General analytical expressions for the observables in $dA$-scattering reaction have been derived in the diffraction approximation. The resulting formulas describe the cross section and polarization states of the deuteron when it scattering by nuclei with zero spin in the ground state. The tabulated distributions of the target nucleus density and the realistic deuteron wave functions calculated on the basis of Nijmegen nucleon-nucleon potentials were used. The nucleon-nucleus phases were calculated in the framework of Glauber formalism and making use of the double-folding potential. The calculated cross sections and analyzing powers in elastic scattering of deuterons by $^{16}\text{O}$ and $^{40}\text{Ca}$ nuclei at 700 MeV are compared with the corresponding experimental data.
P-odd correlations in the deuteron photodesintegration are considered. The $π$-meson exchange is not operative in the case of unpolarized deuterons. For polarized deuterons a P-odd correlation due to the $π$-meson exchange is about $3 \times 10^{-9}$. Short-distance P-odd contributions exceed essentially than the contribution of the $π$-meson exchange.
A model independent theoretical analysis of recent experimental data on deuteron photodisintegration with polarized laser beams is presented. We find that it is important to distinguish between the three isovector E1 amplitudes $E1_v^j$ in reaction channels with total angular momentum $j=0,1,2$ and that the isoscalar M1 amplitude $M1_s$ is non-zero in the photon energy range $3.5 MeV < E_γ< 10 MeV$
Employing the polarization degrees of freedom in the deuteron allows to isolate smaller than average inter-nucleon distances in the deuteron. As a result one can identify set of high $Q^2$ reactions off polarized deuteron which are particularly sensitive to the short range dynamics of strong interaction. We concentrate on the studies of several aspects of the short range phenomena. These are the relativistic dynamics of electron--bound-nucleon scattering, color coherence in high $Q^2$ electro-production as well as the formation of the vector mesons in coherent electro-production from the deute…
The exclusive and inclusive electroproduction off the polarized deuteron is considered at large $Q^2$ and $x \ge 0.5$. It is shown that the use of a polarized target will allow to emphasize smaller than average internucleon distances in the deuteron. As a result, we expect amplification of all the effects (color transparency, relativistic dynamics, etc.) sensitive to small internucleon distances. Numerical estimates are given for the processes $e+ \vec d \rightarrow e +p+n$ and $e+ \vec d \rightarrow e +X$.
Three-nucleon force effects in polarization transfers from the doubly spin-polarized initial neutron-deuteron state to the outgoing neutron in neutron-deuteron scattering
Following precise experimental studies at the Duke Free-Electron Laser Laboratory, we discuss photodisintegration of deuterons with 100% linearly polarized photons using a model independent theoretical approach taking together $M1$ and $E1$ amplitudes simultaneously. The isoscalar $M1_s$ contribution is also taken exactly into account. From the existing experimental measurement on doubly polarized thermal neutron capture, it is seen that the isoscalar $M1_s$ contribution could be of the same order of magnitude as the experimentally measured cross sections at energies relevant to Big Bang Nucle…
A general analytical expression for the double differential cross section of inclusive deuteron stripping reaction on nuclei at intermediate energies of incident particles was obtained in the diffraction approximation. Nucleon-nucleus phases were calculated in the framework of Glauber formalism and making use of the double-folding potential. The exact wave function of deuteron with correct asymptotics at short and long distances between nucleons was used. The calculated angular dependencies of cross sections are in good agreement with corresponding experimental data.
A microscopic formalism for describing observed cross sections for deuteron breakup by three-nucleon nuclei was developed on the basis of the diffraction nuclear model. A general formula that describes the amplitude for the reaction d+3He->3He+p+n and which involves only one adjustable parameter was obtained by using expansions of the integrands involved in terms of a Gaussian basis. This formula was used to analyze experimental data on the exclusive cross sections for deuteron breakup by He-3 nuclei at the projectile energy of 89.4 MeV. The importance of employing, in calculations, a deuteron…
A general analytical expressions for the cross-section and the polarization of nucleons arising in the inclusive deuteron stripping reaction have been derived in the diffraction approximation. The nucleon-nucleus phases were calculated in the framework of Glauber formalism and making use of the double-folding potential. The tabulated distributions of the target nucleus density and the realistic deuteron wave function with correct asymptotic at large nucleon-nucleon distances were used. The calculated angular dependences for the cross-sections and the analyzing powers of the $(\vec{d},p)$ react…
The probability P(Delta-Delta) to find the Delta-Delta component inside the deuteron, where Delta stands for the Delta(1232) resonance, is calculated in the Nambu-Jona-Lasinio model of light nuclei. We obtain P(Delta-Delta) = 0.3%. This prediction agrees good with the experimental estimate P(Delta-Delta) < 0.4% at 90% of CL (D. Allasia et al., Phys. Lett. B174 (1986) 450).
Three-body calculations of (d,p) and (p,d) reactions involving one-neutron halo nuclei 11Be and 15C are performed using the framework of Faddeev-type scattering equations. Important effects of the optical potential nonlocality are found improving the description of the experimental data. The obtained values for the neutron spectroscopic factor are consistent with estimations from other approaches.
A general analytical expression has been obtained in the diffraction approximation for the polarization of nucleons arising in the deuteron stripping reaction on nuclei at intermediate energies of the incident particles. A tabulated density distribution of the target nucleus and a realistic wave function of the deuteron with correct asymptotic limits at large internucleon distances were used in the calculations. The nucleon-nucleus phase shifts were calculated in the Glauber formalism using the double folding potential. The calculated angular dependencies for the vector analyzing power $A_{y}$…
The D-wave state component of the neutron-proton bound state in the deuteron is calculated in the Nambu-Jona-Lasinio model of light nuclei - the relativistically covariant quantum field theoretic approach to the description of low-energy nuclear forces. The theoretical value of the fraction of the D-wave state relative to the S-wave state is equal to eta_d = 0.0238. This agrees well with the phenomenological value eta_d = 0.0256(4) quoted by Kamionkowski and Bahcall (ApJ. 420, 884 (1994)).
A dynamics of low-energy nuclear forces is investigated for low-energy electromagnetic and weak nuclear reactions with the deuteron in the Nambu-Jona-Lasinio model of light nuclei by example of the neutron-proton radiative capture (M1-capture) n + p -> D + photon, the photomagnetic disintegration of the deuteron photon + D -> n + p and weak reactions of astrophysical interest. These are the solar proton burning p + p -> D + positron + nu_e, the pep-process p + electron + p -> D + nu_e and the neutrino and anti-neutrino disintegration of the deuteron caused by charged nu_e + D -> electron + p +…
The process $\overrightarrow{^3{\rm He}}(e,e'\vec{p})d $ (or $\overrightarrow{^3{\rm He}}(e,e'\vec{d})p $) is studied theoretically in a Faddeev treatment with the aim to have access to the spin-dependent momentum distribution of ${\vec p} {\vec d} $ clusters in polarized $^3$He. Final state interactions and meson exchange currents turn out to have a strong influence in the considered kinematical regime (below the pion threshold). This precludes the direct access to the momentum distribution except for small deuteron momenta. Nevertheless, the results for the longitudinal and transverse respon…
The isovector M1 transitions between low-lying T=1 and T=0 states in odd-odd N=Z nuclei are analyzed. Simple analytical expressions for M1 transition strengths are derived within a single-j-shell approximation for both j=l+1/2 and j=l-1/2 cases. The large B(M1) values for the j=l+1/2 case are attributed to quasi-deuteron configurations. The B(M1) values for the j=l-1/2 case are found to be small due to partly cancellation of spin and orbital parts of the M1 matrix element.
The frozen spin method can be effectively used for a high-precision measurement of the tensor electric and magnetic polarizabilities of the deuteron and other nuclei in storage rings. For the deuteron, this method would provide the determination of the deuteron's polarizabilities with absolute precision of order of $10^{-43}$ cm$^3$.
Use of deuteron-induced spallation reactions at intermediate energies has recently been proposed for transmutation of several long-lived fission products (LLFPs). In the design study of a transmutation system using a deuteron primary beam, accurate cross section data of deuteron-induced reactions on the LLFPs are indispensable. Reliable model predictions play an important role in completing the necessary cross section data since currently available experimental data are very limited. Under the circumstances, we have been developing a code system dedicated for deuteron-induced reactions, which …
We compute the distribution of quasideuterons in doubly closed shell nuclei. The ground states of $^{16}$O and $^{40}$Ca are described in $ls$ coupling using a realistic hamiltonian including the Argonne $v_{8}^\prime$ and the Urbana IX models of two-- and three--nucleon potentials, respectively. The nuclear wave function contains central and tensor correlations, and correlated basis functions theory is used to evaluate the distribution of neutron-proton pairs, having the deuteron quantum numbers, as a function of their total momentum. By computing the number of deuteron--like pairs we are abl…
In recent time the deuteron structure at short distances is often treated from the point of view nonnucleonic degrees of freedom. In this paper the measurements of T-odd polarization observables using tensor polarized deuteron beam and polarized proton target or proton polarimeter are proposed to search the quark configurations inside the deuteron.
We compute the distribution of quasideuterons in doubly closed shell nuclei and infinite correlated nuclear matter. The ground states of $^{16}$O and $^{40}$Ca are described in $ls$ coupling using a realistic hamiltonian including the Argonne $v_{8}^\prime$ and the Urbana IX models of two-- and three--nucleon potentials, respectively. The nuclear wave function contains central and tensor correlations, and correlated basis functions theory is used to evaluate the distribution of neutron-proton pairs, having the deuteron quantum numbers, as a function of their total momentum. By computing the nu…
We calculate P-odd difference of the total cross-sections of the deuteron disintegration by left and right polarized photons. The relative magnitude of this difference in the threshold region is about 10^{-7}. Its experimental measurement would give valuable information on the weak nucleon-nucleon interaction at short distances.
Mechanisms of the charge exchange reaction $dp\to \{pp\}_{\!s} Nπ$, where $\{pp\}_{\!s}$ is a two-proton system at low excitation energy, are studied at beam energies 1 -- 2 GeV and for invariant masses $M_X$ of the final $Nπ$ system that correspond to the formation of the $Δ(1232)$ isobar. The direct mechanism, where the initial proton is excited into the $Δ(1232)$, dominates and explains the existing data on the unpolarized differential cross section and spherical tensor analyzing power $T_{22}$ for $M_X> 1.2$ GeV/$c^2$. However, this model fails to describe $T_{20}.
General formulas describing deuteron spin dynamics in storage rings with allowance for the tensor electric and magnetic polarizabilities are derived. It is found that an initially tensor-polarized deuteron beam can acquire a final horizontal vector polarization of the order of 1%. This effect allows one to measure the tensor magnetic polarizability of the deuteron in storage ring experiments. We also confirm an existence of the effect found by Baryshevsky and Gurinovich, hep-ph/0506135 and Baryshevsky, hep-ph/0510158; hep-ph/0603191 that the tensor magnetic polarizability of the deuteron cause…
Formal expressions are developed for the general five-fold differential cross section of incoherent $π$-photoproduction on the deuteron including beam and target polarization. The polarization observables of the cross section are described by various beam, target and beam-target asymmetries for polarized photons and/or polarized deuterons. They are given as bilinear hermitean forms in the reaction matrix elements divided by the unpolarized cross section. In addition, the corresponding observables for the semi-exclusive reaction $\vec d(\vec γ,π)NN$ are also given.
A set of global optical potential parameters, DA1p, for deuterons with the $1p$-shell nuclei is obtained by simultaneously fitting 67 sets of experimental data of deuteron elastic scattering from \nuc{6}{Li}, \nuc{9}{Be}, \nuc{10}{B}, \nuc{11}{B}, \nuc{12}{C}, \nuc{13}{C}, \nuc{14}{N}, \nuc{16}{O} and \nuc{18}{O} with incident energies between 5.25 and 170 MeV. DA1p improves the description of the deuteron elastic scattering from the $1p$-shell nuclei with respect to the existing systematic deuteron potentials and can give satisfactory reproduction to the experimental data with radiative nucle…
The relativistic light-front dynamics (LFD) method has been shown to give a correct description of the most recent data for the deuteron monopole and quadrupole charge form factors obtained at the Jefferson Laboratory for elastic electron-deuteron scattering for six values of the squared momentum transfer between 0.66 and 1.7 (GeV/c)$^{2}$. The good agreement with the data is in contrast with the results of the existing non-relativistic approaches. In this work we firstly make a complementary test of the LFD applying it to calculate another important characteristic, the nucleon momentum distri…
The reactions of nucleon and polarized deuteron scattered off a heavy target at large impact parameter with intermediate energies have been investigated by using the improved quantum molecular dynamics model. It is found that, due to the difference effect of isovector potential on proton and neutron, there is a significant difference between the angle distribution of elastic scattering protons and neutrons. To overcome the lack of monochromatic neutron beam, the reaction of polarized deuteron peripherally scattered off the heavy target is used to replace the reaction of individual proton and n…
The effects of parity violation in the interaction of relativistic polarized protons and deuterons are discussed. Within Glauber's approach, estimates are obtained for P-odd asymmetries in the total and elastic scattering cross sections, in the deuteron dissociation cross section, and in the inelastic cross section with meson production in a final state. It is shown that, from the point of view of the magnitude of the P-odd effects, the interaction of polarized deuterons with unpolarized protons has an advantage over the interaction of polarized protons with unpolarized deuterons. A significan…
We investigate shadowing corrections to the polarized deuteron structure functions g_1^d and b_1. In the kinematic domain of current fixed target experiments we observe that shadowing effects in g_1^d are approximately twice as large as for the unpolarized structure function F_2^d. Furthermore, we find that b_1 is surprisingly large at x < 0.1 and receives dominant contributions from coherent double scattering.
The differential cross section for gamma-deuteron Compton scattering from a tensor polarized deuteron is computed in an effective field theory. The first non-vanishing contributions to this differential cross section are the interference terms between the leading electric coupling diagrams and the subleading single potential pion exchange diagrams or the subleading magnetic moment coupling diagrams. At 90 degree photon scattering angle, only the pion term contributes at this order to the tensor polarized differential cross section. This provides a clean way to study the photon pion dynamics in…
Background: Low-energy transfer reactions in which a proton is stripped from a deuteron projectile and dropped into a target play a crucial role in the formation of nuclei in both primordial and stellar nucleosynthesis, as well as in the study of exotic nuclei using radioactive beam facilities and inverse kinematics. Ab initio approaches have been successfully applied to describe the $^3$H$(d,n)^4$He and $^3$He$(d,p)^4$He fusion processes. Purpose: An ab initio treatment of transfer reactions would also be desirable for heavier targets. In this work, we extend the ab initio description of $(d,…
Following the model independent approach to deuteron photodisintegration with linearly polarized $γ-$rays, we show that the measurements of the tensor analyzing powers on aligned deuterons along with the differential cross section involve five different linear combinations of the isovector $E1^j_v; j=0,1,2$ amplitudes interfering with the isoscalar $M1_s$ and $E2_s$ amplitudes. This is of current interest in view of the recent experimental finding \cite{blackston1} that the three $E1^j_v$ amplitudes are distinct and also the reported experimental observation \cite{sawatzky} on the front-back (…
An analysis of the $^{231}$Pa$(d,3n)$$^{230}$U reaction excitation function at energies around the Coulomb barrier has taken into account the pre-equilibrium and compound-nucleus cross sections corrected for the deuteron-breakup decrease of the total reaction cross section, as well as the inelastic breakup enhancement. The analysis reveals the dominance of the deuteron breakup mechanism unlike a former assessment in this respect of the deuteron-induced fission process.
Relativistic nuclear response theory is formulated for the proton-neutron pairing, or deuteron transfer, channel. The approach is based on the meson-nucleon Lagrangian of Quantum Hadrodynamics (QHD) and advances the relativistic field theory to connect consistently the high-energy scale of heavy mesons, the medium-energy range of the pion and the low-energy domain of emergent collective vibrations (phonons) in a parameter-free way. Mesons and phonons build up the in-medium nucleon-nucleon interaction in spin-isospin transfer channels, in particular, the phonon-exchange part takes care of the l…
Spatial imaging of polarized deuterons at the Electron-Ion Collider
University of Jyväskylä（于韦斯屈莱大学）；Helsinki Institute of Physics（赫尔辛基物理研究所）；Institute for Nuclear Theory, University of Washington（华盛顿大学核理论研究所）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Wayne State University（韦恩州立大学）；RIKEN BNL Research Center（理研布鲁克海文研究中心）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of California, Berkeley（加州大学伯克利分校）
We analyze the energy dependence for two types of parity-non-conserving (PNC) asymmetries in the reaction $γD\to np$ in the near-threshold region. The first one is the asymmetry in reaction with circularly polarized photon beam and unpolarized deuteron target. The second one corresponds to those with an unpolarized photon beam and polarized target. We find that the two asymmetries have quite different energy dependence, and their shapes are sensitive to the PNC-meson exchange coupling constants. The predictions for the future possible experiments to provide definite constraints for the PNC-cou…
We discuss the possible factorization of the tensor asymmetry $A^T_d$ measured for polarized deuteron targets within a relativistic framework. We define a reduced asymmetry and find that factorization holds only in plane wave impulse approximation and if p-waves are neglected. Our numerical results show a strong factorization breaking once final state interactions are included. We also compare the d-wave content of the wave functions with the size of the factored, reduced asymmetry and find that there is no systematic relationship of this quantity to the d-wave probability of the various wave …
The isoscalar $pn$ pair is expected to emerge in nuclei having the similar proton and neutron numbers but there is no clear experimental evidence for it. We aim to clarify the correspondence between the $pn$ pairing strength in many-body calculation and the triple differential cross section (TDX) of proton-induced deuteron knockout ($p,pd$) reaction on $^{16}$O. The radial wave function of the isoscalar $pn$ pair with respect to the center of $^{16}$O is calculated with the energy density functional (EDF) approach and is implemented in the distorted wave impulse approximation (DWIA) framework.…
Polarized electron-deuteron deep-inelastic scattering (DIS) with detection of the spectator proton ("tagged DIS") enables measurements of neutron spin structure with maximal control of nuclear effects. We calculate the longitudinal spin asymmetries in polarized tagged DIS using methods of light-front nuclear structure and study their dependence on the measured proton momentum. Asymmetries can be formed with all three deuteron spin states ($\pm 1, 0$) or the two maximum-spin states only ($\pm 1$, involving tensor polarization). The proton momentum dependence can be used to select pure S-wave co…
Background: DIS on the polarized deuteron with detection of a proton in the nuclear breakup region (spectator tagging) represents a unique method for extracting the neutron spin structure functions and studying nuclear modifications. The tagged proton momentum controls the nuclear configuration during the DIS process and enables a differential analysis of nuclear effects. Such measurements could be performed with the future electron-ion collider (EIC) and forward proton detectors if deuteron beam polarization could be achieved. Purpose: Develop theoretical framework for polarized deuteron DIS …
The possibility of using a tensor polarized deuteron target in electroproduction reactions creates new opportunities for studying different phenomena related to the short-range hadronic and nuclear physics. The use of tensor polarized deuteron allows to isolate smaller than average inter-nucleon distances for the bound two-nucleon system. In this report we consider several of high $Q^2$ reactions which are particularly sensitive to the short-range two-nucleon configurations in the deuteron. The one is the relativistic dynamics of electron-bound-nucleon scattering which can be studied in both i…
The production of light nuclei in relativistic heavy-ion collisions is well described by both the thermal model, where light nuclei are in equilibrium with all other hadron species present in a fireball, and by the coalescence model, where light nuclei are formed due to final state interactions after the fireball decays. A method is proposed to falsify one of the models. We suggest to measure a hadron-deuteron correlation function which carries information about the source of the deuterons and allows one to determine whether a deuteron is directly emitted from the fireball or if it is formed a…
Tensor structure of the deuteron can be studied by deep inelastic scattering and Drell-Yan process to understand it in terms of quark and gluon degrees of freedom. It probes interesting features in the deuteron including a D-wave contribution. In the charged-lepton DIS, twist-two structure functions $b_1$ and $b_2$ are expressed by tensor-polarized parton distribution functions (PDFs). We note that the HERMES experimental measurement of $b_1$ seems to be much different from a conventional theoretical prediction. This puzzling situation should be significantly improved in the near future by an …
Motivated by developments at HIGS at TUNL that include increased photon flux and the ability to circularly polarize photons, we calculate several beam-polarization/target-spin dependent observables for elastic Compton scattering on the deuteron. This is done at energies of the order of the pion mass within the framework of Heavy Baryon Chiral Perturbation Theory. Our calculation is complete to O(Q^3) and at this order there are no free parameters. Consequently, the results reported here are predictions of the theory. We discuss paths that may lead to the extraction of neutron polarizabilities.…
We calculate the asymmetries in parity nonconserving deuteron photodisintegration due to circularly polarized photons gamma+d to n+p with the photon laboratory energy ranging from the threshold up to 10 MeV and the radiative capture of thermal polarized neutrons by protons n+p to gamma+d. We use the leading order electromagnetic Hamiltonian neglecting the smaller nuclear exchange currents. Comparative calculations are done by using the Reid93 and Argonne v18 potentials for the strong interaction and the DDH and FCDH "best" values for the weak couplings in a weak one-meson exchange potential. A…
Polarized electron-deuteron DIS with spectator proton tagging offers a way of measuring the neutron spin structure functions with maximal theoretical control of nuclear effects. We calculate the nuclear structure factors in the longitudinal double-spin asymmetries using methods of light-front nuclear structure. A unique feature of the spin-1 system is that spin asymmetries can be formed either relative to the cross section in all three spin states ($λ_d = \pm 1, 0$) or in the two maximum-spin states only ($\pm 1$, involving tensor polarization). We find that the two-state deuteron spin asymmet…
A general analysis of polarization observables for the $d(γ,π)NN$ reaction with polarized photons and/or oriented deuterons is presented. The unpolarized differential cross section, linear photon asymmetry, vector and tensor target asymmetries are predicted for forthcoming experiments.
Apart from the $pd$ reaction also the scattering of antiprotons with transversal polarization $p_y^p$ on deuterons with tensor polarization $P_{xz}$ provides a null-test signal for time-reversal-invariance violating but parity conserving effects. Assuming that the time-reversal-invariance violating $\bar NN$ interaction contains the same operator structure as the $NN$ interaction, we discuss the energy dependence of the null-test signal in $\bar pd$ scattering on the basis of a calculation within the spin-dependent Glauber theory at beam energies of 50-300 MeV.
Scattering of protons with transversal polarization $p_y^p$ on deuterons with tensor polarization $P_{xz}$ provides a null-test signal for time-reversal (T) invariance violating but parity (P) conserving effects. We calculate the corresponding null-test observable at beam energies 100-1000 MeV within the spin-dependent Glauber theory considering T-violating P-conserving nucleon-nucleon interactions. The S-wave component of the deuteron wave function as well as the D-wave are taken into account and the latter is found to play an important role for the magnitude and the energy dependence of the …
There are four new structure functions for the spin-1 deuteron in comparison with the ones for the spin-1/2 proton, and they are called $b_1$, $b_2$, $b_3$, and $b_4$. The twist-2 structure functions $b_1$ and $b_2$ are expressed by tensor-polarized parton distribution functions in the deuteron. HERMES measurements of $b_1$ are much different from the prediction of the standard deuteron model with D-state admixture. It indicates that the structure functions $b_1$ and $b_2$ probe an interesting new aspect in the deuteron. There is an approved experiment at JLab to measure $b_1$ and it is expect…
We discuss the possibility of finding polarized antiquark flavor asymmetry in Drell-Yan processes. We find that the difference between polarized proton-proton and proton-deuteron Drell-Yan cross sections should provide valuable information on the polarized flavor asymmetry. Numerical results indicate that the asymmetry effects are conspicuous especially in the large-x_F region. Our analysis is important for the transversity distributions because the flavor asymmetry cannot be found by inclusive lepton scattering and W-production processes.
Fresh Look at Polarized Deuterons at the Nuclotron/NICA \& HIAF and Beyond
Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Baldin-Veksler Laboratory of High Energy Physics, Joint Institute for Nuclear Research（杜布纳联合核研究所鲍德温-韦克斯勒高能物理实验室）；L.D. Landau Institute for Theoretical Physics（列夫·朗道理论物理研究所）；Moscow Institute for Physics and Technology（莫斯科物理技术学院）；Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research（杜布纳联合核研究所波戈留博夫理论物理实验室）；Brookhaven National Laboratory（布鲁海文国家实验室）；Research Institute for Nuclear Problems, Belarusian State University（白俄罗斯国立大学核问题研究所）；Dzhelepov Laboratory of Nuclear Problems, Joint Institute for Nuclear Research（杜布纳联合核研究所杰列波夫核问题实验室）；Dubna State University（杜布纳国立大学）；M.V. Lomonosov Moscow State University, Faculty of Physics（莫斯科罗蒙诺索夫国立大学物理系）
