Using the surface tension energy put in dependence on the number of alpha-clusters in the core in a phenomenological model representing a nucleus as a core and a nuclear molecule on its surface leads to widening the number of isotopes to be described from the narrow strip of beta-stability to the isotopes with N >= Z. The number of alpha-clusters in the molecule is obtained from the analysis of experimental binding energies and the specific density of the core binding energy ρand the radii are calculated. It is shown that for the isotopes of one Z with growing A the number of alpha-clusters of the molecule decreases mostly to 3 and ρincreases to reach a saturation value within ρ= 2.5 ÷2.7 MeV/fm^3 at the beta - stable isotopes, so the narrow strip of the binding energies of the beta - stable isotopes with Z <= 84 is outlined by a function of one variable Z.
The n,p-networks model is used to estimate binding energies and radii of proton-rich (N < Z) nuclei. These calculations have been made for some representative examples of even-Z and odd-Z nuclei with nucleon numbers lower than sixty. Good agreement is found in the comparison of these results with experimental data.
A nuclear model is extended to estimate binding energies and radii of neutron-rich nuclei. These calculations have been made for some representative examples of even-Z and odd-Z nuclei with nucleon numbers lower than sixty. A comparison of results with experimental data supports the value and development of the model in nuclear studies.
New formulas to calculate the nuclear charge radii and the nuclear binding energies have been derived in the framework of an alpha-cluster model. The particular features of the model are two assumptions that the proton-neutron pair interactions are responsible for adherence between alpha-clusters and that the proton and the neutron from a proton-neutron pair have equal nuclear potentials. These assumptions allow one to determine the charge and Coulomb radii in dependence on the amount of proton-neutron pairs in the nucleus. Unlike the Weizsacker's formula to calculate nuclear binding energies,…
The alpha-cluster model is based on two assumptions that the proton-neutron pair interactions are responsible for adherence between alpha-clusters and that the NN-interaction in the alpha-clusters is isospin independent. It allows one to estimate the Coulomb energy and the short range inter-cluster bond energy in dependence on the number of clusters. The charge radii are calculated on the number of alpha-clusters too. Unlike the Weizsacker formula in this model the binding energies of alpha-clusters and excess neutrons are estimated separately. The calculated values are in a good agreement wit…
The model of binding alpha-particles in nuclei is suggested. It is shown good (with the accuracy of 1-2%) description of the experimental binding energies in light and medium nuclear systems. Our preliminary calculations show enhancement of the binding energy for super heavy nuclei with Z~120.
In this letter I present further data that show the remarkable evidence for the existence of an alpha-cluster stucture in the ground states of even-even N=Z nuclei. Such a remarkable systematic was observed 20 years ago for these nuclei at A<= 72 and is extended here up to A=100.
We investigate the influence of phenomenological three-nucleon interactions on the systematics of ground-state energies and charge radii throughout the whole nuclear mass range from 4-He to 208-Pb. The three-nucleon interactions supplement unitarily transformed two-body interactions constructed within the Unitary Correlation Operator Method or the Similarity Renormalization Group approach. To be able to address heavy nuclei as well, we treat the many-body problem in Hartree-Fock plus many-body perturbation theory, which is sufficient to assess the systematics of energies and radii, and limit o…
In the framework of a recently developed alpha-cluster model a nucleus is represented as a core (alpha-cluster liquid drop with dissolved excess neutron pairs in it) and a nuclear molecule on its surface. From analysis of experimental nuclear binding energies one can find the number of alpha-clusters in the molecule and calculate the nuclear charge radii. It was shown that for isotopes of one Z with growing A the number of alpha-clusters in the molecule decreases to three, which corresponds to the nucleus 12C for even Z and 15N for odd Z, and the specific density of the core binding energy ρgr…
The Faddeev-Yakubovsky equations for the alpha-particle are solved. Accurate results are obtained for several modern NN interaction models, which include charge-symmetry breaking effects in the NN force, nucleon mass dependences as well as the Coulomb interaction. These models are augmented by three-nucleon forces of different types and adjusted to the 3N binding energy. Our results are close to the experimental binding energy with a slight overbinding. Thus there is only little room left for the contribution of possible 4N interactions to the alpha-particle binding energy. We also discuss mod…
With the goal of developing predictive ab-initio capability for light and medium-mass nuclei, two-nucleon and three-nucleon forces from chiral effective field theory are optimized simultaneously to low-energy nucleon-nucleon scattering data, as well as binding energies and radii of few-nucleon systems and selected isotopes of carbon and oxygen. Coupled-cluster calculations based on this interaction, named NNLO$_{\rm sat}$, yield accurate binding energies and radii of nuclei up to $^{40}$Ca, and are consistent with the empirical saturation point of symmetric nuclear matter. In addition, the low…
Recently an alpha-cluster model based on the pn-pair interactions with using the isospin invariance of nuclear force has been proposed. According to the model the excess neutron pairs fill out the free space in the core determined by the difference in the charge and matter radii of the alpha-clusters. Then the number of excess neutrons in beta-stable nuclei depends on the number of the core alpha-clusters. In such a representation the specific density of binding energy of core is the only parameter to fit the experimental binding energies of beta-stable nuclei and it turned out to be a constan…
We present a systematic study of both nuclear radii and binding energies in (even) oxygen isotopes from the valley of stability to the neutron drip line. Both charge and matter radii are compared to state-of-the-art {\it ab initio} calculations along with binding energy systematics. Experimental matter radii are obtained through a complete evaluation of the available elastic proton scattering data of oxygen isotopes. We show that, in spite of a good reproduction of binding energies, {\it ab initio} calculations with conventional nuclear interactions derived within chiral effective field theory…
An extended pairing plus QQ force model, which has been shown to successfully explain the nuclear binding energy and related quantities such as the symmetry energy, is applied to study the alpha-like four-nucleon correlations in 1f_{7/2} shell nuclei. The double difference of binding energies, which displays a characteristic behavior at $N \approx Z$, is interpreted in terms of the alpha-like correlations. Important roles of proton-neutron interactions forming the alpha-like correlated structure are discussed.
A model investigating the role of geometry on the alpha dose rate of spent nuclear fuel has been developed. This novel approach utilises a new piecewise function to describe the probability of alpha escape as a function of particulate radius, decay range within the material, and position from the surface. The alpha dose rates were produced for particulates of radii 1 $μ$m to 10 mm, showing considerable changes in the 1 $μ$m to 50 $μ$m range. Results indicate that for decreasing particulate sizes, approaching radii equal to or less than the range of the $α$-particle within the fuel, there is a …
Configuration space Faddeev calculations are performed for the binding energy of Lambda-Lambda-6He and Lambda-9Be bound states, here considered as alpha-Lambda-Lambda and alpha-alpha-Lambda clusters respectively, in order to study the dependence of the calculated binding energy on the alpha-Lambda potential input. For Lambda-Lambda-6He, using realistic interactions, the uncertainty in extracting the Lambda-Lambda S=L=0 interaction strength does not exceed 0.1 MeV, which is a fraction of the order of magnitude derived for other theoretical uncertainties. For Lambda-9Be, the dependence of the ca…
In previous work it was shown that the radius of nucleus R is determined by the alpha-cluster structure and can be estimated on the number of alpha-clusters disregarding to the number of excess neutrons. A hypothesis also was made that the radius R_m of a beta-stable isotope, which is actually measured at electron scattering experiments, is determined by the volume occupied by the matter of the core plus the volume occupied by the peripheral alpha-clusters. In this paper it is shown that the condition R_m = R restricts the number of excess neutrons filling the core to provide the beta-stabilit…
We consider the correlation between the binding energies of the triton and the alpha-particle which is empirically observed in calculations employing different phenomenological nucleon-nucleon interactions. Using an effective quantum mechanics approach for short-range interactions with large scattering length |a| >> l, where l is the natural low-energy length scale, we construct the effective interaction potential at leading order in l/|a|. In order to renormalize the four-nucleon system, it is sufficient to include a SU(4)-symmetric one-parameter three-nucleon interaction in addition to the S…
It is shown that the use of a density dependent effective Pauli potential together with a nucleon-nucleon interaction potential plays a crucial role to reproduce not only the binding energies but also the matter root mean square radii of medium mass range spin-isospin saturated nuclei. This study is performed with a semiclassical Monte Carlo many-body simulation within the context of a simplified nucleon-nucleon interaction to focus on the effect of the genuine correlations due to the fermionic nature of nucleons. The procedure obtained is rather robust and it does not depend on the detailed f…
What is the origin of nuclear clustering and how does it emerge from the nuclear interaction? While there is ample experimental evidence for this phenomenon, its theoretical characterization directly from nucleons as degrees of freedom remains a challenge, making it difficult to improve nuclear forces using clustering observables. In this work, a simple ratio of energies based on effective scale arguments is proposed to assess the quality of nuclear forces on alpha clustering (${ {}^{4}\text{He} }$) in bound and narrow ground-state nuclei. The proposed clustering ratio is parameter-free and co…
The total binding energy of compact stars is the sum of the gravitational binding energy $(BE)_g$ and the nuclear binding energy $(BE)_n$, the last being related to the microphysics of the interactions. While the first is positive (binding) both for hadronic stars and for strange quark stars, the second is large and negative for hadronic stars (anti-binding) and either small and negative (anti-binding) or positive (binding) for strange quark stars. A hadronic star can convert into a strange quark star with a larger radius because the consequent reduction of $(BE)_g$ is over-compensated by the …
The binding energies, shapes and sizes of even-even beta-stable nuclei with A >= 40 and a few chains of isotopes with Z=50, 56, 82, 94 protons and isotones with N=50, 82, 126 neutrons are analyzed. The average isospin dependence of the radii of protons and neutrons evaluated within the relativistic mean field theory is studied. A simple, phenomenological formula for neutron radii is proposed.
The artificial neural networks (ANNs) have emerged with successful applications in nuclear physics as well as in many fields of science in recent years. In this paper, by using (ANNs), we have constructed a formula for the nuclear charge radii. Statistical modeling of nuclear charge radii by using ANNs has been seen as to be successful. Also, the charge radii, binding energies and two-neutron separation energies of Sn isotopes have been calculated by implementing of the new formula in Hartree-Fock-Bogoliubov (HFB) calculations. The results of the study shows that the new formula is useful for …
The electromagnetic effects of the finite size of the nucleon are implemented self-consistently on top of the Skyrme Hartree-Fock calculation, where the electric form factors of both protons and neutrons are considered. Furthermore, the vacuum polarization and the electromagnetic spin-orbit interaction are taken into account. The self-consistent finite-size effects give a different Coulomb potential from the conventional one and affect the neutrons as well. The contribution of the finite-size effects to the total energy reaches $ 7 \, \mathrm{MeV} $ in $ {}^{208} \mathrm{Pb} $. The vacuum pola…
Consistent description of 12C and 16O has been a long standing problem of microscopic alpha cluster models, where the wave function is fully antisymmetrized and the effective interaction is applied not between alpha clusters but between nucleons. When the effective interaction is designed to reproduce the binding energy of 16O (four alpha), the binding energy of 12C (three alpha) becomes underbound by about 10 MeV. In the present study, by taking into account the coupling with the jj-coupling shell model components and utilizing Tohsaki interaction, which is phenomenological but has finite-ran…
We study the possibility to use the cluster-daughter overlap as a new probe of alpha-cluster formation in medium-mass and heavy even-even nuclei. We introduce a dimensionless parameter $\mathfrak{O}$, which is the ratio between the root-mean-square (rms) intercluster separation and the sum of rms point radii of the daughter nucleus and the alpha particle, to measure the degree of the cluster-daughter overlap quantitatively. By using this parameter, a large (small) cluster-daughter overlap between the alpha cluster and daughter nucleus corresponds to a small (large) $\mathfrak{O}$ value. The al…
The updated data for the ground-state-to-ground-state alpha-transition half-lives in 401 nuclei and the alpha capture cross sections of 40Ca, 44Ca, 59Co, 208Pb and 209Bi are well described in the framework of the unified model for alpha-decay and alpha-capture. The updated values of the alpha decay half-lives, the binding energies of nuclei, the spins of parent and daughter nuclei, and the surface deformation parameters are used for the reevaluation of the model parameters. The data for the ground-state-to-ground-state alpha-decay half-lives are also well described by the empirical relationshi…
The alpha clustering in the 10Be and 12Be has been studied within the framework of the real-time evolution method (REM). By using the effective interaction tuned to reproduce the charge radii and the threshold energies, we have evaluated the alpha reduced width amplitude (RWA) and spectroscopic factor (S-factor) for the ground and excited states. With several improvements made in this work, comparing with our previous calculations, larger rate of clustering results are obtained for the 10Be and 12Be with correct asymptotic at large distance.
Differences in the charge radii of mirror nuclei have been recently suggested to contain information on the slope of the symmetry energy L. To test this hypothesis, we perform statistical correlation analysis using quantified energy density functionals that are consistent with our previous knowledge on global nuclear observables such as binding energies and charge radii. We conclude that the difference in charge radii between a mirror pair, R_mir, is an inferior isovector indicator compared to other observables, such at the neutron skin or electric dipole polarizability. In particular, this qu…
A phenomenological formula based on liquid drop model has been proposed for ground state binding energies of nuclei. The effect due to bunching of single particle levels has been incorporated through a term resembling the one-body Hamiltonian. The effect of n-p interaction has been included through a function of valence nucleons. A total of 50 parameters has been used in the present calculation. The r.m.s. deviation for the binding energy values for 2140 nuclei comes out to be 0.376 MeV, and that for 1091 alpha decay energies is 0.284 MeV. The correspondence with the conventional liquid drop m…
Recently, precision laser spectroscopy on 6He atoms determined accurately the isotope shift between 4He and 6He and, consequently, the charge radius of 6He. A similar experiment for 8He is under way. We have performed large-scale ab initio calculations for 4,6,8He isotopes using high-precision nucleon-nucleon (NN) interactions within the no-core shell model (NCSM) approach. With the CD-Bonn 2000 NN potential we found point-proton root-mean-square (rms) radii of 4He and 6He 1.45(1) fm and 1.89(4), respectively, in agreement with experiment and predict the 8He point proton rms radius to be 1.88(…
Isospin singlet (pn) pairing as well as quartetting in nuclei is expected to arise near the symmetry line $N=Z$. Empirical values can be deduced from the nuclear binding energies applying special filters. Within the local density approximation, theoretical estimates for finite nuclei are obtained from results for the condensation energy of asymmetric nuclear matter. It is shown that the isospin singlet condensation energy drops down abruptly for |N-Z|~4 for medium nuclei in the region A=40. Furthermore, alpha-like quartetting and the influence of excitations are discussed.
Light nuclei fall within a regime of universal physics governed by the fact that the two-nucleon scattering lengths are large compared to the typical nuclear interaction range set by one-pion exchange. This places nuclear physics near the so-called unitarity limit in which the scattering lengths are exactly infinite. Effective field theory provides a powerful theoretical framework to capture this separation of scales in a systematic way. It is shown here that the nuclear force can be constructed as a perturbative expansion around the unitarity limit and that this expansion has good convergence…
We focus upon the raison d'etre of the alpha-chain states on the basis of the fully microscopic framework, where the Pauli principle among all the nucleons is fully taken into account. Our purpose is to find out the limiting number of alpha clusters, on which the linear alpha-cluster state can stably exist. How many alpha-clusters can stably make an alpha-chain state? We examine the properties of equally separated alpha clusters on a straight line and compare its stability with that on a circle. We also confirm its stability in terms of break-up and binary disintegrations including alpha-decay…
We analyse the impact of the statistical uncertainties of the the nucleon-nucleon interaction, based on the Granada-2013 np-pp database, on the binding energies of the triton and the alpha particle using a bootstrap method, by solving the Faddeev equations for $^3$H and the Yakubovsky equations for $^4$He respectively. We check that in practice about 30 samples prove enough for a reliable error estimate. An extrapolation of the well fulfilled Tjon-line correlation predicts the experimental binding of the alpha particle within uncertainties.
In this paper we examine to what extent traces of alpha-clustering can be found in mean-field ground states of $nα$-nuclei from Be8 through Ar36 as well as in some superdeformed states in S32, Ar36, and Ca40. For this purpose we calculate the overlap of the mean-field Slater determinant with one containg pure Gaussians and perfect spin and isospin symmetry, optimizing the overlap by varying the alpha-particle positions and radii. In some cases a coherent sum over different configurations is also employed. We find quite large overlaps for some of the lighter systems that diminish for nuclei abo…
The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion Monte Carlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference betwe…
We compute the charge radii of even-mass neon and magnesium isotopes from neutron number N = 8 to the dripline. Our calculations are based on nucleon-nucleon and three-nucleon potentials from chiral effective field theory that include delta isobars. These potentials yield an accurate saturation point and symmetry energy of nuclear matter. We use the coupled-cluster method and start from an axially symmetric reference state. Binding energies and two-neutron separation energies largely agree with data and the dripline in neon is accurate. The computed charge radii have an estimated uncertainty o…
The recently developed effective interaction method for the hyperspherical harmonic formalism is extended to noncentral forces. Binding energies and radii of three- and four-body nuclei are calculated with AV6 and AV14 NN potentials. Excellent results for the convergence of the expansion are found, particularly for the three-nucleon system. Due to the higher density the convergence rate is a bit slower for the alpha particle. In comparison to central potential models there is only a very slight deterioration of the convergence due the tensor force, while other potential terms have no visible e…
A phenomenological alpha-cluster model based on np-pair interactions and the charge symmetry of nuclear force allows one to estimate the Coulomb energy, the Coulomb radius R_C, the Coulomb energy of the last proton interaction with the residual nucleus and the radius of its position R_p in a symmetrical nucleus. The values R_C and R_p obtained for the symmetrical nuclei with 5<= Z<=45 are used in a long standing task of determination of the parameters of the Woods-Saxon potential of neuton/proton bound state used in DWBA analysis of direct one nucleon transfer reactions. According to the charg…
In this paper, we investigate the ground state properties ($i.e$ binding energy, nuclear radius, radial density distribution and single particle energies) for $^{4}He$ and $^{12}C$ nuclei at equilibrium and at large static compression at zero temperature by using two realistic different potentials namely, Nijmegen and Reid Soft Core (RSC)potentials. We carry out the calculations in No-Core Shell Model space consisting of six major oscillator shells within the framework of the Constrained Spherical Hartree- Fock (CSHF) approximations. We find out that, the computed equilibrium root mean square …
We study the consistency of the description of charge distributions and radii of nuclear clusters obtained with semiclassical nuclear pasta models. These nuclei are expected to exist in the low density outer crust of neutron stars. Properties of the arising clusterized nucleon matter can be compared to realistic nuclear properties as experimentally extracted on earth. We focus on non iso-symmetric light clusters with nucleon number $8 \le A \le 30$ and use Monte Carlo many-body techniques. We simulate isotopic chains for a set of selected nuclei using a model Hamiltonian consisting of the usua…
A broad extension of periodic system into the sector of antimatter could be possible sometimes in a remote future. We expect that anti-alpha spontaneous emission from an antimatter nucleus will have the same Q-value and half-life as alpha emission from the corresponding mirror nucleus. This is the consequence of the invariance of binding energy as well as of the surface and Coulomb energy when passing from matter to antimatter nuclei with the the same mass number and the same atomic number. The Q-values and half-lives of all measured up to now 27 cluster radioactivities are given together with…
In this work, we study the odd-even effect in binding energies and charge radii, and systematic behavior of differential radii, to identify the underlying components of the effective nuclear interaction. We apply nuclear density functional theory using a family of Fayans and Skyrme energy density functionals fitted to similar datasets but using different optimization protocols. We inspect various correlations between differential charge radii, odd-even staggering in energies and radii, and nuclear matter properties. Detailed analysis is carried out for medium-mass and heavy semi-magic nuclei w…
How do protons and neutrons bind to form nuclei? This is the central question of ab initio nuclear structure theory. While the answer may seem as simple as the fact that nuclear forces are attractive, the full story is more complex and interesting. In this work we present numerical evidence from ab initio lattice simulations showing that nature is near a quantum phase transition, a zero-temperature transition driven by quantum fluctuations. Using lattice effective field theory, we perform Monte Carlo simulations for systems with up to twenty nucleons. For even and equal numbers of protons and …
Dilute multi $α$ cluster condensed states with spherical and axially deformed shapes are studied with the Gross-Pitaevskii equation and Hill-Wheeler equation, where the $α$ cluster is treated as a structureless boson. Applications to self-conjugate $4N$ nuclei show that the dilute $Nα$ states of $^{12}$C to $^{40}$Ca with $J^π=0^+$ appear in the energy region from threshold up to about 20 MeV, and the critical number of $α$ bosons that the dilute $Nα$ system can sustain as a self-bound nucleus is estimated roughly to be $N_{cr}\sim10$. We discuss the characteristics of the dilute $Nα$ states w…
Scrupulous theoretical study of 8Be nucleus states, both clustered and non-clustered, is performed over a wide range of the excitation energies. The quantities which characterize the degree of the alpha-clustering of these states: spectroscopic factors, cluster form factors as well as the alpha-decay widths are computed in the framework of an accurate ab initio approach developed. Other basic properties of 8Be spectrum: the binding and excitation energies, mean values of the isospin are calculated simultaneously. In the majority of instances the results of the computations turn out to be in a …
The Bloch-Horowitz (BH) equation has been successfully applied to calculating the binding energies of the deuteron and 3H/3He systems. For the three-body systems, BH was found to be perturbative for certain choices of the harmonic oscillator (HO) parameter b. We extend upon this work by applying this formalism to the alpha particle and certain five-, six-, and seven-body nuclei in the p-shell. Furthermore, we use only the leading order BH term and work in the smallest allowed included-spaces for each few-body system (0hw and 2hw). We show how to calculate A-body matrix elements within this for…
We discuss the application of an effective theory with contact interactions to the non-relativistic four-body system with short-range interactions. We have computed the binding energies of the 4He tetramer and the alpha-particle. A well-known linear correlation between three- and four-body binding energies can be understood as a result of the absence of a four-body force at leading order within this framework. Further, we give results for the binding energies of the four-boson system in two spatial dimensions.
With the binding energies and configurations determined experimentally, the root-mean-square radii are calculated for a number of single-particle states by numerically solving the Sch{ö}rdinger equations. By studying the relations between the radii and separation energies, the new scaling laws and necessary conditions for neutron halos and proton halos are established, respectively. Especially the existence region of true proton halos is pointed out. It is found that the effects of short-distance behaviours of valence nucleons at the edges of interaction potentials can not be disregarded. More…
We study a particular class of relativistic nuclear energy density functionals in which only nucleon degrees of freedom are explicitly used in the construction of effective interaction terms. Short-distance (high-momentum) correlations, as well as intermediate and long-range dynamics, are encoded in the medium (nucleon density) dependence of the strength functionals of an effective interaction Lagrangian. Guided by the density dependence of microscopic nucleon self-energies in nuclear matter, a phenomenological ansatz for the density-dependent coupling functionals is accurately determined in s…
The interpretation of future precise experiments on atomic parity violation in terms of parameters of the Standard Model could be hampered by uncertainties in the atomic and nuclear structure. While the former can be overcome by measurement in a series of isotopes, the nuclear structure requires knowledge of the neutron density. We use the nuclear Hartree-Fock method, which includes deformation effects, to calculate the proton and neutron densities in {125}Cs-{139}Cs. We argue that the good agreement with the experimental charge radii, binding energies, and ground state spins signifies that th…
In order to study non-zero spin excitations of the recently proposed alpha-cluster condensation in the self-conjugate 4n nuclei, spatial deformation is introduced into the model wave function of the alpha-cluster condensate. The rotational band states of 8Be are investigated as a first step of a test case for the study of the deformation of the alpha-cluster condensate. Calculations reproduce well the binding energy of the 0+ ground state and also the excitation energy of the 2+ state. Our 0+ wave function is found to be almost exactly equal to the 0+ wave function obtained by the generator co…
