Wave Functions Of Nuclei Research Articles

Nuclei with Up to $$\varvec{A=6}$$ Nucleons with Artificial Neural Network Wave Functions

The ground-breaking works of Weinberg have opened the way to calculations of atomic nuclei that are based on systematically improvable Hamiltonians. Solving the associated many-body Schr\"odinger equation involves non-trivial difficulties, due to the non-perturbative nature and strong spin-isospin dependence of nuclear interactions. Artificial neural networks have proven to be able to compactly represent the wave functions of nuclei with up to $A=4$ nucleons. In this work, we extend this approach to $^6$Li and $^6$He nuclei, using as input a leading-order pionless effective field theory Hamiltonian. We successfully benchmark their binding energies, point-nucleon densities, and radii with the highly accurate hyperspherical harmonics method.

Variational Monte Carlo Calculations of A≤4 Nuclei with an Artificial Neural-Network Correlator Ansatz.

The complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrödinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of A≤4 nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually exact Green's function MonteCarlo results.

Nuclear Moment During Nuclear Scattering Using Wave Function of Nucleus

Within the electromagnetic theory, in the present study, we investigate and calculate the magnetic dipole and electric quadrupole moments of J = 1 nuclei using nucleon moment operators and wave function of each nucleus. Then, we made each of the J = 1 nuclei interact with 178O to investigate the potential interaction effect on moment variations.

Knock-out interpretability

A detailed analysis of a nucleon-knockout experiment has put forward a methodological roadmap for overcoming ambiguities in the interpretation of the data — promising access to the nuclear wave functions in unstable nuclei.

Two-neutron knockout as a probe of the composition of states in Mg22,Al23 , and Si24

Simpson and Tostevin proposed that the width and shape of exclusive parallel momentum distributions of the A-2 residue in direct two-nucleon knockout reactions carry a measurable sensitivity to the nucleon single-particle configurations and their couplings within the wave functions of exotic nuclei. We report here on the first benchmarks and use of this new spectroscopic tool. Exclusive parallel momentum distributions for states in the neutron-deficient nuclei $^{22}$Mg, $^{23}$Al, and $^{24}$Si populated in such direct two-neutron removal reactions were extracted and compared to predictions combining eikonal reaction theory and shell-model calculations. For the well-known $^{22}$Mg and $^{23}$Al nuclei, measurements and calculations were found to agree, supporting the dependence of the parallel momentum distribution width on the angular momentum composition of the shell-model two-neutron amplitudes. In $^{24}$Si, a level at 3439(9) keV, of relevance for the important $^{23}$Al(p,$\gamma$)$^{24}$Si astrophysical reaction rate, was confirmed to be the $2^+_2$ state, while the $4^+_1$ state, expected to be strongly populated in two-neutron knockout, was not observed. This puzzle is resolved by theoretical considerations of the Thomas-Ehrman shift, which also suggest that a previously reported 3471-keV state in $^{24}$Si is in fact the ($0^+_2$) level with one of the largest experimental mirror-energy shifts ever observed.

Studying of the Nucleus-Nucleus Interaction Using Wave Function of the Nucleus and Hyperspherical Formalism

Abstract The current study presents the results of the use of the wave function of a nucleus in place of the nucleus density distribution to calculate the nucleus-nucleus interaction potential. The wave function is obtained by solving the D-dimensional wave equation using the hyperspherical formalism. The interaction potential between two nuclei is calculated using the double folding model. The numerical results for the interaction potential and the scattering cross section are presented to evaluate the formalism used to calculate the nucleus wave function.

Asymptotics of three-body bound state radial wave functions of halo nuclei involving two charged particles

Asymptotic expressions for the radial and full wave functions of a three-body bound halo nuclear system with two charged particles in relative coordinates are obtained in explicit form, when the relative distance between two particles tends to infinity. The obtained asymptotic forms are applied to the analysis of the asymptotic behavior of the three-body (pnα) wave functions for the halo (E⁎=3.562 MeV, Jπ=0+, T=1) state of 6Li derived by D. Baye within the Lagrange-mesh method for two forms of the αN-potential. The agreement between the calculated wave function and the asymptotic formula is excellent for distances up to 30 fm. Information about the values of the three-body asymptotic normalization functions is extracted. It is shown that the extracted values of the three-body asymptotic normalization function are sensitive to the form of the αN-potential. The mirror symmetry is revealed for the three-body asymptotic normalization functions derived for the isobaric (6He, 6Li⁎) pair.

Manifestation of cluster effects in the structure of actinides

We developed a cluster model which allows to take into account both shape deformation parameters and cluster degrees of freedom. The model is based on the assumption that the wave function of nucleus can be treated as a superposition of a mononucleus and two-cluster configurations. The model is applied to describe the multiple negative-parity bands in deformed actinides. Special emphasis is made on the investigation of the recently measured positive parity 0+ 2 rotational band of reflection-asymmetric nature in 240 Pu. The results suggest that this band might be understood as the one built on the lowest excited state in mass asymmetry degree of freedom.

Pictures of Particle Production in Proton--Nucleus Collisions

This work focuses on gluon(jet) production in dilute(proton)-dense(nucleus) collisions. Depending on the frame and gauge, gluon production can be viewed as a freeing of gluons coming from either the proton wave function or from the nucleus wave function. These (apparently) very different pictures must lead to the same result and the purpose of this paper is to see how that happens. The focus is on gluons having $k_\perp\sim Q_S$ or gluons in the scaling region $k_\perp/Q_S\gg 1$. In the McLerran-Venugopalan(MV) model with $k_\perp\sim Q_S$ we are able to derive gluon production in a way that (graphically) manifestly shows $k_\perp$-factorization in terms of the number density of gluons in the nuclear wave function. We presume that this picture, and $k_\perp$-factorization, continues to hold in the presence of small-$x$ evolution although we have not been able to explicitly verify this. Our result is in agreement with usual $k_\perp$-factorization where the gluon number density of the nucleus does not appear in an explicit way.

Methodology of projection of wave functions of light nuclei on cluster channels on the example of quantum 11B{alpha-7Li}-system

Methodology of projection of wave functions of light nuclei on cluster channels on the example of quantum 11B{alpha-7Li}-system

Magnetic moments in odd-ACd isotopes and coupling of particles with zero-point vibrations

Background: The coupling of the last nucleon with configurations in the ground state of the even-even core is known to augment the single quasiparticle fragmentation pattern. In a recent experimental study by Yordanov \emph{et al.} the values of the magnetic dipole and electric quadrupole moments of the $11/2^-$ state in a long chain of Cd isotopes were found to follow a simple trend which we try to explain by means of incorporating long-range correlations in the ground state. Purpose: Our purpose is to study the influence of the ground-state correlations (GSC) on the magnetic moments and compare our results with the data for the odd-A Cd isotopes. Method: In order to evaluate if the additional correlations have bearing on the magnetic moments we employ an extension to the quasiparticle-phonon model (QPM) which takes into account quasiparticle$\otimes$phonon configurations in the ground state of the even-even core to the structure of the odd-A nucleus wave function. Results: It is shown that the values for the magnetic moments which the applied QPM extension yields deviate further from the Schmidt values. The latter is in agreement with the measured values for the Cd isotopes. Conclusions: The GSC exert significant influence on the magnetic dipole moments and reveal a potential for reproducing the experimental values for the studied cadmium isotopes.

P-3He elastic scattering at 0.6–1 GeV: some short-range effects

Using a model wave function for 3He nucleus, where the two-body short-range correlation and three-nucleon force are considered, p-3He elastic scattering differential cross section is calculated using two different approaches, the multiple scattering formalism and the optical limit approximation, in the frame work of Glauber model at 0.6, 0.715 and 1 GeV. The results of the two approaches are similar. The principal contribution comes from the two-body short-range correlation and the effect of the three-nucleon force is relatively small. The observed results cannot describe the experimental data in the region, where the multiple scattering is dominant. These discrepancies between the theoretical and experimental results are interpreted as a result of the two-body short-range correlation and the three-nucleon force effects in the used wave function.

Three-body asymptotic normalization factors for halo nuclei and their determination

The explicit forms of the true asymptotics of the three-body (312) bound state radial wave functions of halo nuclei a both with two loosely bound external neutrons and with two charged particles, valid in different parts of the asymptotic region of the configuration space, are presented. The results for three-body asymptotic normalization factors for α + n + n → 6He and n + α + α → 9Be obtained from the comparative analysis of these asymptotic forms with the specific approximate model wave functions for asymptotic regions are also given.

Inelastic proton scattering by the 15N nucleus in the context of diffraction theory

The amplitude of inelastic proton scattering by the 15N nucleus (at a level of J π = 5/2+) is calculated in the context the Glauber diffraction theory. A multifold scattering operator considers the first- and second-order terms. The wave function of 15N nucleus is used in the shell model. The differential sections are calculated for energies of 0.415, 0.8 and 1 GeV. It is shown that the minima in the differential section are due to both the nucleus-target wave function and the destructive interference of the amplitudes of single and double collisions.

Effects of Hindered Rotation on H2Nuclear Spin Conversion on Ag(111)

We investigated the effects of H2 hindered rotation on ortho–para (o–p) H2 conversion. To clarify the adsorption properties of H2 on Ag(111), we performed first-principles calculations based on spin-polarized density functional theory (DFT) with DFT-D2 method. We calculated the wave functions of nuclei of H2 from potential energy curves of H2 on Ag(111). From these results, we found that non-negligible out-of-plane potential anisotropy with a perpendicular orientation preference exists even on non-corrugated Ag(111). We also clarified that o–p H2 conversion is enhanced by H2 hindered rotation on Ag(111). This enhancement is induced by electron transfer from the surface to H2 with the perpendicular orientation preference.

Further improvement in the variational many-body wave functions for light nuclei

An improved variational ansatz is proposed and implemented for variational many-body wave functions for light nuclei with nucleons interacting through Argonne (AV${}_{18}$) and Urbana IX (UIX) three-nucleon interactions. The new ansatz is based upon variationally distinguishing between the various components of the two-body Jastrow and operatorial correlations, which are operated upon by three-body and spin-orbit correlations. We obtain noticeable improvement in the quality of the wave function and lowering of the energies compared to earlier results. The new energies are \ensuremath{-}8.38(1), \ensuremath{-}28.07(1), and \ensuremath{-}29.90(1) MeV for ${}^{3}$H, ${}^{4}$He, and ${}^{6}$Li, respectively. Though, the present improved ansatz still fails to stabilize the ${}^{6}$Li nucleus against a breakup into an \ensuremath{\alpha} particle and a deuteron by 390 KeV; nonetheless, it is an improvement over previous studies.

Spatial entanglement and massive neutrino oscillations produced by orbital electron capture decay

The two-particle wave function of neutrino and recoil nucleus is found as a solution of an initial value problem in the far zone for a time longer than the electron capture decay lifetime of a hydrogenlike ion. The neutrino-recoil entanglement arising in such a process is a consequence of the momentum conservation and is closely related to the wave packet structure of the state. Because of neutrino mixing, the joint wave packet involves the coherent superposition of the neutrino mass eigenstate packets. This is the new physical realization of the Einstein-Podolsky-Rosen thought experiment, which has no analogue in quantum optics and quantum informatics. A class of possible experiments for the registration of a neutrino and a recoil nucleus is proposed. It is shown that due to spatial correlations neutrino oscillations can be observed in the coincidence experiment with the recoil.

Nuclear matter at high density: Phase transitions, multiquark states, and supernova outbursts

Phase transition from hadronic matter to quark-gluon matter is discussed for various regimes of temperature and baryon number density. For small and medium densities, the phase transition is accurately described in the framework of the Field Correlation Method, whereas at high density predictions are less certain and leave room for the phenomenological models. We study formation of multiquark states (MQS) at zero temperature and high density. Relevant MQS components of the nuclear matter can be described using a previously developed formalism of the quark compound bags (QCB). Partial-wave analysis of nucleon-nucleon scattering indicates the existence of 6QS which manifest themselves as poles of $P$-matrix. In the framework of the QCB model, we formulate a self-consistent system of coupled equations for the nucleon and 6QS propagators in nuclear matter and the G-matrix. The approach provides a link between high-density nuclear matter with the MQS components and the cumulative effect observed in reactions on the nuclei, which requires the admixture of MQS in the wave functions of nuclei kinematically. 6QS determine the natural scale of the density for a possible phase transition into the MQS phase of nuclear matter. Such a phase transition can lead to dynamic instability of newly born protoneutron stars and dramatically affect the dynamics of supernovae. Numerical simulations show that the phase transition may be a good remedy for the triggering supernova explosions in the spherically symmetric supernova models. A specific signature of the phase transition is an additional neutrino peak in the neutrino light curve. For a Galactic core-collapse supernova, such a peak could be resolved by the present neutrino detectors. The possibility of extracting the parameters of the phase of transition from observation of the neutrino signal is discussed also.

ON ASYMPTOTICS OF THREE-BODY BOUND STATE RADIAL WAVE FUNCTIONS OF HALO NUCLEI NEAR THE HYPERANGLE φ~0 AND φ~π/2 IN THE CONFIGURATION SPACE AND THREE-BODY ASYMPTOTIC NORMALIZATION FACTORS FOR 6He NUCLEUS IN THE (n+n+α)-CHANNEL

Asymptotic expressions for the bound state radial partial wave functions of three-body (nnc) halo nuclei with two loosely bound valence neutrons (n) are obtained in explicit form, when the relative distance between two neutrons (r) tends to infinity and the relative distance between the center of mass of core (c) and two neutrons (ρ) is too small or vice versa. These asymptotic expressions contain a factor that can strongly influence the asymptotic values of the three-body radial wave function in the vicinity of the hyperangle of φ~0 except 0 (r→∞ and ρ is too small except 0) or φ~π/2 except π/2 (ρ→∞ and r is too small except 0) in the configuration space. The derived asymptotic forms are applied to the analysis of the asymptotic behavior of the three-body (nnα) wave function for 6He nucleus obtained by other authors on the basis of multicluster stochastic variational method using the two forms of the αN-potential. The ranges of r (or ρ) from the asymptotical regions are determined for which the agreement between the calculated wave function and the asymptotics formulae is reached. Information about the values of the three-body asymptotic normalization factors is extracted.

Application of the diffraction theory to proton scattering by the 15C nucleus in inverse kinematics

The calculation of the amplitude of proton elastic scattering by unstable neutron-rich nucleus 15C within the Glauber diffraction theory with the 15C nucleus wave function in the multiparticle shell model is presented. In optical limit approximation (single scattering), the differential cross section of proton elastic scattering is calculated at energies of 0.2, 0.6, and 1 GeV/nucleon. For an energy of 0.2 GeV/nucleon, the contribution of double scattering, determining the differential cross section at angles exceeding 20° is taken into account.