Asymptotics of neutron Cooper pair in weakly bound nuclei

Asymptotic form of neutron Cooper pair penetrating to the exterior of nuclear surface is investigated with the Bogoliubov theory for the superfluid Fermions. Based on a two-particle Schr\"{o}dinger equation governing the Cooper pair wave function and systematic studies for both weakly bound and stable nuclei, the Cooper pair is shown to be spatially correlated even in the asymptotic large distance limit, and the penetration length of the pair condensate is revealed to be universally governed by the two-neutron separation energy $S_{2n}$ and the di-neutron mass $2m$

Pair correlation of giant halo nuclei in continuum Skyrme-Hartree-Fock-Bogoliubov theory

The giant halos predicted in neutron-rich Zr isotopes with $A=124-138$ are investigated by using the self-consistent continuum Skyrme Hartree-Fock-Bogoliubov approach, in which the asymptotic behavior of continuum quasiparticle states is properly treated by the Green's function method. We study in detail the neutron pair correlation involved in the giant halo by analyzing the asymptotic exponential tail of the neutron pair condensate (pair density) in addition to that of the neutron particle density. The neutron quasiparticle spectra associated with these giant halo nuclei are examined. It is found that the asymptotic exponential tail of the neutron pair condensate is dominated by non-resonant continuum quasiparticle states corresponding to the scattering states with low asymptotic kinetic energy. This is in contrast to the asymptotic tail of the neutron density, whose main contributions arise from the resonant quasiparticle states corresponding to the weakly-bound single-particle orbits and resonance orbits in the Hartree-Fock potential

Generalized MICZ-Kepler Problems and Unitary Highest Weight Modules

For each integer $n\ge 1$, we demonstrate that a $(2n+1)$-dimensional generalized MICZ-Kepler problem has an \mr{Spin}(2, 2n+2) dynamical symmetry which extends the manifest \mr{Spin}(2n+1) symmetry. The Hilbert space of bound states is shown to form a unitary highest weight \mr{Spin}(2, 2n+2)-module which occurs at the first reduction point in the Enright-Howe-Wallach classification diagram for the unitary highest weight modules. As a byproduct, we get a simple geometric realization for such a unitary highest weight \mr{Spin}(2, 2n+2)-module.Comment: 27 pages, Refs. update

Impurity effect of Lambda hyperon on collective excitations of atomic nuclei

Taking the ground state rotational band in $^{24}$Mg as an example, we investigate the impurity effect of $\Lambda$ hyperon on collective excitations of atomic nuclei in the framework of non-relativistic energy density functional theory. To this end, we take into account correlations related to the restoration of broken symmetries and fluctuations of collective variables by solving the eigenvalue problem of a five-dimensional collective Hamiltonian for quadrupole vibrational and rotational degrees of freedom. The parameters of the collective Hamiltonian are determined with constrained mean-field calculations for triaxial shapes using the SGII Skyrme force. We compare the low-spin spectrum for $^{24}$Mg with the spectrum for the same nucleus inside $^{25}_{\Lambda}$Mg. It is found that the $\Lambda$ hyperon stretches the ground state band and reduces the $B(E2:2^+_1 \rightarrow 0^+_1)$ value by $\sim 9$, mainly by softening the potential energy surface towards the spherical shape, even though the shrinkage effect on the average proton radius is only $\sim0.5$.Comment: 16 pages, 5 figures, and 1 tabl

Courtyard sound field characteristics by bell sounds in Han Chinese Buddhist temples

The acoustic environments of Han Chinese Buddhist temples have long played an important role in the development of Buddhism. This study explored the effects of layouts and spatial elements of Han Chinese Buddhist temples on courtyard sound fields. First, sound fields of three traditional Han Chinese courtyards were measured, and results were compared with sound field simulations to determine the appropriate acoustic and software parameter setting for ancient building materials in the context of sound field simulation. Next, a sound field model for standard forms of Han Chinese Buddhist temples was built and analysed. Results indicate that in traditional Buddhist temples, spatial elements—such as the height and sound absorption coefficient of temple courtyard walls, position of courtyard partition walls, and the position and height of bell towers—could significantly affect the sound pressure level (SPL), reverberation time (RT), and musical clarity (C80) of each courtyard. However, enclosure materials, such as those used in roofs, on the ground, and in windows of Han Chinese Buddhist temples, had relatively small effects on temple courtyard sound fields

Temperature dependence of the resonance and low energy spin excitations in superconducting FeTe0.6_{0.6}Se0.4_{0.4}

We use inelastic neutron scattering to study the temperature dependence of the low-energy spin excitations in single crystals of superconducting FeTe$_{0.6}$Se$_{0.4}$ ($T_c=14$ K). In the low-temperature superconducting state, the imaginary part of the dynamic susceptibility at the electron and hole Fermi surfaces nesting wave vector $Q=(0.5,0.5)$, $\chi^{\prime\prime}(Q,\omega)$, has a small spin gap, a two-dimensional neutron spin resonance above the spin gap, and increases linearly with increasing $\hbar\omega$ for energies above the resonance. While the intensity of the resonance decreases like an order parameter with increasing temperature and disappears at temperature slightly above $T_c$, the energy of the mode is weakly temperature dependent and vanishes concurrently above $T_c$. This suggests that in spite of its similarities with the resonance in electron-doped superconducting BaFe$_{2-x}$(Co,Ni)$_x$As$_2$, the mode in FeTe$_{0.6}$Se$_{0.4}$ is not directly associated with the superconducting electronic gap.Comment: 7 pages, 6 figure

Pseudospin symmetry in supersymmetric quantum mechanics: Schr\"odinger equations

The origin of pseudospin symmetry (PSS) and its breaking mechanism are explored by combining supersymmetry (SUSY) quantum mechanics, perturbation theory, and the similarity renormalization group (SRG) method. The Schr\"odinger equation is taken as an example, corresponding to the lowest-order approximation in transforming a Dirac equation into a diagonal form by using the SRG. It is shown that while the spin-symmetry-conserving term appears in the single-particle Hamiltonian $H$, the PSS-conserving term appears naturally in its SUSY partner Hamiltonian $\tilde{H}$. The eigenstates of Hamiltonians $H$ and $\tilde{H}$ are exactly one-to-one identical except for the so-called intruder states. In such a way, the origin of PSS deeply hidden in $H$ can be traced in its SUSY partner Hamiltonian $\tilde{H}$. The perturbative nature of PSS in the present potential without spin-orbit term is demonstrated by the perturbation calculations, and the PSS-breaking term can be regarded as a very small perturbation on the exact PSS limits. A general tendency that the pseudospin-orbit splittings become smaller with increasing single-particle energies can also be interpreted in an explicit way.Comment: 31 pages, 11 figures, 2 table

Ticking terahertz wave generation in attoseconds

We perform a joint measurement of terahertz waves and high-order harmonics generated from noble atoms driven by a fundamental laser pulse and its second harmonic. By correlating their dependence on the phase-delay of the two pulses, we determine the generation of THz waves in tens of attoseconds precision. Compared with simulations and models, we find that the laser-assisted soft-collision of the electron wave packet with the atomic core plays a key role. It is demonstrated that the rescattering process, being indispensable in HHG processes, dominant THz wave generation as well but in a more elaborate way. The new finding might be helpful for the full characterization of the rescattering dynamics.Comment: 4 figure