Multi-nucleon Systems Research Articles

Long-distance nuclear matrix elements for neutrinoless double-beta decay from lattice QCD

Neutrinoless double-beta (0νββ) decay is a heretofore unobserved process which, if observed, would imply that neutrinos are Majorana particles. Interpretations of the stringent experimental constraints on 0νββ-decay half-lives require calculations of nuclear matrix elements. This work presents the first lattice quantum chromodynamics (LQCD) calculation of the matrix element for 0νββ decay in a multinucleon system, specifically the nn→ppee transition, mediated by a light left-handed Majorana neutrino propagating over nuclear-scale distances. This calculation is performed with quark masses corresponding to a pion mass of mπ=806 MeV at a single lattice spacing and volume. The statistically cleaner Σ−→Σ+ee transition is also computed in order to investigate various systematic uncertainties. The prospects for matching the results of LQCD calculations onto a nuclear effective field theory to determine a leading-order low-energy constant relevant for 0νββ decay with a light Majorana neutrino are investigated. This work, therefore, sets the stage for future calculations at physical values of the quark masses that, combined with effective field theory and nuclear many-body studies, will provide controlled theoretical inputs to experimental searches of 0νββ decay. Published by the American Physical Society 2024

Formation of large chunk of nuclear matter in heavy-ion collisions

In terrestrial laboratory with existing accelerators, the maximum multinucleon system produced so far is limited to that with total nucleon number being less than the sum of two colliding nuclei. Such situation may hinder our studies on the properties of nuclear many-body system. Here a way of producing large multinucleon system via multi-nucleus collision device Collider Plus in terrestrial laboratory is proposed. It is shown that large chunk of nucleonic matter can be produced through nuclear ternary fusion reactions at lower beam energies and also large block of dense matter can be formed via ternary collisions of heavy nuclei at intermediate energies. These investigations may shed lights on the studies of the synthesis of superheavy elements and the properties of bulk superdense nuclear matter.

Eigenvector continuation as an efficient and accurate emulator for uncertainty quantification

First principles calculations of atomic nuclei based on microscopic nuclear forces derived from chiral effective field theory (EFT) have blossomed in the past years. A key element of such ab initio studies is the understanding and quantification of systematic and statistical errors arising from the omission of higher-order terms in the chiral expansion as well as the model calibration. While there has been significant progress in analyzing theoretical uncertainties for nucleon-nucleon scattering observables, the generalization to multi-nucleon systems has not been feasible yet due to the high computational cost of evaluating observables for a large set of low-energy couplings. In this Letter we show that a new method called eigenvector continuation (EC) can be used for constructing an efficient and accurate emulator for nuclear many-body observables, thereby enabling uncertainty quantification in multi-nucleon systems. We demonstrate the power of EC emulation with a proof-of-principle calculation that lays out all correlations between bulk ground-state observables in the few-nucleon sector. On the basis of ab initio calculations for the ground-state energy and radius in 4He, we demonstrate that EC is more accurate and efficient compared to established methods like Gaussian processes.

Minimally entangled state preparation of localized wave functions on quantum computers

Initializing a single site of a lattice scalar field theory into an arbitrary state with support throughout the quantum register requires $O({2}^{{n}_{Q}})$ entangling gates on a quantum computer with ${n}_{Q}$ qubits per site. It is conceivable that instead initializing to functions that are good approximations to states may have utility in reducing the number of required entangling gates. In the case of a single site of a noninteracting scalar field theory, initializing to a symmetric exponential wave function requires ${n}_{Q}\ensuremath{-}1$ entangling gates, the minimal number necessary to create an entangled state of all ${n}_{Q}$ qubits. This is compared with the ${2}^{{n}_{Q}\ensuremath{-}1}+{n}_{Q}\ensuremath{-}3+{\ensuremath{\delta}}_{{n}_{Q},1}$ required for a symmetric Gaussian wave function. In this work, we explore the initialization of one-site (${n}_{Q}=4$), two-site (${n}_{Q}=3$), and three-site (${n}_{Q}=3$) noninteracting scalar field theories with symmetric exponential wave functions using IBM's quantum simulators and quantum devices (Poughkeepsie and Tokyo). With the digitizations attainable with ${n}_{Q}=3,4$, these tensor-product wave functions are found to have large overlap with a Gaussian wave function and provide a suitable low-noise initialization for improvement and Somma inflation. In performing these simulations, we have employed a workflow that interleaves calibrations to mitigate systematic errors in production. The calibrations allow tolerance cuts on gate performance including the fidelity of the symmetrizing Hadamard gate, both in vacuum (${|\mathbf{0}\ensuremath{\rangle}}^{\ensuremath{\bigotimes}{n}_{Q}}$) and in medium (${n}_{Q}\ensuremath{-}1$ qubits initialized to an exponential function). The results obtained in this work are relevant to systems beyond scalar field theories, such as the deuteron radial wave function, two- and three-dimensional Cartesian-space wave functions, and nonrelativistic multinucleon systems built on a localized eigenbasis.

Measurement of the production and lepton charge asymmetry of [Formula: see text] bosons in Pb+Pb collisions at [Formula: see text] with the ATLAS detector.

A measurement of W boson production in lead-lead collisions at sqrt{s_{mathrm {NN}}}=2.76mathrm { TeV} is presented. It is based on the analysis of data collected with the ATLAS detector at the LHC in 2011 corresponding to an integrated luminosity of 0.14 mathrm {nb}^{-1} and 0.15 mathrm {nb}^{-1} in the muon and electron decay channels, respectively. The differential production yields and lepton charge asymmetry are each measured as a function of the average number of participating nucleons langle N_{mathrm {part}} rangle and absolute pseudorapidity of the charged lepton. The results are compared to predictions based on next-to-leading-order QCD calculations. These measurements are, in principle, sensitive to possible nuclear modifications to the parton distribution functions and also provide information on scaling of W boson production in multi-nucleon systems.

A New Approach for Parameters of Nucleon-Nucleon Scattering at Low Energies in One and Two Dimensions

Many of the important properties of multi-nucleon systems can be found by studying the nucleon- nucleon interactions. In this work, a suitable central and an appropriate noncentral potential have been used to study nucleon- nucleon scattering in one and two dimensions. The phase shift, scattering cross section, length and amplitude are calculated using the Nikiforov-Uvarov (NU) method and WKB approximation. Comparison between the results of the suggested model in this article and the experimental reported values indicates that there is a good consistency between them.

Microscopic Basis of the Interacting Boson Model

The microscopic basis of the IBM is discussed in this paper, presenting a derivation of the IBM system from the multi-nucleon system. Although there could be different approaches to this goal as stated in the preface of this supplement, we focus on two approaches. One is the Otsuka-Arima-Iachello mapping, which works for the spherical and near-spherical nuclei. The other is a mapping for deformed nuclei.

Similarity renormalization group and many-body effects in multiparticle systems

The similarity renormalization group (SRG), based on the simple one-body free harmonic oscillator Hamiltonian, is applied to various nucleon-nucleon realistic interactions to investigate the unitarity of the SRG transformations. Two-body and three-body contributions to the SRG-evolved Hamiltonian are studied in the framework of spectral distribution theory for reasonable SRG cutoffs and in multiparticle systems, with up through 28 particles considered. The outcome points to the first evidence for the overall importance of three-body SRG-induced interactions and especially, of its two-body effective content in multinucleon systems, without the need for large-scale shell model calculations for many light to heavier nuclei.

Publisher’s Note: Microscopic formulation of the interacting boson model for rotational nuclei [Phys. Rev. C83, 041302(R) (2011)

We propose a novel formulation of the Interacting Boson Model (IBM) for rotational nuclei with axially-symmetric strong deformation. The intrinsic structure represented by the potential energy surface (PES) of a given multi-nucleon system has a certain similarity to that of the corresponding multi-boson system. Based on this feature, one can derive an appropriate boson Hamiltonian as already reported. This prescription, however, has a major difficulty in rotational spectra of strongly deformed nuclei: the bosonic moment of inertia is significantly smaller than the corresponding nucleonic one. We present that this difficulty originates in the difference between the rotational response of a nucleon system and that of the corresponding boson system, and could arise even if the PESs of the two systems were identical. We further suggest that the problem can be cured by implementing $\hat{L} \cdot \hat{L}$ term into the IBM Hamiltonian, with coupling constant derived from the cranking approach of Skyrme mean-field models. The validity of the method is confirmed for rare-earth and actinoid nuclei, as their experimental rotational yrast bands are reproduced nicely.

Microscopic formulation of the interacting boson model for rotational nuclei

We propose a novel formulation of the interacting boson model (IBM) for rotational nuclei with axially symmetric, strong deformation. The intrinsic structure represented by the potential-energy surface (PES) of a given multinucleon system has a certain similarity to that of the corresponding multiboson system. Based on this feature, one can derive an appropriate boson Hamiltonian, as already reported. This prescription, however, has a major difficulty in the rotational spectra of strongly deformed nuclei: the bosonic moment of inertia is significantly smaller than the corresponding nucleonic one. We present that this difficulty originates in the difference between the rotational response of a nucleon system and that of the corresponding boson system, and could arise even if the PESs of the two systems were identical. We further suggest that the problem can be solved by implementing the $\mathrm{L\ifmmode \hat{}\else \^{}\fi{}}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{L\ifmmode \hat{}\else \^{}\fi{}}$ term into the IBM Hamiltonian, with the coupling constant derived from the cranking approach of Skyrme mean-field models. The validity of the method is confirmed for rare-earth and actinoid nuclei, as their experimental rotational yrast bands are reproduced nicely.

Astrophysical S factors of reactions with light nuclei

The two-cluster model is a phenomenological semi-microscopic approach to the study of multinucleon nuclear systems. In the framework of this model, interaction of nucleon clusters is described by the local two-body potential determined from the condition of description of data on cluster scattering and properties of their bound states. In this case the many-body character of the problem is taken into account approximately in terms of Pauli-allowed and Pauli-forbidden states of the total nucleon system. Accounting for the dependence of cluster interaction potential on orbital Young schemes characterizing the properties of permutation symmetry in the nucleon system is an important ingredient of the model. This approach is used for examination of photonuclear processes for p2H, p3H, p6Li, p12C and 4He12C, 3He4He, 3H4He, 2H4He systems and corresponding astrophysical S factors. It is demonstrated that this approach provides fairly good description of the data available in the low-energy region, especially for systems with the number of nucleons A > 4 when errors for the phase shifts of cluster scattering extracted from experimental data are minimal.

Formation of multinucleon systems and nuclei with mass numbers of 6 and 7 in 16Op interactions at a momentum of 3.25 GeV/c per nucleon

The results of a comparative analysis of the multiplicities of singly and doubly charged accompanying particles in the channels involving the production of six- and seven-nucleon systems in 16Op collisions at a momentum of 3.25 GeV/c per nucleon are reported. Cross sections for the yield of multinucleon systems and mean multiplicities of accompanying particles are found. The experimental data are compared with the predictions of the cascade—fragmentation—evaporation model.

Development of cluster ideas in the physics of multinucleon and multiquark systems

We review the development of cluster ideas in the following directions: the structural forbiddenness of heavy-nucleus fragmentation, the possibility of “seeing” virtual excited clusters in a nucleus during the quasi-elastic knockout of clusters by ∼1-GeV protons; the role of two-step mechanisms in direct nuclear reactions with clusters; the cluster-cluster potentials with forbidden states; the Moscow NN-interaction potential and quark microscopics; and the quasi-elastic knockout of mesons from a nucleon by high-energy electrons in quark microscopics.

Electroweak matrix elements in the two-nucleon sector from lattice QCD

We demonstrate how to make rigorous predictions for electroweak matrix elements in nuclear systems directly from QCD. More precisely, we show how to determine the short-distance contributions to low-momentum transfer electroweak matrix elements in the two-nucleon sector from lattice QCD. In potential model descriptions of multi-nucleon systems, this is equivalent to uniquely determining the meson-exchange currents, while in the context of nuclear effective field theory, this translates into determining the coefficients of local, gauge-invariant, multi-nucleon-electroweak current operators. The energies of the lowest-lying states of two nucleons on a finite volume lattice with periodic boundary conditions in the presence of a background magnetic field are sufficient to determine the local four-nucleon operators that contribute to the deuteron magnetic moment and to the threshold cross section of n p → d γ . Similarly, the energy-levels of two nucleons immersed in a background isovector axial weak field can be used to determine the coefficient of the leading local four-nucleon operator contributing to the neutral- and charged-current break-up of the deuteron. This is required for the extraction of solar neutrino fluxes at SNO and future neutrino experiments.

Partially quenched nucleon-nucleon scattering

Nucleon-nucleon scattering is studied to next-to-leading order in a partially-quenched extension of an effective field theory used to describe multi-nucleon systems in QCD. The partially-quenched nucleon-nucleon amplitudes will play an important role in relating lattice simulations of the two-nucleon sector to nature.

NN correlations in a multinucleon system

Cross sections for processes involving three or more identical nucleons in the final state are expected to be strongly suppressed near the threshold because of the Pauli exclusion principle. It is shown that the Migdal-Watson effect (final-state interaction between nucleons) removes this suppression.

Microscopic Basis of the Interacting Boson Model

The microscopic basis of the IBM is discussed in this paper, presenting a derivation of the IBM system from the multi-nucleon system. Although there could be different approaches to this goal as stated in the preface of this supplement, we focus on two approaches. One is the Otsuka-Arima-Iachello mapping, which works for the spherical and near-spherical nuclei. The other is a mapping for deformed nuclei. In this paper, we discuss mapping methods for deriving the Interacting Boson Model (IBM). l) We first present a mapping method for spherical and near-spherical nuclei, usually referred to as the Otsuka-Arima-Iachello (OAI) mapping. 2 ), 3 ) The OAI mapping is based on the seniority scheme as will be discussed in detail. This mapping has been developed so that realistic calculations can be carried out as presented in a subsequent paper. In this paper, the basic concepts of the mapping are discussed rather in detail. Furthermore, the proton-neutron Interacting Boson Model (IBM-2) is discussed as a natural consequence of this mapping. 2 ), 3 ) In the second half of this paper, a mapping method for strongly deformed nuclei 8 ) will be reviewed. Although this mapping is for deformed nuclei, it is somewhat related to the OAI mapping. The work on deformed nuclei is much before any sort of completion, and considerable effort should be made in the future. For this purpose, the Quantum Monte Carlo Diagonalization method proposed recently 4 )- 7 ) may be useful. When the IBM was proposed from the phenomenological viewpoint by Arima and Iachello, the microscopic picture of bosons of this model was not known as pointed out in the preface of this supplement. The microscopic theory has made a crucial contribution even to phenomenological studies by the IBM, also as mentioned in the preface. Before starting rather detailed discussions, it may be useful to overview relevant properties of the effective nucleon-nucleon interactions. The short-range nuclear force favors two nucleons lying close to each other. This means that, if the wave functions of the two neutrons have large spatial overlap, the matrix element of this interaction becomes larger. On the other hand, two identical fermions cannot occupy the same quantum state, and this is the case for two neutrons. The next optimum case for gaining energy is that the two neutrons are moving on the same orbital but in opposite directions. Because the direction is opposite, the quantum states of the two neutrons are different. In this case, the total angular momentum of the two-neutron system is zero, because the rotation is completely cancelled. In fact, the

Microscopic calculation of IBM in the Te-Ba region

Recent microscopic calculations of the Proton-Neutron Interacting Boson Model are presented for Te-Xe-Ba isotopes. The IBM-2 Hamiltonian is derived from a nucleon Hamiltonian comprised of single-particle energy, pairing and quadrupole-quadrupole interactions, by carrying out mapping from multinucleon systems to interacting-boson systems. The microscopic origin of the O(6) dynamical symmetry or γ-unstable deformation is discussed.

Neutral strange-particle production in p̄20Ne reactions at 607 MeV/c

The Λ 0 and K 0 s production cross sections have been measured at 607 MeV/ c for the reaction p ̄ + 20 Ne → V 0 + X ( V 0 =Λ, 0 , K 0 s ) . The Λ 0 /K 0 s production ratio is found to be (2.3±0.7). The data are consistent with an evaporative character of the emission mechanism from a multinucleon system for Λ 0 and from one nucleon for K 0 s . The rapidity distributions of negative tracks in K 0 x events are different from those in Λ 0 events without V 0 .

P−presonances: A link between nuclear and hadronic excitations

Evidence of resonant behavior has recently been discovered in $p\ensuremath{-}p$ scattering, and possibly also in $n\ensuremath{-}p$ scattering. In particular, the $p\ensuremath{-}p$ data indicate the existence of $^{1}D_{2}$, $^{3}F_{3}$, and $^{1}G_{4}$ resonances at energies of approximately 2140, 2260, and 2430 MeV. The correlation between increasing $l$ values and increasing energies that is observed in these resonances suggests a form of rotational motion. Since a virtually bound nucleon-nucleon state represents the low-mass limit of a multinucleon (nuclear) system, we logically expect the rotational behavior of this dinucleon state to follow the known systematics of nuclear physics. The rotational motion is highly nonadiabatic for this very light dinucleon system, so that an $l(l+1)$ energy interval rule is expected to apply, where $l$ is the orbital angular momentum quantum number. In support of this idea, we show experimental data plots which reveal that (1) rotational bands in very light nuclei and in the dinucleon follow the expected $l(l+1)$ interval rule, and (2) the experimental moments of inertia of the rotating bandheads exhibit the expected ${A}^{\frac{5}{3}}$ behavior, where $A$ is the atomic weight. We can extend these concepts even farther by formally sorting the observed baryon and meson resonances into nonadiabatic rotational bands. When we do this, we discover that the experimental moments of inertia of these hadron rotational bands, plotted as a function of the bandhead masses, extrapolate smoothly into the moments of inertia of the very light atomic nuclei. Applying the $l(l+1)$ energy interval rule to the observed $^{1}D_{2}$, $^{3}F_{3}$, and $^{1}G_{4}$ $p\ensuremath{-}p$ resonances, and then extrapolating to $l=0$ to obtain the mass of the unobserved $p\ensuremath{-}p$ bandhead, we discover that it corresponds to a virtual $\mathrm{pp}\ensuremath{\pi}$ bound state, which is a characteristic hadronic excitation. Hence the $p\ensuremath{-}p$ resonances form a direct and unique experimental link between nuclear and hadronic excitations: The $p\ensuremath{-}p$ rotational levels, which are nuclear in origin, can be used to pinpoint the mass of the $p\ensuremath{-}p$ bandhead excitation, which is hadronic in origin. The ${C}_{\mathrm{LL}}$, $\ensuremath{\Delta}{\ensuremath{\sigma}}_{L}$, and $\ensuremath{\Delta}{\ensuremath{\sigma}}_{T}$ measurements carried out at Argonne are crucial in the identification of these rather weak $p\ensuremath{-}p$ resonances. Unfortunately, the low-energy limit of these Argonne measurements falls above the predicted energy values of the (unobserved) $l=0$ and $l=1$ levels in the $p\ensuremath{-}p$ rotational band. Thus the present results suggest the usefulness of extending the ${C}_{\mathrm{LL}}$, $\ensuremath{\Delta}{\ensuremath{\sigma}}_{L}$, and $\ensuremath{\Delta}{\ensuremath{\sigma}}_{T}$ experiments at Argonne from the present lower limit of 1.0 GeV/c down to at least 0.8 GeV/c.