The breaking of spin symmetry in the single-particle resonances in deformed nuclei

The exploration of spin symmetry (SS) in nuclear physics has been instrumental in identifying atomic nucleus structures.In this study,we solve the Dirac equation from the relativistic mean field (RMF) in complex momentum representation.We investigated SS and its breaking in single-particle resonant states within deformed nuclei,with a focus on the illustrative nucleus168Er.This was the initial discovery of a resonant spin doublet in a deformed nucleus,with the expectation of the SS approaching the continuum threshold.With increasing single-particle energy,the splitting of the resonant spin doublets widened significantly.This escalating splitting implies diminishing adherence to the SS,indicating a departure from the expected behavior as the energy levels increase.We also analyzed the width of the resonant states,showing that lower orbital angular momentum resonances possess shorter decay times and that SS is preserved within broad resonant doublets,as opposed to narrow resonant doublets.Comparing the radial density of the upper components for the bound-state and resonant-state doublets,it becomes evident that while SS is well-preserved in the bound states,it deteriorates in the resonant states.The impact of nuclear deformation (β_(2)) on SS was examined,demonstrating that an increase in β_(2) resulted in higher energy and width splitting in the resonant spin doublets,which is attributed to increased component mixing.Furthermore,the sensitivity of spin doublets to various potential parameters such as surface diffuseness (a),radius (R),and depth (Σ0) is discussed,emphasizing the role of these parameters in SS.This study provides valuable insights into the behavior of spin doublets in deformed nuclei and their interplay with the nuclear structure,thereby advancing our understanding of SS in the resonance state.

Simplification of Double Folding Model Calculations in Study of Interaction Between Two Deformed Nuclei

The Double Folding （DF） model calculation of the internuclear potential in heavy-ion interactions when the participant nuclei are deformed in their ground states involves a six-dimensional integral. Using the multipole expansion in these calculations, the DF six-dimensional integral reduce to the sum of the products of three single-dimensional integrals. In this paper we have presented a procedure for the calculation of the radius dependent functions in the multipole expansion of the nuclear density and their Fourier transforms. We have also reduced the DF model integrals to the sum of the single dimensional integrals using the obtained relations for the radius dependent functions in the multipole expansion and their Fourier transforms.

Theoretical calculations of proton emission half-lives based on a deformed Gamow-like model

In this study,proton emission half-lives were investigated for deformed proton emitters with 53≤Z≤83based on the presented deformed Gamow-like model,where the deformation effect was included in the Coulomb potential.The experimental half-lives of proton emitters can be reproduced within a factor of 3.45.For comparison,the results from the universal decay law and the new Geiger-Nuttall law are also presented.Furthermore,the relevance of the half-lives to the angular momentum l for ^(117)La,^(121)Pr,^(135)Tb,and ^(141)Ho were analyzed,and the corresponding possible values of l were proposed:l=3,3,4,4.

An angle-dependent potential and alpha-decay half-lives of deformed nuclei for 67≤Z≤91

The half-lives of deformed nuclei are reported for 67≤Z≤91. We consider an angle-dependent potential which yields multiple approximations. The results are in better agreement with the experimental data when the multiple approximation is solely considered for the daughter nuclei.

Rotating deformed halo nuclei and shape decoupling effects

To explore the rotational excitation of deformed halo nuclei,the angular momentum projection(AMP)has been implemented in the deformed relativistic Hartree-Bogoliubov theory in continuum(DRHBc),in which both the mean field and collective wave functions are expanded in terms of Dirac WoodsSaxon basis.The DRHBc+AMP approach self-consistently describes the coupling between single particle bound states and the continuum not only in the ground state but also in rotational states.The rotational modes of deformed halos in ^(42,44)Mg are investigated by studying properties of rotational states such as the excitation energy,configuration,and density distribution.Our study demonstrates that the deformed halo structure persists from the ground state in the intrinsic frame to collective states.Especially,the typical behavior of shape decoupling effects in rotating deformed halo nuclei is revealed.

Analysis of the energy spectra of ground states of deformed nuclei in the rare-earth region

The 62Sm, 64Gd, 66Dy, 70Yb, 72Hf and 74W nuclei are classified as deformed nuclei. Low-lying bands are one of the most fundamental excitation modes in the energy spectra of deformed nuclei. In this paper a theoretical analysis of the experimental data within the phenomenological model is presented. The energy spectra of ground states are calculated. It is found that the low-lying spectra of ground band states are in good agreement with the experimental data.

Investigation of deformed nuclei with a new potential combination

We investigate the alpha-decay half-lives of non-spherical nuclei with the Yukawa potential as the prox- imity potential and an angle-dependent term that accounts for the deformation effects and apply the results to Ho, Tb, Lu, Tin, Ta, Hf, Yb, Re, Ir, Pt, Au, Po, etc. as examples. The comparison with the existing data is encouraging.

Study of Even ^(230-238)U Isotopes by Using Cranked Nilsson Model,Single Particle Schrodinger Fluid and Collective Model

The Cranking Nilsson model is applied to calculate the single-particle energy eigenvalues and eigenfunctions of nuclei in a strongly deformed potential. Accordingly, The L. D. Energy, the Strutinsky inertia, the L. D. inertia, the volume conservation factor , the smoothed energy, the BCS energy, the G-value and the electric quadrupole moment of the five uranium isotopes: 230U, 232U, 234U, 236U and 238U are calculated as functions of the deformation parameter. Furthermore, the single-particle Schrodinger fluid is applied to calculate the rigid-body model, the cranking-model and the equilibrium-model moments of inertia of the five uranium isotopes. Moreover, the collective model is applied to calculate the rotational energies of these isotopes. The best potential and deformation parameters are also given.

Islands of stability and quasi-magic numbers for super- and ultra-heavy nuclei

In the framework of Strutinsky＇s approach, we calculated the shell and the residual pairing correction energies for 5569 even-even nuclei in the range 72 ≤ Z ≤ 282 and 96≤N ≤ 540. Quasi-magic numbers and deformed islands of stability that reside in a range defined by Green＇s formula and the two-neutrons drip line are introduced. We present 36 quasi-magic proton and 53 quasi-magic neutron magic numbers that contribute to the formation of 133 deformed islands of stability along the N-Z space. The quasi-magic proton and neutron magic numbers volatile as the mass number increases and other magic numbers take over. Consequently, the deformed islands of stability fail to exhibit a pattern along the search space covered.

Nuclear longitudinal form factors for axially deformed charge distributions expanded by nonorthogonal basis functions

In this paper,the nuclear longitudinal form factors are systematically studied from the intrinsic charge multipoles.For axially deformed nuclei,two different types of density profiles are used to describe their charge distributions.For the same charge distributions expanded with different basis functions,the corresponding longitudinal form factors are derived and compared with each other.Results show the multipoles C_λ of longitudinal form factors are independent of the basis functions of charge distributions.Further numerical calculations of longitudinal form factors of^（12）C indicates that the C_0 multipole reflects the contributions of spherical components of all nonorthogonal basis functions.For deformed nuclei,their charge RMS radii can also be determined accurately by the C_0 measurement.The studies in this paper examine the model-independent properties of electron scattering,which are useful for interpreting electron scattering experiments on exotic deformed nuclei.

Study of weakly-bound odd-A nuclei with quasiparticle blocking

The coordinate-space Hartree-Fock-Bogoliubov（HFB） approach with quasiparticle blocking has been applied to study the odd-A weakly bound nuclei ^17,19B and ^37Mg,in which halo structures have been reported in experiments.The Skyrme nuclear forces SLy4 and UNEDF1 have been adopted in our calculations.The results with and without blocking have been compared to demonstrate the emergence of deformed halo structures due to blocking effects.In our calculations,^19B and ^37Mg have remarkable features of deformed halos.

Nuclear structure study of some bubble nuclei in the light mass region using mean field formalism

We study the structural properties of some light mass nuclei using two different formalisms（i） a recently developed simple effective interaction in the frame work of microscopic non-relativistic Hartree-Fock method and（ii）the well-known relativistic mean field approach with NL3 parameter set. The bulk properties like binding energy, root mean square radii and quadrupole deformation parameter are estimated and compared with the available experimental data. The predicted results of both the formalisms are well comparable with the experimental observations. The analysis of density profiles of these light mass nuclei suggest that22 O,23F,34 Si and46Ar have bubble like structure.

Projected total energy surface description for axial shape asymmetry in ^(172)W

The projected total energy surface(PTES)approach has been developed based on the triaxial projected shell model(TPSM)hybridized with the macroscopic–microscopic method.The total energy of an atomic nucleus is decomposed into macroscopic,microscopic and rotational terms.The macroscopic and microscopic components are described with the liquid drop model and Strutinsky method,respectively,and the rotational energy is given by the TPSM,the term beyond the mean field.To test theory,the PTES calculations have been carried out for the yrast states of the well deformed rare earth nucleus172W,and the theoretical results are in good agreement with the experimental data.By using the equilibrium quardrupole deformations(ε2andγ)determined by the PTES,the calculation of the transition quardrupole moment(Qt)in function of spin also reproduces the experimental data.A comparison between the PTES and TRS methods has been made for theoretical and application uses.

Systematic dependence of SFE＊B(E2)↑ and ROTE＊B(E2)↑on N_pN_n in the framework of shape fluctuation model

A systematic dependence of shape fluctuation energy product SFE ＊ B（E2）↑ and rotational energy product ROTE ＊ B（E2）↑ on the valence nucleon product Np Nn is carried out in the Z = 50-82,N = 82-126 major shell space.For the shape transitional nuclei,the product SFE＊B（E2）↑ drops to zero and becomes negative,indicating direct dependence on N_pN_n.A relative rise,on the other hand,is observed in the product ROTE＊B（E2） ↑plotted against N_pN_n for all the nuclei in Z = 50-82 and N = 82-126.In the N 〉 104 region,large positive values of the product SFE ＊ B（E2） ↑ are observed for the Pt nucleus,which indicates sphericity.A systematic study of the product SFE ＊ B（E2）↑ and ROTE ＊ B（E2） ↑ with atomic number Z is also discussed.The products SFE ＊ B（E2） ↑and ROTE ＊ B（E2） ↑ vary sharply with Z for the N = 88 isotones.We discuss here for the first time the correlation between SFE ＊ B（E2） ↑ and ROTE ＊ B（E2） ↑ with valence nucleon product N_pN_n.