFB?method to study the structural characteristics of atomic nuclei.It mainly includes two aspects:one is the systematic calculation of the binding energy and charge radius of Sn isotope chain and nuclei near ¹³²Sn;the other is the study of the effect of different correlation processing methods on the nuclear deformation.We have performed Skyrme density functional theory?DFT?calculations of nuclei around ¹³²Sn to study whether the odd-even interlacing behavior around N=82can be reproduced.By using the Skyrme force SLy4 and Sk M*,we test the mixed,volume and surface type of pairing forces with or without the Lipkin-Nogami approximation and particle number projection.The UNEDF parameter sets are also used.We found that for the odd-even mass staggering,the choice of Skyrme forces can change the results quit a lot.UNEDF1 and UNEDF2 DFT can reproduce the trend of the abnormal odd-even staggering around N=82 but UNEDF0 can not.For other related observables in the same nuclear region,the systematics of binding energies are mostly affected by Skyrme forces.By studying the one-neutron and two-neutron separation energies,the drip line position can be influenced by the mean-field and the treatment of pairing correlations,thus the uncertainty is large.For the calculated deformations,without pairing,a larger deformation is prefered,and in the HFB,and HFBLN approximation,a smaller deformation is predicted for the same nuclei.The charge radii by HF approximations are already close to experimental data.The results are further improved by the HFB approximations.However,HFBLN gives larger charge radii and stronger staggerings.We have investigated the effect of different pairing correlations,e.g.,HFB,HFBLN,and particle number projection on HFBLN,etc.,on the potential energy surface?PES?calculations and ground-state energy.We also tested the effect of different pairing force,such as volume-pairing,surface-pairing,mixed-pairing force.We studied typical doubly-magic nuclei,such as ¹⁶O,⁴⁰Ca,¹⁰⁰Sn and ²⁰⁸Pb,which have spherical shape in their ground states.We studied the typical deformed nucleus⁴⁸Cr,and the binding energies of Cr and Fe isotopes.The PES of superheavy nucleus²⁹⁸Fl is also studied.It is learned that the deformed minimum is not changed much by different pairing correlations.The pairing correlations bring about several Me V to the total binding energies.The correlation energy brought by HFBLN is more than that by HFB approximation,and that by projection method is increase further.The softness of the deformed minimum is also changed by pairing correlations.The one by HFBLN is softer than the one by HFB.However,the deformed minimum become explicit by projection method.Pairing correlation can lower down the barrier in the PES.In the same pairing correlation approximation,PESs by mixed-pairing and volume-pairing force are similar.It seems that in the PES calculations,the surface pairing force can bring more pairing correlations,thus the effect of surface pairing force is larger than that volume-and mixed-pairing forces.