Effective Nucleon-nucleon Interaction Research Articles

Irreducible nonlocality of optical model potentials based on realistic NN interactions

We investigate the nonlocal structure of optical model potentials for nucleon-nucleus scattering based on microscopic approaches. To this purpose, \emph{in-medium} folding optical potentials are calculated in momentum space and their corresponding coordinate-space counterpart are examined, paying special attention to their nonlocal shape. The nucleon-nucleon effective interaction consists of the actual full off-shell $g$ matrix in Brueckner-Hartree-Fock approximation. The nonlocality of effective interactions is preserved throughout all stages in the the calculation. Argonne $v_{18}$ bare potential and chiral next-to-next-to-next-to-leading order bare interaction are used as starting point. The study is focused on proton elastic scattering off $^{40}$Ca at beam energies between 30 and 800 MeV. We find that the gradual suppression of high-momentum contributions of the optical potential results in quite different-looking coordinate-space counterparts. Despite this non-uniqueness in their nonlocal structure, the implied scattering observables remain unchanged for momentum cutoff above a critical one, which depends on incident energy of the projectile. We find that coordinate-space potentials with momentum cutoffs at the critical value yield the least structured nonlocal behavior. Implications of these findings are discussed.

Quasi shell gap at 23F

The experimental states of nuclei, close to semi-magic nuclei, having one extra proton on top of closed proton core, in general, connote the arrangement of proton orbitals within a shell. Herein, we have studied the arrangement of proton orbitals (π0d5/2, π1s1/2 and π0d3/2) in sd-shell for Fluorine isotopes within the nuclear shell model framework. The contribution of different components of effective nucleon-nucleon interaction in the evolution of the energies of proton orbitals, and the orbital energy gaps π0d5/2−π1s1/2 and π0d5/2−π0d3/2 at 23,25F has been examined. Results show the evolution of quasi-shell gap at 23F due to key contribution of central force, in particular, of its even-channel, and destructive interference in the contribution of spin–orbit and tensor force. The excitation energies of 121+ and 321+ states of 23F, and 121+ state of 25F are in good agreement with their respective orbital energy gaps. The origin of 321+ state of 25F and its excitation energy has been delineated as an effect of the breakdown of semi-magic core 24O.

Experimental study of the effective nucleon-nucleon interaction using the F21(d,p)F22 reaction

The single-neutron configurations of several low-lying states in $^{22}\mathrm{F}$ have been determined from neutron-adding cross sections of a ($d,p$) reaction using a $^{21}\mathrm{F}$ radioactive beam in inverse kinematics. Final states in $^{22}\mathrm{F}$ consisting of a proton in the $\ensuremath{\pi}0{d}_{5/2}$ orbital coupled to a neutron in either the $\ensuremath{\nu}0{d}_{5/2}$, $\ensuremath{\nu}1{s}_{1/2}$, or $\ensuremath{\nu}0{d}_{3/2}$ orbitals were observed up to an excitation energy of $\ensuremath{\sim}5$ MeV. Spectroscopic factors and strengths were determined from the angular distribution of the cross sections using a distorted wave Born approximation method. The distribution of the $\ensuremath{\nu}0{d}_{5/2}$ and $\ensuremath{\nu}1{s}_{1/2}$ strength was well described by all USD effective shell model interactions, while only the more recent USDA/USDB interactions showed a marked improvement in describing the observed $\ensuremath{\nu}0{d}_{3/2}$ strength. Diagonal two-body matrix elements of the ${(0{d}_{5/2})}_{J=0--5}^{2}$ effective nucleon-nucleon interaction were extracted from the data and compared with previous determinations of the same matrix elements from particle-particle and hole-hole spectra, as well as the calculated results of the USDA interactions. No significant discrepancies were observed. Inspection of the monopole energies showed that an improved agreement between the different empirical matrix elements is found if a mass dependence is included.

New local mass relation for isobaric analogue states and isospin-nonconserving forces

In this paper a new local mass relation is constructed for isobaric analogue states of four relating neighboring nuclei. The standard deviation from a linear fit of experimental data is 20--70 keV. The systematics of the local mass relation is discussed in terms of an empirical Coulomb energy formula and the isobaric multiplet mass equation. The local relation for nuclei in the $pf$ shell is studied in the framework of the microscopic shell model. The results demonstrate the key roles played by the Coulomb interaction and an effective isospin-nonconserving nucleon-nucleon interaction in our new mass relation.

Massive neutron star with strangeness in a relativistic mean-field model with a high-density cutoff

The properties of strangeness neutron star are studied within relativistic mean-field (RMF) model via including a logarithmic interaction as a function of scalar meson field. This logarithmic interaction, named as the $\sigma$-cut potential, can largely reduce the attractive contributions of scalar meson field at high density without any influence on nuclear structure around normal saturation density. In this work, the TM1 parameter set is chosen as the RMF interaction, while the strengths of logarithmic interaction are constrained by the properties of finite nuclei so that we can obtain a reasonable effective nucleon-nucleon interaction. The hyperons, $\Lambda,~\Sigma$, and $\Xi$ are also considered in neutron stars within this framework, whose coupling constants with mesons are determined by the latest hyperon-nucleon and $\Lambda$-$\Lambda$ potentials extracted from the experimental data of hypernuclei. The maximum mass of neutron star can be larger than two solar mass with these hyperons. Furthermore, the nucleon mass at high density will be saturated due to this additional $\sigma$-cut potential, which is consistent with the conclusions from the microscopic calculations such as, Brueckner-Hartree-Fock theory and quark mean-field model.

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.

Microscopic optical potentials within the weak density dependent nucleon-nucleon effective interactions

<p class="tomtat1">The microscopic optical potentials have been investigated in the framework of the nuclear structure approach based on the energy-density functional approaches. The effective phenomenological nucleon-nucleon interaction SLy5 is consistently used to obtain the Hartree-Fock single particle states, the collective motion at small amplitudes of the target, and the coupling between the particle and phonons. The role of the weak density dependent interaction is showed. </p>

Study of the nuclear medium by 12C + 12C elastic scattering analysis at low energy region

The nuclear medium is investigated by studying the 12C + 12C elastic scattering at the low energies in the framework of optical model (OM) potential. Both frozen and adiabatic density approximations are used for the description of the nuclear medium during the colliding process. In the OM calculation, the double folding procedure using the realistic CDM3Y3 effective nucleon-nucleon (NN) interactions and the wave functions of colliding nuclei is employed to describe the nucleus-nucleus potential at low energy region below 10 MeV per nucleon. The obtained results from the elastic scattering analyses show that the adiabatic density approximation is more reasonable than the frozen density approximation to describe the overlapping density (the so-called nuclear medium) for the 12C + 12C system at low energy region.

Asymmetry dependence of Gogny-based optical potential

An analysis of neutron and proton scattering off $^{40,48}$Ca has been carried out. Real and imaginary potentials have been generated using the Nuclear Structure Method (NSM) for scattering with the Gogny D1S nucleon-nucleon effective interaction. Observables are well described by NSM for neutron and proton elastic scattering off $^{40}$Ca and for neutron scattering off $^{48}$Ca. For proton scattering off $^{48}$Ca, NSM yields a lack of absorption. This discrepancy is attributed to double-charge-exchange contribution and coupling to Gamow- Teller mode which are not included in the present version of NSM. A recipe based on a Perey-Buck fit of NSM imaginary potential and Lane model is proposed to overcome this issue in an approximate way.

Microscopic optical potential for He6

The microscopic optical potential for $\phantom{\rule{0.16em}{0ex}}^{6}\mathrm{He}$ with no free parameters is obtained by folding the microscopic optical potentials of its constituent nucleons with the internal wave function of $\phantom{\rule{0.28em}{0ex}}^{6}\mathrm{He}$. We use the isospin-dependent nucleon microscopic optical potential, which is derived by using the Green's function method through the nuclear matter approximation and the local density approximation based on the Skyrme nucleon-nucleon effective interaction. The internal wave function of $^{6}\mathrm{He}$ is described in a harmonic-oscillator form. The $^{6}\mathrm{He}$ microscopic optical potential is used to calculate the reaction cross sections and elastic-scattering angular distributions for target nuclei in the mass range $12\ensuremath{\le}\mathrm{A}\ensuremath{\le}209$ at incident energies up to 350 MeV. The results are compared with the experimental data and those calculated by a global phenomenological optical potential; in most cases, the microscopic optical potential reproduces the experimental data less well than the global potential. The sensitivity of scattering to the potentials as a function of radius has been investigated by using the notch perturbation method. The investigation shows that the scattering is sensitive to the optical potential in the nuclear surface region. It is concluded from the discussion that the microscopic optical potential can be improved by increasing the surface absorption contribution.

Exotic neutron-rich medium-mass nuclei with realistic nuclear forces

We present the first application of the newly developed EKK theory of the effective nucleon-nucleon interaction to shell-model studies of exotic nuclei, including those where conventional approaches with fitted interactions encounter difficulties. This EKK theory enables us to derive the interaction suitable for several major shells ($sd$+$pf$ in this work). By using such an effective interaction obtained from the Entem-Machleidt QCD-based $\chi\mathrm{N}^3\mathrm{LO}$ interaction and the Fujita-Miyazawa three-body force, the energies, E2 properties and spectroscopic factors of low-lying states of neutron-rich Ne, Mg and Si isotopes are nicely described, as the first shell-model description of the "island of inversion" without fit of the interaction. The long-standing question as to how particle-hole excitations occur across the $sd$-$pf$ magic gap is clarified with distinct differences from the conventional approaches. The shell evolution is shown to appear similarly to earlier studies.

Global phenomenological and microscopic optical model potentials for alpha

The global phenomenological and microscopic optical model potentials for alpha with the incident energy up to 400 MeV are obtained. The global phenomenological optical model potential is extracted by simultaneously fitting the experimental data of total reaction cross sections and elastic scattering angular distributions in the mass range of target nuclei 20 ≤ A ≤ 209. The microscopic optical model potential is obtained by the Green function method through nuclear matter approximation and local density approximation based on the effective Skyrme nucleon-nucleon interaction. Both optical model potentials are used to calculate the reaction cross sections and elastic scattering angular distributions for the target nuclei in the mass range 12 ≤ A ≤ 209 at incident alpha energies up to 400 MeV. The calculated results are compared with the experimental data, and the calculated results by phenomenological and microscopic optical model potentials are also compared with each other.

Effect of exact Coulomb-exchange calculations on band-head spectra of odd-proton nuclei

Previous calculations of band-head energy spectra of odd-mass heavy nuclei in the Hartree-Fock-plus-Bardeen-Cooper-Schrieffer (HF-BCS) framework showed that the agreement with data is better for odd-neutron as compared to odd-proton nuclei. The reason for a poorer agreement with data for the latter have been ascribed to the possible usage of the Slater approximation in calculating the Coulomb-exchange term. In this work, we report the effect of exact Coulomb-exchange calculations on band-head energy spectra of two odd-proton nuclei (namely 237 Np and 241 Am) as compared to the results obtained using the Slater approximation. We performed self-consistent blocking calculations while taking the breaking of time-reversal symmetry at the mean-field level into account due to the unpaired nucleon. The SkM* and SIII parametrizations of the Skyrme interaction have been employed to approximate the effective nucleon-nucleon interaction while a seniority force is used for the pairing channel. Contrary to what was expected, our preliminary results show no improvement on the band-head spectra as compared to data when the Coulomb-exchange term is calculated exactly.

Cluster structure and Coulomb shift in two-center mirror systems

The α + 14 C elastic scattering and the nuclear structure of its compound systems, 18 O = α + 14 C, are analyzed on the basis of the semi-microscopic model. The α + 14 C interaction potential is constructed from the double folding (DF) model with the effective nucleon-nucleon interaction of the density-dependent Michigan 3-range Yukawa. The DF potential is applied to the α +14 C elastic scattering in the energy range of Eα /Aα = 5.5 ~ 8.8 MeV, and the observed differential cross sections are reasonably reproduced. The energy spectra of 18 O are calculated by employing the orthogonality condition model (OCM) plus the absorbing boundary condition (ABC). The OCM + ABC calculation predicts the formation of the 0+ resonance around E = 3MeV with respect to the α threshold, which seems to correspond to the 04+ resonance identified in the recent experiment. We also apply the OCM + ABC calculation to the mirror system, such as 18 Ne = α +14 O, and the Coulomb shift of 18 O - 18 Ne is evaluated. We have found that the Coulomb shift is clearly reduced in the excited 0+ state due to the development of the α cluster structure. This result strongly supports that the Coulomb shift is a candidate of new probe to identify the clustering phenomena.

Elastic scattering and breakup of Be11 on deuterons at 26.9A MeV

The elastic scattering and breakup reactions of the halo nucleus Be11 on deuterons at an incident energy of 26.9A MeV are reported for the first time. Special attention has been paid to the determination and subtraction of the proton contaminations in the deuterated polyethylene (CD2)n target (where D2 denotes H22). The cross sections for elastic scattering are analyzed with the systematic optical potentials of Daehnick et al. and DA1p, as well as with single-folding potentials, derived from the Jeukenne-Lejeune-Mahaux effective nucleon-nucleon interaction. An extended version of the continuum-discretized coupled-channels (XCDCC) formalism, including dynamic core excitation (DCX) effects, is applied to analyze the elastic scattering and breakup data. Comparisons of the full XCDCC calculation with that omitting DCX effects indicate that the core excitation plays a remarkable role in reproducing breakup reactions of Be11+d.1 MoreReceived 31 August 2016DOI:https://doi.org/10.1103/PhysRevC.94.064620©2016 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBreakup reactionsDirect reactionsLow & intermediate energy heavy-ion reactionsNuclear reactionsUnstable nuclei induced nuclear reactionsProperties6 ≤ A ≤ 19Nuclear Physics

Medium effect in high-density nuclear matter probed by a systematic analysis of nucleus-nucleus elastic scattering

We investigate the property of the high-density nuclear matter probed by the nucleus-nucleus elastic scattering in the framework of the double-folding (DF) model with the complex $G$-matrix interaction. The medium effect including three-body-force (TBF) effect is investigated with present two methods based on the frozen density approximation (FDA). The medium effect is clearly seen on the potential and the elastic cross section for the $^{16}$O + $^{16}$O system at $E/A =$ 70 MeV. The crucial role of the medium effect is also confirmed with other effective nucleon-nucleon ($NN$) interactions. In addition, the present methods are applied to other heavy-ion elastic scattering systems. Again, the medium effect is clearly seen in the heavy-ion elastic cross section. The medium effect on the elastic cross section becomes invisible with the increase of the target mass and the incident energy (up to $E/A =$ 200 MeV). However, the medium effect is again important to fix the heavy-ion scattering over $E/A =$ 200 MeV. Finally, we make clear the crucial role of the TBF effect up to $k_F =$ 1.6 fm$^{-1}$ in the nucleus-nucleus elastic scattering.

Microscopic effective reaction theory for deuteron-induced reactions

The microscopic effective reaction theory is applied to deuteron-induced reactions. A reaction model-space characterized by a $p+n+{\rm A}$ three-body model is adopted, where A is the target nucleus, and the nucleon-target potential is described by a microscopic folding model based on an effective nucleon-nucleon interaction in nuclear medium and a one-body nuclear density of A. The three-body scattering wave function in the model space is obtained with the continuum-discretized coupled-channels method (CDCC), and the eikonal reaction theory (ERT), an extension of CDCC, is applied to the calculation of neutron removal cross sections. Elastic scattering cross sections of deuteron on $^{58}$Ni and $^{208}$Pb target nuclei at several energies are compared with experimental data. The total reaction cross sections and the neutron removal cross sections at 56 MeV on 14 target nuclei are calculated and compared with experimental values.

Radiative proton capture cross sections in the mass range 40–54

Proton capture cross sections in the energy range of astrophysical interest for mass region 40-54 have been calculated in the Hauser-Feshbach formalism with reaction code TALYS1.6. The density dependent M3Y effective nucleon-nucleon interaction folded with target radial matter densities from relativistic mean field approach is used to obtain the semi-microscopic optical potential. A definite normalization of potential-well depths has been used over the entire mass region. The $(p,\gamma)$ rates of some reactions, important in the astrophysical scenario, are calculated using the potential in the relevant mass region.

The pygmy dipole resonance in neutron-rich nuclei

The pygmy dipole resonance (PDR), which has been observed via the enhancement of the electric dipole strength E1 of atomic nuclei, is studied within a microscopic collective model. The latter employs the Hartree-Fock (HF) method with effective nucleon-nucleon interactions of the Skyrme types plus the random-phase approximation (RPA). The results of the calculations obtained for various even-even nuclei such as 16-28O, 40-58Ca, 100-120Sn, and 182-218Pb show that the PDR is significantly enhanced when the number of neutrons outside the stable core of the nucleus is increased, that is, in the neutron-rich nuclei. As the result, the relative ratio between the energy weighted sum of the strength of the PDR and that of the GDR (giant dipole resonance) does not exceed 4%. The collectivity of the PDR and GDR states will be also discussed.

Low Scale Saturation of Effective NN Interactions and Their Symmetries

The Skyrme force parameters can be uniquely determined by coarse graining the Nucleon-Nucleon (NN) interactions at a characteristic momentum scale. We show how exact V lowk potentials to second order in momenta are saturated with physical NN scattering threshold parameters at Center of Mass (CM) cut-off scales of about Λ = 250 MeV for the S-waves and Λ = 100 MeV for the P-waves. The pattern of Wigner and Serber symmetries unveiled previously and suggested by Quantum Chromodynamics (QCD) large N c contracted symmetry emerges at these scales.