Denis Lacroix
The possibility to use functionals of occupation numbers and natural orbitals for interacting fermions is discussed as an alternative to multi-reference energy density functional method. An illustration based on the two-level Lipkin model is discussed.
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In this work we use the recently measured neutron occupancies in the 76Ge and 76Se nuclei as a guideline to define the neutron quasiparticle states in the 1p0f0g shell. We define the proton quasiparticles by inspecting the odd-mass nuclei adjacent to 76Ge and 76Se. We insert the resulting quasiparticles in a proton-neutron quasiparticle random-phase approximation (pnQRPA) calculation of the nuclear matrix element of the neutrinoless double beta (0-nu-beta-beta) decay of 76Ge. A realistic model space and effective microscopic two-nucleon interactions are used. We include the nucleon-nucleon sho…
The occupancies and vacancies of the valence neutron orbitals across the stable tin isotopic chain from $112\leq A\leq 124$ have been determined. These were inferred from the cross sections of neutron-adding and -removing reactions. In each case, the reactions were chosen to have good angular-momentum matching for transfer to the low- and high-$\ell$ orbitals present in this valence space. These new data are compared to older systematic studies. The effective single-neutron energies are determined by combining information from energy centroids determined from the adding and removing reactions.…
A Fortran program for the calculation of the ground state properties of axially deformed even-even nuclei in the relativistic framework is presented. In this relativistic mean field (RMF) approach a set of coupled differential equations namely the Dirac equation with potential terms for the nucleons and the Glein-Gordon type equations with sources for the meson and the electromagnetic fields are to be solved self-consistently. The well tested basis expansion method is used for this purpose. Accordingly a set of harmonic oscillator basis generated by an axially deformed potential are used in th…
The interplay between the orbital and spin currents in (e,e') excitations of light nuclei is discussed. The microscopic analysis of E1 and M2 resonances was performed within the particle-core coupling approximation (PCC) of the shell model. The comparison of the theoretical results with the available experimental data has shown that the studies of relative contributions of the orbital and different spin components of the nuclear current into the excitation of EJ and MJ resonances could be useful for the identification of their configurational structure.
A simple criterion for the ΔI = 4 bifurcation is applied to thirty superdeformed bands in the A~150 mass region. The analysis allows to differentiate between active and inactive for staggering single-particle states. The consideration is based on additivity of nonaxial hexadecapole moment, which plays a key role in the phenomenon.
A method to calculate the hole spectral function in the discrete part of the spectrum is suggested within the natural orbital representation of the one-body density matrix of $A$-nucleon system using its relationship with the overlap functions of the eigenstates in the $(A-1)$-nucleon system.
Nuclear scissors modes are considered in the frame of Wigner function moments method generalized to take into account spin degrees of freedom and pair correlations simultaneously. A new source of nuclear magnetism, connected with counter-rotation of spins up and down around the symmetry axis (hidden angular momenta), is discovered. Its inclusion into the theory allows one to improve substantially the agreement with experimental data in the description of energies and transition probabilities of scissors modes in rare earth nuclei.
The natural orbitals and natural occupation numbers of various N = Z, sp and sd shell nuclei are calculated by applying a correlated one-body density matrix. The correlated density matrix has been evaluated by considering central correlations of Jastrow type and an approximation named factor cluster expansion. The correlation effects on the natural orbitals, natural occupation numbers and the Fermi sea depletion are discussed and analysed. In addition, an approximate expression for the correlated one-body density matrix of the nuclear matter has been used for the evaluation of the relative mom…
The structure of nuclei with $Z\sim100$ is investigated systematically by the Cranked Shell Model (CSM) with pairing correlations treated by a Particle-Number Conserving (PNC) method. In the PNC method, the particle number is conserved and the Pauli blocking effects are taken into account exactly. By fitting the experimental single-particle spectra in these nuclei, a new set of Nilsson parameters ($κ$ and $μ$) is proposed. The experimental kinematic moments of inertia and the band-head energies are reproduced quite well by the PNC-CSM calculations. The band crossing, the effects of high-$j$ in…
Isomer triplets in odd-odd transitional rare earth nuclei: unique features, orbital systematics and characterization
本研究通过核数据调查揭示轻稀土区奇-奇过渡核中存在低能长寿同质异能三重态，结合双准粒子转子模型分析其轨道系统性，明确高自旋闯入中子轨道对其形成的关键作用。
An approximate SU(3) symmetry appears in heavy deformed even-even nuclei, by omitting the intruder Nilsson orbital of highest total angular momentum and replacing the rest of the intruder orbitals by the orbitals which have escaped to the next lower major shell. The approximation is based on the fact that there is a one-to-one correspondence between the orbitals of the two sets, based on pairs of orbitals having identical quantum numbers of orbital angular momentum, spin, and total angular momentum. The accuracy of the approximation is tested through calculations in the framework of the Nilsso…
Within the unified model of Bohr and Mottelson we derive the following linear energy weighted sum rule for low energy orbital 1$^+$ excitations in even-even deformed nuclei $$S_{\rm LE}^{\rm lew} (M_1^{\rm orb}) \cong (6/5) ε(B(E2; 0^+_1 \rightarrow 2_1^+ K=0)/Z e^2<r^2>^2) μ^2_N$$ with B(E2) the E2 strength for the transition from the ground state to the first excited state in the ground state rotational band, $<r^2>$ the charge r.m.s. radius squared and $ε$ the binding energy per nucleon in the nuclear ground state. It is shown that this energy weighted sum rule is in good agreement with ava…
The relationship between the deformed harmonic oscillator and the formation of molecular cluster structures, whereby valence neutrons are exchanged between cluster cores, is examined. It is found that there is a strong connection between the properties of the valence orbitals associated with deformed structures in the deformed harmonic oscillator and the molecular orbitals created by linear combinations of single-centre orbitals around nuclear clusters. The conclusion is that in addition to the appearance of clustering in the deformed harmonic oscillator that \emph{every} prolate deformed clus…
$Δl =1$ coupling of single-particle orbitals in octupole deformed nuclei
研究揭示了八极变形核中$Δl=1$耦合的重要性，通过Nilsson模型分析单粒子轨道混合比，并利用粒子-转子模型验证了$Δl=1$对旋转结构的影响，提出八极耦合协同驱动反射不对称性。
Radial and orbital decomposition of charge radii of Ca nuclei:Comparative study of Skyrme and Fayans functionals
本研究在密度泛函理论框架下分解Ca核电荷半径的径向与轨道贡献，比较Skyrme和Fayans泛函，揭示Fayans泛函在N<20和20≤N≤28区域行为的共同起源，强调需同时描述两个区域。
We have considered the possibility to describe the astrophysical S-factors of some light atomic nuclei on the basis of the potential cluster model by taking into account the supermultiplet symmetry of wave functions and splitting the orbital states according to Young's schemes. Such an approach allows analyzing the structure of inter-cluster interactions, to determine the presence of allowed and forbidden states in the interaction potential and so the number of nodes of the orbital wave function of cluster relative motion.
Deformed natural orbitals for ab initio calculations
本文研究了自然基在对称破缺多体计算中的应用，展示了其在提高计算效率方面的优势。
Two important ingredients of nuclear shell-structure, kinetic energy and spin-orbit splitting, are studied as a function of orbital angular momenta \ell and binding energies, when binding energies of neutrons decrease towards zero. If we use the standard parameters of the Woods-Saxon potential in βstable nuclei and approach the limit of zero binding energy from 10 MeV, the spin-orbit splitting for n=1 orbitals decreases considerably for \ell=1, while for \ell > 2 little decreasing is observed in the limit. In contrast, the kinetic energy decreases considerably for \ell \simleq 3. The smaller t…
We show that within the proxy-SU(3) scheme the wave functions of the normal parity orbitals in a given nuclear shell are affected very little as a result of the replacement of the abnormal parity orbitals by their 0[110] proxy-SU(3) counterparts.
A low-energy magnetic dipole $(M1)$ spin-scissors resonance (SSR) located just below the ordinary orbital scissors resonance (OSR) was recently predicted in deformed nuclei within the Wigner Function Moments (WFM) approach. We analyze this prediction using fully self-consistent Skyrme Quasiparticle Random Phase Approximation (QRPA) method. Skyrme forces SkM*, SVbas and SG2 are implemented to explore SSR and OSR in $^{160,162,164}$Dy and $^{232}$Th. Accuracy of the method is justified by a good description of M1 spin-flip giant resonance. The calculations show that isotopes $^{160,162,164}$Dy i…
A phenomenological method based on the natural orbital representation is applied to construct the ground state one-body density matrix which describes correctly both density and momentum distributions in $^{4}He$, $^{16}O$ and $^{40}Ca$ nuclei. The parameters of the matrix are fixed by a best fit to the experimental density distribution and to the correlated nucleon momentum distribution. The method allows the natural orbitals, the occupation probabilities and the depletion of the Fermi sea to be obtained. Ground-state characteristics of $^{4}He$, $^{16}O$ and $^{40}Ca$ nuclei, such as rms rad…
Proton momentum distributions of the $^{12}C$, $^{16}O$, $^{40}Ca$, $^{56}Fe$ and $^{208}$Pb nuclei are calculated by a model using the natural orbital representation and the experimental data for the momentum distribution of the $^{4}He$ nucleus. The model allows realistic momentum distributions to be obtained using only hole-state natural orbitals (or mean-field single-particle wave functions as a good approximation to them). To demonstrate the model two different sets of wave functions were employed and the predictions were compared with the available empirical data and other theoretical re…
We show that fully aligned neutron-proton pairs play a crucial role in the low-energy spectroscopy of nuclei. with valence nucleons in a high-j orbital. Their dominance is valid in nuclei with valence neutrons and protons in different high-j orbitals as well as in N = Z nuclei, where all nucleons occupy the same orbital. We demonstrate analytically this generic feature of the neutron-proton interaction for a variety of systems with four valence nucleons interacting through realistic, effective forces. The dominance of fully aligned neutron-proton pairs results from the combined effect of (i) a…
Role of tensor forces in nuclei
基于高精度核力数据，研究张量力导致核子形成低势能团簇，解释^8Be寿命、Hoyle态等核现象。
Employing a cranking Hamiltonian, in the static path approximation to the partition function, we have studied the behaviour of the moment of inertia of $^{64}Zn$ at a few values of temperatures as a function of the rotation frequency. At a low temperature T = 0.5 MeV and J=16 rotational alignment of $0g_{9/2}$ orbitals takes place. But at a high temperature T = 2.0 MeV about 40 - 45$\%$ of all the angular momenta are generated by the alignment of the same orbitals. This should imply a decrease in collectivity for all the spins at high temperatures.
Machine learning orbital-free density functional theory: taming quantum shell effects in deformed nuclei
本文提出机器学习无轨道密度泛函理论方法，首次成功高精度描述球形16O和变形20Ne核的基态性质与势能曲线，证明无轨道能量密度泛函可实际驯服变形核中的量子壳效应。
Natural and Dyson orbitals in small helium drops
研究小氦滴中自然和迪逊轨道的性质，采用超球面簇模型计算波函数，通过非本地单体密度矩阵对角化获得自然轨道，通过两滴波函数重叠得到迪逊轨道，讨论其形状、占据和演化特性，发现自然轨道在表示密度时更优。
Neutron shell-structure and the resulting possible deformation in the neighborhood of neutron-drip-line nuclei are systematically discussed, based on both bound and resonant neutron one-particle energies obtained from spherical and deformed Woods-Saxon potentials. Due to the unique behavior of weakly-bound and resonant neutron one-particle levels with smaller orbital angular-momenta $\ell$, a systematic change of the shell structure and thereby the change of neutron magic-numbers are pointed out, compared with those of stable nuclei expected from the conventional j-j shell-model. For spherical…
The effects of varying the spin-orbit and tensor components of a realistic interaction on $M1$ excitation rates and $B(E2)'s$ are studied on nuclei in the $0p$ and $1s-0d$ shells. Not only the total $M1$ but also the spin and orbital parts separately are studied. The single-particle energies are first calculated with the same interaction that is used between the valence nucleons. Later this stringent condition is relaxed somewhat and the $1s$ level is raised relative to $0d$. For nuclei up to $^{28}Si$, much better results i.e stronger $B(M1)$ rates are obtained by increasing the strength of t…
Effects of rotation and valence nucleons in molecular-like $α$-chain nuclei
基于协变密度泛函理论的三维格点推转模型研究表明，转动诱导价核子由 π 轨道跃迁至 σ 轨道，可稳定线性 α 链结构。
A relativistic mean-field model is used to study the ground-state properties of neutron-rich nuclei. Nonlinear isoscalar-isovector terms, unconstrained by present day phenomenology, are added to the model Lagrangian in order to modify the poorly known density dependence of the symmetry energy. These new terms soften the symmetry energy and reshape the theoretical neutron drip line without compromising the agreement with existing ground-state information. A strong correlation between the neutron radius of 208Pb and the binding energy of valence orbitals is found: the smaller the neutron radius …
Isoscalar, isovector and orbital contributions in $M1$ transitions from analogous $M1$ and Gamow-Teller transitions in $T=\frac{1}{2}$ mirror nuclei
本文研究了质量数23至37的奇A、T=1/2镜像核，通过比较类似M1与Gamow-Teller跃迁计算轨道贡献，并利用同位旋非守恒相互作用及ab initio有效相互作用进行分析。
Different steps leading to the new functional for pairing based on natural orbitals and occupancies proposed in ref. [D. Lacroix and G. Hupin, arXiv:1003.2860] are carefully analyzed. Properties of quasi-particle states projected onto good particle number are first reviewed. These properties are used (i) to prove the existence of such a functional (ii) to provide an explicit functional through a 1/N expansion starting from the BCS approach (iii) to give a compact form of the functional summing up all orders in the expansion. The functional is benchmarked in the case of the picked fence pairing…
A survey of the available single-proton data in $A\leq17$ nuclei, along with calculations using a Woods-Saxon potential, show that the ordering of the $0d_{5/2}$ and $1s_{1/2}$ proton orbitals are determined primarily by the proximity of the $s$-state proton energy to the Coulomb barrier. This is analogous to the dependence of the corresponding neutron orbitals in proximity to the neutron threshold, that was previously discussed.
Effects of the density dependence of the nuclear symmetry energy on ground-state properties of superheavy nuclei are studied in the relativistic mean-field theory. It is found that the softening of the symmetry energy plays an important role in the empirical shift [Phys. Rev. C 67, 024309 (2003)] of spherical orbitals in superheavy nuclei. The calculation based on the relativistic mean-field models NL3 and FSUGold supports the double shell closure in $^{292}120$ with the softening of the symmetry energy. In addition, the significant effect of the density dependence of the symmetry energy on th…
The enhancement observed below 2 MeV in the radiative strength function of nuclei near closed shells is explained by shell model calculations as M1 transitions between excited states. In the open-shell a change to a bimodal structure composed of the zero energy spike and a scissors resonance is found. The features are caused by realignment of high-j orbitals.
Based on the Relativistic continuum Hartree-Bogoliubov (RCHB) theory, the pseudo-spin approximation in exotic nuclei is investigated in Zr and Sn isotopes from the proton drip line to the neutron drip line. The quality of the pseudo-spin approximation is shown to be connected with the competition between the centrifugal barrier (CB) and the pseudo-spin orbital potential (PSOP). The PSOP depends on the derivative of the difference between the scalar and vector potentials $dV/dr$. If $dV/dr = 0$, the pseudo-spin symmetry is exact. The pseudo-spin symmetry is found to be a good approximation for …
Relation between E2 transitions in even--even and odd-mass nuclei
本文研究偶偶核中B(E2;2_1^+ -> 0_1^+)值与相邻奇质量核中对应B(E2;J_i -> J_f)值之间的关系，在单j轨道和核子-核子相互作用保持seniority的假设下得到简单关系，并考虑多个非简并轨道时的扰动，应用于缺中子锡同位素的最新测量。
Correlations between low-lying electric dipole (E1) strength and neutron skin thickness are systematically investigated with the fully self-consistent random-phase approximation using the Skyrme energy functionals. The presence of strong correlation among these quantities is currently under dispute. We find that the strong correlation is present in properly selected nuclei, namely in spherical neutron-rich nuclei in the region where the neutron Fermi levels are located at orbits with low orbital angular momenta. The significant correlation between the fraction of the energy-weighted sum value …
Effect of the charge asymmetry and orbital angular momentum in the entrance channel on the hindrance to complete fusion
本研究通过DNS模型研究重离子碰撞中完全融合的阻碍，发现其与准裂变相关，并展示了电荷不对称性和角动量的作用，通过与实验数据比较验证了入射道质量不对称性的影响。
Quantum entanglement patterns in the structure of atomic nuclei within the nuclear shell model
本文利用量子信息工具在核壳层模型内分析了轻质量与中等质量同位素的量子纠缠模式，揭示了纠缠与能量、角动量及同位旋的关系，为NISQ时代设计更高效的量子算法提供了指导。
Ab initio calculations of nuclei face the challenge of simultaneously describing strong short-range internucleon correlations and the long-range properties of weakly-bound halo nucleons. Natural orbitals, which diagonalize the one-body density matrix, provide a basis which is better matched to the physical structure of the many-body wave function. We demonstrate that the use of natural orbitals significantly improves convergence for ab initio no-core configuration interaction calculations of the neutron halo nucleus 6He, relative to the traditional oscillator basis.
Calculations of B(E2)'s and quadruplole moments in the g_{9/2 region below ^{100} Sn are hampered by the fact that the inclusion of the g_{7/2}configuration leads to model spaces that are too large to handle. We therefore examine lighter nuclei if the fp region where one can easily include all the orbitals, f,{}_{7/2}, p_{3/2}, p_{1/2}and f_{5/2} . We perform such calculations but then take a step back and exclude the f_{5/2} orbital. By comparing the 2 calculations we can hope to get insight into the importance of the missing spin-orbit partner in other regions.
Orbital-free Density Functional Theory: differences and similarities between electronic and nuclear systems
本文首次尝试将无轨道密度泛函理论（OF-DFT）应用于原子核，通过实现无轨道动能并求解相关薛定谔方程，探讨了电子与核系统的差异及OF-DFT在核物理中的实际应用与未决问题。
Exploring Short-Range Correlations in Symmetric Nuclei: Insights into Contacts and Entanglement Entropy
本文研究对称核中核子短程关联的轨道纠缠熵与Tan接触之间的关系，发现质子-质子对与中子-质子对的纠缠熵比值近似为2.0，并提出该标度关系对所有对称核普遍成立的可能解释。
The apparent splitting between orbitals that are spin-orbit partners can be substantially influenced by the effects of finite binding. In particular, such effects can account for the observed decrease in separation of the neutron $1p_{3/2}$ and $1p_{1/2}$ orbitals between the $^{41}$Ca and $^{35}$Si isotopes. This behavior has been the subject of recent experimental and theoretical works and cited as evidence for a proton "bubble" in $^{34}$Si causing an explicit weakening of the spin-orbit interaction. The results reported here suggest that the change in the separation between the $1p_{3/2}$ …
The rotational bands in nuclei with $Z \approx 100$ are investigated systematically by using a cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method, in which the blocking effects are taken into account exactly. By fitting the experimental single-particle spectra in these nuclei, a new set of Nilsson parameters ($κ$ and $μ$) and deformation parameters ($\varepsilon_2$ and $\varepsilon_4$) are proposed. The experimental kinematic moments of inertia for the rotational bands in even-even, odd-$A$ and odd-odd nuclei, and the bandhead energies …
We survey approaches to nonrelativistic density functional theory (DFT) for nuclei using progress toward ab initio DFT for Coulomb systems as a guide. Ab initio DFT starts with a microscopic Hamiltonian and is naturally formulated using orbital-based functionals, which generalize the conventional local-density-plus-gradients form. The orbitals satisfy single-particle equations with multiplicative (local) potentials. The DFT functionals can be developed starting from internucleon forces using wave-function based methods or by Legendre transform via effective actions. We describe known and unres…
The calculation of a statistical measure of complexity and the Fisher-Shannon information in nuclei is carried out in this work. We use the nuclear shell model in order to obtain the fractional occupation probabilities of nuclear orbitals. The increasing of both magnitudes, the statistical complexity and the Fisher-Shannon information, with the number of nucleons is observed. The shell structure is reflected by the behavior of the statistical complexity. The magic numbers are revealed by the Fisher-Shannon information.
Nuclear level density at low excitation energies is proposed as an indicator of the first order phase transitions in nuclei. The new signature, a maximum value of the level density at the critical point, appears to be sensitive to the detailed way the phase transition takes place in different nuclear regions: it is consistent with phase coexistence in the N=90 region, and with a rapid crossing of the two phases, without their coexistence/mixing at the critical point in the N=60 region, respectively. Candidates for critical point nuclei are proposed for odd-mass and odd-odd nuclei, using correl…
Machine learning is employed to build an energy density functional for self-bound nuclear systems for the first time. By learning the kinetic energy as a functional of the nucleon density alone, a robust and accurate orbital-free density functional for nuclei is established. Self-consistent calculations that bypass the Kohn-Sham equations provide the ground-state densities, total energies, and root-mean-square radii with a high accuracy in comparison with the Kohn-Sham solutions. No existing orbital-free density functional theory comes close to this performance for nuclei. Therefore, it provid…
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