分类： 物理学 >> 核物理学 提交时间： 2017-08-22
摘要： The shapes of light normal nuclei and Λ hypernuclei are investigated in the (β,γ) deformation plane by using a newly developed constrained relativistic mean field (RMF) model. As examples, the results of some C, Mg, and Si nuclei are presented and discussed in details. We found that for normal nuclei the present RMF calculations and previous Skyrme-Hartree-Fock models predict similar trends of the shape evolution with the neutron number increasing. But some quantitative aspects from these two approaches, such as the depth of the minimum and the softness in the γ direction, differ a lot for several nuclei. For Λ hypernuclei, in most cases, the addition of a Λ hyperon alters slightly the location of the ground state minimum towards the direction of smaller β and softer γ in the potential energy surface E ∼ (β,γ). There are three exceptions, namely, 13C, 23C, and ΛΛ 31Si in which the polarization effect of the additional Λ is so strong that the shapes of these three Λ hypernuclei are drastically different from their corresponding core nuclei.
分类： 物理学 >> 核物理学 提交时间： 2017-08-22
摘要： For the first time the potential energy surfaces of actinide nuclei in the (β20, β22, β30) deformation space are obtained from a multi-dimensional constrained covariant density functional theory. With this newly developed theory we are able to explore the importance of the triaxial and octupole shapes simultaneously along the whole fission path. It is found that besides the octupole deformation, the triaxiality also plays an important role upon the second fission barriers. The outer barrier as well as the inner barrier are lowered by the triaxial deformation compared with axially symmetric results. This lowering effect for the reflection asymmetric outer barrier is 0.5 ∼ 1 MeV, accounting for 10 ∼ 20% of the barrier height. With the inclusion of the triaxial deformation, a good agreement with the data for the outer barriers of actinide nuclei is achieved.
分类： 物理学 >> 核物理学 提交时间： 2017-08-22
摘要： The pseudospin symmetry is a relativistic dynamical symmetry connected with the small com- ponent of the Dirac spinor. The origin of pseudospin symmetry in single particle bound states in atomic nuclei has been revealed and studied extensively. By examining the zeros of Jost functions corresponding to the small components of Dirac wave functions and phase shifts of continuum states, we show that the pseudospin symmetry in single particle resonant states in nuclei is conserved when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. The exact conservation and the breaking of pseudospin symmetry are illustrated for single particle resonances in spherical square-well and Woods-Saxon potentials.
分类： 物理学 >> 核物理学 提交时间： 2017-08-22
摘要： The non-axial reflection-asymmetric β32 shape in some transfermium nuclei with N = 150, namely 246Cm, 248Cf, 250Fm, and 252No are investigated with multidimensional constrained covariant den- sity functional theories. By using the density-dependent point coupling covariant density functional theory with the parameter set DD-PC1 in the particle-hole channel, it is found that, for the ground states of 248Cf and 250Fm, the non-axial octupole deformation parameter β32 > 0.03 and the energy gain due to the β32 distortion is larger than 300 keV. In 246Cm and 252No, shallow β32 minima are found. The occurrence of the non-axial octupole β32 correlations is mainly from a pair of neutron orbitals [734]9/2 (νj15/2) and [622]5/2 (νg9/2) which are close to the neutron Fermi surface and a pair of proton orbitals [521]3/2 (πf7/2) and [633]7/2 (πi13/2) which are close to the proton Fermi surface. The dependence of the non-axial octupole effects on the form of energy density functional and on the parameter set is also studied.
分类： 物理学 >> 核物理学 提交时间： 2017-07-30
摘要： Multi-dimensional constrained covariant density functional theories were developed recently. In these theories, all shape degrees of freedom βλμ deformations with even μ are allowed, e.g., β20, β22, β30, β32, β40, β42, β44, and so on and the CDFT functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent couplings. In this contri- bution, some applications of these theories are presented. The potential energy surfaces of actinide nuclei in the (β20 , β22 , β30 ) deformation space are investigated. It is found that besides the octupole deformation, the triaxiality also plays an important role upon the second fission barriers. The non-axial reflection-asymmetric β32 shape in some transfermium nuclei with N = 150, namely 246Cm, 248Cf, 250Fm, and 252No are studied.
分类： 物理学 >> 核物理学 提交时间： 2017-07-30
摘要： In this contribution we present some results on the study of pseudospin symmetry (PSS) in single particle resonant states. The PSS is a relativistic dynamical symmetry connected with the small component of the nucleon Dirac wave function. Many efforts have been made to study this symmetry in bound states. We recently gave a rigorous justification of the PSS in single particle resonant states by examining the zeros of Jost functions corresponding to the small components of the radial Dirac wave functions and phase shifts of continuum states [1]. We have shown that the PSS in single particle resonant states in nuclei is conserved when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. Examples of exact conservation and breaking of this symmetry in single particle resonances are given for spherical square-well and Woods-Saxon potentials.
分类： 物理学 >> 核物理学 提交时间： 2017-07-30
摘要： We have developed multi-dimensional constrained covariant density functional theories (MDC-CDFT) for finite nuclei in which the shape degrees of freedom βλμ with even μ, e.g., β20, β22, β30, β32, β40, etc., can be described simultaneously. The functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent couplings. For the pp channel, either the BCS approach or the Bogoliubov transformation is implemented. The MDC-CDFTs with the BCS approach for the pairing (in the following labelled as MDC-RMF models with RMF standing for “relativistic mean field”) have been applied to investigate multi-dimensional potential energy surfaces and the non-axial octupole Y32-correlations in N = 150 isotones. In this contribution we present briefly the formalism of MDC-RMF models and some results from these models. The potential energy surfaces with and without triaxial deformations are compared and it is found that the triaxiality plays an important role upon the second fission barriers of actinide nuclei. In the study of Y32-correlations in N = 150 isotones, it is found that, for 248Cf and 250Fm, β32 > 0.03 and the energy is lowered by the β32 distortion by more than 300 keV; while for 246Cm and 252No, the pocket with respect to β32 is quite shallow.
分类： 物理学 >> 核物理学 提交时间： 2017-07-30
摘要： Background: The pseudospin symmetry (PSS) has been studied extensively for bound states. Recently we justified rigorously that the PSS in single particle resonant states is exactly conserved when the attractive scalar and repulsive vector potentials of the Dirac Hamiltonian have the same magnitude but opposite sign [Phys. Rev. Lett. 109, 072501 (2012)]. Purpose: To understand more deeply the PSS in single particle resonant states, we focus on several issues related to the exact conservation and breaking mechanism of the PSS in single particle resonances. In particular, we are interested in how the energy and width splittings of PS partners depend on the depth of the scalar and vector potentials. Methods: We investigate the asymptotic behaviors of radial Dirac wave functions. Spherical square well poten- tials are employed in which the PSS breaking part in the Jost function can be well isolated. By examining the zeros of Jost functions corresponding to small components of the radial Dirac wave functions, general properties of the PSS are analyzed. Results: By examining the Jost function, the occurrence of intruder orbitals is explained and it is possible to trace continuously the PSS partners from the PSS limit to the case with a finite potential depth. The dependence of the PSS in resonances as well as in bound states on the potential depth is investigated systematically. We find a threshold effect in the energy splitting and an anomaly in the width splitting of pseudospin partners when the depth of the single particle potential varies from zero to a finite value. Conclusions: The conservation and the breaking of the PSS in resonant states and bound states share some similar properties. The appearance of intruder states can be explained by examining the zeros of Jost functions. Origins of the threshold effect in the energy splitting and the anomaly in the width splitting of PS partners, together with many other problems, are still open and should be further investigated.
分类： 物理学 >> 核物理学 提交时间： 2017-07-30
摘要： The pseudospin symmetry (PSS) is a relativistic dynamical symmetry directly connected with the small component of the nucleon Dirac wave function. Much effort has been made to study this symmetry in bound states. Recently, a rigorous justification of the PSS in single particle resonant states was achieved by examining the asymptotic behaviors of the radial Dirac wave functions: The PSS in single particle resonant states in nuclei is conserved exactly when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. Several issues related to the exact conservation and breaking mechanism of the PSS in single particle resonances were investigated by employing spherical square well potentials in which the PSS breaking part can be well isolated in the Jost function. A threshold effect in the energy splitting and an anomaly in the width splitting of pseudospin partners were found when the depth of the square well potential varies from zero to a finite value.
分类： 物理学 >> 核物理学 提交时间： 2017-07-30
摘要： In this contribution we present some results of potential energy sur- faces of actinide and transfermium nuclei from multi-dimensional constrained relativistic mean field (MDC-RMF) models. Recently we developed multi-dimensional constrained covariant density func- tional theories (MDC-CDFT) in which all shape degrees of freedom βλμ with even μ are allowed and the functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the non-linear or density-dependent cou- plings. In MDC-RMF models, the pairing correlations are treated with the BCS method. With MDC-RMF models, the potential energy surfaces of even-even actinide nuclei were investigated and the effect of triaxiality on the fission barriers in these nuclei was discussed. The non-axial reflection-asymmetric β32 shape in some βλμ =0 β22 ̸=0 β20 >0 β30 ̸=0 β20 0 β20 ≫0 transfermium nuclei with N = 150, namely and 252No were also studied.
分类： 物理学 >> 核物理学 提交时间： 2017-07-30
摘要： Background: Many different shape degrees of freedom play crucial roles in determining the nuclear ground state and saddle point properties and the fission path. For the study of nuclear potential energy surfaces, it is desirable to have microscopic and self-consistent models in which all known important shape degrees of freedom are included. Purpose: By breaking both the axial and the spatial reflection symmetries simultaneously, we develop multidimensionally-constrained relativistic mean field (MDC-RMF) models. Methods: The nuclear shape is assumed to be invariant under the reversion of x and y axes, i.e., the intrinsic symmetry group is V4 and all shape degrees of freedom βλμ with even μ, such as β20, β22, β30, β32, β40, ..., are included self-consistently. The single-particle wave functions are expanded in an axially deformed harmonic oscillator (ADHO) basis. The RMF functional can be one of the following four forms: the meson exchange or point-coupling nucleon interactions combined with the nonlinear or density-dependent couplings. The pairing effects are taken into account with the BCS approach. Results: The one-, two, and three-dimensional potential energy surfaces of 240Pu are illustrated for numerical checks and for the study of the effect of the triaxiality on the fission barriers. Potential energy curves of even-even actinide nuclei around the first and second fission barriers are studied systematically. Besides the first ones, the second fission barriers in these nuclei are also lowered considerably by the triaxial deformation. This lowering effect is independent of the effective interactions used in the RMF functionals. Further discussions are made about different predictions on the effect of the triaxiality between the macroscopic-microscopic and MDC-RMF models, possible discontinuities on PES’s from self-consistent approaches, and the restoration of broken symmetries. Conclusions: MDC-RMF models give a reasonably good description of fission barriers of even-even actinide nuclei. It is important to include both the nonaxial and the reflection asymmetric shapes simultaneously for the study of potential energy surfaces and fission barriers of actinide nuclei and of those in unknown mass regions such as, e.g., superheavy nuclei.
分类： 物理学 >> 核物理学 提交时间： 2017-07-30
摘要： We study the superdeformed (SD) states and corresponding SD hypernuclei of Ar isotopes with the multidimensionally-constrained relativistic mean field (MDC-RMF) models which can accommodate various shape degree of freedom. We found that the density profiles of SD states in Ar isotopes show a strong localization with a ring structure near the surface, while the central part of the density is dilute showing a hole structure. This localization of SD density induces an appreciable deformation in the hyperon wave function and results in a large overlap between the core and the hyperon in the SD hypernuclei of Ar isotopes. Then the Λ separation energy of SD state becomes larger than that of normally deformed or spherical ground state. This feature is different from that found in other nuclei such as 32S, 56Ni, and 60Zn in which the Λ separation energy of larger deformed state is smaller. In this context, the measurement of the Λ separation energy may provide an important information on the localization of the density profile of SD states.
分类： 物理学 >> 核物理学 提交时间： 2017-07-30
摘要： Background: Potential energy surfaces (PES’s) of actinide nuclei are characterized by a two-humped barrier structure. At large deformations beyond the second barrier the occurrence of a third one was predicted by macroscopic-microscopic model calculations in the 1970s, but contradictory results were later reported by number of studies that used different methods. Purpose: Triple-humped barriers in actinide nuclei are investigated in the framework of covariant density func- tional theory (CDFT). Methods: Calculations are performed using the multidimensionally-constrained relativistic mean field (MDC- RMF) model, with the nonlinear point-coupling functional PC-PK1 and the density-dependent meson exchange functional DD-ME2 in the particle-hole channel. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. Results: Two-dimensional PES’s of 226,228,230,232Th and 232,234,236,238U are mapped and the third minima on these surfaces are located. Then one-dimensional potential energy curves along the fission path are analyzed in detail and the energies of the second barrier, the third minimum, and the third barrier are determined. The functional DD-ME2 predicts the occurrence of a third barrier in all Th nuclei and 238U. The third minima in 230,232Th are very shallow, whereas those in 226,228Th and 238U are quite prominent. With the functional PC- PK1 a third barrier is found only in 226,228,230 Th. Single-nucleon levels around the Fermi surface are analyzed in 226Th, and it is found that the formation of the third minimum is mainly due to the Z = 90 proton energy gap at β20 ≈ 1.5 and β30 ≈ 0.7. Conclusions: The possible occurrence of a third barrier on the PES’s of actinide nuclei depends on the effective interaction used in multidimensional CDFT calculations. More pronounced minima are predicted by the DD-ME2 functional, as compared to the functional PC-PK1. The depth of the third well in Th isotopes decreases with increasing neutron number. The origin of the third minimum is due to the proton Z = 90 shell gap at relevant deformations.
分类： 物理学 >> 核物理学 提交时间： 2017-07-30
摘要： Background: Studies of fission dynamics, based on nuclear energy density functionals, have shown that the coupling between shape and pairing degrees of freedom has a pronounced effect on the nonperturbative collective inertia and, therefore, on dynamic (least-action) spontaneous fission paths and half-lives. Purpose: To analyze effects of particle-number fluctuation degree of freedom on symmetric and asymmetric spontaneous fission (SF) dynamics, and compare with results of recent studies based on the self-consistent Hartree- Fock-Bogoliubov (HFB) method. Methods: Collective potentials and nonperturbative cranking collective inertia tensors are calculated using the multidimensionally-constrained relativistic mean-field (MDC-RMF) model. Pairing correlations are treated in the BCS approximation using a separable pairing force of finite range. Pairing fluctuations are included as a collective variable using a constraint on particle-number dispersion. Fission paths are determined with the dynamic programming method by minimizing the action in multidimensional collective spaces. Results: The dynamics of spontaneous fission of 264Fm and 250Fm are explored. Fission paths, action integrals and corresponding half-lives computed in the three-dimensional collective space of shape and pairing coordinates, using the relativistic functional DD-PC1 and a separable pairing force of finite range, are compared with results obtained without pairing fluctuations. Results for 264Fm are also discussed in relation with those recently obtained using the HFB model. Conclusions: The inclusion of pairing correlations in the space of collective coordinates favors axially symmetric shapes along the dynamic path of the fissioning system, amplifies pairing as the path traverses the fission barriers, significantly reduces the action integral and shortens the corresponding SF half-life.
提交时间： 2017-07-30
摘要： We develop a multidimensionally constrained relativistic Hartree-Bogoliubov (MDC-RHB) model in which the pairing correlations are taken into account by making the Bogoliubov transformation. In this model, the nuclear shape is assumed to be invariant under the reversion of x and y axes; i.e., the intrinsic symmetry group is V4 and all shape degrees of freedom βλμ with even μ are included self-consistently. The RHB equation is solved in an axially deformed harmonic oscillator basis. A separable pairing force of finite range is adopted in the MDC-RHB model. The potential energy curves of neutron-rich even-even Zr isotopes are calculated with relativistic functionals DD-PC1 and PC-PK1 and possible tetrahedral shapes in the ground and isomeric states are investigated. The ground state shape of 110Zr is predicted to be tetrahedral with both functionals and so is that of 112Zr with the functional DD-PC1. The tetrahedral ground states are caused by large energy gaps around Z = 40 and N = 70 when β32 deformation is included. Although the inclusion of the β30 deformation can also reduce the energy around β20 = 0 and lead to minima with pear-like shapes for nuclei around 110Zr, these minima are unstable due to their shallowness.
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