Nucleon Core Research Articles

Electron Scattering from Stable and Exotic Li Isotopes

The nuclear shell model was used to investigate the bulk properties of lithium isotopes (6,7,8,9,11Li), i.e., the ground state density distributions and C0 and C2 components of charge form factors. The theoretical treatment was based on supposing that the Harmonic-oscillator (HO) potential governs the core nucleons while the valence nucleon(s) move through Hulthen potential. Such assumptions were applied for both stable and exotic lithium isotopes. The HO size parameters ( and ), the core radii ( ) and the attenuation parameters ( and ) were fixed to recreate the available empirical size radii for lithium isotopes under study.

Core of F25 studied by the F25(−p ) proton-removal reaction

The $^{9}\mathrm{Be}(^{25}\phantom{{}^{B}e}\mathrm{F}(5/{2}^{+}),^{24}\phantom{{}^{B}e}\mathrm{O}$)X proton-removal reaction was studied at the NSCL using the S800 spectrometer. The experimental spectroscopic factor for the ground-state to ground-state transition indicates a substantial depletion of the proton ${d}_{5/2}$ strength compared to shell-model expectations, similar to the findings of an inverse-kinematics $(p,2p)$ measurement performed at RIBF. The $^{25}\phantom{{}^{B}e}\mathrm{F}$ to $^{24}\phantom{{}^{B}e}\mathrm{O}$ ground-states overlap is considerably less than anticipated if the core nucleons behaved as rigid, doubly-magic $^{24}\phantom{{}^{B}e}\mathrm{O}$ within $^{25}\phantom{{}^{B}e}\mathrm{F}$. We interpret the new results within the framework of the Particle-Vibration Coupling (PVC) model, of a ${d}_{5/2}$ proton coupled to a quadrupole phonon of an effective core. This approach provides a good description of the experimental data, requiring an effective $^{24}\phantom{{}^{B}e}\mathrm{O}^{*}$ core with a phonon energy of $\ensuremath{\hbar}{\ensuremath{\omega}}_{2}$= 3.2 MeV and a $B(E2)\ensuremath{\approx}2.7$ W.u. -- softer and more collective than a bare $^{24}\phantom{{}^{B}e}\mathrm{O}$. Both the Nilsson deformed mean field and the PVC models appear to capture the properties of the effective core of $^{25}\phantom{{}^{B}e}\mathrm{F}$, suggesting that the additional proton polarizes $^{24}\phantom{{}^{B}e}\mathrm{O}$ in such a way that it becomes either slightly deformed or a quadrupole vibrator.

Calculation of magnetic moments of Λ-hypernuclei c , o and ca

The magnetic moments of Λ-hypernuclei are the most interesting observables which provide a highly sensitive probe of lambda in the hypernuclei structure and also supply direct information on hyperon-nucleon interactions. In this work, we derive the magnetic moments of Λ-hypernuclei such as O , C and Ca employing a relativistic approach in the presence of the Dirac equation and the spin-orbital potential in their ground and excited states, i.e. the 1S1/2, 1P3/2 and 1P1/2 states. We, then, extract an analytic solution for the wave function of hyperon which is needed for computing the magnetic moments of Λ-hypernuclei. The hypernuclei magnetic moments are the magnetic moment of the last unpaired baryon for the odd mass hypernuclei, therefore, in our work we study the hypernuclear magnetic moment with one Lambda added to a closed-shell core of nucleons. Since Λ-hypernuclei is an isoscalar particle it is possible to directly probe the modified core current electromagnetically.

Nuclear surface parameters revisited

The atomic nucleus is a leptodermous system in which the related densities fade gradually through the surface region. The surface is usually described by two parameters, one to describe the radius and the second to describe the surface width. In this study, we present a clear definition of the nucleons distribution surface based on the investigation of the surface region independent of the nuclear core. We also present an improved method for calculating the surface width relying only on the surface nucleons, avoiding the effect of the core nucleons. The proposed surface parameters are tested for centrally depressed, and centrally raised, distributions and the results confirmed the improvement in the surface description and the elimination of the exaggerated effect of core density on the values of surface parameters. The surface radii and surface widths, based on the proposed method, are presented for experimental proton distributions of 64 nuclei. Including the surface width by the proposed method in the nuclear proximity model improved the calculation of fusion barrier height and position compared to the experimental results.

Transport coefficients of nucleon neutron star cores for various nuclear interactions within the Brueckner-Hartree-Fock approach

We consider the thermal conductivity, shear viscosity, and momentum relaxation rates in the nucleon cores of the neutron stars. We study how the choice of the nuclear interaction and the model for three-body forces may affect these transport coefficients calculated within the Brueckner-Hartree-Fock many-body nuclear theory. We find that at relatively large densities the model dependence of the results is substantial. In addition we provide the analytical approximations which allow to incorporate our results in practical simulations.

Magnetic field dissipation in nucleonic neutron star cores

AbstractWe study the long-term heating due to magnetic field decay in the core of neutron star. Two cases for the nucleonic core are considered: normal and strongly superconducting. We give simple scaling relations (depending on the internal stellar temperature and the averaged magnetic field in the core) to estimate the magnetic field decay rate for the most important dissipation processes. Comparison to properties of observed neutron stars suggests that heating due to the magnetic field decay is (at least partially) responsible for the thermal states of middle-aged magnetars and highly-magnetized isolated neutron stars with ages of 1 — 10 Myr.

Dynamically generated momentum space shell structure of quarkyonic matter via an excluded volume model

The phase space structure of zero temperature Quarkyonic Matter is a Fermi sphere of Quark Matter, surrounded by a shell of Nucleonic Matter. We construct a quasi particle model of Quarkyonic Matter based on the constituent quark model, where the quark and nucleon masses are related by m_Q = m_N/N_c, and N_c is the number of quark colors. The region of occupied states is for quarks k_Q < k_F/N_c, and for nucleons k_F < k_N < k_F + \Delta. We first consider the general problem of Quarkyonic Matter with hard core nucleon interactions. We then specialize to a quasi-particle model where the hard core nucleon interactions are accounted for by an excluded volume. In this model, we show that the nucleonic shell forms past some critical density related to the hard core size, and for large densities becomes a thin shell. We explore the basic features of such a model, and argue this model has the semi-quantitative behaviour needed to describe neutron stars.

Spin–isospin properties of $$\varvec{N=Z}$$ odd–odd nuclei from a core+$$\varvec{pn}$$ three-body model including core excitations

For $$N=Z$$ odd–odd nuclei, a three-body model assuming two valence particles and an inert core can provide insight into pairing correlations in the ground state and spin–isospin excitations. However, since residual core–nucleon interactions can have a significant impact, the inclusion of core excitations in the model is essential for a detailed understanding of both the ground state and spin–isospin properties. To qualitatively understand the effect of core excitation on the ground state and spin–isospin excitations of $$N=Z$$ odd–odd nuclei, we solve the three-body core–nucleon–nucleon problem including core vibrational states described by the random-phase approximation. We pay a particular attention to the magnetic dipole and Gamow–Teller transitions between $$0^+$$ and $$1^+$$ states of $$N=Z$$ nuclei and discuss it in terms of the SU(4) multiplet. We also discuss the effect of coupling to the core vibration on low energy spectra of even–odd nuclei, the spatial distribution, core contributions to the ground state, and possible uncertainties in the present framework.

Strong Interaction in the Presence of Chemical Potential and AdS/CFT Correspondence

In this paper, we use AdS/CFT correspondence to consider holographic model of QCD and study repulsive core of nucleons in the presence of chemical potential. Such low range interaction between nucleons may be calculated using the string theory in the context of AdS/CFT correspondence. We find that variation of nucleon potential with chemical potential at the large $$N_\mathrm{c}$$ limit is very slow; however, we find that nuclear potential affected by non-trivial chemical potential, which yields to more agreement with experiment and lattice results at a very short distances.

Studying the Ground States of 6, 7, 9, 11Li Nuclei by Feynman Continual Integrals Method

The energy and the square of the wave function modulus for the ground state of 6, 7, 11Li nuclei are calculated using Feynman continual integrals in the model of the interaction between a nuclear core and external nucleons. The obtained energy values are in good agreement with the experimental data. The appearance of deuteron and triton clusters was demonstrated in the structure of 6Li and 7Li nuclei, respectively. Calculations in the shell model of a deformed nucleus are also performed for 7, 9, 11Li nuclei. Both models help explain the strong deformation of the 7Li nucleus.

Elastic transverse electron scattering form factors of 11Li exotic nucleus

The elastic transverse electron scattering form factors have been studied for the 11Li nucleus using the Two- Frequency Shell Model (TFSM) approach. The single-particle wave functions of harmonic-oscillator (HO) potential are used with two different oscillator parameters bcore and bhalo. According to this model, the core nucleons of 9Li nucleus are assumed to move in the model space of spsdpf. The outer halo (2-neutron) in 11Li is assumed to move in the pure 1p1/2, 1d5/2, 2s1/2 orbit. The shell model calculations are carried out for core nucleons using the spsdpf-interaction. The elastic magnetic electron scattering of the stable 7Li and exotic 11Li nuclei are also investigated through Plane Wave Born Approximation (PWBA). It is found that the difference between the total form factors of unstable isotope (11Li halo) and stable isotope 7Li is in magnitude. The measured value of the magnetic moment is also reproduced.

Elastic electron scattering from 17Ne and 27P exotic nuclei

The ground state proton, neutron and matter densities andcorresponding root mean square radii of unstable proton-rich 17Neand 27P exotic nuclei are studied via the framework of the twofrequencyshell model. The single particle harmonic oscillator wavefunctions are used in this model with two different oscillator sizeparameters core b and halo , b the former for the core (inner) orbitswhereas the latter for the halo (outer) orbits. Shell model calculationsfor core nucleons and for outer (halo) nucleons in exotic nuclei areperformed individually via the computer code OXBASH. Halostructure of 17Ne and 27P nuclei is confirmed. It is found that thestructure of 17Ne and 27P nuclei have 25 / 2 (1d ) and 1/ 2 2s -dominantconfigurations, respectively. Elastic electron scattering form factorsof these exotic nuclei are also studied using the plane wave Bornapproximation. Effects of the long tail behavior of the proton densitydistribution on the proton form factors of 17Ne and 27P areanalyzed. It is found that the difference between the proton formfactor of 17Ne and that of stable 20Ne (or of 27P and that of stable31P) comes from the difference in the proton density distribution ofthe last two protons (or of the last proton) in the two nuclei. It isconcluded that elastic electron scattering will be an efficient tool (inthe near future) to examine proton-halo phenomena of proton-richnuclei.

Wobbling motion in Lu within a semi-classical framework

The results obtained for Lu with a semi-classical formalism are presented. Properties like excitation energies for the super-deformed bands TSD1, TSD2, TSD3, in 165Lu, and TSD1 and TSD2 for 167Lu, inter- and intra-band B(E2) and B(M1), the mixing ratios, transition quadrupole moments are compared either with the corresponding experimental data or with those obtained for 163Lu. Also alignments, dynamic moments of inertia, relative energy to a reference energy of a rigid symmetric rotor with an effective moment of inertia and the angle between the angular momenta of the core and odd nucleon were quantitatively studied. One concludes that the semi-classical formalism provides a realistic description of all known wobbling features in Lu.

Three-nucleon force contribution in the distorted-wave theory of (d,p) reactions

The distorted-wave theory of A ( d , p ) B reactions, widely used to analyze experimental data, is based on a Hamiltonian that includes only two-nucleon interactions. However, numerous studies of few-nucleon systems and many modern developments in nuclear structure theory show the importance of the three-nucleon ( 3 N ) force. The purpose of this paper is to study the contribution of the 3 N force of the simplest possible form to the A ( d , p ) B reaction amplitude. This contribution is given by a new term that accounts for the interaction of the neutron and proton in the incoming deuteron with one of the target nucleons. This term involves a new type of nuclear matrix elements containing an infinite number of target excitations in addition to the main part associated with the traditional overlap function between A and B . The nuclear matrix elements are calculated for double-closed shell targets within a mean field theory where target excitations are shown to be equivalent to exchanges between valence and core nucleons. These matrix elements can be readily incorporated into available reaction codes if the 3 N interaction has a spin-independent zero-range form. Distorted-wave calculations are presented for a contact 3 N force with the volume integral fixed by the chiral effective field theory at the next-to-next-to-leading order. For this particular choice, the 3 N contribution is noticeable, especially at high deuteron incident energies. No 3 N effects are seen for incident energies below the Coulomb barrier. The finite range can significantly affect the 3 N contribution to the ( d , p ) cross sections. Finite-range studies require new formal developments and, therefore, their contribution is preliminarily assessed within the plane-wave Born approximation, together with sensitivity to the choice of the deuteron model.

Rapid Neutrino Cooling in the Neutron Star MXB 1659-29.

We show that the neutron star in the transient system MXB 1659-29 has a core neutrino luminosity that substantially exceeds that of the modified Urca reactions (i.e., n+n→n+p+e^{-}+ν[over ¯]_{e} and inverse) and is consistent with the direct Urca (n→p+e^{-}+ν[over ¯]_{e} and inverse) reaction occurring in a small fraction of the core. Observations of the thermal relaxation of the neutron star crust following 2.5yr of accretion allow us to measure the energy deposited into the core during accretion, which is then reradiated as neutrinos, and infer the core temperature. For a nucleonic core, this requires that the nucleons are unpaired and that the proton fraction exceeds a critical value to allow the direct Urca reaction to proceed. The neutron star in MXB 1659-29 is the first with a firmly detected thermal component in its x-ray spectrum that needs a fast neutrino-cooling process. Measurements of the temperature variation of the neutron star core during quiescence would place an upper limit on the core specific heat and serve as a check on the fraction of the neutron star core in which nucleons are unpaired.

Neutrino luminosities and heat capacities of neutron stars in analytic form

We derive analytic approximations for the neutrino luminosities and the heat capacities of neutron stars with isothernal nucleon cores as functions of the mass and radius of stars. The neutrino luminosities are approximated for the three basic neutrino emission mechanisms, and the heat capacities for the five basic combinations of the partial heat capacities. The approximations are valid for for a wide class of equations of state of dense nucleonmatter. The results significantly simplify the theoretical interpretation of observations of cooling neutron stars as well as of quasistationary thermal states of neutron stars in X-ray transients. For illustration, we present an analysis of the neutrino cooling functions of nine isolated neutron stars taking into account the effects of their magnetic fields and of the presence of light elements in their heat blanketing envelopes. These results allow one to investigate the superfluid properties of neutron star cores.

Combined mean-field and three-body model tested on the O26 nucleus

We combine few- and many-body degrees of freedom in a model applicable to both bound and continuum states and adaptable to different subfields of physics. We formulate a self-consistent three-body model for a core-nucleus surrounded by two valence nucleons. We treat the core in the mean-field approximation and use the same effective Skyrme interaction between both core and valence nucleons. We apply the model to $^{26}$O where we reproduce the known experimental data as well as phenomenological models with more parameters. The decay of the ground state is found to proceed directly into the continuum without effect of the virtual sequential decay through the well reproduced $d_{3/2}$-resonance of $^{25}$O.

Mirror Nuclei of17O and17F in Relativistic and Nonrelativistic Shell Model

We have investigated energy levels mirror nuclei of the17O and17F in relativistic and nonrelativistic shell model. The nuclei17O and17F can be modeled as a doubly magic17O = n + (N = Z = 8) and17F = p + (N = Z = 8), with one additional nucleon (valence) in the ld5/2level. Then we have selected the quadratic Hellmann potential for interaction between core and single nucleon. Using Parametric Nikiforov-Uvarov method, we have calculated the energy levels and wave function in Dirac and Schrodinger equations for relativistic and nonrelativistic, respectively. Finally, we have computed the binding and excited energy levels for mirror nuclei of17O and17F and compare with other works. Our results were in agreement with experimental values and hence this model could be applied for similar nuclei.

Calculation of energy and charge radius for doubly-magic nuclei of 41Ca and 41Sc with extra nucleon

We have studied some static properties of 41Ca and 41Sc in the relativistic shell model. The nuclei 41Ca and 41Sc can be modeled as a doubly-magic 41Ca=n+(N=Z=20) and 41Sc=p+(N=Z=20), with one additional nucleon (valence) in the lf7/2 level. Then we have selected the modified Eckart plus Hulthen potentials for interaction between core and single nucleon. By using the Parametric Nikiforov–Uvarov method, we have calculated the energy values and wave function. Finally we calculated the charge radius for 41Ca and 41Sc. Our results were in agreement with experimental values and hence this model could be applied for similar nuclei.

Reactions with a10Be beam to study the one-neutron halo nucleus11Be

Halo nuclei are excellent examples of few-body systems consisting of a core and weakly-bound halo nucleons. Where there is only one nucleon in the halo, as in 11Be, the many-body problem can be reduced to a two-body problem. The contribution of the 1s1/2 orbital to the ground state configuration in 11Be, characterized by the spectroscopic factor, S, has been extracted from direct reaction data by many groups over the past five decades with discrepant results. An experiment was performed at the Holifield Radioactive Ion Beam Facility using a 10Be primary beam at four different energies with the goal of resolving the discrepancy through a consistent analysis of elastic, inelastic, and transfer channels. Faddeev-type calculations, released after the publication of the experimental results, show that dynamic core excitation in the transfer process can lead to reduced differential cross sections at higher beam energies. This reduction would lead to the extraction of decreasing values of S with increasing beam energy. A 10Be(d,p) measurement at Ed greater than 25 MeV is necessary to investigate the effects of core excitation in the reaction.