This work introduces into the Interacting Boson Model, which was created in 1974 by F. Iachello and A. Arima and then extended by numerous papers. Many-body configurations with s- and d-boson states are described and creation- and annihilation-operators for bosons are introduced. States with defined total angular momentum are dealt with and the Hamilton operator of the IBM1-model is expressed in terms of Casimir operators. Level energies and electromagnetic transition probabilities are compared with measured data. A short introduction to Lie algebras and their application to the IBM1-model are given. In the IBM2- model protons and neutrons are treated separately and in IBFM single nucleons are added to the boson model. Comparison with experimental results.
The rate for the photon emission accompanying orbital 1S electron capture by the atomic nucleus is recalculated. While a photon can be emitted by the electron or by the nucleus, the use of the length gauge significantly suppresses the nuclear contribution. Our calculations resolve the long standing discrepancy of theoretical predictions with experimental data for $ΔJ=2$ forbidden transitions. We illustrate the results by comparison with the data established experimentally for the first forbidden unique decays of $^{41}$Ca and $^{204}$Tl.
The spin symmetry of anti-Lambda spectrum in nucleus $^{16}$O has been studied in the relativistic mean field theory. The spin-orbit splittings of spin doublets are found to be around 0.03-0.07 MeV and the dominant components of the Dirac spinor for the anti-Lambda spin doublets are found to be near identical. It indicates that there is an even better spin symmetry in the anti-Lambda spectrum than that in the anti-nucleon spectrum.
The connection of synthesis of long-lived superheavy nuclei and existence of the island of stability with the choice of realistic nuclear potential is discussed: the behaviour of the average field of nuclei is an important element of nuclear models. It is also shown that it is just Dubna that possesses the priority both in the recent synthesis of a superheavy nucleus with charge Z=114 and in its theoretical prediction made 35 years ago. Possible sizes of the island of stability of superheavy nuclei are considered.
Experimental values of Coulomb sums for q > 2 fm^(-1) are considered. Assuming that a part of nucleons is modified in the nucleus, an approach is offered, in the framework of which the calculation is in agreement with the experimental data. It gives the nuclear matter density value, above which the nucleon changes its properties. The radius of a modified proton is estimated, the possibilities for a further investigation into its properties are discussed.
Event-by-event multiplicity fluctuations in central C+C, S+S, In+In, and Pb+Pb as well as p+p collisions at bombarding energies from 10 to 160 AGeV are studied within the HSD and UrQMD microscopic transport approaches. Our investigation is directly related to the future experimental program of the NA61 Collaboration at the SPS for a search of the QCD critical point. The dependence on energy and atomic mass number of the scaled variances for negative, positive, and all charged hadrons is presented and compared to the results of the model of independent sources. Furthermore, the nucleus-nucleus …
Analytical expressions for the elastic and dynamic form factors (FFs) are derived in the shell model (SM) with a potential well of finite depth. The consideration takes into account the motion of the target-nucleus center of mass (CM). Explanation is suggested for a simultaneous shrinking of the density and momentum distributions of nucleons in nuclei. The convenient working formulae are given to handle the expectation values of relevant multiplicative operators in case of the 1s-1p shell nuclei.
The work deals with one of the topics of collective motion. In the frame of Nuclear Fluid Dynamics, a model which portrays the nuclear matter as a quantum elastic body, the torus-like motions and their associated energies are computed using the thirteen moment approximation. The spin-dependent collective excitations, with toroidal electromagnetic structure, are studied by means of the Generalized Goldhaber-Teller model, with emphasize on the 1$^{-}$ spin-flip mode and its excitation in spherical nuclei by inelastic electron scattering. We discuss the importance of toroidal contributions in the…
The $K^-$-nucleus optical potential is revisited to investigate its global feature phenomenologically. It is a puzzle that the energy shift is found to be repulsive in all of the observed kaonic atom, although the $K^-N$ interaction is known to be so attractive as to form the $Λ(1405)$ resonance. To solve this puzzle, we examine the $K^-$ optical potential in the linear density approximation and determine the potential parameters of each kaonic atom so as to reproduce the observed energy shift and absorption width. We find two types of the potentials. One potential has a so large real part as …
The charge-dependent realistic nuclear Hamiltonian for a nucleus, composed of neutrons and protons, can be successfully approximated by a charge-independent one. The parameters of such a Hamiltonian, i.e., the nucleon mass and the NN potential, depend upon the mass number A, charge Z and isospin quantum number T of state of the studied nucleus.
What is the size of the atomic nucleus? This deceivably simple question is difficult to answer. While the electric charge distributions in atomic nuclei were measured accurately already half a century ago, our knowledge of the distribution of neutrons is still deficient. In addition to constraining the size of atomic nuclei, the neutron distribution also impacts the number of nuclei that can exist and the size of neutron stars. We present an ab initio calculation of the neutron distribution of the neutron-rich nucleus $^{48}$Ca. We show that the neutron skin (difference between radii of neutro…
We study a production of Coulomb-assisted $Σ^-$-nucleus bound states by nuclear ($K^-$, $π^+$) reactions within a distorted-wave impulse approximation, so as to examine several types of the $Σ$-nucleus potentials that are consistent with the available $Σ^-$ atomic X-ray data and nuclear ($π^-$, $K^+$) data. We theoretically demonstrate the inclusive ($K^-$, $π^+$) spectra of the $Σ^-$ unstable bound states on $^{28}$Si, $^{58}$Ni, and $^{208}$Pb targets at incident $K^-$ lab momenta $p_{K}= 400\text{--}800$ MeV/c. The results show that the near-recoilless ($K^-$, $π^+$) reaction on the $^{58}$…
We perform a global sensitivity analysis of the binding energy and the charge radius of the nucleus $^{16}$O to identify the most influential low-energy constants in the next-to-next-to-leading order chiral Hamiltonian with two- and three-nucleon forces. For this purpose we develop a subspace-projected coupled-cluster method using eigenvector continuation [Frame D. et al., Phys. Rev. Lett. 121, 032501 (2018)]. With this method we compute the binding energy and charge radius of $^{16}$O at more than one million different values of the 16 low-energy constants in one hour on a standard laptop. Fo…
Atomic Parity Violation (APV) is usually quantified in terms of the weak nuclear charge $Q_W$ of a nucleus, which depends on the coupling strength between the atomic electrons and quarks. In this work, we review the importance of APV to probing new physics using effective field theory. Furthermore, using $SU(2)$ invariance, we correlate our findings with those from neutrino-nucleus coherent scattering. Moreover, we investigate signs of parity violation in polarized electron scattering and show how precise measurements on the Weinberg angle, $\sin θ_W$, will give rise to competitive bounds on l…
We report a quantum simulation of the deuteron binding energy on quantum processors accessed via cloud servers. We use a Hamiltonian from pionless effective field theory at leading order. We design a low-depth version of the unitary coupled-cluster ansatz, use the variational quantum eigensolver algorithm, and compute the binding energy to within a few percent. Our work is the first step towards scalable nuclear structure computations on a quantum processor via the cloud, and it sheds light on how to map scientific computing applications onto nascent quantum devices.
Further exploration of the machine-learning-based nuclear mass table
College of Physics, Henan Normal University（河南师范大学物理学院）；School of Science, Huzhou University（湖州学院理学院）；Institute of Nuclear Science and Technology, Henan Academy of Sciences（河南省科学院核科学与技术研究所）；China Institute of Atomic Energy（中国原子能科学研究院）
A scheme of solving the proton-neutron interacting boson model (IBM-2) in terms of the SU(3) basis is introduced, by which the IBM-2 coupled with an octupole boson is applied to describe the low-energy structure of the critical point nucleus, $^{152}$Sm. The results indicate that the spectral properties of both the positive-parity bands and negative-parity bands in this nucleus can be well captured by the IBM-2 calculations through a simple Hamiltonian, thus providing an example of the IBM-2 in a unified description of quadrupole and octupole states in a transitional system. In addition, a sta…
The Gamow-Teller transition operator is written as a polynomial in the dipole proton-neutron and quadrupole charge conserving QRPA boson operators, using the prescription of the boson expansion technique of Belyaev-Zelevinski type. Then, the $2νββ$ process ending on the first $2^+$ state in the daughter nucleus is allowed via one, two and three boson states describing the odd-odd intermediate nucleus. The approach uses a single particle basis which is obtained by projecting out the good angular momentum from an orthogonal set of deformed functions. The basis for mother and daughter nuclei have…
In nuclear physics, the relativistic mean-field theory describes the nucleus as a system of Dirac nucleons which interact via meson fields. In a static case and without nonlinear self-coupling of the $σ$ meson, the relativistic mean-field equations become a system of Dirac equations where the potential is given by the meson and photon fields. The aim of this work is to prove the existence of solutions of these equations. We consider a minimization problem with constraints that involve negative spectral projectors and we apply the concentration-compactness lemma to find a minimizer of this prob…
We considered the characteristic features of SU(3) partial dynamical symmetry in the interacting boson model framework to demonstrate the relevance of this technique in the nuclear spectroscopy of Dy (A=160) nucleus. The predictions of SU(3)-PDS for energy spectrum and B(E2)transition probabilities were compared with the most recent experimental data which an acceptable degree of agreement is achieved.
The nuclear interactions of atomic and low energy antiprotons are studied. Measurements of level shifts and widths in the lightest elements are analyzed and compared with new results obtained in heavy nuclei. Simple geometric properties of antiproton - nucleus interactions are demonstrated. Upon this background one finds some anomalies that indicate strong energy dependence in the subthreshold antiproton - nucleon interactions. The use of of antiproton in studies of the nuclear surface is briefly discussed.
The microscopic origin of the $γ$-softness (fluctuations in the triaxiality parameter $γ$ of the nuclear shape) observed in atomic nuclei is studied in the framework of the triaxial projected shell model approach, which is based on the deformed mean-field picture with multi-quasiparticle configuration space. It is demonstrated that the coupling to quasiparticle excitations drives the system from a $γ$-rigid to a $γ$-soft pattern. As an illustrative example for a $γ$-soft nucleus, a detailed study has been performed for the $^{104}$Ru nucleus. The experimental energies and a large sample of mea…
The physics of neutrino-nucleus cross sections is a critical probe of the Standard Model and beyond. A precise understanding is also needed to accurately deduce astrophysical neutrino spectra. At energies above $\sim 5$ GeV, the cross section is dominated by deep inelastic scattering, mediated by weak bosons. In addition, there are subdominant processes where the hadronic coupling is through virtual photons, $γ^\ast$: (on-shell) $W$-boson production (e.g., where the underlying interaction is $ν_\ell + γ^\ast \rightarrow \ell^- + W^+$) and trident production (e.g., where it is $ν+ γ^\ast \right…
We study the spectral fluctuations of the $^{208}$Pb nucleus using the complete experimental spectrum of 151 states up to excitation energies of $6.20$ MeV recently identified at the Maier-Leibnitz-Laboratorium at Garching, Germany. For natural parity states the results are very close to the predictions of Random Matrix Theory (RMT) for the nearest-neighbor spacing distribution. A quantitative estimate of the agreement is given by the Brody parameter $ω$, which takes the value $ω=0$ for regular systems and $ω\simeq 1$ for chaotic systems. We obtain $ω=0.85 \pm 0.02$ which is, to our knowledge,…
A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1,1) x SO(5) dynamical group. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code enables a wide range of model Hamiltonians to be analysed. This range includes essentially all Hamiltonians that are rational functions of the model's quadrupole moments $q_M$ and are at most quadratic in the corresponding conjugate mo…
Atomic electrons are sensitive to the properties of the nucleus they are bound to, such as nuclear mass, charge distribution, spin, magnetization distribution, or even excited level scheme. These nuclear parameters are reflected in the atomic transition energies. A very precise determination of atomic spectra may thus reveal information about the nucleus, otherwise hardly accessible via nuclear physics experiments. This work reviews theoretical and experimental aspects of the nuclear effects that can be identified in atomic structure data. An introduction to the theory of isotope shifts and hy…
This paper gives an extended model of the atomic nucleus - we call it the YY model, which allows a new description for strong forces from the well-known Standard Model. The forces that hold the nucleus together (protons and neutrons) can be expressed in a new way. Based on the YY model, more structural description details for an atomic nucleus will be possible than is the case with the conventional description. The YY model is compatible with the standard model. However, it allows for very delicate considerations when modelling the distribution of protons and neutrons within or around an atomi…
We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator techniques directly linked to the characteristic function of the probability distribution. The method is illustrated in atomic nuclei. The nature of the particle number fluctuations from small to large volumes compared to the system size are carefully analyzed in three cases: normal systems, superfluid systems and superfluid systems with total particle number rest…
In this paper, we used a transitional Hamiltonian which has $U(5)\leftrightarrow(6)$ transition to improve theoretical predictions for energy spectra and quadrupole transition rates of $^{112}$Cd nucleus. To this aim, the transitional Hamiltonian in the affine $SU(1,1)$ algebra has been extended by adding the $O(6)$-Casimir operator and mixing Hamiltonian to increase exactness in the description of 4$^+_2$ and 2$^+_3$ intruder levels of this nucleus. We also considered the wave functions of both regular and intruder states, as a combination in the $N$ and $N+2$ boson spaces. The results confir…
The influence of the diffuse surface layer of a finite nucleus on the mean square radii and their isotopic shift is investigated. We present the calculations within the Gibbs-Tolman approach using the experimental values of the nucleon separation energies. Results are compared with that obtained by means of direct variational method based on Fermi-like trial functions.
Double-$γ$ vibrations in deformed nuclei are studied in the context of the interacting boson model with special reference to their anharmonic character. It is shown that large anharmonicities can be obtained with interactions that are (at least) of three-body nature between the bosons. As an example the $γ$ vibrations of the nucleus $^{166}_{\phantom{0}68}$Er$^{\phantom{00}}_{98}$ are studied in detail.
When an atom is placed into an oscillating electric field with frequency far from atomic resonances, the atomic electrons partly shield this field at the nucleus. It is conjectured that when the frequency of electric field reaches an atomic resonance, the electric field at the nucleus may be significantly enhanced. In this paper, we systematically study the mechanisms of this enhancement and show that it may reach five orders in magnitude in particular cases. As an application, we consider laser-assisted neutron capture in 139-Lanthanum nucleus and screening and resonance enhancement of nuclea…
The hyperfine interaction as a probe of the microscopic structure of the atomic nucleus
Center for Quantum Nanoscience, Institute for Basic Science（量子纳米科学中心，基础科学研究院）；Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg（斯特拉斯堡大学，法国国家科学研究中心，斯特拉斯堡材料物理与化学研究所）；Ewha Womans University（梨花女子大学）；Université de Strasbourg, CNRS, Institut de Chimie（斯特拉斯堡大学，法国国家科学研究中心，化学研究所）；Université de Strasbourg, CNRS, Institut pluridisciplinaire Hubert Curien（斯特拉斯堡大学，法国国家科学研究中心，于贝尔·居里跨学科研究所）
Cross sections for the concurrent production of pairs of quarkonia (J/psi, Upsilon) and/or gauge bosons (W, Z) from double-parton scatterings (DPS) in high-energy proton-nucleus and nucleus-nucleus collisions at the LHC are calculated. The estimates are based on next-to-leading-order perturbative QCD predictions, including nuclear modifications of the parton densities, for the corresponding single-scattering cross sections. Expected event rates for J/psi+J/psi, J/psi+Upsilon, J/psi+W, J/psi+Z, Upsilon+Upsilon, Upsilon+W, Upsilon+Z, and same-sign W+W production in their (di)leptonic decay modes…
We explore for the first time the possibilities to measure an intermediate-mass (mH = 115-140 GeV/c^2) Standard-Model Higgs boson in electromagnetic proton-lead (pPb) interactions at the CERN Large Hadron Collider (LHC) via its b-bbar decay. Using equivalent Weizsaecker-Williams photon fluxes and Higgs effective field theory for the coupling gamma-gamma --> H, we obtain a leading-order cross section of the order of 0.3 pb for exclusive Higgs production in elastic (pPb --> gamma-gamma --> p H Pb) and semielastic (pPb --> gamma-gamma --> Pb H X) processes at sqrt(s) = 8.8 TeV. After applying var…
Low-lying collective excitations in even-even vibrational and transitional nuclei may be described semi-classically as quadrupole running waves on the surface of the nucleus ("tidal waves"), and the observed vibrational-rotational behavior can be thought of as resulting from a rotating condensate of interacting $d$ bosons. These concepts have been investigated by measuring lifetimes of the levels in the yrast band of the $^{102}$Pd nucleus with the Doppler Shift Attenuation Method. The extracted $B(E2)$ reduced transition probabilities for the yrast band display a monotonic increase with spin,…
The neutron-rich $^{213}$Pb isotope was produced in the fragmentation of a primary 1 GeV $A$ $^{238}$U beam, separated in FRS in mass and atomic number, and then implanted for isomer decay $γ$-ray spectroscopy with the RISING setup at GSI. A newly observed isomer and its measured decay properties indicate that states in $^{213}$Pb are characterized by the seniority quantum number that counts the nucleons not in pairs coupled to angular momentum $J=0$. The conservation of seniority is a consequence of the Berry phase associated with particle-hole conjugation, which becomes gauge invariant and t…
We delineate, as an analog of two-flavor dense quark matter, the phase structure of a many-body mixture of atomic bosons and fermions in two internal states with a tunable boson-fermion attraction. The bosons b correspond to diquarks, and the fermions f to unpaired quarks. For weak b-f attraction, the system is a mixture of a Bose-Einstein condensate and degenerate fermions, while for strong attraction composite b-f fermions N, analogs of the nucleon, are formed, which are superfluid due to the N-N attraction in the spin-singlet channel. We determine the symmetry breaking patterns at finite te…
The concept of compound nucleus was proposed by Niels Bohr in 1936 to explain narrow resonances observed in scattering of a slow neutron off atomic nuclei. A compound nucleus is a metastable state with a long lifetime, in which all the degrees of freedom are in a sort of thermal equilibrium. Fusion reactions are defined as reactions to form such compound nucleus by merging two atomic nuclei. Here a short description of heavy-ion fusion reactions at energies close the Coulomb barrier is presented. This includes: (i) an overview of a fusion process, (ii) a strong interplay between nuclear struct…
Tagged jet measurements provide a promising experimental channel to quantify the similarities and differences in the mechanisms of jet production in proton-proton and nucleus-nucleus collisions. We present the first calculation of the transverse momentum asymmetry of $Z^0/γ^*$-tagged jet events and the momentum imbalance of $γ$-tagged jet events in $\sqrt{s}=2.76$ TeV reactions at the LHC. Our results combine the ${\cal O}(G_Fα_s^2)$, ${\cal O}(G_Fα_s^2)$ perturbative cross sections with the radiative and collisional processes that modify parton showers in the presence of dense QCD matter. We …
We compute the $β$-decay $ft$-values within the frameworks of the energy density functional (EDF) and the interacting boson model (IBM). Based on the constrained mean-field calculation with the Gogny-D1M EDF, the IBM Hamiltonian for an even-even nucleus and essential ingredients of the interacting boson-fermion-fermion model (IBFFM) for describing the neighboring odd-odd nucleus are determined in a microscopic way. Only the boson-fermion and residual neutron-proton interaction strengths are determined empirically. The Gamow-Teller (GT) and Fermi (F) transition rates needed to compute the $β$-d…
Recent data on the nuclear modification of W and Z boson production measured by the ATLAS collaboration in PbPb collisions at $\sqrt{s_{\rm nn}}=5.02$ TeV show an enhancement in peripheral collisions, seemingly contradicting predictions of the Glauber model. The data were previously explained by arguing that the nucleon-nucleon cross section may be shadowed in nucleus-nucleus collisions, and hence suppressed compared to the proton-proton cross section at the same collision energy. This interpretation has quite significant consequences for the understanding of heavy-ion data, in particular in t…
The interacting boson model with configuration mixing, with parameters derived from the self-consistent mean-field calculation employing the microscopic Gogny energy density functional, is applied to the systematic analysis of the low-lying structure in Hg isotopes. Excitation energies, electromagnetic transition rates, deformation properties, and ground-state properties of the $^{172-204}$Hg nuclei are obtained by mapping the microscopic deformation energy surface onto the equivalent IBM Hamiltonian in the boson condensate. These results point to the overall systematic trend of the transition…
Shell model calculations using realistic interactions reveal that the ground and low-lying yrast states of the $N=Z$ nucleus $^{92}_{46}$Pd are mainly built upon isoscalar neutron-proton pairs each carrying the maximum angular momentum J=9 allowed by the shell $0g_{9/2}$ which is dominant in this nuclear region. This structure is different from the ones found in the ground and low-lying yrast states of all other even-even nuclei studied so far. The low-lying spectrum of excited states generated by such correlated neutron-proton pairs has two distinctive features: i) the levels are almost equid…
Low-mass (sub-eV) spin-0 dark matter particles, which form a coherently oscillating classical field $ϕ= ϕ_0 \cos(m_ϕt)$, can induce oscillating variations in the fundamental constants through their interactions with the Standard Model sector. We calculate the effects of such possible interactions, which may include the linear interaction of $ϕ$ with the Higgs boson, on atomic and molecular transitions. Using recent atomic clock spectroscopy measurements, we derive new limits on the linear interaction of $ϕ$ with the Higgs boson, as well as its quadratic interactions with the photon and light q…
