arXiv subjects

F. R. Xu

Publications and source records attributed to F. R. Xu.

At least 55 records · Page 3Linked to original sources

arXiv2018

Ab initio Rayleigh-Schrödinger perturbation calculation including three-body force

We first derive the Rayleigh-Schrödinger many-body perturbation theory up to third order (RSPT3) for Hamiltonians with three-body interaction. The structure of closed-shell nuclei in a wide mass range from 4He to 48Ca has been investigated by the RSPT3 with explicit NN+3N Hamiltonian. The RSPT3 calculations are performed within Hartree-Fock bases. The perturbative contribution of antisymmetrized Goldstone diagrams (diagrammatic expansion for RSPT) with normal-ordered interaction has been analyzed. We demonstrate that the normal-ordered two-body level (NO2B) approximation which neglects the residual three-body term can catch the main effect of full three-body force in RSPT calculation. We also present rigorous benchmarks for RSPT3 with non-perturbative coupled cluster and in-medium similarity renormalization group using the same chiral NNLOsat NO2B interaction. The three methods are in good agreement with each other for binding energies and radii. However, the RSPT3 provides an alternative that is computationally inexpensive but comparable in accuracy to state-of-the-art non-perturbative many-body methods.

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arXiv2018

$p$-shell hypernuclear structures using the Gogny-interaction shell model

We have systematically investigated the excitation spectra of $p$-shell hypernuclei within the shell model based on the nucleon-nucleon and hyperon-nucleon interactions. For the effective nucleon-nucleon interaction, we adopt the Gogny force instead of the widely-used empirical $p$-shell Cohen-Kurath interaction, while the hyperon-nucleon interaction takes the $ΛN$ interaction including the $ΛN$-$ΣN$ coupling effect. We find that the shell model with the Gogny force can give reasonable descriptions of both spectra and binding energies of the $p$-shell nuclei. With this confidence, combined with the $ΛN$ interaction, we have performed shell-model calculations for the $p$-shell hypernuclei. We compare our results with $γ$-ray data as well as various theoretical calculations, and explain recent experimental hypernuclear excitation spectra observed at JLab.

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arXiv2018

Resonances of unbound quantum many-body systems of nuclei

Resonance is a general phenomenon which can happen in classic or quantum systems. An unbound many-body quantum system can undergo a self-resonant process. It has long been a challenge how to describe unbound many-body quantum systems in resonances. In this paper, we develop a novel first-principles method that is capable of describing resonant quantum systems. We exploit, for the first time, the advanced in-medium similarity renormalization group (IMSRG) in the complex-energy Gamow-Berggren representation with resonance and non-resonant continuum. The ab initio Gamow IMSRG has broad applications, such as, to the electromagnetic-interaction systems of atoms, molecules or quantum dots, and strong-interaction atomic nuclei. In the present work, we apply the method to loosely bound or unbound nuclear systems. Carbon and oxygen isotopes have been investigated with an optimized chiral effective field theory potential. The resonant states observed in neutron-rich 22O and 24O are well reproduced. The loose halo structure of the Borromean nucleus 22C is clearly seen by the density calculation, in which the continuum s-waves play a crucial role. Further, we predict low-lying resonant excited states in 22C. This method provides rigorous and tractable theoretical calculations for weakly-bound or unbound open quantum systems.

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arXiv2018

Realistic shell-model calculations for p-shell nuclei including contributions of a chiral three-body force

In this paper we present an evolution of our derivation of the shell-model effective Hamiltonian, namely introducing effects of three-body contributions. More precisely, we consider a three-body potential at next-to-next-to-leading order in chiral perturbation theory, and the induced three-body forces that arise from many-body correlations among valence nucleons. The first one is included, in the derivation of the effective Hamiltonian for one- and two-valence nucleon-systems, at first order in the many-body perturbation theory. Namely, we include only the three-body interaction between one or two valence nucleons and those belonging to the core. For nuclei with more than two valence particles, both induced - turned on by the two-body potential - and genuine three-body forces come into play. Since it is difficult to perform shell-model calculations with three-body forces, these contributions are estimated for the ground-state energy only. In order to establish the reliability of our approximations, we focus attention on nuclei belonging to the p shell, aiming to benchmark our calculations against those performed with the ab initio no-core shell-model. The obtained results are satisfactory, and pave the way to the application of our approach to nuclear systems with heavier masses.

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arXiv2018

The Masses of the $T_z=-3/2$ Nuclei $^{27}$P and $^{29}$S

Isochronous mass spectrometry has been applied in the storage ring CSRe to measure the masses of the $T_z=-3/2$ nuclei $^{27}$P and $^{29}$S. The new mass excess value $ME$($^{29}$S) $=-3094(13)$~keV is 66(52)~keV larger than the result of the previous $^{32}$S($^3$He,$^{6}$He)$^{29}$S reaction measurement in 1973 and a factor of 3.8 more precise. The new result for $^{29}$S, together with those of the $T=3/2$ isobaric analog states (IAS) in $^{29}$P, $^{29}$Si, and $^{29}$Al, fit well into the quadratic form of the Isobaric Multiplet Mass Equation IMME. The mass excess of $^{27}$P has been remeasured to be $ME(^{27}$P$)=-685(42)$ keV. By analyzing the linear and quadratic coefficients of the IMME in the $T_z=-3/2$ $sd$-shell nuclei, it was found that the ratio of the Coulomb radius parameters is $R\approx0.96$ and is nearly the same for all $T=3/2$ isospin multiplets. Such a nearly constant $R$-value, apparently valid for the entire light mass region with $A>9$, can be used to set stringent constraints on the isovector and isotensor components of the isospin non-conserving forces in theoretical calculations.

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arXiv2018

{\it Ab initio} perturbation calculations of realistic effective interactions in the Hartree--Fock basis

We perform two types of {\it ab initio} perturbation calculations of effective interactions in the Hartree--Fock (HF) basis instead of the harmonic-oscillator basis: one is called the Brillouin--Wigner (BW) perturbation and another is called the Rayleigh--Schrödinger (RS) perturbation. It is shown that the HF basis provides good convergences. We also benchmark the perturbation calculations with the in-medium similarity renormalization group (IM-SRG) which is a nonperturbative method. In the HF basis some-type perturbation diagrams can be cancelled out, while the cancellation does not happen in the harmonic-oscillator basis. We have investigated the {\it sd} shell using the chiral N$^3$LO potential softened by $V_{\text{low-}k}$. With the low-momentum N$^3$LO potential, we first perform the spherical HF calculations for the $^{16}$O core of the {\it sd} shell, and the realistic effective two-body interactions for the HF {\it sd}-shell space can be derived by the perturbation calculations. The calculations give simultaneously effective single-particle energies and excitation spectra of two valence particle systems (i.e., $^{18}$O, $^{18}$F, and $^{18}$Ne in the {\it sd} shell). Convergences have been analyzed order by order. The perturbation calculations are in fairly good agreement with nonperturbative method IM-SRG. We find that the HF RS perturbation gives even better results compared with the BW perturbation. The HF realistic effective interactions derived by the perturbations can be used for further shell-model calculations.

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arXiv2018

A New Measurement of the Intruder Configuration in 12Be

A new $^{11}$Be($d,p$)$^{12}$Be transfer reaction experiment was carried out in inverse kinematics at 26.9$A$ MeV, with special efforts devoted to the determination of the deuteron target thickness and of the required optical potentials from the present elastic scattering data. In addition, a direct measurement of the cross sections for the 0$_2^+$ state was realized by applying an isomer-tagging technique. The s-wave spectroscopic factors of 0.20(0.04) and 0.41(0.11) were extracted for the 0$_1^+$ and 0$_2^+$ states, respectively, in $^{12}$Be. Using the ratio of these spectroscopic factors, together with the previously reported results for the p-wave components, the single-particle component intensities in the bound 0$^+$ states of $^{12}$Be were deduced, allowing a direct comparison with the theoretical predictions. It is evidenced that the ground-state configuration of $^{12}$Be is dominated by the d-wave intruder, exhibiting a dramatic evolution of the intruding mechanism from $^{11}$Be to $^{12}$Be, with a persistence of the $N = 8$ magic number broken.

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arXiv2018

Mass Measurements of Neutron-Deficient Y, Zr, and Nb Isotopes and Their Impact on $rp$ and $νp$ Nucleosynthesis Processes

Using isochronous mass spectrometry at the experimental storage ring CSRe in Lanzhou, the masses of $^{82}$Zr and $^{84}$Nb were measured for the first time with an uncertainty of $\sim 10$ keV, and the masses of $^{79}$Y, $^{81}$Zr, and $^{83}$Nb were re-determined with a higher precision. %The latter differ significantly from their literature values. The latter are significantly less bound than their literature values. Our new and accurate masses remove the irregularities of the mass surface in this region of the nuclear chart. Our results do not support the predicted island of pronounced low $α$ separation energies for neutron-deficient Mo and Tc isotopes, making the formation of Zr-Nb cycle in the $rp$-process unlikely. The new proton separation energy of $^{83}$Nb was determined to be 490(400)~keV smaller than that in the Atomic Mass Evaluation 2012. This partly removes the overproduction of the $p$-nucleus $^{84}$Sr relative to the neutron-deficient molybdenum isotopes in the previous $νp$-process simulations.

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arXiv2018

Evidence for rotational to vibrational evolution along the yrast line in the odd-A rare-earth nuclei

The phase transition of nuclei to increasing angular momentum (or spin) and excitation energy is one of the most fundamental topics of nuclear structure research. The odd-N nuclei with A equal 160 are widely considered belonging to the well-deformed region, and their excitation spectra are energetically favored to exhibit the rotational characteristics. In the present work, however, there is evidence indicating that the nuclei can evolve from rotation to vibration along the yrast lines while increasing spin. The simple method, named as E-Gamma Over Spin (E-GOS) curves, would be used to discern the evolution from rotational to vibrational structure in nuclei as a function of spin. In addition, in order to get the insight into the rotational-like properties of nuclei, theoretical calculations have been performed for the yrast bands of the odd-A rare-earth nuclei using the total Routhian surfaces (TRS) model. The TRS plots indicate that the 165Yb and 157Dy isotopes have stable prolate shapes at low spin states. At higher rotational frequency (larger than 0.50 MeV), a distinct decrease in the quadrupole deformation is predicted by the calculations, and the isotopes becomes rigid in the gamma deformation.

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arXiv2018

Chiral NNLO$_{\text{sat}}$ descriptions of nuclear multipole resonances within the random phase approximation

We study nuclear multipole resonances in the framework of the random phase approximation using the chiral potential NNLO$_{\text{sat}}$. This potential includes two- and three-body terms that has been simultaneously optimized to low-energy nucleon-nucleon scattering data and selected nuclear structure data. Our main foci have been the isoscalar monopole, isovector dipole, and isoscalar quadrupole resonances of the closed-shell nuclei, $^4$He, $^{16,22,24}$O, and $^{40,48}$Ca. These resonance modes have been widely observed in experiment. In addition, we use a renormalized chiral potential $V_{\text{low-}k}$, based on the N$^3$LO two-body potential by Entem and Machleidt [Phys. Rev. \textbf{C68}, 041001 (2011)]. This introduces a dependency on the cutoff parameter used in the normalization procedure as reported in previous works by other groups. While NNLO$_{\text{sat}}$ can reasonably reproduce observed multipole resonances, it is not possible to find a single cutoff parameter for the $V_{\text{low-}k}$ potential that simultaneously describe the different types of resonance modes. The sensitivity to the cutoff parameter can be explained by missing induced three-body forces in the calculations. Our results for neutron-rich $^{22,24}$O show a mixing nature of isoscalar and isovector resonances in the dipole channel at low energies. We predict that $^{22}$O and $^{24}$O have low-energy isoscalar quadrupole resonances at energies lower than 5 MeV.

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arXiv2017

Effects of tensor and $T=0$ pairing interactions on nuclear $β^+$/EC decay

The Hartree-Fock-Bogolyubov (HFB) plus proton-neutron quasiparticle random phase approximation (pnQRPA) approach based on Skyrme interaction is applied to study the nuclear $β^+$/EC decay for nuclei near the proton magic numbers $Z=$20, 28, and 50. With properly selected Skyrme interactions that include the tensor terms, and the $T=0$ pairing interaction, the experimental $β^+$/EC decay half-lives of these nuclei can be systematically reproduced quite well. It is shown that the tensor and $T=0$ pairing interactions play different roles in different nuclei. The specific effect is relevant to the configurations that contribute to the decay. The attractive and repulsive properties of tensor interaction for the GT state is also studied. The present results indicate that it works repulsively on the GT states dominated by the configurations from $πj_\gtrless$ to $νj_\gtrless$ orbits, while working attractively for those mainly composed of the configurations from $πj_\gtrless$ to $νj_\lessgtr$ orbits.

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arXiv2017

Structure and decays of nuclear three-body systems: the Gamow coupled-channel method in Jacobi coordinates

${\bf Background:}$ Weakly bound and unbound nuclear states appearing around particle thresholds are prototypical open quantum systems. Theories of such states must take into account configuration mixing effects in the presence of strong coupling to the particle continuum space. ${\bf Purpose:}$ To describe structure and decays of three-body systems, we developed a Gamow coupled-channel (GCC) approach in Jacobi coordinates by employing the complex-momentum formalism. We benchmarked the new framework against the complex-energy Gamow Shell Model (GSM). ${\bf Methods:}$ The GCC formalism is expressed in Jacobi coordinates, so that the center-of-mass motion is automatically eliminated. To solve the coupled-channel equations, we use hyperspherical harmonics to describe the angular wave functions while the radial wave functions are expanded in the Berggren ensemble, which includes bound, scattering and Gamow states. ${\bf Results:}$ We show that the GCC method is both accurate and robust. Its results for energies, decay widths, and nucleon-nucleon angular correlations are in good agreement with the GSM results. ${\bf Conclusions:}$ We have demonstrated that a three-body GSM formalism explicitly constructed in cluster-orbital shell model coordinates provides similar results to a GCC framework expressed in Jacobi coordinates, provided that a large configuration space is employed. Our calculations for $A=6$ systems and $^{26}$O show that nucleon-nucleon angular correlations are sensitive to the valence-neutron interaction. The new GCC technique has many attractive features when applied to bound and unbound states of three-body systems: it is precise, efficient, and can be extended by introducing a microscopic model of the core.

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arXiv2016

Radiation reaction induced spiral attractors in ultra-intense colliding laser beams

The radiation reaction effects on electron dynamics in counter-propagating circularly polarized laser beams are investigated through the linearization theorem and the results are in great agreement with numeric solutions. For the first time, the properties of fixed points in electron phase-space were analyzed with linear stability theory, showing that center nodes will become attractors if the classical radiation reaction is considered. Electron dynamics are significantly affected by the properties of the fixed points and the electron phase-space densities are found to be increasing exponentially near the attractors. The density growth rates are derived theoretically and further verified by particle-in-cell simulations, which can be detected in experiments to explore the effects of radiation reaction qualitatively. The attractor can also facilitate to realize a series of nanometer-scaled flying electron slices via adjusting the colliding laser frequencies.

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arXiv2016

Identification of the Lowest $T=2$, $J^{π=}0^+$ Isobaric Analog State in $^{52}$Co and Its Impact on the Understanding of $β$-Decay Properties of $^{52}$Ni

Masses of $^{52g,52m}$Co were measured for the first time with an accuracy of $\sim 10$ keV, an unprecedented precision reached for short-lived nuclei in the isochronous mass spectrometry. Combining our results with the previous $β$-$γ$ measurements of $^{52}$Ni, the $T=2$, $J^π=0^+$ isobaric analog state (IAS) in $^{52}$Co was newly assigned, questioning the conventional identification of IASs from the $β$-delayed proton emissions. Using our energy of the IAS in $^{52}$Co, the masses of the $T=2$ multiplet fit well into the Isobaric Multiplet Mass Equation. We find that the IAS in $^{52}$Co decays predominantly via $γ$ transitions while the proton emission is negligibly small. According to our large-scale shell model calculations, this phenomenon has been interpreted to be due to very low isospin mixing in the IAS.

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arXiv2016

Brueckner-Hartree-Fock and its renormalized calculations for finite nuclei

We have performed self-consistent Brueckner-Hartree-Fock (BHF) and its renormalized theory to the structure calculations of finite nuclei. The $G$-matrix is calculated within the BHF basis, and the exact Pauli exclusion operator is determined by the BHF spectrum. Self-consistent occupation probabilities are included in the renormalized Brueckner-Hartree-Fock (RBHF). Various systematics and convergences are studies. Good results are obtained for the ground-state energy and radius. RBHF can give a more reasonable single-particle spectrum and radius. We present a first benchmark calculation with other {\it ab initio} methods using the same effective Hamiltonian. We find that the BHF and RBHF results are in good agreement with other $\it{ab}$ $\it{initio}$ methods.

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arXiv2016

Searching for high-$K$ isomers in the proton-rich $A\sim80$ mass region

Configuration-constrained potential-energy-surface calculations have been performed to investigate the $K$ isomerism in the proton-rich $A\sim80$ mass region. An abundance of high-$K$ states are predicted. These high-$K$ states arise from two and four-quasi-particle excitations, with $K^π=8^{+}$ and $K^π=16^{+}$, respectively. Their excitation energies are comparatively low, making them good candidates for long-lived isomers. Since most nuclei under studies are prolate spheroids in their ground states, the oblate shapes of the predicted high-$K$ states may indicate a combination of $K$ isomerism and shape isomerism.

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arXiv2015

Identification of new transitions and mass assignments of levels in $^{143-153}$Pr

The previously reported levels assigned to 151,152,153Pr have recently been called into question regarding their mass assignment. The above questioned level assignments are clarified by measuring g-transitions tagged with A and Z in an in-beam experiment in addition to the measurements from 252Cf spontaneous fission (SF) and establish new spectroscopic information from $N=84$ to $N=94$ in the Pr isotopic chain. The isotopic chain 143-153Pr has been studied from the spontaneous fission of 252Cf by using Gammasphere and also from the measurement of the prompt g-rays in coincidence with isotopically-identified fission fragments using VAMOS++ and EXOGAM at GANIL. The latter were produced using 238U beams on a 9Be target at energies around the Coulomb barrier. The g-g-g-g data from 252Cf (SF) and those from the GANIL in-beam A- and Z-gated spectra were combined to unambiguously assign the various transitions and levels in 151,152,153Pr and other isotopes. New transitions and bands in 145,147,148,149,150Pr were identified by using g-g-g and g-g-g-g coincidences and A and Z gated g-g spectra. The transitions and levels previously assigned to 151,153Pr have been confirmed by the (A,Z) gated spectra. The transitions previously assigned to 152Pr are now assigned to 151Pr on the basis of the (A,Z) gated spectra. Two new bands with 20 new transitions in 152Pr and one new band with 7 new transitions in 153Pr are identified from the g-g-g-g coincidence spectra and the (A,Z) gated spectrum. In addition, new g-rays are also reported in 143-146Pr. New levels of 145,147-153Pr have been established, reliable mass assignments of the levels in 151,152,153Pr have been reported and new transitions have been identified in 143-146Pr showing the new avenues that are opened by combining the two experimental approaches.

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arXiv2015

Configuration mixing effects in neutron-rich carbon isotopes

Shell model calculations are done to study the structure of neutron-rich carbon isotopes. For both even-A and odd-A neutron-rich carbon isotopes, the energy levels are strongly affected by the configuration mixing of valence neutrons. The calculated energy levels in the nucleus $^{17}$C are significantly improved compared with experimental values when the model space of the three valence neutrons is enlarged from pure $ν(0d_{5/2})^{3}$ configuration to full $sd$ space. We also investigate the configuration mixing effect on the $B(E2)$ values in even-even nuclei $^{16-20}$C.

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