CD-Bonn Potential Research Articles

$$\Lambda -\alpha $$ Potential by Folding $$\Lambda $$-Nucleon Interaction with Realistic $$\alpha $$ Wave Function

We construct a folding potential between the \(\alpha \) and \(\Lambda \) particles based on underlying nucleon-nucleon and hyperon-nucleon interactions. Starting from a phenomenological \(\Lambda \)-N potential and a Gaussian form of the \(\alpha \)-particle wave function we obtain the \(\alpha \)-\(\Lambda \) potential and with this potential the binding energy of \(^5_\Lambda \)He is (3.10 MeV), which is consistent with recent experimental data \(3.12 \pm 0.02\) MeV. When in turn an exact solution of the four-body Faddeev-Yakubovsky equation for the \(\alpha \)-particle calculated with the CDBonn, Nijmegen or Argonne V18 realistic nucleon-nucleon potential is used and the phenomenological Gaussian \(\Lambda \)-N potential is replaced by the realistic (e.g. Nijmegen NSC97f) potential approximated by a rank-1 separable form, then \(^5_\Lambda \)He is overbound. In particular, its binding energy given by the folding potential generated with the \(\alpha \) particle wave function based on the CDBonn potential is 7.47 MeV. Although the rank-1 separable \(\Lambda \)-N potential reproduces the exact scattering length and the effective range of the original \(\Lambda \)-N potential, the \(\Lambda \)-\(\alpha \) folding potential results from these \(\Lambda \)-N potential give a large binding energy of \(^5_\Lambda \)He .

Lifetimes and structures of low-lying negative-parity states of Po209

The $5/{2}_{1}^{\ensuremath{-}}$, $9/{2}_{1}^{\ensuremath{-}}$, and $11/{2}_{1}^{\ensuremath{-}}$ states in $^{209}\mathrm{Po}$ were populated in the $\ensuremath{\beta}$ decay of $^{209}\mathrm{At}$ and their lifetimes measured using the electronic $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ fast timing technique. The lifetime of the $9/{2}_{1}^{\ensuremath{-}}$ state is measured for first time. The lifetime of the $5/{2}_{1}^{\ensuremath{-}}$ is measured to be shorter than the value adopted in the literature while the lifetime of the $11/{2}_{1}^{\ensuremath{-}}$ state agrees well with the previous measurement. In order to get deeper insight into the structure of the states, a shell-model calculation was carried out adopting a microscopic effective interaction derived from the realistic CD-Bonn potential. The comparison between theoretical and experimental data for the low-lying negative-parity states of $^{209}\mathrm{Po}$ supports the reliability of the predicted wave functions, which are found to be dominated by the coupling of a neutron hole to the yrast states of $^{210}\mathrm{Po}$. However, it also points to the important role played by minor wave-function components in describing the reduced electromagnetic strengths, suggesting the need of additional configuration mixing for achieving a better quantitative agreement.

Effect of Fock terms on nuclear symmetry energy based on Lorentz-covariant decomposition of nucleon self-energies

Using the Lorentz-covariant decomposition of nucleon self-energies with relativistic mean-field approximation, we study the effect of Fock terms on the density dependence of nuclear symmetry energy, E sym. It is found that the Fock contribution suppresses the potential part of E sym at higher densities, and the constraint from the heavy-ion collision data is in favor of the present result including exchange terms with the cutoff parameters given by the CD-Bonn potential. In addition, not only the isovector-vector (ρ) meson but also the isoscalar (σ, ω) and π mesons give influence on the potential part of E sym through the exchange diagram.

Neutron-rich calcium isotopes within realistic Gamow shell model calculations with continuum coupling

Based on the realistic nuclear force of the high-precision CD-Bonn potential, we have performed comprehensive calculations for neutron-rich calcium isotopes using the Gamow shell model (GSM) which includes resonance and continuum. The realistic GSM calculations produce well binding energies, one- and two-neutron separation energies, predicting that $^{57}$Ca is the heaviest bound odd isotope and $^{70}$Ca is the dripline nucleus. Resonant states are predicted, which provides useful information for future experiments on particle emissions in neutron-rich calcium isotopes. Shell evolutions in the calcium chain around neutron numbers \textit{N} = 32, 34 and 40 are understood by calculating effective single-particle energies, the excitation energies of the first $2^+$ states and two-neutron separation energies. The calculations support shell closures at $^{52}$Ca (\textit{N} = 32) and $^{54}$Ca (\textit{N} = 34) but show a weakening of shell closure at $^{60}$Ca (\textit{N} = 40). The possible shell closure at $^{70}$Ca (\textit{N} = 50) is predicted.

Three beta-decaying states in 128In and 130In resolved for the first time using Penning-trap techniques

Isomeric states in 128In and 130In have been studied with the JYFLTRAP Penning trap at the IGISOL facility. By employing state-of-the-art ion manipulation techniques, three different beta-decaying states in 128In and 130In have been separated and their masses measured. JYFLTRAP was also used to select the ions of interest for identification at a post-trap decay spectroscopy station. A new beta-decaying high-spin isomer feeding the 15− isomer in 128Sn has been discovered in 128In at 1797.6(20) keV. Shell-model calculations employing a CD-Bonn potential re-normalized with the perturbative G-matrix approach suggest this new isomer to be a 16+ spin-trap isomer. In 130In, the lowest-lying (10−) isomeric state at 58.6(82) keV was resolved for the first time using the phase-imaging ion cyclotron resonance technique. The energy difference between the 10− and 1− states in 130In, stemming from parallel/antiparallel coupling of (π0g9/2−1)⊗(ν0h11/2−1), has been found to be around 200 keV lower than predicted by the shell model. Precise information on the energies of the excited states determined in this work is crucial for producing new improved effective interactions for the nuclear shell model description of nuclei near 132Sn.

Gamow shell-model calculations of neutron-rich lithium isotopes

<p indent="0mm">The calculations of neutron-rich lithium isotopes have been performed using the Gamow shell model (GSM). In the present work, the shell model basis is generated by solving the one-body Schrödinger equation of the Woods-Saxon (WS) potential in the complex momentum space. The resulting single-particle basis is composed of bound, resonant and non-resonant continuum states, which is also called the Berggren ensemble. Two-body interaction between nucleons in the Berggren ensemble is derived from the realistic nuclear force CD-Bonn potential with the many-body perturbation theory named the <inline-formula id="INLINE7" content-type="pic"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mover accent="true"><mml:mi other="0">Q</mml:mi><mml:mo other="1" stretchy="true">^</mml:mo></mml:mover></mml:mrow></mml:math></inline-formula>-box folded diagrams. The model space consists of the 0p_3/2 bound state, 0p_1/2 resonant state and p_1/2 non-resonant continuum states for neutrons, and 0p_3/2, 0p_1/2 bound states for protons, respectively. The real and imaginary parts of the complex eigenvalues of the shell model Hamiltonian represent the excitation energies and resonance widths of resonant states, respectively. The p-shell neutron-rich lithium isotopes ^7–10Li have been studied. The results of GSM calculations with CD-Bonn potential are compared with traditional shell model with PWT interaction and GSM with surface Gaussian interaction (SGI). The low-lying spectra and resonance widths of resonant states are discussed, as well as the influences of the continuum states on these observables. In terms of the low-lying spectra of well-bound nuclei, the GSM calculations reproduce the excitation energies of ^7–9Li with good accuracy, except for the states with <sc>4 MeV</sc> or higher energies of ⁷Li, which decay through α-particle emission. In the calculation of the unbound nucleus ¹⁰Li, the GSM calculation proves that continuum effect is crucial in its low-lying spectrum. The shell model calculation with PWT interaction of ¹⁰Li overestimates the excitation energies by almost 100%, and by introducing the continuum states, GSM calculation can give more accurate values. Similar phenomenon was also observed in the shell model calculation with USDB interaction of the unbound nucleus ²⁶O, and was explained by the continuum effect as well. As for the resonance widths, the present calculations extend to higher levels of the studied nuclei compared with GSM calculations with the SGI interaction, and obtain reasonable resonance widths of the resonant states. Though the widths of the α-emitting states of ⁷Li cannot be explained by the current GSM, the resonant states among the excited states of ^8–9Li are reproduced in the present work. The GSM calculation with realistic nuclear force also gives correct resonant property of the first 1⁺ state of ¹⁰Li, while the GSM calculation with SGI yields a non-resonant state. The excited state of ¹⁰Li with unknown angular momentum and resonance width is also reproduced, which is predicted to be a 0⁺ state, with <sc>0.13 MeV</sc> width. In the present work, it is proved that the continuum effect is crucial in shell-model calculations of unbound ¹⁰Li. Through treating the continuum effect microscopically, the GSM calculations with properly renormalized realistic nuclear force can reproduce the observed low-lying spectra and resonance widths of both bound and unbound nuclei with high accuracy. On the other hand, the GSM with realistic nuclear force is based on a relatively small model space, and can thus be used to systems with more valence particles. The GSM with realistic nuclear force is proved to be a promising tool for future research on weakly bound or unbound nuclei.

Quark degrees of freedom and nuclear matter saturation

It has been found in previous works [M. Baldo and K. Fukukawa, Phys. Rev. Lett. 113, 241501 (2014); K. Fukukawa, M. Baldo, G. F. Burgio, L. Lo Monaco and H.-J. Schulze, Phys. Rev. 92, 065802 (2015)] that the nucleon–nucleon potential of [Y. Fujiwara, M. Kohno, C. Nakamoto and Y. Suzuki Phys. Rev. C 64, 054001 (2001); Y. Fujiwara et al., Phys. Rev. C 65, 014002 (2001)] gives an accurate saturation point in symmetric nuclear matter once the three hole-line contributions are included in the Brueckner–Bethe–Goldstone expansion without the addition of three-body forces in the nuclear Hamiltonian. The potential is based on a quark model of nucleons and on the quark–quark interaction together with quark exchange processes. These features introduce an intrinsic nonlocality of the nucleon–nucleon interaction. In order to clarify the role of the quark degrees of freedom and of the nonlocality in the saturation, we perform a comparative study of this potential and the traditional meson exchange models, exemplified in the CD-Bonn potential. We find that at the Brueckner–Hartree–Fock approximation, which corresponds to the two hole-line level of approximation, the dominant modification of the nucleon–nucleon interaction with respect to CD-Bonn is incorporated in the s-wave channels, where the quark degrees of freedom should be more relevant, in particular for the short range quark exchange processes. However, when the three hole-line contribution is included, we find that the higher partial waves play a relevant role, mainly in the term that describes the effect of the medium on the off-shell propagation of the nucleon.

The charge-dependent Bonn potentials with pseudovector pion-nucleon coupling * * Supported by National Natural Science Foundation of China (11775119, 11405116, 11675083)

In order to use high-precision realistic nucleon-nucleon (NN) potentials in relativistic many-body problems, new versions of the charge-dependent Bonn (CD-Bonn) NN potential are constructed with pseudovector pion-nucleon coupling, instead of pseudoscalar coupling used in the original CD-Bonn potential as given by Machleidt . To describe precisely the charge dependence in the NN scattering data, two effective scalar mesons are introduced, whose coupling constants with nucleons are independently determined for each partial wave and for the total angular momentum . The coupling constants between the vector and pseudovector mesons and a nucleon are identical in all channels. Three revised CD-Bonn potentials with the pseudovector pion-nucleon coupling (pvCD-Bonn) are generated by fitting the Nijmegen PWA phase shift data and the deuteron binding energy with different pion-nucleon coupling strengths. The potentials reproduce the phase shifts in the spin-single channels and the low-energyNNscattering parameters very well, but result in significantly different mixing parameters in the spin-triplet channels. The D-state probabilities for the deuteron range from 4.22% to 6.05%, demonstrating that the potentials contain different components of the tensor force, which is useful when considering the role of the tensor force in nuclear few- and many-body systems.

Unitary limit and linear scaling of neutrons in harmonic trap with tuned CD-Bonn and square-well interactions

We study systems of finite-number neutrons in a harmonic trap at the unitary limit. Two very different types of neutron-neutron interactions are applied, namely, the meson-theoretic CD-Bonn potential and hard-core square-well interactions, all tuned to possess an infinite scattering length, and with effective ranges comparable to the trap size. The potentials are renormalized to equivalent, scattering-length preserving low-momentum potentials, Vlow−k, with which the particle-particle hole-hole ring diagrams are summed to all orders to yield the ground-state energy E0 of the finite neutron system. We find the ratio E0/E0free (where E0free denotes the ground-state energy of the corresponding non-interacting system) to be remarkably independent from variations of the harmonic trap parameter, the type and effective range of the unitarity interaction, and the decimation momentum of Vlow−k. Our results support a special linear scaling relation of E0 versus the trap parameter ħω. Certain properties of Landau's quasi-particles for trapped neutrons at the unitary limit are also discussed.

Spectral functions of nuclear matter using self-consistent Green’s function approach based on three-body force

A self-consistent Green’s Function approach is used to study the influence of short-range correlations beyond the mean-field approach of nuclear matter. The ladder equation, including both particle-particle and hole-hole propagation, is solved in nuclear matter for a realistic interaction derived from the CD-Bonn potential. The hole-hole interaction is used to calculate the spectral functions that describe the distribution of holes below Fermi level. The nucleon spectral functions are calculated from the momentum- and energy-dependent self-energy. For comparison, the calculations are investigated by including nuclear three-body force. These spectral functions directly reflect the effects of the nucleon-nucleon correlations and can be explored by the analysis of nucleon knock-out experiments like $ ({\rm e, e' p})$ .

Continuum effect in resonance spectra of neutron-rich oxygen isotopes**Supported by the National Key R&D Program of China (2018YFA0404401), the National Natural Science Foundation of China (11320101004, 11575007), the China Postdoctoral Science Foundation (2018M630018), the CUSTIPEN (China-U.S. Theory Institute for Physics with Exotic Nuclei) funded by the U.S. Department of Energy, Office of Science (DESC0009971), and High-performance Computing Platform of Peking

Starting from the CD-Bonn potential, we have performed Gamow shell-model calculations for neutron-rich oxygen isotopes, investigating excitation spectra and their resonant properties. The Gamow shell model is based on the Berggren ensemble, which is capable of treating the continuum effect reasonably in weakly bound or unbound nuclei. To calculate heavier-mass oxygen isotopes, we choose 16O as a frozen core in the Gamow shell-model calculations. The first 2+ excitation energies of the even-even O isotopes are calculated, and compared with those obtained by the conventional shell model using the empirical USDB interaction. The continuum effect is proved to play an important role in the shell evolution near the drip line. We also discuss the effect of the Berggren contour choice. We improve the approximation in the contour choice to give more precise calculations of resonance widths.

Exclusive $$\varvec{\pi ^{-}}$$ Electroproduction Off the Neutron in Deuterium in the Resonance Region

The goal of our research is to provide the exclusive \({\gamma }^{*}n(p) \rightarrow p{\pi }^{-} (p)\) reaction cross section from deuterium data. The existing \({\gamma }^{*}n \rightarrow p{\pi }^{-}\) event generator based on MAID (Drechsel et al. in Nucl Phys A 645:145, 1999) is modified to include the spectator (proton) information based via the CD-Bonn potential (Entem and Machleidt in Phys Rev C 68:041001, 2003) to simulate the quasi-free production process. With this method, the exclusive quasi-free process has been isolated successfully as demonstrated by the comparison of the spectator momentum distribution of the simulation with the missing momentum distribution of the data, and a kinematical final-state-interaction contribution factor \(R_{FSI}\) is extracted directly from the data according to the ratio between the exclusive quasi-free and full cross sections. Furthermore, the corresponding structure functions are extracted from those cross sections as well. The experiment was done in Hall B at the Thomas Jefferson National Laboratory (JLab) by using the CEBAF Large Acceptance Spectrometer (CLAS) detector, the “e1e” run data off a liquid deuterium target will provide final results with a kinematic coverage for the hadronic invariant mass (W) up to \(1.825\,\text {GeV}\) and in the momentum transfer (\(Q^{2}\)) range of 0.4–\(1.0\,\text {GeV}/c^{2}\).

Temperature Effects on the Equation of State and Symmetry Energy at Low and High Densities

Thermal properties of symmetric nuclear matter and pure neutron matter are studied in a selfconsistent Green’s function and Brueckner–Hartree–Fock approaches with the inclusion of the contact interaction using CDBONN potential. Also we investigate the temperature dependence of the symmetry energy. The symmetry energy at fixed density is found to generally decrease with temperature. The temperature effects on the nuclear matter symmetry energy are found to be stronger at lower densities while become much weaker at higher densities. The results of several microscopic approaches are compared. Also the results are compared with recent experimental data. There is good agreement between the experimental symmetry energy and those calculated in the Brueckner–Hartree–Fock approach.

Nucleon-pair approximation with particle-hole excitations

In this paper, the formalism for the nucleon-pair approximation (NPA) with particle-hole excitations is developed. By using this approach, one is able to perform multiple-major-shell calculations. In this formulation, we use a particle-hole mixed representation, i.e., the particle-hole conjugate transformation is used for operators of the lower major shells, while operators of the upper major shells remain unchanged. We consider collective valence-particle pairs in the upper major shells, collective valence-hole pairs in the lower major shells, and collective pairs consisting of one valence particle in the upper shells and one valence hole in the lower shells to construct our model space. Matrix elements for the shell-model Hamiltonian, both for effective interactions and for phenomenological pairing plus multipole-multipole interactions, are derived in the nucleon-pair basis. As a special case, analytical formulas for doubly magic nuclei with excitations up to two-particle--two-hole are presented. To exemplify this approach, we calculate $^{100}\mathrm{Sn}$ considering both proton and neutron up to four-particle--four-hole excitations, where valence particles are in the 50-82 major shell and valence holes in the 28-50 major shell, with the low-momentum nucleon-nucleon interaction derived from the CD-Bonn potential.

Realistic Gamow shell model for resonance and continuum in atomic nuclei

The Gamow shell model can describe resonance and continuum for atomic nuclei. The model is established in the complex-moment (complex-k) plane of the Berggren coordinates in which bound, resonant and continuum states are treated on equal footing self-consistently. In the present work, the realistic nuclear force, CD Bonn, has been used. We have developed the full -box folded-diagram method to derive the realistic effective interaction in the model space which is nondegenerate and contains resonance and continuum channels. The CD-Bonn potential is renormalized using the Vlow-k method. With choosing 16O as the inert core, we have applied the Gamow shell model to oxygen isotopes.

Large–scale shell model calculations for 140Xe

This paper presents the results of a large-scale shell model calculations of the yrast spectrum of 140Xe. We extend the previous calculations confined to low-lying angular momenta to high-spin states apply- ing the same importance sampling iterative matrix diagonalization algorithm. Excitation energies and transi- tion probabilities are obtained by using an effective nucleon-nucleon interaction derived from the CD-Bonn nucleon-nucleon potential. A satisfactory agreement with the experimental data and the previous results for low lying states is achieved.

On the Mechanism of Nucleon-Nucleon Attraction by Pion Exchange

A formula is derived for the central nucleon-nucleon potential, based on an analysis of the physical origin of the nucleon-nucleon attraction by pion exchange. The decrease of the dynamical mass of the interaction field, exchanged pion in this case, is the principal mechanism responsible for the nuclear attraction in a similar way that the decrease of the kinetic energy of the exchange electron in the diatomic molecule is directly responsible for the covalent molecular attraction. The minimum value of this central nucleon-nucleon potential and the position of the minimum are similar with the values reported in literature for a potential calculated by lattice QCD, which shares the features of the phenomenological nucleon-nucleon potentials. The Schrodinger equation with this central nucleon-nucleon potential was solved numerically for different values of the pion mass. The binding energy increases with the decrease of the pion mass. For masses higher than the real pion mass the nucleon-nucleon system is unbound. We discuss on the two pion exchange and hard core repulsion. The minimum value of the potential for two pion exchange is comparable with the minimum value of the CD Bonn potential. For a hard core radius of 0.5 fm the binding energy is equal to the deuteron binding energy.

Resonance and continuum Gamow shell model with realistic nuclear forces

Starting from realistic nuclear forces, we have developed a core Gamow shell model which can describe resonance and continuum properties of loosely-bound or unbound nuclear systems. To describe properly resonance and continuum, the Berggren representation has been employed, which treats bound, resonant and continuum states on equal footing in a complex-momentum (complex-k) plane. To derive the model-space effective interaction based on realistic forces, the full Qˆ-box folded-diagram renormalization has been, for the first time, extended to the nondegenerate complex-k space. The CD-Bonn potential is softened by using the Vlow-k method. Choosing 16O as the inert core, we have calculated sd-shell neutron-rich oxygen isotopes, giving good descriptions of both bound and resonant states. The isotopes 25,26O are calculated to be resonant even in their ground states.

The Thermal Properties of Asymmetric Nuclear Matter within the Extended Brueckner–Hartree–Fock Approach

The single-particle potentials and other properties at absolute zero temperature in isospin asymmetric nuclear matter are investigated in the frame of an extended Brueckner theory. Also thermal quantities are calculated in asymmetric nuclear matter using CD-Bonn potential and the Urbana three-body forces (3BF). Also, the effects of the hole–hole contributions are investigated within the self-consistent Greens function approach. The inclusion of 3BF or the hole–hole contributions improves the predicted saturation property of symmetric nuclear matter within the Brueckner–Hartree–Fock approach and it leads to a significant stiffening of the density dependence of symmetry energy at high densities but the exact saturation point is not reproduced. This is of great importance in astrophysical calculation. A phenomenological term simulating the three-body interaction is introduced to assure the empirical saturation property. The hot properties of asymmetric nuclear matter such as the internal energy and the press...

Green’s function calculations of light nuclei

The influence of short-range correlations in nuclei was investigated with realistic nuclear force. The nucleon-nucleon interaction was renormalized with $V_{\text{low}k}$ technique and applied to the Green's function calculations. The Dyson equation was reformulated with algebraic diagrammatic constructions. We also analyzed the binding energy of $^4$He, calculated with chiral potential and CD-Bonn potential. The properties of Green's function with realistic nuclear forces are also discussed.