Nucleon Pair Research Articles

A Hartree-Fock-Bogoliubov Study on the Pairing Correlations of the Isotopes of Cobalt

Background: The phenomena of nucleon pairing could be outlined from the Bethe-Weizäcker semi-empirical formula, from which the nuclear properties, viz. the binding energy, stability, shape etc. could be clearly sketched. Though the pairing correlation seems to be a small correction to the binding energy term, it plays a determinative role in defining the structure of nuclear systems. The addition to the binding energy in turn affects the position of the isotope on the dripline and hence increases the stability.
 Purpose: To study the effects of pairing on the ground state properties of the isotopes of Cobalt.
 Methods: We use Hartree-Fock-Bogoliubov (HFB) theory for the study. The general wave functions for the HFB approach are determined from variational principle. The eigen functions for the Hamiltonian are connected with the particle operators through the Bogoliubov transformations. The Hartree-Fock energy is obtained through the minimization of the variational parameter and the HFB equation is solved by iterative diagonalization by restoring the particle number symmetry.
 Results: The HFB analysis substantiates the effect of pairing correlation on binding energies, neutron and proton pairing energies, neutron and proton pairing gaps and one- and two-neutron separation energies of the Cobalt isotopes. The binding energies and one and two-neutron separation energies match with the experimental values and for pairing energies and pairing gaps, the regions where pairing is significant and the effects of shell closure at the vicinity of magic configuration of neutrons could be recognized.
 Conclusion: The Hartree-Fock-Bogoliubov calculations of the effects of pairing could be used as an efficient tool to study the nuclear structure. It can be ascertained that pairing plays an important role in determining the ground state properties of atomic nuclei.

Nature of particles azimuthal anisotropy at low and high transverse momenta in ultrarelativistic A + A collisions

LHC data on the correlations of the elliptic flow v 2 of particles at low and high transverse momenta p T from Pb+Pb collisions at center-of-mass energy per nucleon pair TeV are analyzed in the framework of the HYDJET++ model. This model includes soft and hard components which allows to describe the region of both low and high transverse momenta. The origin of v 2 values in different p T regions is investigated at different centralities. It is shown that the experimentally observed correlations between v 2 at low and high p T in peripheral lead-lead collisions is due to correlation of particles in jets.

Even-even Nd isotopes in an SD -pair shell model

Nucleon pair shell model truncated to $SD$ collective pair subspace (SDPSM) was applied to study the properties of the low-lying states of the even-even $^{144--156}\mathrm{Nd}$ isotopes. It is found that, within the $M$ scheme, the systems with the number ${N}_{\ensuremath{\nu}}=7$ of neutron pairs (or the number ${N}_{\ensuremath{\pi}}=7$ of proton pairs) can be studied in the SDPSM for the first time. The results show that the properties of the low-lying states of the even-even Nd isotopes can be reproduced approximately, and the even-even $^{144--156}\mathrm{Nd}$ isotopes may be a good candidate for the first-order shape phase transition.

Observation of B[formula omitted] mesons and measurement of the B[formula omitted]/B+ yield ratio in PbPb collisions at TeV

The Bs0 and B+ production yields are measured in PbPb collisions at a center-of-mass energy per nucleon pair of 5.02 TeV. The data sample, collected with the CMS detector at the LHC, corresponds to an integrated luminosity of 1.7 nb−1. The mesons are reconstructed in the exclusive decay channels B→s0J/ψ(μ+μ−)ϕ(K+K−) and B→+J/ψ(μ+μ−)K+, in the transverse momentum range 7–50GeV/c and absolute rapidity 0–2.4. The Bs0 meson is observed with a statistical significance in excess of five standard deviations for the first time in nucleus-nucleus collisions. The measurements are performed as functions of the transverse momentum of the B mesons and of the PbPb collision centrality. The ratio of production yields of Bs0 and B+ is measured and compared to theoretical models that include quark recombination effects.

Study of neutrino-nucleus reactions with crisp model ( 0<Eν<3 GeV )

The neutrino-nucleus reactions are studied at energies from 0 to 3 GeV, using the CRISP program. To simulate these reactions, CRISP uses the Monte Carlo method through an intranuclear cascade model. Quase-elastic and baryonic resonance formation channels for the neutrino-nucleon interaction are considered. The total and differential particle emission cross-sections were obtained, obtaining a good agreement with the values reported by the MiniBooNE experiment. The influence of nuclear effects on the studied reactions, such as fermionic motion, the Pauli blocking mechanism, and the nucleonic separation energy, was shown. It was not possible to simultaneously reproduce the $\nu_\mu + D$ and $\nu_\mu + ^{12}C$ reactions using the same axial mass value. For the charged current quasi-elastic channel, $M_A = 0.95 \ GeV$ for the $\nu_\mu + D$ reaction, and $M_A = 1.35 \ GeV$ for the $\nu_\mu + ^{12}C$ reaction. This can be solved if one considers, in addition to the neutrino-nucleon interaction, the neutrino interaction with a pair of nucleons, just as we demonstrate in the last part of this work.

J/ψ photoproduction in Pb-Pb peripheral collisions at sNN=5 TeV

The photoproduction of J/ψ mesons at low transverse momentum is studied in peripheral lead-lead collisions collected by the LHCb Collaboration at a center-of-mass energy per nucleon pair of 5TeV, corresponding to an integrated luminosity of 210 μb−1. The J/ψ candidates are reconstructed through the prompt decay into two muons of opposite charge in the rapidity region of 2.0<y<4.5. The results significantly improve previous measurements and are compared to the latest theoretical prediction.Received 9 August 2021Accepted 14 February 2022DOI:https://doi.org/10.1103/PhysRevC.105.L032201Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.©2022 CERN, for the LHCb CollaborationPhysics Subject Headings (PhySH)Research AreasPhotonuclear reactionsPhysical SystemsQuarkoniaNuclear Physics

Measurement of prompt [formula omitted]-meson production and azimuthal anisotropy in Pb–Pb collisions at [formula omitted

The production yield and angular anisotropy of prompt Ds+ mesons were measured as a function of transverse momentum (pT) in Pb–Pb collisions at a centre-of-mass energy per nucleon pair sNN=5.02TeV collected with the ALICE detector at the LHC. Ds+ mesons and their charge conjugates were reconstructed at midrapidity (|y|<0.5) from their hadronic decay channel Ds+→ϕπ+, with ϕ→K−K+, in the pT intervals 2<pT<50GeV/c and 2<pT<36GeV/c for the 0–10% and 30–50% centrality intervals. For pT>10GeV/c, the measured Ds+-meson nuclear modification factor RAA is consistent with the one of non-strange D mesons within uncertainties, while at lower pT a hint for a Ds+-meson RAA larger than that of non-strange D mesons is seen. The enhanced production of Ds+ relative to non-strange D mesons is also studied by comparing the pT-dependent Ds+/D0 production yield ratios in Pb–Pb and in pp collisions. The ratio measured in Pb–Pb collisions is found to be on average higher than that in pp collisions in the interval 2<pT<8GeV/c with a significance of 2.3σ and 2.4σ for the 0–10% and 30–50% centrality intervals. The azimuthal anisotropy coefficient v2 of prompt Ds+ mesons was measured in Pb–Pb collisions in the 30–50% centrality interval and is found to be compatible with that of non-strange D mesons. The main features of the measured RAA, Ds+/D0 ratio, and v2 as a function of pT are described by theoretical calculations of charm-quark transport in a hydrodynamically expanding quark–gluon plasma including hadronisation via charm-quark recombination with light quarks from the medium. The pT-integrated production yield of Ds+ mesons is compatible with the prediction of the statistical hadronisation model.

Thermal Freeze-Out Parameters and Pseudoentropy from Charged Hadron Spectra in High-Energy Collisions

We collected the transverse momentum (mass) spectra of charged hadrons ( π − , π + , K − , K + , p ¯ , and p ) produced in collisions over a center-of-mass energy range from 2.70 to 200 GeV (per nucleon pair). The modified Tsallis–Pareto-type function (the TP-like function) with average transverse flow velocity is used to describe the contribution of participant or constituent quarks to transverse momentum of considered hadron. The experimental spectra of π ∓ and K ∓ (or p ¯ and p ) are fitted by the convolution of two (or three) TP-like functions due to the fact that two (or three) constituent quarks are regarded as two (or three) energy resources in the formation of considered hadron. From the reasonable fits to the spectra, the thermal freeze-out parameters are extracted, and the pseudoentropy is newly defined and extracted. Some parameters quickly change in the energy range of less than 7.7 GeV, and slowly change in the energy range of greater than 7.7 GeV, indicating the variation of collision mechanism at around 7.7 GeV.

γγ decay as a probe of neutrinoless ββ decay nuclear matrix elements

We study double gamma (γγ) decay nuclear matrix elements (NMEs) for a wide range of nuclei from titanium to xenon, and explore their relation to neutrinoless double-beta (0νββ) NMEs. To favor the comparison, we focus on double-magnetic dipole transitions in the final ββ nuclei, in particular the γγ decay of the double isobaric analog of the initial ββ state into the ground state. For the decay with equal-energy photons, our large-scale nuclear shell model results show a good linear correlation between the γγ and 0νββ NMEs. Our analysis reveals that the correlation holds for γγ transitions driven by the spin or orbital angular momentum due to the dominance of zero-coupled nucleon pairs, a feature common to 0νββ decay. Our shell-model findings point out the potential of future γγ decay measurements to constrain 0νββ NMEs, which are key to answer fundamental physics questions based on 0νββ experiments.

An iterative approach for the exact solution of the pairing Hamiltonian

A new iterative algorithm is established for the exact solution of the standard pairing problem, based on the Richardson-Gaudin method using the polynomial approach. It provides efficient and robust solutions for both spherical and deformed systems at a large scale. The key to its success is that the initial guess for the solutions of such a large set of the non-linear equations is provided in a physically meaningful and controllable manner. Moreover, one reduces the large-dimensional problem to a one-dimensional Monte Carlo sampling procedure, which improves the algorithm's efficiency and avoids the non-solutions and numerical instabilities that persist in most existing approaches. We calculated the ground state and low-lying excited states of equally spaced systems at different pairing strengths G. We then applied the model to study the quantum phase transitional Sm isotopes and the actinide nuclei Pu isotopes, where an excellent agreement with experimental data is obtained. Program summaryProgram Title: IterV1.mCPC Library link to program files:https://doi.org/10.17632/rjnbhgk2p6.1Licensing provisions: GPLv3Programming language: MathematicaNature of problem: The program calculates exact pairing energies based on a new iterative algorithm. The key is the procedure of determining the initial guesses for the large-set non-linear equations involved in a controllable and physically motivated manner. It provides an efficient and robust solver for both spherical and deformed systems in super large model spaces.Solution method: The new iterative algorithm approach starts with simple systems with k nucleon pairs and n=k levels, which can be solved iteratively by including one pair and one level at each step using the Newton-Raphson algorithm with a Monte Carlo sampling procedure. Then it takes the solutions of those systems as initial values and obtain the converged results for the full space by gradually adding the remaining levels. In this way, one reduces the k-dimensional Monte Carlo sampling procedure to a one-dimensional sampling, which improves the efficiency of the algorithm and avoids the non-solutions and numerical instabilities.

Evidence for X(3872) in Pb-Pb Collisions and Studies of its Prompt Production at sqrt[s_{NN}]=5.02 TeV.

The first evidence for X(3872) production in relativistic heavy ion collisions is reported. The X(3872) production is studied in lead-lead (Pb-Pb) collisions at a center-of-mass energy of sqrt[s_{NN}]=5.02 TeV per nucleon pair, using the decay chain X(3872)→J/ψπ^{+}π^{-}→μ^{+}μ^{-}π^{+}π^{-}. The data were recorded with the CMS detector in 2018 and correspond to an integrated luminosity of 1.7 nb^{-1}. The measurement is performed in the rapidity and transverse momentum ranges |y|<1.6 and 15<p_{T}<50 GeV/c. The significance of the inclusive X(3872) signal is 4.2 standard deviations. The prompt X(3872) to ψ2S yield ratio is found to be ρ^{Pb-Pb}=1.08±0.49(stat)±0.52(syst), to be compared with typical values of 0.1 for pp collisions. This result provides a unique experimental input to theoretical models of the X(3872) production mechanism, and of the nature of this exotic state.

Analyzing Transverse Momentum Spectra by a New Method in High-Energy Collisions

We analyzed the transverse momentum spectra of positively and negatively charged pions (π+ and π−), positively and negatively charged kaons (K+ and K−), protons and antiprotons (p and p¯), as well as ϕ produced in mid-(pseudo)rapidity region in central nucleus–nucleus (AA) collisions over a center-of-mass energy range from 2.16 to 2760 GeV per nucleon pair. The transverse momentum of the considered particle is regarded as the joint contribution of two participant partons which obey the modified Tsallis-like transverse momentum distribution and have random azimuths in superposition. The calculation of transverse momentum distribution of particles is performed by the Monte Carlo method and compared with the experimental data measured by international collaborations. The excitation functions of effective temperature and other parameters are obtained in the considered energy range. With the increase of collision energy, the effective temperature parameter increases quickly and then slowly. The boundary appears at around 5 GeV, which means the change of reaction mechanism and/or generated matter.

Evidence for X(3872) in PbPb collisions and studies of its prompt production at √SNN = 5.02 TeV with CMS

The first evidence for X(3872) production in relativistic heavy ion collisions, with a significance of 4.2 standard deviations, is reported. The X(3872) production is studied in lead-lead (PbPb) collisions at a center-of-mass energy of √SNN = 5.02 TeV per nucleon pair with the CMS detector. The measurement is performed in the rapidity and transverse momentum ranges |y| &lt; 1.6 and 15 &lt; pT &lt; 50 GeV/c. The prompt X(3872) to ψ(2S) yield ratio is found to be ρPbPb = 1.08 ± 0.49(stat.) ± 0.52(syst.), to be compared with typical values of 0.1 for pp collisions. This provides new input to theoretical models of the X(3872) production mechanism, and of the nature of this exotic state.

First measurement of the Bc+ meson nuclear modification factor in PbPb collisions with CMS

The Bc+ meson is observed in lead-lead and proton-proton collisions at a center-of-mass energy per nucleon pair of √SNN = 5.02 TeV, via the Bc+ → (J/ψ → μ+μ−)μ+vμ decay and using 2017 and 2018 data from the CMS detector. The resulting Bc+ nuclear modification factor is measured in two bins of the trimuon transverse momentum and of the collision centrality. Less suppression is observed than for other quarkonia and most open heavy flavour mesons. This first observation of the Bc+ meson in heavy ion collisions will shed light on the interplay of suppression and enhancement mechanisms in the production of heavy-flavor mesons in the quark-gluon plasma.

Prompt D0, D+, and D*+ production in Pb\u2013Pb collisions at sqrt{s_{mathrm{NN}}} = 5.02 TeV

The production of prompt D0, D+, and D*+ mesons was measured at midrapidity (|y| < 0.5) in Pb–Pb collisions at the centre-of-mass energy per nucleon–nucleon pair sqrt{s_{mathrm{NN}}} = 5.02 TeV with the ALICE detector at the LHC. The D mesons were reconstructed via their hadronic decay channels and their production yields were measured in central (0–10%) and semicentral (30–50%) collisions. The measurement was performed up to a transverse momentum (pT) of 36 or 50 GeV/c depending on the D meson species and the centrality interval. For the first time in Pb–Pb collisions at the LHC, the yield of D0 mesons was measured down to pT = 0, which allowed a model-independent determination of the pT-integrated yield per unit of rapidity (dN/dy). A maximum suppression by a factor 5 and 2.5 was observed with the nuclear modification factor (RAA) of prompt D mesons at pT = 6–8 GeV/c for the 0–10% and 30–50% centrality classes, respectively. The D-meson RAA is compared with that of charged pions, charged hadrons, and J/ψ mesons as well as with theoretical predictions. The analysis of the agreement between the measured RAA, elliptic (v2) and triangular (v3) flow, and the model predictions allowed us to constrain the charm spatial diffusion coefficient Ds. Furthermore the comparison of RAA and v2 with different implementations of the same models provides an important insight into the role of radiative energy loss as well as charm quark recombination in the hadronisation mechanisms.

Hunting for tetraquarks in ultraperipheral heavy ion collisions

Ultra-peripheral heavy ion collisions constitute an ideal setup to look for exotic hadrons because of their low event multiplicity and the possibility of an efficient background rejection. We propose to look for four-quark states produced by photon-photon fusion in these collisions at center-of-mass energy per nucleon pair $\sqrt{s_{\rm NN}}=5.5~{\rm TeV}$. In particular, we focus on those states that would represent a definite smoking gun for the compact tetraquark model. We show that the $X(6900)$, a likely $cc\bar{c}\bar{c}$ compact state, is a perfect candidate for this search, and estimate a production cross section ranging from around $250$ nb to $1150$ nb, depending on its quantum numbers. Furthermore, we discuss the importance of ultra-peripheral collisions to the search for the scalar and tensor partners of the $X(3872)$ predicted by the diquarkonium model, and not yet observed. The completion of such a flavor-spin multiplet would strongly speak in favor of the compact tetraquark model.

Unified Picture of Nucleon Pairs Playing Leading Roles in Nuclear Collectivity

Published from 1956, the Bulgarian Journal of Physics accepts articles in the fields of: General and Mathematical Physics; Particle Physics and Field Theory; Atomic and Molecular Physics; Nuclear Physics; Fundamental Areas of Phenomenology; Theory of Relativity and Astrophysics; Condensed Matter, Statistical Physics; Cross-Disciplinary Physics; and Related Areas of Science and Technology.

Λc+ production in pp and in p -Pb collisions at sNN=5.02 TeV

The production cross section of prompt $\mathrm{\Lambda_{c}^{+}}$ charm baryons was measured with the ALICE detector at the LHC at midrapidity in proton-proton (pp) and proton-lead (p-Pb) collisions at a centre-of-mass energy per nucleon pair of $\sqrt{s_\mathrm{NN}} = 5.02$ TeV. The $\mathrm{\Lambda_{c}^{+}}$ and $\rm {\overline{\Lambda}{}_c^-}$ baryons were reconstructed in the hadronic decay channels $\rm \Lambda_{c}^{+} \rightarrow p K^{-}\pi^{+}$ and $\rm \Lambda_{c}^{+}\to p K^{0}_{S}$ and respective charge conjugates. The measured differential cross sections as a function of transverse momentum ($p_{\rm T}$) and the $p_{\rm T}$-integrated $\mathrm{\Lambda_{c}^{+}}$ production cross section in pp and in p-Pb collisions are presented. The $\mathrm{\Lambda_{c}^{+}}$ nuclear modification factor ($R_\mathrm{pPb}$), calculated from the cross sections in pp and in p-Pb collisions, is presented and compared with the $R_\mathrm{pPb}$ of D mesons. The $\mathrm {\Lambda_{c}^{+}}/\mathrm {D^0}$ ratio is also presented and compared with the light-flavour baryon-to-meson ratios p$/\pi$ and $\Lambda /\mathrm {K^0_S}$, and measurements from other LHC experiments. The results are compared to predictions from model calculations and Monte Carlo event generators.

Measurement of J/\u03c8 production cross-sections in pp collisions at sqrt{s} = 5 TeV

The production cross-sections of J/ψ mesons in proton-proton collisions at a centre-of-mass energy of sqrt{s} = 5 TeV are measured using a data sample corresponding to an integrated luminosity of 9.13 ± 0.18 pb−1, collected by the LHCb experiment. The cross-sections are measured differentially as a function of transverse momentum, pT, and rapidity, y, and separately for J/ψ mesons produced promptly and from beauty hadron decays (nonprompt). With the assumption of unpolarised J/ψ mesons, the production cross-sections integrated over the kinematic range 0 < pT< 20 GeV/c and 2.0 < y < 4.5 areσpromptJ/ψ=8.154±0.010±0.283μb,σnonpromptJ/ψ=0.820±0.003±0.034μb,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ {\\displaystyle \\begin{array}{c}{\\sigma}_{\\mathrm{prompt}}\\ J/\\psi =8.154\\pm 0.010\\pm 0.283\\ \\upmu \\mathrm{b},\\\\ {}{\\sigma}_{\\mathrm{nonprompt}}\\ J/\\psi =0.820\\pm 0.003\\pm 0.034\\ \\upmu \\mathrm{b},\\end{array}} $$\\end{document}where the first uncertainties are statistical and the second systematic. These cross-sections are compared with those at sqrt{s} = 8 TeV and 13 TeV, and are used to update the measurement of the nuclear modification factor in proton-lead collisions for J/ψ mesons at a centre-of-mass energy per nucleon pair of sqrt{s_{mathrm{NN}}} = 5 TeV. The results are compared with theoretical predictions.

Kaon–proton strong interaction at low relative momentum via femtoscopy in Pb–Pb collisions at the LHC

In quantum scattering processes between two particles, aspects characterizing the strong and Coulomb forces can be observed in kinematic distributions of the particle pairs. The sensitivity to the interaction potential reaches a maximum at low relative momentum and vanishing distance between the two particles. Ultrarelativistic heavy-ion collisions at the LHC provide an abundant source of many hadron species and can be employed as a measurement method of scattering parameters that is complementary to scattering experiments. This study confirms that momentum correlations of particles produced in Pb–Pb collisions at the LHC provide an accurate measurement of kaon–proton scattering parameters at low relative momentum, allowing precise access to the K−p→K−p process. This work also validates the femtoscopic measurement in ultrarelativistic heavy-ion collisions as an alternative to scattering experiments and a complementary tool to the study of exotic atoms with comparable precision. In this work, the first femtoscopic measurement of momentum correlations of K−p(K+p‾) and K+p(K−p‾) pairs in Pb–Pb collisions at centre-of-mass energy per nucleon pair of sNN=5.02 TeV registered by the ALICE experiment is reported. The components of the K−p complex scattering length are extracted and found to be ℜf0=−0.91±0.03(stat)−0.03+0.17(syst) and ℑf0=0.92±0.05(stat)−0.33+0.12(syst). The results are compared with chiral effective field theory predictions as well as with existing data from dedicated scattering and exotic kaonic atom experiments.