Realistic Two-body Forces Research Articles

Coexistence of quartets and pairs in even-even N > Z nuclei

We analyse the structure of the ground states of even-even N>Z nuclei with nucleons moving in the same major shell and interacting via realistic two-body forces of shell model type. We describe the ground states of these nuclei as a product of two terms, one representing the proton-neutron subsystem with an equal number of protons and neutrons and the other one associated with the excess neutrons. The first term is expressed by means of quartets made of two neutrons and two protons coupled to total isospin T=0. The second term is represented as a neutron pair condensate. Quartets and pairs are constructed variationally. The accuracy of this approximation is discussed for nuclei with valence nucleons in the sd and pf major shells.

Extending the VDPC+BCS formalism by including three-body forces* *Supported by the National Natural Science Foundation of China (11405109)

Recently, Jia proposed a formalism to apply the variational principle to a coherent-pair condensate for a two-body Hamiltonian. The present study extends this formalism by including three-body forces. The result is the same as the so-called variation after particle-number projection in the BCS case, but now, the particle number is always conserved, and the time-consuming projection is avoided. Specifically, analytical formulas of the average energy are derived along with its gradient for a three-body Hamiltonian in terms of the coherent-pair structure. Gradient vanishment is required to obtain analytical expressions for the pair structure at the energy minimum. The new algorithm iterates on these pair-structure expressions to minimize energy for a three-body Hamiltonian. The new code is numerically demonstrated when applied to realistic two-body forces and random three-body forces in large model spaces. The average energy can be minimized to practically any arbitrary precision.

Rotating hybrid stars with the Dyson-Schwinger quark model

We study rapidly rotating hybrid stars with the Dyson-Schwinger model for quark matter and the Brueckner-Hartree-Fock many-body theory with realistic two-body and three-body forces for nuclear matter. We determine the maximum gravitational mass, equatorial radius, and rotation frequency of stable stellar configurations by considering the constraints of the Keplerian limit and the secular axisymmetric instability, and compare with observational data. We also discuss the rotational evolution for constant baryonic mass, and find a spinup phenomenon for supramassive stars before they collapse to black holes.

Nuclear and neutron matters at low density

In this study, symmetric and asymmetric nuclear matter, as well as pure neutron matter in the low-density regime, where the density ranges 0.01 fm−3ρ 0.13 fm−3, have been investigated. Two different realistic and accurate two-body forces are considered. These include Argonne V18 and the CD-Bonn, which give quite different equations of state. The binding energy per nucleon as a function of the density is calculated using the Brueckner-Hartree-Fock approximation. Both the conventional (gap) and continuous choice of single-particle energies are utilized. For the sake of comparison, the equation of state within the self-consistent Green’s function approach is calculated using the CD-Bonn potential. The contribution of the hole-hole terms leads to a repulsive contribution to the energy per nucleon which increases with the nuclear density. Significantly, very good agreement between the experimental symmetry energy values and those calculated in the self-consistent Green’s function and BHF approaches especially at low density, has been accomplished. Finally, The results are compared with those from various many-body approaches, such as variational and relativistic mean field approaches.

Detailed description of exclusive muon capture rates using realistic two-body forces

Starting from state-by-state calculations of exclusive rates of the ordinary muon capture (OMC), we evaluated total muon-capture rates for a set of light- and medium-weight nuclear isotopes. We employed a version of the proton-neutron quasi-particle random phase approximation (pn-QRPA, for short) which uses as realistic nuclear forces the Bonn C-D one boson exchange potential. Special attention was paid on the percentage contribution to the total muon-capture rate of specific low-spin multipolarities resulting by summing over the corresponding multipole transitions. The nuclear method used offers the possibility of estimating separately the individual contributions to the total and partial rates of the polar-vector and axial-vector components of the weak interaction Hamiltonian for each accessible final state of the daughter nucleus. One of our main goals is to provide a reliable description of the charge changing transitions matrix elements entering the description of other similar semileptonic nuclear processes like the charged-current neutrino-nucleus reactions, the electron capture on nuclei, the single \b{eta}-decay mode, etc., which play important role in currently interesting laboratory and astrophysical applications like the neutrino-detection through lepton- nucleus interaction probes, and neutrino-nucleosynthesis. Such results can be also be useful in various ongoing muon-capture experiments at PSI, Fermilab, JPARC and RCNP.

Neutral-current neutrino-nucleus reactions and their impact to supernova physics

We study neutral-current neutrino-nucleus reactions in nuclei that are relevant for supernova (SN) simulations and for terrestrial experiments aiming at neutrino astrophysics as well as ν-nucleus scattering cross sections measurements. Such studies allow us to improve estimates of nuclear responses to low energy neutrinos in light of the operation of nuclear v-detectors with very-low threshold and very high sensitivity. The adopted ν-energy range is extended to rather high energies (up to 100 MeV) so as to consider allowed and forbidden multipole contributions to cross sections. Both contributions are calculated within the quasi-particle random phase approximation by using realistic two-body forces (Bonn CD potential) for the residual interaction of the nuclear Hamiltonian. As a special application the 56Fe isotope is chosen due to its significant role in SN physics and ν-detection.

Nuclear responses of64,66Zn isotopes to supernova neutrinos

Nuclear responses to energy spectra of supernova (SN) neutrinos are studied by folding original $\ensuremath{\nu}$-nucleus cross sections calculated in the context of the quasiparticle random-phase approximation using realistic two-body forces. To this purpose, we employ two-parameter neutrino-energy distributions of Fermi-Dirac and power-law shapes for various SN neutrino scenarios. As concrete examples of promising neutrino detectors we have chosen the ${}^{64,66}$Zn isotopes, contents of (i) the semiconductor CdZnTe (COBRA experiment) and (ii) the crystal scintillators ZnMoO${}_{4}$ and ZnWO${}_{4}$. These materials are quite advantageous for measuring double-$\ensuremath{\beta}$-decay events and for potential use in studying current neutrino physics issues. We concentrate on the evaluation of folded differential cross sections, ${[d\ensuremath{\sigma}(\ensuremath{\omega})/d\ensuremath{\omega}]}_{\mathrm{fold}}$, and flux-averaged cumulative cross sections, ${[d\ensuremath{\sigma}(\ensuremath{\omega})/d\ensuremath{\omega}]}_{\mathrm{fold}}^{\mathrm{cum}}$, as well as total cross sections, $\ensuremath{\langle}{\ensuremath{\sigma}}_{\mathrm{tot}}\ensuremath{\rangle}$, of the above Zn isotopes by adopting several realistic SN neutrino models parametrized by the neutrino temperature or the mean neutrino energy and the width of the aforementioned distributions.

Hybrid stars with the Dyson-Schwinger quark model

We study the hadron-quark phase transition in the interior of neutron stars. For the hadronic sector, we use a microscopic equation of state involving nucleons and hyperons derived within the Brueckner-Hartree-Fock many-body theory with realistic two-body and three-body forces. For the description of quark matter, we employ the Dyson-Schwinger approach and compare with the MIT bag model. We calculate the structure of neutron star interiors comprising both phases and find that with the Dyson-Schwinger model, the hadron-quark phase transition takes place only when hyperons are excluded, and that a two-solar-mass hybrid star is possible only if the nucleonic equation of state is stiff enough.

Neutrino and anti-neutrino scattering off Zn isotopes with quasi-particle RPA calculations

We performed detailed calculations for the cross-sections of (anti)neutrinos with Zn isotopes, contents of the COBRA double beta decay detector at Gran Sasso. We utilized a quasi-particle random phase approximation (QRPA) relying on realistic two-body forces. We present and discuss original double and single differential cross-sections of the neutral current reactions 64 , 66 Zn ( ν , ν ′ ) 64 , 66 Zn ∗ and 64 , 66 Zn ( ν ˜ , ν ˜ ′ ) 64 , 66 Zn ∗ . The response of these isotopes to the energy-spectra of supernova neutrinos is studied by convoluting the original cross-sections with the two-parameter Fermi–Dirac neutrino energy distribution for various mean neutrino energies.

Neutral current neutrino–98Mo reaction cross sections at low and intermediate energies

Inelastic neutrino–nucleus reaction cross sections at low and intermediate neutrino energies are studied. The required many-body nuclear wavefunctions are calculated in the context of a quasi-particle random phase approximation that uses realistic two-body forces. The results presented here refer to the differential, integrated and total cross sections of the neutral-current-induced reaction of νe with the 98Mo nucleus. Exploiting the obtained results, we investigate the response of this isotope as a supernova neutrino detector, assuming a two-parameter Fermi–Dirac distribution for the supernova neutrino energy spectra.

Supernova neutrino detection by terrestrial nuclear detectors

We present and discuss differential cross sections for the 128,130Te isotopes, contents of the COBRA double beta decay detector. The response of these isotopes to energy spectra of supernova neutrinos is explored by convoluting the original results, calculated in the context of the quasi-particle random phase approximation (QRPA) using realistic two-body forces, with a two-parameter Fermi–Dirac (FD) and a Power-Law (PL) neutrino energy distributions.

Investigating the nuclear response of Te isotopes to SN-neutrinos

The response of Te isotopes to the energy-spectra of supernova neutrinos is explored by applying the folding procedure. We present double differential cross sections for 128,130Te isotopes convoluted with a two-parameter Fermi-Dirac (FD) and a Power-Law (PL) neutrino energy distributions. The original cross sections are calculated in the context of the quasi particle random phase approximation (QRPA) by using realistic two-body forces.

Dependence of the nuclear equation of state on two-body and three-body forces

The nuclear equation of state is calculated within the Bethe–Brueckner–Goldstone expansion with the inclusion of three-body forces. Two different realistic and accurate two-body forces are considered, the CD Bonn and the Argonne v18, which give quite different EOS. Surprisingly, the inclusion of the same three-body forces in the calculation produces two EOS's which are close to each other not only around saturation but also up to density as large as five times the saturation one. The results suggest that the nuclear EOS is, to some extent, unique within the microscopic many-body theory with accurate realistic two-body forces.

Spin correlation parameterCyyofp+He3elastic backward scattering

We measured the differential cross section and the spin correlation parameter C{sub yy} of the p-vector+{sup 3}He-vector elastic backward scattering at 200, 300, and 400 MeV at {theta}=180 deg. in the center-of-mass frame to study the mechanism of the reaction and to examine the validity of the {sup 3}He wave functions based on two different realistic two-body forces. This is the first measurement of the spin correlation parameter C{sub yy} of the p-vector+{sup 3}He-vector EBS at intermediate energies. The experimental results were compared with few-body calculations, including three reaction mechanisms: two-nucleon-pair exchange, pion exchange, and direct pp scattering. It was found that few-body calculations describe the differential cross-section data reasonably well. The spin correlation parameter C{sub yy} shows clear evidence for the two-nucleon-pair exchange processes in the reaction, demonstrating that the spin observables are helpful for deeper understanding of the reaction mechanism.

Improved short-range correlations and0νββnuclear matrix elements ofGe76andSe82

We calculate the nuclear matrix elements of the neutrinoless double beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decays of $^{76}\mathrm{Ge}$ and $^{82}\mathrm{Se}$ for the light neutrino exchange mechanism. The nuclear wave functions are obtained by using realistic two-body forces within the proton-neutron quasiparticle random-phase approximation (pnQRPA). We include the effects that come from the finite size of a nucleon, from the higher-order terms of nucleonic weak currents, and from the nucleon-nucleon short-range correlations. Most importantly, we improve on the presently available calculations by replacing the rudimentary Jastrow short-range correlations by the more advanced unitary correlation operator method (UCOM). The UCOM-corrected matrix elements turn out to be notably larger in magnitude than the Jastrow-corrected ones. This has drastic consequences for the detectability of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay in present and future double beta experiments.

Hybrid protoneutron stars with the MIT bag model

We study the hadron-quark phase transition in the interior of protoneutron stars. For the hadronic sector, we use a microscopic equation of state involving nucleons and hyperons derived within the finite-temperature Brueckner-Bethe-Goldstone many-body theory, with realistic two-body and three-body forces. For the description of quark matter, we employ the MIT bag model both with a constant and a density-dependent bag parameter. We calculate the structure of protostars with the equation of state comprising both phases and find maximum masses below 1.6 solar masses. Metastable heavy hybrid protostars are not found.

The shell model as a unified view of nuclear structure

The last decade has witnessed both quantitative and qualitative progresses in Shell Model studies, which have resulted in remarkable gains in our understanding of the structure of the nucleus. Indeed, it is now possible to diagonalize matrices in determinantal spaces of dimensionality up to 10^9 using the Lanczos tridiagonal construction, whose formal and numerical aspects we will analyze. Besides, many new approximation methods have been developed in order to overcome the dimensionality limitations. Furthermore, new effective nucleon-nucleon interactions have been constructed that contain both two and three-body contributions. The former are derived from realistic potentials (i.e., consistent with two nucleon data). The latter incorporate the pure monopole terms necessary to correct the bad saturation and shell-formation properties of the realistic two-body forces. This combination appears to solve a number of hitherto puzzling problems. In the present review we will concentrate on those results which illustrate the global features of the approach: the universality of the effective interaction and the capacity of the Shell Model to describe simultaneously all the manifestations of the nuclear dynamics either of single particle or collective nature. We will also treat in some detail the problems associated with rotational motion, the origin of quenching of the Gamow Teller transitions, the double beta-decays, the effect of isospin non conserving nuclear forces, and the specificities of the very neutron rich nuclei. Many other calculations--that appear to have ``merely'' spectroscopic interest--are touched upon briefly, although we are fully aware that much of the credibility of the Shell Model rests on them.

Hybrid stars with the color dielectric and the MIT bag models

We study the hadron-quark phase transition in the interior of neutron stars (NS). For the hadronic sector, we use a microscopic equation of state (EOS) involving nucleons and hyperons derived within the Brueckner-Bethe-Goldstone many-body theory, with realistic two-body and three-body forces. For the description of quark matter, we employ both the MIT bag model with a density dependent bag constant, and the color dielectric model. We calculate the structure of NS interiors with the EOS comprising both phases, and we find that the NS maximum masses are never larger than 1.7 solar masses, no matter the model chosen for describing the pure quark phase.

Neutron densities and the equation of state for neutron-rich matter

We present predictions for energies, proton and neutron rms radii, and neutron skins of some closed-shell nuclei based upon a microscopic model of the equation of state for asymmetric nuclear matter which is used as input for a mass formula. We employ realistic two-body forces and the Dirac-Brueckner-Hartree-Fock approach to nuclear matter. We compare with experimental information, when available, and point out the need for accurate determinations of neutron densities and skins.

Hadron-quark phase transition in dense matter and neutron stars

We study the hadron-quark phase transition in the interior of neutron stars (NS's). We calculate the equation of state (EOS) of hadronic matter using the Brueckner-Bethe-Goldstone formalism with realistic two-body and three-body forces, as well as a relativistic mean field model. For quark matter we employ the MIT bag model constraining the bag constant by using the indications coming from the recent experimental results obtained at the CERN SPS on the formation of a quark-gluon plasma. We find necessary to introduce a density dependent bag parameter, and the corresponding consistent thermodynamical formalism. We calculate the structure of NS interiors with the EOS comprising both phases, and we find that the NS maximum masses fall in a relatively narrow interval, $1.4 M_\odot \leq M_{\rm max} \leq 1.7 M_\odot$. The precise value of the maximum mass turns out to be only weakly correlated with the value of the energy density at the assumed transition point in nearly symmetric nuclear matter.