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 correctly identify basic alpha clustering features in light nuclei. It is found that in nuclei ranging from ${ {}^{6}\text{Li} }$ to ${ {}^{14}\text{C} }$, state-of-the-art \textit{ab initio} nuclear forces underestimate the degree of alpha clustering in key nuclei such as ${ {}^{8}\text{Be} }$ and ${ {}^{12}\text{C} }$. Stringent constraints on binding energies are then provided by back-propagating 10\% relative uncertainties on the experimental clustering ratios using a parallel Markov chain Monte Carlo algorithm. It is demonstrated that the binding energies of the nuclei $^{6,7}$Li, $^7$Be, $^{10,11}$B, and $^{11}$C need to be obtained within tens of keV precision by nuclear forces to ensure a proper reproduction of basic alpha clustering features in light nuclei. This study provides a new and practical path to guide future optimizations of nuclear forces with a potential impact for medium-mass nuclei.
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.
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…
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…
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.
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 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…
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,…
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…
The optimized point-coupling interaction for the relativistic energy density functional of Hartree-Bogoliubov approach quantifying the nuclear bulk properties
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.
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…
Background: Modern ab initio theory combined with high-quality nucleon-nucleon (NN) and three-nucleon (3N) interactions from chiral effective field theory (EFT) can provide a predictive description of low-energy light-nuclei reactions relevant for astrophysics and fusion-energy applications. However, the high cost of computations has so far impeded a complete analysis of the uncertainty budget of such calculations. Purpose: Starting from NN potentials up to fifth order (N4LO) combined with leading-order 3N forces, we study how the order-by-order convergence of the chiral expansion and confiden…
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 …
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…
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.
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…
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…
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…
We present new calculations of the $α$-particle which are based on the most modern nucleon-nucleon interactions alone and combined with the Tucson-Melbourne or the Urbana IX three-nucleon interaction. Results for the binding energies and some properties of the wavefunction are given. On that phenomenological level little room is left for the action of a possible four-nucleon force.
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.
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…
We study the effect of the tensor correlation in the alpha clustering in 8Be. We take as the wave function of the alpha particle the one calculated by the charge- and parity-projected Hartree- Fock method, which was proposed by us recently. We use the wave function in a cluster-model calculation. The expectation value of the potential energy from the tensor force is almost double of that in the alpha particle. The energy surface as the function of the relative distance of two alpha particles becomes much steeper in an inner region by the inclusion of the tensor correlation in the wave function…
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…
The onset of quartetting, i.e. alpha-particle condensation, in symmetric nuclear matter is studied with the help of an in-medium modified four nucleon equation. It is found that at very low density quartetting wins over pairing, because of the strong binding of the alpha-particles. The critical temperature can reach values up to around 6 MeV. Also the disappearance of alpha-particles with increasing density, i.e. the Mott transition, is investigated. In finite nuclei the Hoyle state, that is the 0_2^+ of 12C, is identified as an "alpha-particle condensate" state. It is conjectured that such st…
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.
Description of a nuclear system in its ground state and at low excitations based on the equation of state (EoS) around normal density is presented. In the expansion of the EoS around the saturation point additional spin polarization terms are taken into account. These terms, together with the standard symmetry term, are responsible for appearance of the $α$-like clusters in the ground state configurations of the N=Z even-even nuclei. At the nuclear surface these clusters can be identified as alpha particles. A correction for the surface effects is introduced for atomic nuclei. Taking into acco…
We consider the non-relativistic four-body system with large scattering length and short-range interactions within an effective theory with contact interactions only. We compute the binding energies of the 4He tetramer and of alpha-particle. The well-known linear correlation between the three-body binding energies and the four-body binding energies of these physical systems can be understood as a consequence of the absence of a four-body force at leading order.
There is an increasing interest in quantifying the predictive power in nuclear structure calculations. We discuss how both experimental and systematic errors at the NN-level can be used to estimate the theoretical uncertainties by rather simple means and without solving the full nuclear many body problem. We emphasize the role of effective interactions defined by coarse graining the NN potential to length scales of the order of the minimal de Broglie wavelength probed between nucleons in nuclei. We find an a priori error of \DeltaB/A \sim 0.1 - 0.4MeV for the binding energy per particle throug…
An effective field theory is used to describe light nuclei, calculated from quantum chromodynamics on a lattice at unphysically large pion masses. The theory is calibrated at leading order to two available data sets on two- and three-body nuclei for two pion masses. At those pion masses we predict the quartet and doublet neutron-deuteron scattering lengths, and the alpha-particle binding energy. For $m_π=510~$MeV we obtain, respectively, $^4a_{\rm nD}=2.3\pm 1.3~$fm, $^2a_{\rm nD}=2.2\pm 2.1~$fm, and $B_α^{}=35\pm 22~$MeV, while for $m_π=805~$MeV $^4a_{\rm nD}=1.6\pm 1.3~$fm, $^2a_{\rm nD}=0.6…
Deeply bound KNN, KNNN and KNNNN states are discussed. The effective force exerted by the K meson on the nucleons is calculated with static nucleons. Next the binding energies are obtained by solving the Schrodinger equation or by variational calculations. The dominant attraction comes from the S-wave Lambda(1405) and an additional contribution is due to Sigma(1385). The latter state is formed at the nuclear peripheries and absorbs a sizable piece of the binding energy. It also generates new branches of quasi-bound states. The lowest binding energies based on a phenomenological KN input fall i…
We solve the Faddeev-Yakubovsky equations for 3N and 4N bound states based on the most modern realistic nucleon-nucleon interactions. We include different realistic 3N forces. It is shown that all 3N force models can remove the underbinding of the triton and alpha-particle which one obtains with existing NN interactions. The agreement of theoretical predictions and the experimental binding energy is quite good and there is little room left for the action of four-nucleon forces in the alpha-particle. The effect of 3N forces on the wave function is investigated.
We present the virial equation of state of low-density nuclear matter composed of neutrons, protons and alpha particles. The virial equation of state is model-independent, and therefore sets a benchmark for all nuclear equations of state at low densities. We calculate the second virial coefficients for nucleon-nucleon, nucleon-alpha and alpha-alpha interactions directly from the relevant binding energies and scattering phase shifts. The virial approach systematically takes into account contributions from bound nuclei and the resonant continuum, and consequently provides a framework to include …
The large values of the singlet and triplet scattering lengths locate the two-nucleon system close to the unitary limit, the limit in which these two values diverge. As a consequence, the system shows a continuous scale invariance which strongly constrains the values of the observables, a well-known fact already noticed a long time ago. The three-nucleon system shows a discrete scale invariance that can be observed by correlations of the triton binding energy with other observables as the doublet nucleon-deuteron scattering length or the alpha-particle binding energy. The low-energy dynamics o…
We show how nuclear effective field theory (EFT) and ab initio nuclear-structure methods can turn input from lattice quantum chromodynamics (LQCD) into predictions for the properties of nuclei. We argue that pionless EFT is the appropriate theory to describe the light nuclei obtained in recent LQCD simulations carried out at pion masses much heavier than the physical pion mass. We solve the EFT using the effective-interaction hyperspherical harmonics and auxiliary-field diffusion Monte Carlo methods. Fitting the three leading-order EFT parameters to the deuteron, dineutron and triton LQCD ener…
The Hoyle state plays a crucial role in the helium burning of stars that have reached the red giant stage. The close proximity of this state to the triple-alpha threshold is needed for the production of carbon, oxygen, and other elements necessary for life. We investigate whether this life-essential condition is robust or delicately fine-tuned by measuring its dependence on the fundamental constants of nature, specifically the light quark mass and the strength of the electromagnetic interaction. We show that there exist strong correlations between the alpha-particle binding energy and the vari…
