Properties Of Light Nuclei Research Articles

Signature of magic numbers in light exotic nuclei

The advent of technology widened the study of shell closure for nuclei lying far away from the stability line. The classic shell closures are observed to be valid for nuclei near the stability line. The light exotic nuclei exhibit unique behavior compared to those of stable ones. The objective of this work is to study the shell closure in light nuclei near the neutron drip-line to the proton drip-line region. The systematics of two nucleon separation energy difference ([Formula: see text]) between calculated and experimental data are taken as a tool to study the shell closure of light nuclei. Nucleon separation energy is determined using the liquid drop model (LDM) expression with modified asymmetry and pairing energy terms. The light mass numbered isotopes and isotones as a function of even neutron and even proton numbers were considered for this work. The shell structure predicted by [Formula: see text] systematics is compared with the first excitation energy [Formula: see text]. The modified LDM is successful in identifying the shell structure properties of light nuclei in exotic region. The study supports the emergence of new shell closure and the disappearance of existing classic shell closure for both neutron and proton numbers. The shell structure predicted by [Formula: see text] systematics for isotopes (isotones) of magic nucleon number [Formula: see text] was in agreement with the results of [Formula: see text] analysis.

θ -dependence of light nuclei and nucleosynthesis

We investigate the impact of the QCD vacuum at nonzero $\theta$ on the properties of light nuclei, Big Bang nucleosynthesis, and stellar nucleosynthesis. Our analysis starts with a calculation of the $\theta$-dependence of the neutron-proton mass difference and neutron decay using chiral perturbation theory. We then discuss the $\theta$-dependence of the nucleon-nucleon interaction using a one-boson-exchange model and compute the properties of the two-nucleon system. Using the universal properties of four-component fermions at large scattering length, we then deduce the binding energies of the three-nucleon and four-nucleon systems. Based on these results, we discuss the implications for primordial abundances of light nuclei, the production of nuclei in stellar environments, and implications for an anthropic view of the universe.

Akmal-Pandharipande-Ravenhall equation of state for simulations of supernovae, neutron stars, and binary mergers

Differences in the equation of state (EOS) of dense matter translate into differences in astrophysical simulations and their multimessenger signatures. Thus, extending the number of EOSs for astrophysical simulations allows us to probe the effect of different aspects of the EOS in astrophysical phenomena. In this work, we construct the EOS of hot and dense matter based on the Akmal, Pandharipande, and Ravenhall (APR) model and thereby extend the open-source SROEOS code which computes EOSs of hot dense matter for Skyrme-type parametrizations of the nuclear forces. Unlike Skrme-type models, in which parameters of the interaction are fit to reproduce the energy density of nuclear matter and/or properties of heavy nuclei, the EOS of APR is obtained from potentials resulting from fits to nucleon-nucleon scattering and properties of light nuclei. In addition, this EOS features a phase transition to a spin-isospin ordered state of nucleons, termed a neutral pion condensate, at supranuclear densities. We show that differences in the effective masses between EOSs have consequences for the properties of nuclei in the subnuclear inhomogeneous phase of matter. We also test the new EOS of APR in spherically symmetric core-collapse of massive stars with $15\phantom{\rule{0.28em}{0ex}}{M}_{\ensuremath{\bigodot}}$ and $40\phantom{\rule{0.28em}{0ex}}{M}_{\ensuremath{\bigodot}}$, respectively. We find that the phase transition in the EOS of APR speeds up the collapse of the star. However, this phase transition does not generate a second shock wave or another neutrino burst as reported for the hadron-to-quark phase transition. The reason for this difference is that the width of the coexistence region and the latent heat in the EOS of APR are substantially smaller than in the quark-to-hadron transition employed earlier, which results in a significantly smaller softening of the high density EOS.

Quantum Monte Carlo methods for nuclear physics

Quantum Monte Carlo methods have proved very valuable to study the structure and reactions of light nuclei and nucleonic matter starting from realistic nuclear interactions and currents. These ab-initio calculations reproduce many low-lying states, moments and transitions in light nuclei, and simultaneously predict many properties of light nuclei and neutron matter over a rather wide range of energy and momenta. We review the nuclear interactions and currents, and describe the continuum Quantum Monte Carlo methods used in nuclear physics. These methods are similar to those used in condensed matter and electronic structure but naturally include spin-isospin, tensor, spin-orbit, and three-body interactions. We present a variety of results including the low-lying spectra of light nuclei, nuclear form factors, and transition matrix elements. We also describe low-energy scattering techniques, studies of the electroweak response of nuclei relevant in electron and neutrino scattering, and the properties of dense nucleonic matter as found in neutron stars. A coherent picture of nuclear structure and dynamics emerges based upon rather simple but realistic interactions and currents.

Statistical (?) decay of light hot nuclei

The reaction 12 C+ 12 C at 95 MeV beam energy has been measured using the GARFIELD+RCo apparatuses at Laboratori Nazionali di Legnaro LNL - INFN, Italy, in the framework of an experimental campaign proposed by the NUCL-EX collaboration. The aim is to progress in the understanding of statistical properties of light nuclei at excitation energies above particle emission thresholds, by measuring exclusive fusion-evaporation data. A theoretical study of the system, performed with a newly developed Monte Carlo Hauser-Feshbach code, is shown, together with preliminary results of the data analysis.

NUCLEAR FORCES AND FEW NUCLEON SYSTEMS IN CHIRAL EFFECTIVE FIELD THEORY

Using chiral effective field theory (EFT) with explicit Δ degrees of freedom we calculated nuclear forces up to next-to-next-to-leading order (N2LO). We find a much improved convergence of the chiral expansion in all peripheral partial waves. We also present a novel lattice EFT method developed for systems with larger number of nucleons. Combining Monte Carlo lattice simulations with EFT allows one to calculate the properties of light nuclei, neutron and nuclear matter. Accurate description of two-nucleon phase-shifts and ground state energy ratio of dilute neutron matter up to corrections of higher orders show that lattice EFT is a promising tool for quantitative studies of low-energy few- and many-body systems.

Nonlocal inverse-scattering nucleon-nucleon interaction and spectra of s-and p-shell nuclei

Nucleon-nucleon interaction is constructed in the J-matrix inverse scattering approach developed by us. The interaction has the form of a matrix in the oscillator basis in each partial wave. The rank of the matrix is not large though the description of the NN scattering data is comparable in quality with that provided by the best modern NN interaction potentials (x2/datum = 1.03). Various phase-equivalent transformations (PETs) that do not affect the description of the scattering data are then used. They allow, in particular, all experimentally known deuteron characteristics to be reproduced with this interaction. The interaction is used in calculations of properties of light nuclei (to A = 16) by the no-core shell model (NCSM), where all nucleons are spectroscopically active. In the NCSM calculations the ultimate fit of the interaction is performed: using PETs, we make it capable of describing binding energies and spectra of all nuclei in question. Note that three-nucleon forces are not used in our approach.

New developments within the no-core shell model

We review recent developments in the ab initio no-core shell model, such as the influence of 3NFs on the binding energies and excitation spectra of light nuclei. Our calculations permit us to compare the effect of different choices for the theoretical 3NF on the properties of light nuclei. This is of particular interest in determining the best choice of the values for the contact terms in 3NFs derived from Chiral Perturbation Theory. Other recent developments in the NCSM include an investigation of the renormalization properties of physical operators, besides the nuclear Hamiltonian, as well as the Lorentz integral transform approach to the description of select reaction observables in light nuclei.

A New Antisymmetrized Molecular Dynamics Approach to Few-Nucleon Systems

A new method in the study of antisymmetrized molecular dynamics (AMD) is proposed. This method consists of a Jacobi-coordinate-basis AMD with the generator coordinate method (GCM). A simple example is presented for the case of in few-nucleon systems with the Volkov potential. Bound states for 2N, 3N, and 4N systems are compared with those obtained using the “primary AMD” and some other methods. We find this to be a promising method for investigating light nuclear systems. During the past decade, since the primary antisymmetrized molecular dynamics (AMD) was proposed, 1)–3) it has been successfully extended to systematic studies of neutron-rich nuclei, 4)–6) as well as excited states of nuclei. 7) Further developments of the AMD method have been realized by introducing several conventional ideas of conventional nuclear structure physics. 8)–19) The physical approaches mentioned above were formulated by making improvements of the AMD in Refs. 4)–7); for instance, a variational calculation was carried out after application of the spin parity projection (VAP) in order to investigate excited states 15) and the existence of exotic clusters in excited states of neutronrich nuclei. 16)–19) Another improvement realized through use of the superposition of selected Slater determinants was made in the AMD triple-S model, which can quantitatively describe properties of light nuclei. 10),11) These improvements were made in methods treating medium light nuclei in which the wave function is expressed in terms of a superposition of Slater determinants. However, this method has not yet been successfully applied to few-body problems. In order to allow for the application of the AMD method to few-body and very light nuclei, we present one modified AMD method which was developed using the Jacobi-coordinate-basis AMD plus the GCM technique. 20),21) One of the aims of this work is to introduce the N-body correlations in a “single Slater determinant”. The second is to remove the ambiguity of the zero-point oscillation energy. The third is to reduce the number of variational parameters in the AMD effectively with the GCM technique; using this technique, a very large number of the variational parameters can be fixed in the eigenvalue problem. Let us start from the trial wave function primary AMD. The wave function of N -nucleon system Ψ is given by

Comment on “Extension of the Bethe-Weizsäcker mass formula to light nuclei and some new shell closures”

Some general features of the Bethe-Weizsacker mass formula recently extended to light nuclei have been explored. Though this formula improves fits to the properties of light nuclei and it does seem to work well in delineating the positions of all old and new magic numbers found in that region, yet it is not well tuned for predicting finer details. The mass predictions have also been found to be less accurate compared to those by the macroscopic-microscopic calculations. It is concluded that such semi-empirical mass formulae can not be a substitute for more fundamental mass formulae having its origin based upon the basic nucleon-nucleon effective interaction.

Deformation and Clustering in Even-Z Nuclei Up to Mg Studied Using AMD with the Gogny Force

Employing the Gogny force as an effective force, we study the ground state properties of light nuclei using antisymmetrized molecular dynamics (AMD). In a previous paper, we discussed the nuclear binding energies and nuclear radii of He, Be, C, O, Ne and Mg isotopes. In this paper, we mainly consider the deformation properties and the clustering nature of these isotopes. By comparing the calculated results with the AMD results by use of the Skyrme-III (SIII) force, we investigated the differences and similarities between the SIII force and the Gogny force. We find that the Gogny force yields rather better binding energy and larger deformation than the SIII force. We carry out the parity-projected calculations. Parity projection enhances the parity-violating deformation and the cluster structure of certain nuclei. Shape of the deformation energy surface is also changed by parity projection. This causes a competition between the mean-field-like structure and the cluster-like structure. A modified version of AMD, which employs deformed Gaussian wave packets instead of spherical ones, is shown to give large quadrupole moments in the case of Mg isotopes.

Maximally incompressible neutron star matter

Relativistic kinetic theory, based on the Grad method of moments as developed by Israel and Stewart, is used to model viscous and thermal dissipation in neutron star matter and determine an upper limit on the maximum mass of neutron stars. In the context of kinetic theory, the equation of state must satisfy a set of constraints in order for the equilibrium states of the fluid to be thermodynamically stable and for perturbations from equilibrium to propagate causally via hyperbolic equations. Application of these constraints to neutron star matter restricts the stiffness of the most incompressible equation of state compatible with causality to be softer than the maximally incompressible equation of state that results from requiring the adiabatic sound speed to not exceed the speed of light. Using three equations of state based on experimental nucleon-nucleon scattering data and properties of light nuclei up to twice normal nuclear energy density, and the kinetic theory maximally incompressible equation of state at higher density, an upper limit on the maximum mass of neutron stars averaging 2.64 solar masses is derived.

Study of Light Nuclei in the Relativistic Mean Field Theory and the Non-Relativistic Skyrme-Hartree-Fock Theory

We study the ground state properties of light nuclei in the relativistic mean field theory and the non-relativistic Skyrme·Hartree-Fock theory. The systematics of the experimental binding energies are reproduced well in both theories, while the results for the matter radii have rather clear model dependence. We find that the isovector part of the nuclear interaction plays an important role to induce the inversion of 2s and 1d single particle levels, which causes the rapid increase of matter radii. In the light mass region, due to the smallness of the number of nucleons, the center-of·mass correction becomes important. In addition, through the self·consistency, the nuclear potential for some nucleus differs clearly from those of the neighboring nuclei. In fact, we find some cases where these ingredients make it possible to reproduce the instability against particle emission without considering the effect of residual interaction.

The Maximum Mass of a Neutron Star

Observational identification of black holes as members of binary systems requires the knowledge of the upper limit on the gravitational mass of a neutron star. We use modern equations of state for neutron star matter, fitted to experimental nucleon-nucleon scattering data and the properties of light nuclei, to calculate, within the framework of Rhoades & Ruffini (1974), the minimum upper limit on a neutron star mass. Regarding the equation of state as valid up to twice nuclear matter saturation density, ρnm, we obtain a secure upper bound on the neutron star mass equal to 2.9 M☉. We also find that in order to reach the lowest possible upper bound of 2.2 M☉, we need to understand the physical properties of neutron matter up to a density of ~4ρnm.

Alpha-particle reactions

Recent work using the concept of alpha-clustering in studies of nuclear structure and nuclear reactions is reviewed. The high symmetry and binding energy of the alpha-particle makes it likely that nucleons inside the nucleus can condense into alpha particles and live long enough to affect many properties of nuclei and also the cross-sections of nuclear reactions, particularly those with alpha-particles as the projectile or ejectile. The alpha-particles inside the nucleus may escape, and the resulting alpha decay is now quite well understood. An incident projectile may collide with a transient alpha-particle in the nucleus and knock it out, thus providing information on the degree of clustering. This model enables the direct part of the cross-sections of (n, α) reactions to be calculated. The alpha-particle mean field unifies many of the characteristics of alpha-particle structure and alpha-particle scattering. Many properties of light nuclei may be simply explained using the concept of alpha-clustering.

Self-weakening of the tensor interaction in a nucleus.

We examine several ``landmarks'' for the effects of the tensor interaction on the properties of light nuclei. These were usually discussed in the context of small-space shell-model calculations. We show, using $G$ matrices derived from a realistic nucleon-nucleon potential, that when the model space is small (e.g., $0\hbar\omega$), these effects are overestimated, indicating that the tensor interaction is too strong. However, when larger spaces are used, there is a diminishing of these effects, which, in general, leads to better agreement with experiment.

Laser spectroscopy and the properties of light nuclei near the neutron drip line

The interesting nuclear structure phenomena observed in some light nuclei at the neutron drip line suggest the measurement of basic ground state properties such as spins, magnetic moments and electric quadrupole moments. Here it will be discussed what experiments are presently feasable using laser spectroscopy. For the outstanding example of a “halo” nucleus,11Li, the development of a technique combining β-asymmetry detected optical pumping in a fast beam with NMR spectroscopy has yielded pertinent results, the most recent of which is an experimental value of the nuclear quadrupole moment.

Elastic and inelastic form factors of light nuclei in the method of hyperspherical functions

Consideration is given to the properties of light nuclei in the method of hyperspherical functions with central realistic potentials. In general, the following set of parameters can be described satisfactorily for the nuclei: binding energy, excitation energy of monopole resonance, RMS radius, elastic and inelastic form factors. The detailed reproduction of the relevant data for each nucleus necessitates the solution of the inverse problem and requires that the corresponding nucleon-nucleon potential (which will probably vary from nucleus to nucleus) be found.

Investigation of Nuclear Three- and Four-Body Systems with Soft-Core Nucleon-Nucleon Potentials

The nuclear three- and four-body systems are investigated with a variational method and various soft-core nucleon-nucleon potentials. A Monte Carlo method is used to compute the multidimensional integrals involved. The results show that (i) a soft-core potential and a hard-core potential which give the same effective-range parameters and $S$-wave phase shifts yield very nearly the same values for the binding energies and rms radii of ${\mathrm{H}}^{3}$ and ${\mathrm{He}}^{4}$, and (ii) as far as the ground-state properties of ${\mathrm{H}}^{3}$ and ${\mathrm{He}}^{4}$ are concerned, the fitting of the high-energy ($\ensuremath{\gtrsim}100$-MeV) $S$-wave phase shifts need not be seriously considered in choosing a nucleon-nucleon potential. Also, it is shown that by paying less attention to the higher-energy ($\ensuremath{\gtrsim}50$-MeV) nucleon-nucleon scattering data, a soft-core potential can be found which yields nearly correct values for the binding energies, rms radii, and form factors up to about 10 ${\mathrm{F}}^{\ensuremath{-}2}$ for both ${\mathrm{H}}^{3}$ and ${\mathrm{He}}^{4}$. The soft-core potentials proposed by Eikemeier and Hackenbroich and by Volkov have also been briefly considered. Here the results indicate that the mathematical approximations used by Hackenbroich et al. to investigate the properties of light nuclei are inaccurate, while the binding energy of ${\mathrm{He}}^{4}$ calculated by Volkov is too small by about 2 MeV.

The Dependence of Nuclear Forces on Velocity

It is shown that the Majorana force may be considered as a special case of a neutron-proton interaction dependent on velocity and angular momentum. Any interaction of this more general form, which is non-Wignerian, and represents attraction, accounts for the saturation properties of nuclear binding in the same way as do the Heisenberg and Majorana potentials. An analysis of the binding in heavy nuclei in terms of angular momentum is given on the basis of the Fermi-Thomas statistical model. An illustration is given showing that the assumption of velocity dependent forces is also consistent with the properties of light nuclei: a particular form of interaction, containing two parameters, is found to give results much the same as those of the ordinary Majorana theory. Finally, the most general dependence of two-particle forces on spin, separation, and velocity, consistent with the conservation laws, is determined, and it is pointed out that experiments on the scattering of fast neutrons in hydrogen are capable of deciding between Majorana forces and a more general form of velocity dependence.