I explore weakly-collective singly-closed shell nuclei with high-j shells where active valence neutrons and particle-particle correlations may be the dominant collective degree of freedom. The combination of large and close-lying proton and neutron pairing gaps extracted from experimental masses seems to charaterize the origin of the weak collectivity observed in Ni and Sn superfluids with $N\approx Z$. The trend of $E2$ transition strengths, i.e., $B(E2; 2^+_1\rightarrow 0^+_1)$ values, in these nuclei is predicted from proton and neutron pairing-gap information. The agreement with the Ni isotopes is excellent and recent experimental results support the trend in the Sn isotopes. This work emphasizes the importance of atomic masses in elucidating nuclear-structure properties. In particular, it indicates that many-body microscopic properties such as nuclear collectivity could be directly inferred from more macroscopic average properties such as atomic masses.
We briefly review highlights for ultra-relativistic light-heavy collisions (p-Pb, d-Au, 3He-Au, 12C-Au) which display collective evolution, with the same very characteristic features as in the A-A systems.
Inelastic neutron scattering was used to study the low-lying nuclear structure of $^{132}$Xe. A comprehensive level scheme is presented, as well as new level lifetimes, multipole mixing ratios, branching ratios, and transition probabilities. Comparisons of these data as well as previously measured $E2$ strengths and $g$ factors are made with new shell-model calculations for $^{132,134,136}$Xe to explore the emergence of collectivity in the Xe isotopes with $N$ < 82 near the closed shell.
Long-lived opposite-parity states and the onset of octupole collectivity in atomic nuclei
San Diego State University（圣地亚哥州立大学）；Ho Chi Minh City University of Education（胡志明市教育大学）；Institute for Basic Science（基础科学研究院）；Tel Aviv University（特拉维夫大学）
Radioactive $^{129}$Sb, which can be treated as a proton plus semi-magic $^{128}$Sn core within the particle-core coupling scheme, was studied by Coulomb excitation. Reduced electric quadrupole transition probabilities, $B(E2)$, for the $2^+$ $\times$ $πg_{7/2}$ multiplet members and candidate $πd_{5/2}$ state were measured. The results indicate that the total electric quadrupole strength of $^{129}$Sb is a factor of 1.39(11) larger than the $^{128}$Sn core, which is in stark contrast to the expectations of the empirically successful particle-core coupling scheme. Shell-model calculations perf…
Hanbury Brown--Twiss interferometry (HBT) provides crucial insights into both the space-time structure and the momentum-space evolution of ultrarelativistic nuclear collisions at freeze-out. In particular, the dependence of the HBT radii on the transverse pair momentum $K_T$ and the system charged multiplicity $dN_{\mathrm{ch}}/dη$ may reflect the mechanisms driving collective behavior in small systems. This paper argues that certain features observed in the multiplicity dependence of the HBT radii can be naturally understood if small systems evolve hydrodynamically at high-multiplicity. This …
We show and interpret three examples of nontrivial results obtained in numerical simulations of many-body systems: exponential convergence of low-lying energy eigenvalues in the process of progressive truncation of huge shell-model matrices, apparently ordered spectra generated by random interactions, and regular behavior of complex many-body energies in a system with single-particle orbitals in continuum. The possible practical applications and new approaches are suggested.
The bulk motion of nuclear matter at the ultra-high temperatures created in heavy-ion collisions at the Relativistic Heavy Ion Collider and the Large Hadron Collider is well described in terms of nearly inviscid hydrodynamics, thereby establishing this system of quarks and gluons as the most perfect fluid in nature. A revolution in the field is underway, spearheaded by the discovery of similar collective, fluid-like phenomena in much smaller systems including p+p, p+A, d+Au, and $^3$He$+$Au collisions. We review these exciting new observations and their implications.
The neutron-rich isotopes $^{58-63}$Cr were produced for the first time at the ISOLDE facility and their masses were measured with the ISOLTRAP spectrometer. The new values are up to 300 times more precise than those in the literature and indicate significantly different nuclear structure from the new mass-surface trend. A gradual onset of deformation is found in this proton and neutron mid-shell region, which is a gateway to the second island of inversion around \emph{N}=40. In addition to comparisons with density-functional theory and large-scale shell-model calculations, we present predicti…
A variable combination of realistic and random two-body interactions allows the study of collective properties, such as the energy spectra and B(E2) transition strengths in 44Ti, 48Cr and 24Mg. It is found that the average energies of the yrast band states maintain the ordering for any degree of randomness, but the B(E2) values lose their quadrupole collectivity when randomness dominates the Hamiltonian. The high probability of the yrast band to be ordered in the presence of pure random forces exhibits the strong correlations between the different members of the band.
We consider several topics concerning static magnetic dipole and electric quadrupole moments ($μ$ and $Q$) as signatures of the onset of nuclear collectivity. Having previously noted that in $^{50}\mbox{Cr}$ there is an abrupt change of sign in $Q$ of yrast states with $J^π=10^+, 12^+$, and $14^+$ relative to lower $J$ states, we discuss whether these states are oblate or prolate. We next show that configuration mixing leads to much larger changes in $Q$ than in $μ$. We then look for other bands of interest in $^{50}\mbox{Cr}$. Finally we discuss the Jolos-von Brentano relationship which relat…
The mechanism of collectivity coexisting with chaos is investigated on the quantum level. The complex spectra are represented in the basis of two-particle two-hole states describing the nuclear double-charge exchange modes in $^{48}$Ca. An example of $J^π=0^-$ excitations shows that the residual interaction, which generically implies chaotic behavior, under certain specific and well identified conditions may create transitions stronger than those corresponding to the pure mean-field picture. Therefore, for this type of excitations such an effect is not generic and in most cases the strength of…
The principal component analysis (PCA) of different parameters affecting collectivity of nuclei predicted to be candidate of the interacting boson model dynamical symmetries are performed. The results show that, the use of PCA within nuclear structure can give us a simple way to identify collectivity together with the parameters simultaneously affecting it.
The mechanism of collectivity coexisting with chaos in a finite system of strongly interacting fermions is investigated. The complex spectra are represented in the basis of two-particle two-hole states describing the nuclear double-charge exchange modes in $^{48}$Ca. An example of $J^π=0^-$ excitations shows that the residual interaction, which generically implies chaotic behavior, under certain specific and well identified conditions may create strong transitions, even much stronger than those corresponding to a pure mean-field picture. Such an effect results from correlations among the off-d…
Nuclear collectivity and the harmonic spectrum of two-body correlations
Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS（巴黎萨克雷大学理论物理研究所）；Theoretical Physics Department, CERN（欧洲核子研究中心理论物理部）；INFN-TIFPA Trento Institute of Fundamental Physics and Applications（特伦托基础物理与应用研究所）；Physics Division, Argonne National Laboratory（阿贡国家实验室物理部）；Computational Science Division, Argonne National Laboratory（阿贡国家实验室计算科学部）
We study the multiplicity and rapidity dependence of thermal and prompt photon production in p+Pb collisions at 5.02 TeV, using a (3+1)D viscous hydrodynamic framework. Direct photon anisotropic flow coefficients $v^γ_{2,3}$ and nuclear modification factor $R^γ_\mathrm{pPb}(p_T)$ are presented in both the p-going (backward) and the Pb-going (forward) directions. The interplay between initial state cold nuclear effect and final state thermal enhancement at different rapidity regions is discussed. The proposed rapidity dependent thermal photon enhancement and direct photon anisotropic flow obser…
Background: Type II shell evolution has recently been identified as a microscopic cause for nuclear shape coexistence. Purpose: Establish a low-lying rotational band in 96-Zr. Methods: High-resolution inelastic electron scattering and a relative analysis of transition strengths are used. Results: The B(E2; 0_1^+ -> 2_2^+) value is measured and electromagnetic decay strengths of the secdond 2^+ state are deduced. Conclusions: Shape coexistence is established for 96-Zr. Type II shell evolution provides a systematic and quantitative mechanism to understand deformation at low excitation energies.
Two important pieces of nuclear structure are many-body collective deformations and single-particle spin-orbit splitting. The former can be well-described microscopically by simple SU(3) irreps, but the latter mixes SU(3) irreps, which presents a challenge for large-scale, ab initio calculations on fast modern computers. Nonetheless, SU(3)-like phenomenology remains even in the face of strong mixing. The robustness of band structure is reminiscent of robust, pairing collectivity that arises from random two-body interactions.
The transition rates for the 2_{1}^{+} states in 62,64,66Fe were studied using the Recoil Distance Doppler-Shift technique applied to projectile Coulomb excitation reactions. The deduced E2 strengths illustrate the enhanced collectivity of the neutron-rich Fe isotopes up to N=40. The results are interpreted by the generalized concept of valence proton symmetry which describes the evolution of nuclear structure around N=40 as governed by the number of valence protons with respect to Z~30. The deformation suggested by the experimental data is reproduced by state-of-the-art shell calculations wit…
Ab Initio Emergence and Collapse of Nuclear Collectivity near N = Z = 40
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, Sun Yat-sen University（中山大学广东省量子计量与传感重点实验室）；School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University（北京大学物理学院及核物理与核技术国家重点实验室）
Background: Response to spin-dependent operators has been investigated in the magnetic dipole and Gamow-Teller transitions, which provides magnetic properties of a nuclear system. Purpose: I investigate an isotopic dependence of the collectivity generated by the spin-dependent interactions in the Ca and Ni isotopes through the isovector (IV) spin-flip excitations. The responses in the neutral $(t_z)$ and charge-exchange $(t_{\pm})$ channels are considered in a unified way. Method: A nuclear energy-density functional approach is employed for calculating the response functions based on the Skyrm…
We discuss emulators from the ab initio symmetry-adapted no-core shell-model framework for studying the formation of alpha clustering and collective properties without effective charges. We present a new type of an emulator, one that utilizes the eigenvector continuation technique but is based on the use of symplectic symmetry considerations. This is achieved by using physically relevant degrees of freedom, namely, the symmetry-adapted basis, which exploits the almost perfect symplectic symmetry in nuclei. Specifically, we study excitation energies, point-proton root-mean-square radii, along w…
We studied nucleus-nucleus collision in strong magnetic field based on a transport model. It is found that neutrons and protons can be separated from a nucleus by strong magnetic field and neutron-rich high density nuclear matter and low density proton collectivity matter can be formed during nucleus-nucleus collision. The electric field produced by proton collectivity can accelerate proton and charged meson up to very high energies. Besides the studies of isospin physics such as symmetry energy, these results may help us to understand the acceleration mechanisms of high energy charged particl…
Background: The $γ$ vibrational mode of excitation is an acknowledged collective mode in deformed nuclei. The collectivity depends on the details of the shell structure around the Fermi levels, in particular the presence of the orbitals that have the enhanced transition matrix elements of the non-axial quadrupole excitation. Quite recently, a sudden decrease in the excitation energy of the $γ$ vibration was observed at RIKEN RIBF for the neutron-rich Dy isotopes at $N=106$. Purpose: In the present work, by studying systematically the microscopic structure of the $γ$ vibration in the neutron-ri…
Enhanced proton-neutron interactions occur in heavy nuclei along a trajectory of approximately equal numbers of valence protons and neutrons. This is also closely aligned with the trajectory of the saturation of quadrupole deformation. The origin of these enhanced p-n interactions is discussed in terms of spatial overlaps of proton and neutron wave functions that are orbit-dependent. It is suggested for the first time that nuclear collectivity is driven by synchronized filling of protons and neutrons with orbitals having parallel spins, identical orbital and total angular momenta projections, …
New polarization potentials have been determined based on: 1) the latest photo-neutron cross section evaluation and a missing factor of two in previous work, and 2) the mass dependency of the symmetry energy, $a_{sym}(A)$. The magnitude of the first one is 35\% stronger than the currently accepted polarization potential. The second one opens up the possibility for a parameter-free polarization potential. Both polarization potentials are essentially the same for heavy nuclei. The polarization effect on quadrupole collectivity is more substantial than previously assumed for light nuclei. Particu…
Calculations of the spectra of various even-even nuclei in the fp shell ({44}Ti, {46}Ti, {48}Ti, {48}Cr and {50}Cr) are performed with two sets of two-body interaction matrix elements. The first set consists of the matrix elements of the FPD6 interaction. The second set has the same T=1 two-body matrix elements as the FPD6 interaction, but all the T=0 two-body matrix elements are set equal to zero (T0FPD6). Surprisingly, the T0FPD6 interaction gives a semi-reasonable spectrum (or else this method would make no sense). A consistent feature for even-even nuclei, e.g. {44,46,48}Ti and {48,50}Cr, …
The isospin character, the collective or single-particle nature, and the sensitivity to the slope of the nuclear symmetry energy of the low-energy isovector dipole response (known as pygmy dipole resonance) are nowadays under debate. In the present work we study, within the fully self-consistent non-relativistic mean field (MF) approach based on Skyrme Hartree-Fock plus Random Phase Approximation (RPA), the measured even-even nuclei ${}^{68}$Ni, ${}^{132}$Sn and ${}^{208}$Pb. To analyze the model dependence in the predictions of the pygmy dipole strength, we employ three different Skyrme param…
With the aim of understanding the phase structure of nuclear matter created in high-energy nuclear collisions at finite baryon density, a beam energy scan program has been carried out at Relativistic Heavy Ion Collider (RHIC). In this mini-review, most recent experimental results on collectivity, criticality and heavy flavor productions will be discussed. The goal here is to establish the connection between current available data and future heavy-ion collision experiments in a high baryon density region.
Proton Collectivity in Au+Au Collisions at $\sqrt{s_{\rm NN}}=2.4-4.5$~GeV from a Unified Purely Hadronic EOS without QCD Phase Transition
School of Physics and Electronic Science, Guizhou Normal University（贵州师范大学物理与电子科学学院）；Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing, Guizhou Normal University（贵州师范大学贵州省射电天文与数据处理重点实验室）；Department of Physics, Tsinghua University（清华大学物理系）；Center for High Energy Physics, Tsinghua University（清华大学高能物理中心）
Qualitative features of multiparticle correlations in light-heavy ion ($p+A$) collisions at RHIC and LHC are reproduced in a simple initial state model of partons in the projectile coherently scattering off localized domains of color charge in the heavy nuclear target. These include i) the ordering of the magnitudes of the azimuthal angle $n$th Fourier harmonics of two-particle correlations $v_n\{2\}$, ii) the energy and transverse momentum dependence of the four-particle Fourier harmonic $v_2\{4\}$, and iii) the energy dependence of four-particle symmetric cumulants measuring correlations bet…
We celebrate the legacies of our friend and mentor Professor Lianshou Liu who was one of the pioneers for the phenomenology of multi-particle interactions and initiated the physics of relativistic heavy-ion collisions in China. In this article, we discuss some of the recent exciting experimental observations on the collective phenomena including collectivity, chirality, criticality, strangeness production, and thermal equilibrium in high-energy nuclear collisions. Future directions, especially the physics at high baryon density, will be discussed with a focus on the first-order phase boundary …
Applications of configuration mixing methods for nuclei near the proton and neutron drip lines are discussed. A short review of magic numbers is presented. Prospects for advances in the regions of four new "outposts" are highlighted: $^{28}$O, $^{42}$Si, $^{60}$Ca and $^{78}$Ni. Topics include: shell gaps, single-particle properties, islands-of-inversion, collectivity, neutron decay, neutron halos, two-proton decay, effective charge, and quenching in knockout reactions.
The description of the energiy spectra of $0^{+}$ states for rare-earth nuclei has been done involving the degree of the collectivity of corresponding $0^{+}$-state as a systematics parameter. Holshtein-Primakoff representation leads to very good agreement with experiment. Within the framework of this approach the parameter of the collectivity is mainly determined by pairs of particles constructed on single ''effective'' level. The results may be helpful both for nuclear structure experimentalists and theorists in their investigations of low-lying states structure and transition probabilities.
The quadrupole vibrational modes of neutron-rich $N$=28 isotones ($^{48}$Ca, $^{46}$Ar, $^{44}$S and $^{42}$Si) are investigated using the canonical-basis time-dependent Hartree-Fock-Bogoliubov theory with several choice of energy density functionals, including nuclear pairing correlation. It is found that the quenching of $N$=28 shell gap and the proton holes in the $sd$-shell trigger quadrupole correlation and increase the collectivity of the low-lying 2$^+$ state in $^{46}$Ar. It is also found that the pairing correlation plays an important role to increase the collectivity. We also demonst…
An abrupt change in $α$ decay systematics around the N=126 neutron shell closure is discussed. It is explained as a sudden hindrance of the clustering of the nucleons that eventually form the $α$ particle. This is because the clustering induced by the pairing mode acting upon the four nucleons is inhibited if the configuration space does not allow a proper manifestation of the pairing collectivity.
We present calculations of the N N -> N Delta cross section in nuclear matter within the one-pion exchange model taking into account pion collectivity, vertex renormalization by the contact nuclear interactions and Dirac effective masses of the baryons due to coupling with the scalar sigma field. Introducing the Dirac effective masses leads to an in-medium reduction of the cross section. The experimental data on pion multiplicities from the collisions of Ca+Ca, Ru+Ru and Au+Au at 0.4-1.5 A GeV are well described by BUU calculations with the in-medium cross section.
We search for nonlinear effects in nuclear giant resonances (GRs), in particular the isovector dipole and the isoscalar quadrupole modes. To that end, we employ a spectral analysis of time-dependent Hartree-Fock (TDHF) dynamics using Skyrme forces. Based on TDHF calculations over a wide range of excitation amplitudes, we explore the collectivity and degree of harmonic motion in these modes. Both GR modes turn out to be highly harmonic in heavy nuclei from A=100 on. There is no trace of a transition to irregular motion and multiple resonances are predicted. Slight anharmonicities are seen for l…
Multifractal scaling analysis of nuclear giant resonance transition probability distributions is performed within the approximation which takes into account the one-particle-one-hole (1p-1h) and 2p-2h states. A new measure to determine the fractal dimensions of the spectra is introduced. It is found that chaotic dynamics governing the decay leads to non-trivial multifractal scaling properties. Such a kind of scaling is absent in the case of regular dynamics. The degree of collectivity is another element which worsens the scaling.
A brief overview is given of the Continuum Shell Model, a novel approach that extends the traditional nuclear shell model into the domain of unstable nuclei and nuclear reactions. While some of the theoretical aspects, such as role and treatment of one- and two-nucleon continuum states, are discussed more in detail, a special emphasis is made on relation to observed nuclear properties, including definitions of the decay widths and their relation to the cross sections, especially in the cases of non-exponential decay. For the chain of He isotopes we demonstrate the agreement of theoretical resu…
Continuum quasiparticle random-phase approximation for $(n,γ)$ reactions on neutron-rich nuclei: collectivity and resonances in low-energy cross section
Reflection asymmetric, octupole shapes in nuclei are a prominent aspect of nuclear structure, and have been recurrently studied over the decades. Recent experiments using radioactive-ion beams have provided evidence for stable octupole shapes. A variety of nuclear models have been employed for the related theoretical analyses. We review recent studies on the nuclear octupole shapes and collective excitations within the interacting boson model. A special focus is placed on the microscopic formulation of this model by using the mean-field method that is based on the framework of nuclear density …
We report on measurements of the hyperfine $A, B$ and $C$-constants of the $3d4s^2 ~^2D_{5/2}$ and $3d4s^2 ~^2D_{3/2}$ atomic states in $^{45}$Sc. High-precision atomic calculations of the hyperfine fields of these states and second-order corrections are performed, and are used to extract $C_{5/2}=-0.06(6)$ kHz and $C_{3/2}=+0.04(3)$ kHz from the data. These results are one order of magnitude more precise than the available literature. From the combined analysis of both atomic states, we infer the nuclear magnetic octupole moment $Ω= -0.07(53) μ_N b$, including experimental and atomic structur…
By using the general triaxial rotor model (TRM) and the phonon-configuration mixing scheme within an anharmonic-vibrator(AHV) framework, a series of global correlations between electromagnetic properties of nuclear $2^+_1$ and $2^+_2$ states are analytically established. The correlations from both models can roughly describe the experimental data involving quadrupole collectivity with few exceptions. Furthermore, there seems to be a robust orthogonal transformation between the AHV and TRM bases for realistic nuclear systems, suggesting that the two models may in fact be describing the collecti…
A mixed-symmetry nuclear shell-model scheme for carrying out calculations in regimes where there is a competition between two or more modes is proposed. A one-dimensional toy model is used to demonstrate the concept. The theory is then applied to $^{24}Mg$ and $^{44}Ti$. For lower pf-shell nuclei such as $^{44-48}Ti$ and $^{48}Cr$ there is strong SU(3) symmetry breaking due to the spin-orbit interaction. However, the quadrupole collectivity as measured by B(E2) transition strengths in the yrast band remain high even though SU(3) appears to be broken. Some results for the so-called X(5) symmetr…
Nuclear forces and the nuclear many-body problem have been some of Gerry Brown's main topics in his so productive life as a theoretical physicist. In this talk, I outline how Gerry's work laid the foundations of the modern theory of nuclear forces and ab initio calculations of atomic nuclei. I also present some recent developments obtained in the framework of nuclear lattice simulations.
