We extend the recently developed Jacobi no-core shell model to hypernuclei. Based on the coefficients of fractional parentage for ordinary nuclei, we define a basis where the hyperon is the spectator particle. We then formulate transition coefficients to states that single out a hyperon-nucleon pair which allow us to implement a hypernuclear many-baryon Hamiltonian for $p$-shell hypernuclei. As a first application, we use the basis states and the transition coefficients to calculate the ground states of $^{4}_Λ$He, $^{4}_Λ$H, $^{5}_Λ$He, $^{6}_Λ$He, $^{6}_Λ$Li, and $^{7}_Λ$Li and, additionally, the first excited states of $^{4}_Λ$He, $^{4}_Λ$H, and $^{7}_Λ$Li. In order to obtain converged results, we employ the similarity renormalization group (SRG) to soften the nucleon-nucleon and hyperon-nucleon interactions. Although the dependence on this evolution of the Hamiltonian is significant, we show that a strong correlation of the results can be used to identify preferred SRG parameters. This allows for meaningful predictions of hypernuclear binding and excitation energies. The transition coefficients will be made publicly available as HDF5 data files.
Empirical data on the spectra of light hypernuclei, especially the data from recent gamma-ray experiments, is used to constrain the parameters which govern the p(nucleon)s(Lambda) and p(nucleon)p(Lambda) two-body matrix elements that enter into shell-model calculations.
We introduce a mean field model based on realistic 2-body baryon interactions and calculate spectra of a set of p-shell and sd-shell Λ hypernuclei - 13ΛC, 17ΛO, 21ΛNe, 29ΛSi and 41ΛCa. The hypernuclear spectra are compared with the results of a relativistic mean field (RMF) model and available experimental data. The sensitivity of Λ single-particle energies to the nuclear core structure is explored. Special attention is paid to the effect of spin-orbit ΛN interaction on the energy splitting of the Λ single particle levels 0p3/2 and 0p1/2. In particular, we analyze the contribution of the symme…
Halo Structures in p-Shell Hypernuclei with Natural Orbitals
Technische Universität Darmstadt（达姆施塔特工业大学）；Institut für Kernphysik, Fachbereich Physik, Technische Universität Darmstadt（达姆施塔特工业大学物理系核物理研究所）；Helmholtz Forschungsakademie Hessen für FAIR, GSI Helmholtzzentrum（黑森FAIR亥姆霍兹研究中心GSI亥姆霍兹中心）
We evaluate pionic decay widths of Lambda hypernuclei using a shell model for, both the nuclear bound and the continuum nucleon wave functions in the final state, and distorted waves for the outgoing pion. An excellent agreement with the recent KEK measurement of $π^-$-decay widths of $^{12}_Λ$C and $^{28}_Λ$Si is found. Besides, results for $^{56}_Λ$Fe are consistent with the existing upper bound.
Energy spectra of $0s$-orbit $Λ$ states in $p$-shell $Λ$ hypernuclei ($^{A}_ΛZ$) and those in $^{19}_Λ\textrm{F}$ are studied with the microscopic cluster model and antisymmetrized molecular dynamics using the $G$-matrix effective $ΛN$ ($ΛNG$) interactions. Spin-dependent terms of the ESC08a version of the $ΛNG$ interactions are tested and phenomenologically tuned to reproduce observed energy spectra in $p$-shell $^{A}_ΛZ$. Spin-dependent contributions of the $ΛN$ interactions to spin-doublet splitting and excitation energies are discussed. Energy spectra for unobserved excited states in $p$-s…
Variational calculations for s-shell hypernuclei are performed by explicitly including $Σ$ degrees of freedom. Four sets of YN interactions (SC97d(S), SC97e(S), SC97f(S) and SC89(S)) are used. The bound-state solution of $_Λ^5$He is obtained and a large energy expectation value of the tensor $ΛN-ΣN$ transition part is found. The internal energy of the $^4$He subsystem is strongly affected by the presence of a $Λ$ particle with the strong tensor $ΛN-ΣN$ transition potential.
Information on Lambda-7Li, Lambda-9Be, Lambda-10B, Lambda-11B, Lambda-12C, Lambda-15N, and Lambda-16O from the Ge detector array Hyperball is interpreted in terms of shell-model calculations that include both Lambda and Sigma configurations with p-shell cores. It is shown that the data puts strong constraints on the effective Lambda-N interaction.
$0s$-orbit $Λ$ states in $p$-shell double-$Λ$ hypernuclei ($^{\ \,A}_{ΛΛ}Z$), $^{\ \,8}_{ΛΛ}\textrm{Li}$, $^{\ \,9}_{ΛΛ}\textrm{Li}$, $^{10,11,12}_{\ \ \ \ \ ΛΛ}\textrm{Be}$, $^{12,13}_{\ \ ΛΛ}\textrm{B}$, and $^{\,14}_{ΛΛ}\textrm{C}$ are investigated. Microscopic cluster models are applied to core nuclear part and a potential model is adopted for $Λ$ particles. The $Λ$-core potential is a folding potential obtained with effective $G$-matrix $Λ$-$N$ interactions, which reasonably reproduce energy spectra of $^{A-1}_{\,Λ}Z$. System dependence of the $Λ$-$Λ$ binding energies is understood by the…
Grand Accélérateur National d’Ions Lourds (GANIL), CEA/DSM - CNRS/IN2P3（大重离子加速器（GANIL））；Department of Physics, Tohoku University（东北大学物理系）；Nishina Center, RIKEN（理化学研究所西村中心）；Université Paris-Saclay, CNRS/IN2P3, IJClab（巴黎萨克雷大学）；School of Nuclear Science and Technology, University of Chinese Academy of Sciences（中国科学院大学核科学与技术学院）
We investigated structures of low-lying $0s$-orbit $Λ$ states in $p$-shell $Λ$ hypernuclei ($^A_ΛZ$) by applying microscopic cluster models for nuclear structure and a single-channel folding potential model for a $Λ$ particle. For $A>10$ systems, the size reduction of core nuclei is small, and the core polarization effect is regarded as a higher-order perturbation in the $Λ$ binding. The present calculation qualitatively describes the systematic trend of experimental data for excitation energy change from $^{A-1} Z$ to $^A_ΛZ$, in $A>10$ systems. The energy change shows a clear correlation wit…
The interpretation of hypernuclear gamma-ray data for p-shell hypernuclei in terms of shell-model calculations that include the coupling of Lambda- and Sigma-hypernuclear states is briefly reviewed. Next, Lambda 8Li, Lambda 8Be, and Lambda 9Li are considered, both to exhibit features of Lambda-Sigma coupling and as possible source of observed, but unassigned, hypernuclear gamma rays. Then, the feasibility of measuring the ground-state doublet spacing of Lambda 10Be, which, like Lambda 9Li, could be studied via the (K-,pi0 gamma) reaction, is investigated. Structural information relevant to the…
We generalize the Jacobi no-core shell model (J-NCSM) to study double-strangeness hypernuclei. All particle conversions in the strangeness $S=-1,-2$ sectors are explicitly taken into account. In two-body space, such transitions may lead to the coupling between states of identical particles and of non-identical ones. Therefore, a careful consideration is required when determining the combinatorial factors that connect the many-body potential matrix elements and the free-space two-body potentials. Using second quantization, we systematically derive the combinatorial factors in question for $S=0,…
It is shown how the recent shell-model determination of Lambda-N spin dependent interaction terms in Lambda hypernuclei allows for a reliable deduction of Lambda-Lambda separation energies in Lambda-Lambda hypernuclei across the nuclear p shell. Comparison is made with the available data, highlighting 11(Lambda-Lambda)Be and 12(Lambda-Lambda)Be which have been suggested as possible candidates for the KEK-E373 Hida event.
We describe {\it ab initio} calculations of doubly strange, $S=-2$, $s$-shell hypernuclei ($^4_{ΛΛ}$H, $^5_{ΛΛ}$H, $^5_{ΛΛ}$He and $^6_{ΛΛ}$He) as a first attempt to explore the few-body problem of the {\it full}-coupled channel scheme for these systems. The wave function includes $ΛΛ$, $ΛΣ$, $NΞ$ and $ΣΣ$ channels. Minnesota $NN$, D2$^\prime$ $YN$, and simulated $YY$ potentials based on the Nijmegen hard-core model, are used. Bound state solutions of these systems are obtained. We find that a set of phenomenological $B_8B_8$ interactions among the octet baryons in $S=0, -1$ and -2 sectors, wh…
In present study, we search the lambda magic number in hypernuclei within the framework of relativistic mean field theory (RMF) with inclusion of hyperon-nucleon and hyperon-hyperon potentials. Based on one- and two-lambda separation energy and two-lambda shell gap, 2, 8, 14, 18, 20, 28, 34, 40, 50, 58, 68, 70 and 82 are suggested to be the $Λ$ magic number within the present approach. The weakening strength of $Λ$ spin-orbit interaction is responsible for emerging the new lambda shell closure other than the model scheme. The predicted $Λ$ magic numbers are in remarkable agreement with earlier…
Shell-model calculations that include both Lambda and Sigma configurations with p-shell cores are used to interpret gamma-ray transitions in Lambda-7Li, -9Be, -10B, -11B, -12C, -15N, and -16O observed with the Hyperball array of Ge detectors. It is shown that the data puts strong constraints on the spin dependence of the Lambda-N effective interaction and that the Lambda-Sigma coupling plays an important role.
$ΛN$ spin-spin and spin-orbit splittings in low-lying excitation spectra are investigated for $p$-shell $Λ$ hypernuclei on the basis of the microscopic structure calculation within the antisymmetrized molecular dynamics, where the $ΛN$ $G$-matrix interaction derived from the baryon-baryon interaction model ESC (extended soft core) is used. It is found that the ground-state spin-parity is systematically reproduced in the $p$-shell $Λ$ hypernuclei by tuning the $ΛN$ spin-spin and spin-orbit interactions so as to reproduce the experimental data of $^{4}_Λ$H, $^{7}_Λ$Li and $^9_Λ$Be. Furthermore, …
This research article is a follow up of earlier work by M. Ikram et al., reported in International Journal of Modern Physics E {\bf{25}}, 1650103 (2016) wherein we searched for $Λ$ magic numbers in experimentally confirmed doubly magic nucleonic cores in light to heavy mass region (ie.$^{16}O - ^{208}Pb$) by injecting $Λ$'s into them. In present manuscript, working within the state-of-art relativistic mean field theory with inclusion of $ΛN$ and $ΛΛ$ interaction in hypernuclei using the predicted doubly magic nucleonic cores ie. $^{292}$120, $^{304}$120, $^{360}$132, $^{370}$132, $^{336}$138, …
Recent experimental evidence presented by the FINUDA Collaboration for a particle-stable Lambda-6H has stirred renewed interest in charting domains of particle-stable neutron-rich Lambda hypernuclei, particularly for unbound nuclear cores. We have studied within a shell-model approach several neutron-rich Lambda hypernuclei in the nuclear p shell that could be formed in (pi-,K+) or in (K-,pi+) reactions on stable nuclear targets. Hypernuclear shell-model input is taken from a theoretically inspired successful fit of gamma-ray transitions in p-shell Lambda hypernuclei which includes also Lambda…
We present the first ab initio calculations for p-shell single-Lambda hypernuclei. For the solution of the many-baryon problem, we develop two variants of the no-core shell model with explicit $Λ$ and $Σ^+$, $Σ^0$, $Σ^-$ hyperons including $Λ$-$Σ$ conversion, optionally supplemented by a similarity renormalization group transformation to accelerate model-space convergence. In addition to state-of-the-art chiral two- and three-nucleon interactions, we use leading-order chiral hyperon-nucleon interactions and a recent meson-exchange hyperon-nucleon interaction. We validate the approach for s-she…
Charge symmetry breaking (CSB) is particularly strong in the A=4 mirror hypernuclei $_Λ^4$H--$_Λ^4$He. Recent four-body no-core shell model calculations that confront this CSB by introducing $Λ$-$Σ^0$ mixing to leading-order chiral effective field theory hyperon-nucleon potentials are reviewed, and a shell-model approach to CSB in p-shell $Λ$ hypernuclei is outlined.
A nonperturbative field theoretic calculation has been made for the $s$-shell hypernuclei. Here we dress the $Λ$- and $Σ$- hypernuclei with off-mass shell pion pairs. The analysis replaces the scalar isoscalar potential by quantum coherent states. The binding energies of $^{4+nΛ}$He $(n=0,1,2)$ agree quite well with the RMF result of Greiner. The experimental binding energies of $^4$He and $^3$He are reasonably well reproduced in our calculation. A satisfactory description of the relevant experimental $Λ$- and $Σ$- separation energies has been obtained.
Explicit expressions for the parity-violating s-wave and the parity-conserving p-wave contributions to pi- weak-decay rates of Lambda hypernuclei in the 1p shell are given in the weak-coupling limit, to update previous shell-model calculations and to compare with recent pi- spectra and total decay rates measured by the FINUDA Collaboration. A useful sum rule for the summed strength of Lambda_{1s} --> pi- + proton_{1p} weak decays is derived. Fair agreement between experiment and calculations is reached, using the primary s-wave amplitude and Cohen-Kurath nuclear wavefunctions. The role of the …
We explore the systematics of ground-state and excitation energies in singly-strange hypernuclei throughout the helium and lithium isotopic chains --- from $^5_Λ$He to $^{11}_Λ$He and from $^7_Λ$Li to $^{12}_Λ$Li --- in the ab initio no-core shell model with importance truncation. All calculations are based on two- and three-baryon interaction from chiral effective field theory and we employ a similarity renormalization group transformation consistently up to the three-baryon level to improve the model-space convergence. While the absolute energies of hypernuclear states show a systematic vari…
We employ a feed-forward artificial neural network to extrapolate at large model spaces the results of {\it ab-initio} hypernuclear No-Core Shell Model calculations for the $Λ$ separation energy $B_Λ$ of the lightest hypernuclei, $^3_Λ$H, $^4_Λ$H and $^4_Λ$He, obtained in computationally accessible harmonic oscillator basis spaces using chiral nucleon-nucleon, nucleon-nucleon-nucleon and hyperon-nucleon interactions. The overfitting problem is avoided by enlarging the size of the input dataset and by introducing a Gaussian noise during the training process of the neural network. We find that a…
We describe full-coupled-channel ab initio calculations among the octet baryons for S=-2 s-shell hypernuclei,_{LambdaLambda}^4H,_{LambdaLambda}^5H and_{LambdaLambda}^6He. The wave function includes Lambda Lambda, Lambda Sigma, N Xi, and Sigma Sigma channels. Minnesota NN, D2^\prime YN and Nijmegen model D simulated YY interactions are used. This is the first attempt to explore the few-body problem of the full-coupled channel scheme for A=4-6, S=-2 multistrangeness hypernuclear systems. Bound state solutions of the Lambda Lambda hypernuclei,_{LambdaLambda}^4H,_{LambdaLambda}^5H and _{LambdaLamb…
A general shell model formalism for the nonmesonic weak decay of the hypernuclei has been developed.It involves a partial wave expansion of the emitted nucleon waves,preserves naturally the antisymmetrization between the escaping particles and the residual core, and contains as a particular case the weak Lambda-core coupling formalism. The hypernuclei are grouped having in view their A-1 cores, that is in those with even-even, even-odd and odd-odd cores.It is shown that in all three cases the nuclear structure manifests itself basically through Pauli Principle, and very simple expressions are …
Using as a tool the s-wave approximation (sWA), this work demonstrates that the nonmesonic weak decay transition rates $Γ_{n}$ and $Γ_{p}$ can be expressed in all hypernuclei up to $^{29}_Λ$Si (and very likely in heavier ones too) in the same way as in the s-shell hypernuclei, i.e. as a linear combination of only three elementary transition rates. This finding leads to the analytic prediction that, independently of the transition mechanism, all hypernuclei that are on the stability line (N = Z), i.e. $^5_Λ$He, $^7_Λ$Li, $^9_Λ$Be, $^{11}_Λ$B, $^{13}_Λ$C, $^{17}_Λ$O, $^{29}_Λ$Si, etc should roug…
We investigate the role of two- and three-body $Λ$-nucleon forces by computing the ground state of a few $Λ$-hypernuclei with the Auxiliary Field Diffusion Monte Carlo algorithm. Calculations have been performed for masses up to A=41, including some open-shell hypernuclei. The results show that the use of a bare hyperon-nucleon force fitted on the available scattering data yields a consistent overestimate of the $Λ$-separation energy $B_Λ$. The inclusion of a hyperon-nucleon-nucleon interaction systematically reduces $B_Λ$, leading to a qualitatively good agreement with experimental data over …
Machine learning the single-$Λ$ hypernuclei with neural-network quantum states
Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute of Modern Physics, Fudan University（复旦大学现代物理研究所核物理与离子束应用教育部重点实验室）；State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University（北京大学物理学院核物理与技术国家重点实验室）；Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生部）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（上海理论核物理研究中心（国家自然科学基金委与复旦大学））
Background: The calculation of the hyperon binding energy in hypernuclei is crucial to understanding the interaction between hyperons and nucleons. Purpose: We assess the relative importance of two- and three-body hyperon-nucleon force by studying the effect of the hyperon-nucleon-nucleon interaction in closed shell Λ-hypernuclei from A=5 to 91. Methods: The Λ-binding energy has been calculated using the auxiliary field diffusion Monte Carlo method for the first time, to study light and heavy hypernuclei within the same model. Results: Our results show that including a three-body component in …
In this review we discuss the present status of strange nuclear physics, with special attention to the weak decay of Lambda hypernuclei. The models proposed for the evaluation of the Lambda decay widths are summarized and their results are compared with the data. Despite the recent intensive investigations, the main open problem remains a sound theoretical interpretation of the large experimental values of the ratio G_n/G_p. Although recent works offer a step forward in the solution of the puzzle, further efforts must be invested in order to understand the detailed dynamics of the non-mesonic …
We study the properties of hypernuclei containing one lambda hyperon in the framework of the correlated basis function theory with Jastrow correlations. Fermi hypernetted chain integral equations are derived and used to evaluate energies and one-body densities of lambda hypernuclei having a doubly closed shell nucleonic core in the jj coupling scheme, from Carbon to Lead. We also study hypernuclei having the least bound neutron substituted by the lambda particle. The semi-realistic Afnan and Tang nucleon-nucleon potential and Bodmer and Usmani lambda-nucleon potential are adopted. The effect o…
The large charge symmetry breaking (CSB) implied by the $Λ$ binding energy difference $ΔB^{4}_Λ(0^+_{\rm g.s.})\equiv B_Λ(_Λ^4$He)$-$$B_Λ(_Λ^4$H) = 0.35$\pm$0.06 MeV of the $A=4$ mirror hypernuclei ground states, determined from emulsion studies, has defied theoretical attempts to reproduce it in terms of CSB in hyperon masses and in hyperon-nucleon interactions, including one pion exchange arising from $Λ-Σ^0$ mixing. Using a schematic strong-interaction $ΛN\leftrightarrowΣN$ coupling model developed by Akaishi and collaborators for $s$-shell $Λ$ hypernuclei, we revisit the evaluation of CSB …
Previous studies of proton and neutron spectra from Non-Mesonic Weak Decay of eight Lambda-Hypernuclei (A = 5-16) have been revisited. New values of the ratio of the two-nucleon and the one-proton induced decay widths, Gamma_2N/Gamma_p, are obtained from single proton spectra, Gamma_2N/Gamma_p = 0.50 +/- 0.24, and from neutron and proton coincidence spectra, Gamma_2N/Gamma_p = 0.36 +/- 0.14stat +0.05sys -0.04sys , in full agreement with previously published ones. With these values, a method is developed to extract the one-proton induced decay width in units of the free Lambda decay width, Gamm…
The relativistic mean-field theory with Green's function method is extended to study $Λ$ hypernuclei. Taking hypernucleus $^{61}_Λ$Ca as an example, the single-particle resonant states for $Λ$ hyperons are investigated by analyzing density of states and the corresponding energies and widths are given. Different behaviors are observed for the resonant states, i.e., the distributions of the very narrow $1f_{5/2}$ and $1f_{7/2}$ states are very similar as bound states while that of the wide $1g_{7/2}$ and $1g_{9/2}$ states are like scattering states. Besides, the impurity effect of $Λ$ hyperons o…
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 wit…
The impurity effect of hyperon on atomic nuclei has received a renewed interest in nuclear physics since the first experimental observation of appreciable reduction of $E2$ transition strength in low-lying states of hypernucleus $^{7}_Λ$Li. Many more data on low-lying states of $Λ$ hypernuclei will be measured soon for $sd$-shell nuclei, providing good opportunities to study the $Λ$ impurity effect on nuclear low-energy excitations. We carry out a quantitative analysis of $Λ$ hyperon impurity effect on the low-lying states of $sd$-shell nuclei at the beyond-mean-field level based on a relativi…
We introduce an algorithm to obtain coefficients of fractional parentage for light $p$-shell nuclei. The coefficients enable to use Jacobi coordinates in no-core shell model calculations separating off the center-of-mass motion. Fully antisymmetrized basis states are given together with recoupling coefficients that allow one to apply two- and three-nucleon operators. As an example, we study the dependence on the harmonic oscillator frequency of $^3$H, $^4$He, $^6$He, $^6$Li and $^7$Li and extract their binding and excitation energies. The coefficients will be made openly accessible as HDF5 dat…
After a short introduction to the nonmesonic weak decay (NMWD) $ΛN\go nN$ of $Λ$-hypernuclei we discuss the long-standing puzzle on the ratio $Γ_n/Γ_p$, and some recent experimental evidences that signalized towards its final solution. Two versions of the Independent-Particle-Shell-Model (IPSM) are employed to account for the nuclear structure of the final residual nuclei. They are: (a) IPSM-a, where no correlation, except for the Pauli principle, is taken into account, and (b) IPSM-b, where the highly excited hole states are considered to be quasi-stationary and are described by Breit-Wigner …
We report on a novel ab initio approach for nuclear few- and many-body systems with strangeness. Recently, we developed a relevant no-core shell model technique which we successfully applied in first calculations of lightest $Λ$ hypernuclei. The use of a translationally invariant finite harmonic oscillator basis allows us to employ large model spaces, compared to traditional shell model calculations, and use realistic nucleon-nucleon and nucleon-hyperon interactions (such as those derived from EFT). We discuss formal aspects of the methodology, show first demonstrative results for ${}_Λ^3$H, $…
Charge symmetry breaking (CSB) in the $Λ$-nucleon strong interaction generates a charge dependence of $Λ$ separation energies in mirror hypernuclei, which in the case of the $A=4$ mirror hypernuclei $0^+$ ground states is sizable, $ΔB^{J=0}_Λ\equiv B^{J=0}_Λ (_Λ^4{\rm He}) -B^{J=0}_Λ(_Λ^4{\rm H})=230\pm 90$ keV, and of opposite sign to that induced by the Coulomb repulsion in light hypernuclei. Recent ab-initio calculations of the ($_Λ^4{\rm H},{_Λ^4{\rm He}}$) mirror hypernuclei $0^+_{\rm g.s.}$ and $1^+_{\rm exc}$ levels have demonstrated that a $Λ- Σ^0$ mixing CSB model due to Dalitz and vo…
We present the first ab initio calculations for $p$-shell hypernuclei including hyperon-nucleon-nucleon (YNN) contributions induced by a Similarity Renormalization Group transformation of the initial hyperon-nucleon interaction. The transformation including the YNN terms conserves the spectrum of the Hamiltonian while drastically improving model-space convergence of the Importance-Truncated No-Core Shell Model, allowing a precise extraction of binding and excitation energies. Results using a hyperon-nucleon interaction at leading order in chiral effective field theory for lower- to mid-$p$-she…
Unitary transformations of a Hamiltonian generally induce interaction terms beyond the particle rank present in the untransformed Hamiltonian that have to be captured and included in a many-body calculation. In systems with strangeness such as hypernuclei, the three-body terms induced by the hyperon-nucleon interaction are strong, so their inclusion is crucial. We present in detail a procedure for computing hyperon-nucleon-nucleon interaction terms that are induced during a similarity renormalization group (SRG) flow. The SRG is carried out in a basis spanned by antisymmetric harmonic-oscillat…
The energy levels of light hypernuclei are experimentally accessible observables that contain valuable information about the interaction between hyperons and nucleons. In this work we study strangeness $S = -1$ systems $^{3,4}_Λ$H and $^{4,5}_Λ$He using the ab initio no-core shell model (NCSM) with realistic interactions obtained from chiral effective field theory ($χ$EFT). In particular, we quantify the finite precision of theoretical predictions that can be attributed to nuclear physics uncertainties. We study both the convergence of the solution of the many-body problem (method uncertainty)…
We extend the No-Core Shell Model (NCSM) methodology to incorporate strangeness degrees of freedom and apply it to single-$Λ$ hypernuclei. After discussing the transformation of the hyperon-nucleon (YN) interaction into Harmonic-Oscillator (HO) basis and the Similarity Renormalization Group transformation applied to it to improve model-space convergence, we present two complementary formulations of the NCSM, one that uses relative Jacobi coordinates and symmetry-adapted basis states to fully exploit the symmetries of the hypernuclear Hamiltonian, and one working in a Slater determinant basis o…
${\bf Background:}$ 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 expre…
We derive expressions for cluster overlap integrals or channel cluster form factors for ab initio no-core shell model (NCSM) wave functions. These are used to obtain the spectroscopic factors and can serve as a starting point for the description of low-energy nuclear reactions. We consider the composite system and the target nucleus to be described in the Slater determinant (SD) harmonic oscillator (HO) basis while the projectile eigenstate to be expanded in the Jacobi coordinate HO basis. This is the most practical case. The spurious center of mass components present in the SD bases are remov…
We present a translationally invariant formulation of the no-core shell model approach for few-nucleon systems. We discuss a general method of antisymmetrization of the harmonic-oscillator basis depending on Jacobi coordinates. The use of a translationally invariant basis allows us to employ larger model spaces than in traditional shell-model calculations. Moreover, in addition to two-body effective interactions, three- or higher-body effective interactions as well as real three-body interactions can be utilized. In the present study we apply the formalism to solve three and four nucleon syste…
