We present finite temperature Dirac-Hartree-Bogoliubov (FTDHB) calculations for the tin isotope chain to study the dependence of pseudospin on the nuclear temperature. In the FTDHB calculation, the density dependence of the self-consistent relativistic mean fields, the pairing, and the vapor phase that takes into account the unbound nucleon states are considered self-consistently. The mean field potentials obtained in the FTDHB calculations are fit by Woods-Saxon (WS) potentials to examine how the WS parameters are related to the energy splitting of the pseudospin pairs as the temperature increases. We find that the nuclear potential surface diffuseness is the main driver for the pseudospin splittings and that it increases as the temperature grows. We conclude that pseudospin symmetry is better realized when the nuclear temperature increases. The results confirm the findings of previous works using RMF theory at $T=0$, namely that the correlation between the pseudospin splitting and the parameters of the Woods-Saxon potentials implies that pseudospin symmetry is a dynamical symmetry in nuclei. We show that the dynamical nature of the pseudospin symmetry remains when the temperature is considered in a realistic calculation of the tin isotopes, such as that of the Dirac-Hartree-Bogoliubov formalism.
We investigated the role of a pairing correlation in the chemical composition of the inner crust of a neutron star with the extended Thomas-Fermi method, using the Strutinsky integral correction. We compare our results with the fully self-consistent Hartree-Fock-Bogoliubov approach, showing that the resulting discrepancy, apart from the very low density region, is compatible with the typical accuracy we can achieve with standard mean-field methods.
Symmetry-projected Hartree-Fock-Bogoliubov (HFB) equations are derived using the variational ansatz for the generalized one-body density-matrix in the Valatin form. It is shown that the projected-energy functional can be completely expressed in terms of the HFB density-matrix and the pairing-tensor. The variation of this projected-energy is shown to result in HFB equations with modified expressions for the pairing-potential and the Hartree-Fock field. The expressions for these quantities are explicitly derived for the case of particle number-projection. The numerical applicability of this proj…
The transfer reaction between two nuclei in the superfluid phase is studied with the Time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. In order to restore the symmetry of the relative gauge angle a set of independent TDHFB evolutions is done. Then the transfer probability is computed using a triple projection method. This method is first tested to determine the transfer probabilities on a toy model and compared to the exact solution. It is then applied to the reactions $^{20}$O+$^{20}$O and $^{14}$O+$^{20}$O in a realistic framework with a Gogny interaction.
In a previous work [Int. J. Mod. Phys. E 24, 1550073 (2015)], hereafter referred as paper I, we have investigated the ground-state properties of Nd, Ce and Sm isotopes within Hartree-Fock-Bogoliubov method with SLy5 skyrme force in which the pairing strength has been generalized with a new proposed formula. However, that formula is more appropriate for the region of Nd. In this work, we have studied the ground-state properties of both even-even and odd Mo and Ru isotopes. For this, we have used Hartree- Fock-Bogoliubov method with SLy4 skyrme force, and a new formula of the pairing strength wh…
Grassmann integral and Balian-Brézin decomposition in Hartree-Fock-Bogoliubov matrix elements
提出了一个计算多重准粒子激发下Hartree-Fock-Bogoliubov态一般么正算符矩阵元的新公式。在推导中使用了酉算子的Balian-Brézin分解（Il Nuovo Cimento B 64，37（1969））。我们发现这种分解非常适合于在准粒子基下的费米子相干态和格拉斯曼积分的应用。由此产生的公式是用Pfweian公式来表示的，并且显示出与我们先前在裸粒子基础上导出的公式相似的二分结构（Phys. Lett. B 707，305（2012））。
The coordinate-space representation of the Hartree-Fock-Bogoliubov theory is the method of choice to study weakly bound nuclei whose properties are affected by the quasiparticle continuum space. To describe such systems, we developed a three-dimensional Skyrme-Hartree-Fock-Bogoliubov solver HFBFFT based on the existing, highly optimized and parallelized Skyrme-Hartree-Fock code Sky3D. The code does not impose any self-consistent spatial symmetries such as mirror inversions or parity. The underlying equations are solved in HFBFFT directly in the canonical basis using the fast Fourier transform.…
Ground state properties of even-even and odd Nd,Ce and Sm isotopes in Hartree-Fock-Bogoliubov method
本文采用Hartree-Fock-Bogoliubov方法，在SLy 5 Skyrme力的作用下，研究了Nd的奇偶同位素的基态性质。计算了束缚能、双中子分离能、四极形变、电荷、中子和质子半径。对Ce和Sm进行了类似的计算，以验证我们的配对强度公式的有效性。计算结果与已有的实验数据、基于D1 S Gogny有效核子-核子相互作用的Hartree-Fock-Bogoliubov计算结果以及有限程液滴模型（FRDM）和相对论平均场（RMF）等核模型的预言进行了比较。
We describe the new version 4.0 of the code hfbtho that solves the nuclear Hartree-Fock-Bogoliubov problem by using the deformed harmonic oscillator basis in cylindrical coordinates. In the new version, we have implemented the restoration of rotational, particle number, and reflection symmetry. The restoration of rotational symmetry does not require using bases closed under rotation. Furthermore, the SeaLL1 functional was added and the calculation of the Coulomb potential was improved. Finally, the code has been refactored to facilitate maintenance and future developments.
