Matrix elements of a two-body interaction between states of the jn configutation (n identical nucleons in the j-orbit) are functions of two-body energies. In some cases, diagonal matrix elements are linear combinations of two-body energies. The coefficients of these linear combinations are rational and non-negative numbers, independent of the two-body interaction. It is shown that if in the jn configuration there is only one state with given spin J, its eigenvalue (the diagonal matrix element) is equal to a linear combination of two-body energies with rational and non-negative coefficients. These coefficients have the same values for any two-body interaction (solvable eigenvalues). If there are several J-states in the jn configuration, they define a sub-matrix of the interaction which should be diagonalized to yield eigenvalues and eigenstates. Bases of these states are constructed from which the sub-matrix characterized by J may be obtained for any two-body interaction. The diagonal elements are linear combinations of two-body energies whose coefficients are independent of the two-body interaction and the non-vanishing ones are rational and positive. Aslo in the non-diagonal elements the coefficients have a simple form. States in the seniority scheme are shown to form such bases. If one of them is an eigenstate of any two-body interaciton its eigenvalue is shown to be solvable.
The Alt-Grassberger-Sandhas N-body theory is used to study interaction of eta-mesons with d, 3He, and 4He. Separable expansion of the subamplitudes is adopted to convert the integral equations into the quasi-two-body form. The resulting formalism is applied to fit the existing data for low-energy eta production on few-nucleon targets. On the basis of this fitting procedure the scattering lengths a_{eta d}, a_{eta 3He}, a_{eta 4He} as well as the subthreshold behaviour of the elementary eta-N scattering amplitude are obtained.
Four-body Faddeev-Yakubovsky calculation of polarization transfer coefficient $\bm{K}_y^{y'}$ in the $^2$H$(\vec{\bm{d}}, \vec{\bm{p}})^3$H reaction at very low energies
Using separable potentials for $\bar{K}N-πΣ$ interaction, we investigated four-body kaonic nuclear systems such as $K^{-}ppn$ and $K^{-}K^{-}pp$, with the Faddeev AGS method in the momentum representation. The Faddeev calculations are based on the quasi-particle method and the method of the energy dependent pole expansion was used to obtain the separable representation for the integral kernels in the three- and four-body equations. Different types of $\bar{K}N-πΣ$ potentials based on phenomenological and chiral SU(3) approach are used and it was shown that the kaonic nuclear systems under cons…
We present a new framework to treat the dissipation and fluctuation dynamics associated with nucleon-nucleon scattering in heavy-ion collisions. The two-body collision processes are effectively described in terms of the diffusion of nucleons in viscous nuclear media, governed by a set of Langevin equations in momentum space. The new framework combined with the usual mean field dynamics can be used to simulate heavy-ion collisions at intermediate energies. As a proof of principle, we simulate Au + Au reactions and obtain results consistent with other existing codes under the same constrained co…
We use the recently introduced single-particle states obtained from localized Deuteron wave-functions as a basis for nuclear many-body calculations. We show that energies can be substantially lowered if the natural orbits obtained from this basis are used. We use this modified basis for ${}^{10}B$, ${}^{16}O$ and ${}^{24}Mg$ employing the bare $NNLO_{opt}$ Nucleon-Nucleon interaction. The lowering of the energies increases with the mass. Although in principle natural orbits require a full scale preliminary many-body calculation, we found that an approximate preliminary many-body calculation, w…
We make variational estimates for the binding energies of $^2H,~^3H,~^4He,~^{16}O,~^{40}Ca$, showing their running with the Similarity Renormalization Group (SRG) cutoff towards the infrared region and show the generalized Tjon lines that emerge from the calculations. We infer the SRG evolution of the three-body contributions for the $^3H$ and $^4He$ binding energies by computing the two-body contributions with a variational approach assuming that four-body forces are negligible. At any given SRG cutoff, the three-body contributions may then be inferred as being the experimental value minus th…
破裂截面的Borromean核22 C确定通过使用四体程函模型，包括库仑修正。在超球坐标系下，在20 C + n + n三体模型中构造了束缚态和连续态。我们通过R-矩阵方法计算具有正确渐近行为的连续态。对于n+ n势，我们使用明尼苏达相互作用。由于21 C没有精确的实验数据，我们对20 C + n势定义了不同的参数集。这些参数组提供不同的散射长度，和预期的3/2+激发态的共振能量。然后我们分析了22 C基态能量和均方根半径，以及E1强度分布和破裂截面。E1强度分布在低能量下呈现增强。它的振幅与低结合能有关，而不是与三体共振有关。我们发现，在低能量的截面的形状是敏感的基态性质。此外，我们建议存在一个低能量的2+共振，这应该是可观察到的分裂实验。
通过将我们最近发展的$p d \to ^3$ He $η$反应的两步模型推广到高能，验证了三体机制产生$η$介子的有效性，该模型成功地再现了阈附近数据的能量依赖性.该模型中的$η$生产通过$p p \to πd$和$πN \to ηp$反应分两步进行，中间体颗粒脱壳。利用几个体方程构造了$η^3$ He弹性散射的$T$矩阵，并将末态相互作用（FSI）引入其中。在计算的角分布与一些最近可用的数据的比较，我们发现在高能量的模型的局限性。
Nuclear Many-Body Theory of Electroweak Interactions with Nuclei at Intermediate Energies
将文献\cite{GNO97}中的核包容电子模型的准弹性（QE）贡献推广到研究电弱荷电电流（CC）引起的中能核反应，为将来的中微子振荡实验提供理论依据.长程核关联（RPA），最终状态相互作用（FSI）和库仑修正包括在模型中。RPA的相关性在整个中微子能量范围内发挥着至关重要的作用，高达500兆电子伏，在这项工作中研究。通过元素周期表和反应$^{12}$ C $(ν_μ,μ^-)X$和$^{12}$ C $(ν_e,e^-)X$阈值附近的包容μ子捕获的预测也给出了。
Cross sections for elastic and inelastic scattering of the weakly-bound $^9$Be nucleus on a $^{120}$Sn target have been measured at seven bombarding energies around and above the Coulomb barrier. The elastic angular distributions are analyzed with a four-body continuum-discretized coupled-channels (CDCC) calculation, which considers $^9$Be as a three-body projectile ($α$ + $α$ + n). An optical model analysis using the São Paulo potential is also shown for comparison. The CDCC analysis shows that the coupling to the continuum part of the spectrum is important for the agreement with experimental…
We study the structure of $^9_Λ$Be in the framework of three body $α+α+Λ$ cluster model using YNG-NF interaction with the Gaussian expansion method. Employing the complex scaling method, we obtain the energies of bound states as well as energies and decay widths of the resonant states. By analyzing our wave functions of bound states and resonant states, we confirm three analogue states of $^9_Λ$Be pointed out by Band${\rm \bar{o}}$ and Motoba {\it et al.} \cite{motoba1983,motoba1985,bando1983}, $^8$Be analogue states, $^9_Λ$Be genuine states and $^9$Be analogue states. The new states of $^9_Λ$…
A new dispersion (asymptotic) theory is proposed for the peripheral sub- and above-barrier charged particle transfer $A(x,y)B$ reaction in the three-body ($A$, $a$ and $y$) model where $ x= y +a$ and $B=A+a$, and $ a$ is a transferred particle. It is based on the combination of the dispersion theory and the conventional DWBA method. The explicit forms have been derived for the exact three-body pole amplitude and differential cross section in which the contribution of the three-body ($A$, $a$ and $y$) Coulomb dynamics of the transfer mechanism in the peripheral partial amplitudes, corresponding…
The even-even Ti isotopic chain, from A = 42 to 70, has been studied within the nuclear shell-model framework by employing an effective Hamiltonian which is derived by way of many-body perturbation theory from a chiral potential with two- and three-body forces, and includes three-body contributions which account for Pauli principle violations in nuclei with more than two valence particles. We consider 40Ca as a closed core and a model space spanned by the neutron and proton 0f1p orbitals with the addition of the 0g9/2 orbital for neutrons. Calculated two-neutron separation energies and excitat…
Impact of correlations on nuclear binding energies
KU Leuven（荷语鲁汶大学）；ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH（极端物质研究所EMMI，GSI重离子研究中心有限公司）；Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）；IRFU, CEA, Université Paris-Saclay（IRFU，法国原子能和替代能源委员会，巴黎萨克雷大学）；CEA, DES, IRESNE, DER, SPRC, LEPh（法国原子能和替代能源委员会，DES，IRESNE，DER，SPRC，LEPh）；Technische Universität Darmstadt（达姆施塔特工业大学）
We apply a quark combination model to study yield densities and transverse momentum ($p_{T}$) spectra of strange (anti-)hadrons at mid-rapidity in central Au+Au collisions at $\sqrt{s_{NN}}=$ 7.7, 11.5, 19.6, 27, 39 and 200 GeV. We show that experimental data for $p_{T}$ spectra of (anti-)hadrons in these collisions can be systematically described by the equal velocity combination of constituent quarks and antiquarks at hadronization. We obtain $p_{T}$ spectra of quarks and antiquarks at hadronization and study their collision energy dependence. We also reproduce the yield densities of hadrons…
Two-body correlations in N=8 and 10 nuclei and effective neutron-neutron interactions in Tamm-Dancoff and two-particle RPA models
本文用粒子-粒子RPA模型研究了~（14）C，~（12）Be，~（11）Li和~（14）Be的双中子价波函数的性质。RPA模型考虑了堆芯中的两体相关性，因此它比假设中子闭合壳（或子壳）堆芯的模型更好地描述了能量和振幅。用Gogny中子-中子有效相互作用或等效密度依赖的δ力，我们能够再现这些核和相应核中的两中子分离能，但9-Li除外。计算结果表明，~（12）Be_（13）Be与~（11）Be具有相同的2s-1 p ~（12）壳层反转。
We explore the possibility to perform symmetry restoration with the variation after projection technique on a quantum computer followed by additional post-processing. The final goal is to develop configuration interaction techniques based on many-body trial states pre-optimized on a quantum computer. We show how the projection method used for symmetry restoration can prepare optimized states that could then be employed as initial states for quantum or hybrid quantum-classical algorithms. We use the quantum phase estimation and quantum Krylov approaches for the post-processing. The latter metho…
We present an effective field theory (EFT) at leading order to describe light single-$Λ$ hypernuclei. Owing to the weak $Λ$ binding and to the $ΛN$ short interaction range, meson exchange forces are approximated by contact interactions within a pionless EFT where the only degrees of freedom are baryons. At leading order, the $Λ$-nuclear interaction contains two 2-body (singlet and triplet) and three 3-body interaction terms, a total of 5 terms associated with 5 coupling strengths or low energy constants (LECs). We adopt the 2-body LECs from hyperon-nucleon scattering data and interaction model…
The charged-current quasi-elastic (CCQE) scattering of muon neutrinos on a carbon target is analyzed using the relativistic distorted-wave impulse approximation (RDWIA) taking into account the contribution of the two-particle and two-hole meson exchange current ($2p-2h$ MEC) to the weak response functions. A fit the RDWIA+MEC model to the MiniBooNE neutrino data is performed and the best fit value of nucleon axial mass $M_A=1.2 \pm 0.06$ GeV is obtained. We also extract the values of the axial form factor $F_A(Q^2)$ as a function of the squared momentum transfer $Q^2$ from the measured $dσ/dQ^…
