Effect Of Tensor Force Research Articles

The role of tensor force in heavy-ion fusion dynamics

The tensor force is implemented into the time-dependent Hartree–Fock (TDHF) theory so that both exotic and stable collision partners, as well as their dynamics in heavy-ion fusion, can be described microscopically. The role of tensor force on fusion dynamics is systematically investigated for Ca40+Ca40, Ca40+Ca48, Ca48+Ca48, Ca48+Ni56, and Ni56+Ni56 reactions which vary by the total number of spin-unsaturated magic numbers in target and projectile. A notable effect on fusion barriers and cross sections is observed by the inclusion of tensor force. The origin of this effect is analyzed. The influence of isoscalar and isovector tensor terms is investigated with the TIJ forces. These effects of tensor force in fusion dynamics are essentially attributed to the shift of low-lying vibration states of colliding partners and nucleon transfer in the asymmetric reactions. Our calculations of above-barrier fusion cross sections also show that tensor force does not significantly affect the dynamical dissipation at near-barrier energies.

Effects of tensor forces in nuclear spin–orbit splittings from ab initio calculations

A systematic and specific pattern due to the effects of the tensor forces is found in the evolution of spin–orbit splittings in neutron drops. This result is obtained from relativistic Brueckner–Hartree–Fock theory using the bare nucleon–nucleon interaction. It forms an important guide for future microscopic derivations of relativistic and nonrelativistic nuclear energy density functionals.

Nuclear structure investigation of neutron-rich Mn isotopes

Structural evolution of odd-even and odd-odd Mn isotopes from the valley of stability up to neutron dripline is studied in the framework of the self-consistent mean-field theory of Hartree–Fock–Bogoliubov. Three Skyrme effective interactions, namely, SLy4, SLy5 and SLy5T, are employed to investigate the tensor force effect on the ground-state properties. It is shown that the calculated quantities with the SLy4 interaction correctly reproduce the available experimental data and agree well with finite range droplet model and relativistic mean-field predictions. An inconsistency has been observed between the curves of the separation energies and that of the charge radius around N = 40. It is explained by the flatness of the potential energy curves in this region. The SLy5 and SLy5T results point to the necessity to refit all the Skyrme parameters after including the tensor terms.

Tensor force effect on the evolution of single-particle energies in some isotopic chains in the relativistic Hartree–Fock approximation

Within a nonlinear relativistic Hartree–Fock approximation combined with the BCS method, we study the effect of the nucleon–nucleon tensor force of the π-exchange potential on the spin- and pseudospin–orbit doublets along the Ca and Sn isotopic chains.We show how the self-consistent tensor force effect modifies the splitting of both kinds of doublets in an interdependent form, leading, quite generally, to opposite effects in the accomplishment of the spin and pseudospin symmetries (the one is restored, the other one deteriorates and vice versa). The ordering of the single-particle energy levels is crucial to this respect.Also, we observe a mutual dependence on the evolution of the shell closure gap Z = 50 and the energy band outside the core, along the Sn chain, as due to the tensor force. In fact, when the shell gap is quenched the outside energy band is enlarged, and vice versa. A reduction of the strength of the pion tensor force with respect to its experimental value from the nucleon–nucleon scattering is needed to get results closer to the experiment. Pairing correlations act to some extent in the opposite direction of the tensor term of the one-pion-exchange force.

Hybridization of tensor-optimized and high-momentum antisymmetrized molecular dynamics for light nuclei with bare interaction

Many-body correlations play an essential role in the ab initio description of nuclei with nuclear bare interactions. We propose a new framework to describe light nuclei by the hybridization of the tensor-optimized antisymmetrized molecular dynamics (TOAMD) and the high-momentum AMD (HM-AMD), which we call “HM-TOAMD.” In this framework, we describe the many-body correlations in terms of not only the correlation functions in TOAMD, but also the high-momentum pairs in the AMD wave function. With the bare nucleon–nucleon interaction AV8|$^\prime$|⁠, we sufficiently reproduce the energy and radius of the |${^3}$|H nucleus in HM-TOAMD. The effects of tensor force and short-range repulsion in the bare interaction are nicely described in this new framework. We also discuss the convergence in calculation and flexibility of the model space for this new method.

Inelastic Longitudinal C2 Form Factors with Core-Polarization Effects for 10B Nucleus

An effective two-body density operator for point nucleon system folded with the full two-body correlations (which include the tensor correlations and short-range correlations), which take account of the effect of the strong tensor force and the strong short-range repulsion in the nucleon–nucleon forces, is produced and used to derive an explicit form for ground-state two-body charge density distributions. The inelastic longitudinal form factors C2 are calculated using this transition charge density with excitation of the levels in 10B (J π , T):(1+, 0) at E x = 0.718 MeV, (1+, 0) at E x = 2.154 MeV, (2+, 0) at E x = 3.587 MeV, (3+, 0) at E x = 4.774 MeV, (2+, 0) at E x = 5.920 MeV, and (4+, 0) at E x = 6.025 MeV. In this work, the core-polarization transition density is evaluated by adopting the shape of Tassie model together with the derived form of the ground-state two-body charge density distributions with the effect of higher occupation probabilities η. It is noticed that the core-polarization effects which represent the collective modes are essential in obtaining a remarkable agreement between the calculated inelastic longitudinal F(q)s and those of the experimental data.

Skyrme tensor force in the collision16O+40Ca

The role of tensor force is investigated by using the time-dependent Hartree-Fock (TDHF) theory in the collision 16 O+40 Ca. The full tensor force is incorporated in our TDHF implementation. The calculations are performed in three-dimensional Cartesian coordinate without any symmetry restrictions. We study the effect of tensor force on Coulomb barrier, upper fusion threshold energy, and energy contribution of the time-odd and tensor terms in Skyrme energy functional. The Coulomb barrier obtained from the energy functional with frozen density approximation is compared with the available experimental data. We find that the tensor force may change the upper fusion threshold energy in the order of a few MeV for the collision 16 O+40 Ca. The tensor force has a non-negligible effect in heavy-ion collisions.

Effects of a realistic tensor force on nuclear quadrupole deformation near the “shore” of the island of inversion

The M3Y-type semirealistic interaction is applied to deformed nuclei for the first time. Constrained Hartree-Fock calculations assuming axial symmetry are implemented for the $N=20$ isotones $^{30}\mathrm{Ne}$, $^{32}\mathrm{Mg}$, $^{34}\mathrm{Si}$ and the $N=28$ isotones $^{40}\mathrm{Mg}$, $^{42}\mathrm{Si}$, $^{44}\mathrm{S}$ with the M3Y-P6 interaction. The results match the experimental data well. Effects of the realistic tensor force on the nuclear quadrupole deformation are investigated in relation to the loss of the $N=20$ and 28 magic numbers. The tensor force is confirmed to favor the deformation for the $N=28$ nuclei owing to the closure of the $jj$ shell (i.e., $n0{f}_{7/2}$), while favoring the sphericity for the $N=20$ nuclei owing to the $\ensuremath{\ell}s$ closure of $N=20$.

Interplay between tensor force and deformation in even–even nuclei

In this work we study the effect of the nuclear tensor force on properties related with deformation. We focus on isotopes in the Mg, Si, S, Ar, Sr and Zr chains within the Hartree–Fock–Bogoliubov theory using the D1ST2a Gogny interaction. Contributions to the tensor energy in terms of saturated and unsaturated subshells are analyzed. Like–particle and proton–neutron parts of the tensor term are independently examinated. We found that the tensor term may considerably modify the potential energy landscapes and change the ground state shape. We analyze too how the pairing characteristics of the ground state change when the tensor force is included.

Effect of a tensor force on the proton bubble structure ofHg206

The proton density distribution of $^{206}\mathrm{Hg}$ is calculated in the framework of the Skyrme-Hartree-Fock approach with the SLy5, SLy5 + T, and SLy5 + ${\mathrm{T}}_{w}$ interactions. It is shown that the central density drops strongly with the SLy5 and SLy5 + T interactions due to the vacancy of the $3{s}_{1/2}$ orbital. This means that the density depression in the interior of the nucleus is not so much influenced by the tensor force of the SLy5 + T interaction. However, with the SLy5 + ${\mathrm{T}}_{w}$ interaction the bubble structure does not exist because the tensor force effect of this interaction leads to the inversion between the single-proton states $3{s}_{1/2}$ and $1{h}_{11/2}$ $(3{s}_{1/2}\ensuremath{-}1{h}_{11/2}$ inversion) so that the $3{s}_{1/2}$ state is fully occupied by protons. In addition, a detailed discussion on the antibubble effect from the pairing interaction is performed by using the Skyrme-Hartree-Fock-Bogoliubov approach. It is found that a proton bubble structure in $^{206}\mathrm{Hg}$ is unlikely to appear because of the paring correlation.

Effect of tensor force on the density dependence of symmetry energy within the BHF framework

The effect of tensor force on the density dependence of nuclear symmetry energy has been investigated within the framework of the Brueckner-Hartree-Fock (BHF) approach. It is shown that the tensor force manifests its effect via the tensor 3SD1 channel. The density dependence of symmetry energy Esym turns out to be determined essentially by the tensor force from the π meson and ρ meson exchanges via the 3SD1 coupled channel. Increasing the strength of the tensor component due to the ρ-meson exchange tends to enhance the repulsion of the equation of state of symmetric nuclear matter and leads to the reduction of symmetry energy. The present results confirm the dominant role played by the tensor force in determining nuclear symmetry energy and its density dependence within the microscopic BHF framework.

Tensor force effect on incompressibility of bubble nucleus

The tensor force effect on the isoscalar giant monopole resonance (ISGMR) of 46 Ar is investigated in the framework of Hartree–Fock (HF) + random phase approximation (RPA) approach with the Skyrme interactions SLy5, SLy5+T and SLy5+ T w. By using the ISGMR excitation energy, the incompressibility value of 46 Ar is extracted. It is shown that the incompressibility is enhanced with the SLy5+T interaction compared to the one with the SLy5 interaction. However, the SLy5+ T w interaction makes the incompressibility smaller because of the bubble structure of 46 Ar .

Tensor Force Effect on Shape Coexistence of N = 28 Neutron-Rich Isotones

The tensor force effect on potential energy surfaces of the N = 28 neutron-rich isotones is investigated by using the deformed Skyrme—Hartree—Fock—Bogoliubov approach with the T22 interaction. It is found that, without the tensor force, 40Mg and 46Ar have prolate and spherical ground states, respectively. The ground states of 42Si and 44S are oblate. The shape coexistence in 40Mg, 42Si and 44S is evident. However, the ground state deformations of these isotones are not changed and the shape coexistence in 42Si and 44S vanishes when the tensor force is switched on. Taking 42Si as an example, the disappearance of the shape coexistence is understood by analyzing the tensor force effect on the shell correction energies.

Tensor force effect on single-proton energy levels of oxygen isotopes

In the framework of the Hartree-Fock approach the proton spin-orbital splittings of the 1p orbits and the shell gaps in the oxygen isotopes are investigated with the interactions SLy5+T,SLy5+Tw, SGII+Te1, SGII+Te2, SGII+Te3 and many sets of the TIJ interactions. All of the interactions are the Skyrme interactions and contain a tensor component (tensor force). It is shown that the evolution of the single-proton levels for the oxygen isotopes is sensitive to a parameter β T which is associated with the tensor force strength of the Skyrme interactions. To understand this phenomenon, we systematically analyze the dependence of the spin-orbit splittings and shell gaps on the parameter β T in terms of the spin-orbit potential and the corresponding wave function. We find that the Skyrme interactions can be classified into two groups: (a) T21, T32, T43, T54, SLy5+T, SLy5+Tw, SGII+Te1 and SGII+Te2, which can roughly reproduce the experimental shell gaps of the oxygen isotopes; (b) T1J and SGII+Te3, which can not reproduce the experimental shell gaps.

Effect of tensor force on dissipation dynamics in time-dependent Hartree-Fock theory

The role of tensor force on the collision dynamics of 16O+16O is investigated in the framework of a fully three-dimensional time-dependent Hartree-Fock theory. The calculations are performed with modern Skyrme energy functional plus tensor terms. Particular attention is given on the analysis of dissipation dynamics in heavy-ion collisions. The energy dissipation is found to decrease as an initial bombarding energy increases in deep-inelastic collisions for all the Skyrme parameter sets studied here because of the competition between the collective motion and the single-particle degrees of freedom. We reveal that the tensor forces may either enhance or reduce the energy dissipation depending on the different parameter sets. The fusion cross section without tensor force overestimates the experimental value by about 25%, while the calculation with tensor force T11 has good agreement with experimental cross section.

Tensor force effects and high-momentum components in the nuclear symmetry energy

We analyze microscopic many-body calculations of the nuclear symmetry energy and its density dependence. The calculations are performed in the framework of the Brueckner-Hartree-Fock and the Self-Consistent Green's Functions methods. Within Brueckner-Hartree-Fock, the Hellmann-Feynman theorem gives access to the kinetic energy contribution as well as the contributions of the different components of the nucleon-nucleon interaction. The tensor component gives the largest contribution to the symmetry energy. The decomposition of the symmetry energy in a kinetic part and a potential energy part provides physical insight on the correlated nature of the system, indicating that neutron matter is less correlated than symmetric nuclear matter. Within the Self-Consistent Green's Function approach, we compute the momentum distributions and we identify the effects of the high momentum components in the symmetry energy. The results are obtained for the realistic interaction Argonne V18 potential, supplemented by the Urbana IX three-body force in the Brueckner-Hartree-Fock calculations.

Effect of Tensor Force on the Halo Structure of 29Ne and 31Ne

The structure of Ne isotopes has been investigated by using deformed Skyrme—Hartree—Fock (SHF) method and BCS approximation. Especially the effect of tensor force on the halo structure of 29Ne and 31Ne is discussed. To this end, the tensor contributions are considered to the energy density function and the single particle potential in SHF theory. For comparison, four Skyrme interactions are used: SLy5 and SGII without tensor force, and SLy5+T and SGII+T with tensor force. The results indicate that the inclusion of tensor force shows a more pronounced halo structure for 31Ne.

DETAILED INVESTIGATION OF THE TENSOR FORCE ON THE EVALUATION OF THE SINGLE PARTICLE LEVELS OF Z = 28 AND Z = 82 NUCLEI

In this work, effects of tensor force on the evaluation of shell structure of Z = 28 and Z = 82 isotopes are investigated in the framework of Hartree–Fock+BCS approach. Skyrme type SLy5 and SIII interactions are used with and without tensor interaction. The effect of tensor force on the gap evaluation, single particle energies and spin-orbit splittings of the selected isotopic chain are presented. Pairing energy results are also discussed. It is shown that tensor force plays a crucial role in the evaluation of the single particle states and changing spin-orbit splittings of Nickel and Lead isotopic chain.

Tensor force effect on proton shell structure in neutron-rich Ca isotopes

In the framework of the Skyrme-Hartree-Fock approach with 36 sets of the TIJ parameterizations, the tensor force effect on the evolution of the single-proton states in the calcium isotopes is systematically investigated. It is shown that the single-proton states with higher angular momenta are influenced significantly by the tensor force and the trend in the evolution of somesingle-particle energy differences with the mass number of the isotopes depends sensitively on a parameter β T associated with the intensity of the tensor force. To understand this phenomenon, we analyze the spin-orbit potentials and the radial wave functions of relevant single-proton orbits in detail. In addition, it is found that some TIJ interactions could cause the 2s1/2-1d3/2 energy level inversion in 48Ca.

Tensor-force effects on single-particle levels and proton bubble structure around theZorN=20magic number

Applying the semirealistic $NN$ interactions that include a realistic tensor force to the Hartree-Fock calculations, we investigate tensor-force effects on the single-particle levels in Ca isotopes. The semirealistic interactions successfully describe the experimental difference between $\ensuremath{\varepsilon}(p1{s}_{1/2})$ and $\ensuremath{\varepsilon}(p0{d}_{3/2})$ (denoted by $\ensuremath{\Delta}{\ensuremath{\varepsilon}}_{13}$) both at ${}^{40}$Ca and ${}^{48}$Ca, confirming the importance of the tensor force. The tensor force plays a role in the $N$ dependence of $\ensuremath{\Delta}{\ensuremath{\varepsilon}}_{13}$ also in neutron-rich Ca nuclei. While the $p1{s}_{1/2}$--$p0{d}_{3/2}$ inversion is predicted in heavier Ca nuclei as in ${}^{48}$Ca, it takes place only for $N\ensuremath{\ge}46$, delayed by the tensor force. We further investigate the possibility of proton bubble structure in Ar, which is suggested by the $p1{s}_{1/2}$--$p0{d}_{3/2}$ inversion in ${}^{48}$Ca and more neutron rich Ca nuclei, by using spherical Hartree-Fock-Bogolyubov calculations. Even with the inversion at ${}^{48}$Ca the pair correlation prohibits prominent bubble distribution in ${}^{46}$Ar. Bubble structure in Ar is unlikely also near the neutron drip line because of either unboundness or deformation. However, ${}^{34}$Si remains a candidate for proton bubble structure, owing to the large shell gap between $p1{s}_{1/2}$ and $p0{d}_{5/2}$.