Pb Nuclei Research Articles

Production of 4He and 4[formula omitted] in Pb–Pb collisions at [formula omitted] at the LHC

Results on the production of 4He and ▪ nuclei in Pb–Pb collisions at sNN=2.76TeV in the rapidity range |y|<1, using the ALICE detector, are presented in this paper. The rapidity densities corresponding to 0–10% central events are found to be dN/dyHe4=(0.8±0.4(stat)±0.3(syst))×10−6 and ▪, respectively. This is in agreement with the statistical thermal model expectation assuming the same chemical freeze-out temperature (Tchem=156MeV) as for light hadrons. The measured ratio of ▪ is 1.4±0.8(stat)±0.5(syst).

Identification of rotating and vibrating tetrahedrons in the heavy nucleus 208Pb

Ten known states in the heavy nucleus 208Pb at $2.6 < E_{x} < 7.9$ MeV are described by rotating and vibrating tetrahedrons. The $ 3^{-}$ and $ 4^{+}$ yrast states are the first members of the rotational band. A $ 2^{\pm}$ doublet state with the $ 2^{+}$ yrast state as one member and the newly recognized $ 2^{-}$ yrast state as the other member, the $ 1^{-}$ yrast state, and the third $ 0^{+}$ state are the heads of the three elementary tetrahedral rotating and vibrating bands. The newly recognized state at $ E_{x} = 4142$ keV was assigned spin 2 in 1975 and is suggested to have negative parity by the absent 208Pb $(\alpha, \alpha')$ excitation. Four more states at $5.7< E_{x}< 7.9$ MeV are identified as the next members of the three elementary tetrahedral rotating and vibrating bands. The ambiguous spin assignment to the state at $E_{x}= 7020$ keV is settled with $ 3^{-}$ , the state at $ E_{x} = 7137$ keV is assigned $ 4^{-}$ .

Self-consistent description of EL transitions between one-phonon states in magic nuclei

Transition probabilities between low-lying one-phonon states of magic nuclei are for the first time computed self-consistently within an approach to anharmonic effects based on the quantum theory of many-body systems. In the adopted approach, three-quasiparticle correlations in the ground state are taken into account, and the nuclear mean field is interrelated with the effective nucleon–nucleon interaction. These quantities are derived using the energy density functional method with known parameters of the Fayans functional. The E1 and E2 transitions in the 132Sn and 208Pb nuclei are considered as an example, and a reasonably good agreement with the data on these nuclei is reached. Three-quasiparticle correlations in the ground state are shown to make a significant contribution to the probabilities of the discussed transitions.

Self-consistent Hartree–Fock RPA calculations in 208Pb

The nuclear structure of 208Pb is studied in the framework of the self-consistent random phase approximation (SCRPA). The Hartree–Fock mean field and single particle states are used to implement a completely SCRPA with Skyrme-type interactions. The Hamiltonian is diagonalised within a model space using five Skyrme parameter sets, namely LNS, SkI3, SkO, SkP and SLy4. In view of the huge number of the existing Skyrme-force parameterizations, the question remains which of them provide the best description of data. The approach attempts to accurately describe the structure of the spherical even–even nucleus 208Pb. To illustrate our approach, we compared the binding energy, charge density distribution, excitation energy levels scheme with the available experimental data. Moreover, we calculated isoscalar and isovector monopole, dipole, and quadrupole transition densities and strength functions.

Coherent fragmentation of 12C nuclei of momentum 4.5 GeV/c per nucleon through the 8Beg.s.+4He channel in a nuclear photoemulsion containing lead nuclei

A two-particle channel in which an unbound nucleus of 8Be in the ground state (8Beg.s.) was one of the fragments was selected among events where 12C nuclei of momentum 4.5 GeV/c per nucleon undergo coherent dissociation into three alpha particles. The events in question were detected in a track nuclear photoemulsion containing lead nuclei, which was irradiated at the synchrophasotron of the Laboratory of High Energies at the Joint Institute for Nuclear Research (JINR, Dubna). The average transverse momentum of alpha particles produced upon the decay of 8Beg.s. nuclei was 87±6 MeV/c, while that for “single” alpha (αs) particles was 123±15 MeV/c. The average value of the transverse-momentum transfer in the reaction being considered, Pt(12C), was 223 ± 20 MeV/c. The average value of the cross section for this channel involving Ag and Br target nuclei was 13 ± 4 mb, while the cross section for the reaction on the Pb nucleus was 40 ± 15 mb. The Coulomb dissociation contribution evaluated on the basis of the number of events where the momentum P t(12C) did not exceed 0.1 GeV/c saturated about 20%. In nine events, the measured total transverse energy of the fragments in the reference frame comoving with the decaying carbon nucleus did not exceed 0.45 MeV, which did not contradict the excitation of the participant 12C nucleus to the level at 7.65 MeV. The average value of the transverse momentum in those events was 234 ± 25 MeV/c.

Inelastic scattering of neutrinos on nuclei

The cross section of inelastic neutrino interaction with 56Fe and 208Pb nuclei is calculated. Investigation of these processes caused by neutral currents is essential for considering phenomena that occur during Supernova explosions and designing astrophysical neutrino detectors. The inelastic neutrino scattering cross section is calculated using the model independent approach, which is based on experimental data on nuclear structure. The values of the matrix elements of the considered reaction are determined from the characteristics of electromagnetic dipole М1 transitions in nuclei, obtained by means of nuclear resonance fluorescence.

Equation of state and radii of finite nuclei in the presence of a diffuse surface layer

The definitions of nuclear surface and nuclear radii are considered within the Gibbs-Tolman-Rowlinson-Widom (GTW) approach. We demonstrate the nonmonotonic behavior of the nuclear equimolar radii, which is due to the shell effects in the chemical potential of finite nuclei. The direct variational method within the extended Thomas-Fermi approximation is used to establish the equation of state for finite nuclei. We have studied the influence of the polarization effect caused by the neutron excess on the particle density and the nuclear radii. This effect increases with the asymmetry parameter $X$ and can be responsible for the appearance of large neutron halos in nuclei well away from the $\ensuremath{\beta}$ stability line. We have performed new calculations of the $A$ dependence of the radii $R(A)$ of nucleon distribution, which are based on the use of the experimental data for the nuclear binding energy. We demonstrate the presence of the quantum shell effects in $R(A)$. We have analyzed the value of the neutron-skin thickness $\mathrm{\ensuremath{\Delta}}{r}_{np}$ in the isotopes of the Na, Sn, and Pb nuclei within the GTW approach and show the appearance of nonmonotonic behavior of $\mathrm{\ensuremath{\Delta}}{r}_{np}$ as a function of the neutron excess. We discuss the relative contributions to the neutron-skin thickness $\mathrm{\ensuremath{\Delta}}{r}_{np}$ from the skin and the halo effects.

The Impact of Chronic Sleep Restriction on Neuronal Number and Volumetric Correlates of the Dorsal Respiratory Nuclei in a Rat Model.

Sleep restriction can result in a range of neurophysiological consequences in the brain including some brain stem nuclei. This study aimed to evaluate the effects of chronic sleep restriction (CSR) on quantitative aspects of brain stem respiratory centers using stereological methods. Male rats were randomly assigned into experimental group (CSR through a modified multiple platform apparatus), corresponding apparatus-control group (grid-floor control) and cage controls. In the grid-floor control group, animals were placed on wire-mesh grids positioned upon CSR apparatus and were then allowed to retain the opportunity to sleep. On day 21, all rats were euthanized with their brains removed for stereological assessments. The nuclei which are known to be involved in respiration rhythm including nucleus tractus solitarius (NTS), parabrachial nuclei (PB), and Kölliker-Fuse nucleus (KF) were evaluated. Compared to the control groups, stereological findings in CSR rats revealed a decrease by 5.2 ± 0.01%, 7.1 ± 0.007%, 3.9 ± 0.004%, and 6.3 ± 0.002% (mean ± standard error of the mean [SEM], p < .01 for all) in the volume of NTS, medial PB, lateral PB, and KF nuclei, respectively. Also, the total neuronal number of NTS, medial PB, lateral PB, and KF showed a significant decrease by 10.2 ± 21.4%, 6.3 ± 5.2%, 11.8 ± 8.6%, and 9.3 ± 2.5% (mean ± SEM, p < .05 for all), respectively. CSR may potentially induce neuronal loss and structural changes in the dorsal respiratory nuclei.

Identification of the one-quadrupole phonon [formula omitted] state of 204Hg

One-phonon states of vibrational nuclei with mixed proton–neutron symmetry have been observed throughout the nuclear chart besides the mass A≈200 region. Very recently, it has been proposed that the 22+ state of 212Po is of isovector nature. This nucleus has two valence protons and two valence neutrons outside the doubly-magic 208Pb nucleus. The stable isotope 204Hg, featuring two valence-proton and valence-neutron holes, with respect to 208Pb, is the particle-hole mirror of 212Po. In order to compare the properties of low-lying isovector excitations in these particle-hole mirror nuclei, we have studied 204Hg by using the projectile Coulomb-excitation technique. The measured absolute B(M1;22+→21+) strength of 0.20(2)μN2 indicates that the 22+ level of 204Hg is at least the main fragment of the 21,ms+ state. For the first time in this mass region, both lowest-lying, one-quadrupole phonon excitations are established together with the complete set of their decay strengths. This allows for a microscopic description of their structures, achieved in the framework of the Quasi-particle Phonon Model.

Temperature dependence of the symmetry energy and neutron skins in Ni, Sn, and Pb isotopic chains

The temperature dependence of the symmetry energy for isotopic chains of even-even Ni, Sn, and Pb nuclei is investigated in the framework of the local density approximation (LDA). The Skyrme energy density functional with two Skyrme-class effective interactions, SkM* and SLy4, is used in the calculations. The temperature-dependent proton and neutron densities are calculated through the HFBTHO code that solves the nuclear Skyrme-Hartree-Fock-Bogoliubov problem by using the cylindrical transformed deformed harmonic-oscillator basis. In addition, two other density distributions of $^{208}$Pb, namely the Fermi-type density determined within the extended Thomas-Fermi (TF) method and symmetrized-Fermi local density obtained within the rigorous density functional approach, are used. The kinetic energy densities are calculated either by the HFBTHO code or, for a comparison, by the extended TF method up to second order in temperature (with $T^{2}$ term). Alternative ways to calculate the symmetry energy coefficient within the LDA are proposed. The results for the thermal evolution of the symmetry energy coefficient in the interval $T=0-4$ MeV show that its values decrease with temperature. The temperature dependence of the neutron and proton root-mean-square radii and corresponding neutron skin thickness is also investigated, showing that the effect of temperature leads mainly to a substantial increase of the neutron radii and skins, especially in the more neutron-rich nuclei, a feature that may have consequences on astrophysical processes and neutron stars.

Examination of experimental evidence of chaos in the bound states of Pb208

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 $\omega$, which takes the value $\omega=0$ for regular systems and $\omega \simeq 1$ for chaotic systems. We obtain $\omega=0.85 \pm 0.02$ which is, to our knowledge, the closest value to chaos ever observed in experimental bound states of nuclei. By contrast, the results for unnatural parity states are far from RMT behavior. We interpret these results as a consequence of the strength of the residual interaction in $^{208}$Pb, which, according to experimental data, is much stronger for natural than for unnatural parity states. In addition our results show that chaotic and non-chaotic nuclear states coexist in the same energy region of the spectrum.

Recent results on light nuclei production from the NA49 experiment

Production of d and 3 He nuclei in central Pb+Pb interactions was studied at five collision energies (√sNN = 6.3, 7.6, 8.8, 12.3, and 17.3 GeV) with the NA49 detector at the CERN SPS. Transverse momentum spectra and rapidity distributions were measured. Yields are compared to predictions of statistical models. Phase-space distributions of light nuclei are discussed and compared to those of protons in the context of a coalescence approach. The coalescence parameters B 2 and B 3 for d and 3 He were determined at all energies.

The single-particle characteristics of Pb isotopes near the drip lines calculated within the dispersive optical model

The neutron and proton dispersive optical potential for the 208Pb nucleus has been determined for the energy region from–70 to +60 MeV and used to calculate the differential elastic scattering, the total interaction and reaction cross sections, as well as the single-particle characteristics, the neutron and charge densities, rms radii, and the thickness of the nucleus skin. The calculated results are in good agreement with the experimental data. The proton dispersive optical model potential for the spherical and close to spherical Pb isotopes within the neutron and proton drip lines has been obtained by a similar method. The calculation predicts a trend towards the growth of the proton particle-hole gap, which corresponds to Z = 82 shell closure as Z approaches the proton drip line.

D-meson production in p-Pb collisions at sNN=5.02 TeV and in pp collisions at s=7 TeV

The production cross sections of the prompt charmed mesons D$^0$, D$^+$, D$^{*+}$ and D$_s$ were measured at mid-rapidity in p-Pb collisions at a centre-of-mass energy per nucleon pair $\sqrt{s_{\rm NN}}=5.02$ TeV with the ALICE detector at the LHC. D mesons were reconstructed from their decays D$^0\rightarrow{\rm K}^-\pi^+$, D$^+\rightarrow{\rm K}^-\pi^+\pi^+$, D$^{*+}\rightarrow D^0\pi^+$, D$_s^+\rightarrow\phi\pi^+\rightarrow{\rm K}^-{\rm K}^+\pi^+$, and their charge conjugates. The $p_{\rm T}$-differential production cross sections were measured at mid-rapidity in the interval $1<p_{\rm T}<24$ GeV/$c$ for D$^0$, D$^+$ and D$^{*+}$ mesons and in $2<p_{\rm T}<12$ GeV/$c$ for D$_s$ mesons, using an analysis method based on the selection of decay topologies displaced from the interaction vertex. The production cross sections of the D$^0$, D$^+$ and D$^{*+}$ mesons were also measured in three $p_{\rm T}$ intervals as a function of the rapidity $y_{\rm cms}$ in the centre-of-mass system in $-1.26<y_{\rm cms}<0.34$. In addition, the prompt D$^0$ cross section was measured in pp collisions at $\sqrt{s}=7$ TeV and p-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV down to $p_{\rm T}=0$ using an analysis technique that is based on the estimation and subtraction of the combinatorial background, without reconstruction of the D$^0$ decay vertex. The nuclear modification factor $R_{\rm pPb}(p_{\rm T})$, defined as the ratio of the $p_{\rm T}$-differential D-meson cross section in p-Pb collisions and that in pp collisions scaled by the mass number of the Pb nucleus, was calculated for the four D-meson species and found to be compatible with unity within experimental uncertainties. The results are compared to theoretical calculations that include cold-nuclear-matter effects and to transport model calculations incorporating the interactions of charm quarks with an expanding deconfined medium.

Unitary version of the particle–hole dispersive optical model

For the particle–hole dispersive optical model developed recently, a method is proposed for restoring unitarity weakly violated by a phenomenological description of the spreading effect. The method is implemented by performing a quantitative analysis of the energy-averaged isoscalar monopole double transition density and strength functions over a broad energy range including the isoscalar giant monopole resonance and its overtone in the 208Pb nucleus.

Application of a folding-model optical potential to analyzing inelastic pion–nucleus scattering and the in-medium effect on a pion–nucleon amplitude

The folding-model optical potential is generalized in such a way as to apply it to calculating the cross sections for inelastic scattering of π±-mesons on 28Si, 40Ca, 58Ni, and 208Pb nuclei at the energies of 162, 180, 226, and 291 MeV leading to the excitation of the 2+ and 3− collective states. In doing this, use is made of known nucleon-density distributions in nuclei and the pion–nucleon scattering amplitude whose parameters were obtained previously by fitting the elastic scattering cross sections for the same nuclei. Thus, the values of quadrupole (β2) and octupole (β3) deformations of nuclei appear here as the only adjustable parameters. The scattering cross section is calculated by solving the relativistic wave equation, whereby effects of relativization and distortion in the entrance and exit scattering channels are taken exactly into account. The cross sections calculated in this way for inelastic scattering are in good agreement with respective experimental data. The importance of the inclusion of in-medium effects in choosing parameters of the pion–nucleon amplitude is emphasized.

E2 transitions between excited single-phonon states: Role of ground-state correlations

The probabilities for E2 transitions between low-lying excited 3− and 5− single-phonon states in the 208Pb and 132Sn magic nuclei are estimated on the basis of the theory of finite Fermi systems. The approach used involves a new type of ground-state correlations, that which originates from integration of three (rather than two, as in the random-phase approximation) single-particle Green’s functions. These correlations are shown to make a significant contribution to the probabilities for the aforementioned transitions.

Production of deuterium, tritium, andHe3in central Pb + Pb collisions at20A,30A,40A,80A, and158A GeV at the CERN Super Proton Synchrotron

Production of $d$, $t$, and $^3$He nuclei in central Pb+Pb interactions was studied at five collision energies ($\sqrt{s_{NN}}=$ 6.3, 7.6, 8.8, 12.3, and 17.3 GeV) with the NA49 detector at the CERN SPS. Transverse momentum spectra, rapidity distributions, and particle ratios were measured. Yields are compared to predictions of statistical models. Phase-space distributions of light nuclei are discussed and compared to those of protons in the context of a coalescence approach. The coalescence parameters $B_2$ and $B_3$, as well as coalescence radii for $d$ and $^3$He were determined as a function of transverse mass at all energies.

LCAO-based theoretical study of PbTiO3 crystal to search for parity and time reversal violating interaction in solids.

An experiment towards the search for the interaction of the Schiff moment (S) of the (207)Pb nuclei with electrons in PbTiO3 crystal which violates the time reversal (T) and space parity (P) symmetries was proposed by Mukhamedjanov and Sushkov [Phys. Rev. A 72, 034501 (2005)]. The interpretation of the experiment in terms of the Schiff moment requires knowledge of an electronic density gradient parameter (usually designated as X) on the Pb nucleus in the crystal, which is determined by the electronic structure of the crystal. Here we propose a theoretical approach to calculate the properties in solids which are directly sensitive to the changes of valence electron densities in atomic cores but not in the valence spatial regions (Mössbauer parameters, hyperfine structure (HFS) constants, parameters of T,P-odd Hamiltonians, etc. [L. V. Skripnikov and A. V. Titov, Phys. Rev. A 91, 042504 (2015)]). It involves constructing the crystalline orbitals via the linear combination of atomic orbitals and employs a two-step concept of calculating such properties that was earlier proposed by us for the case of heavy-atom molecules. The application of the method to the PbTiO3 crystal results in the energy shift, Δε=0.82×10(6)S((207)Pb)eaB (3)eV, due to the T,P-odd interactions. The value is compared to the corresponding parameter in diatomic molecules (TlF, RaO, PbO), which have been proposed and used in the past decades in the search for the nuclear Schiff moment. We also present the calculation of the electric field gradient at the Pb nucleus in PbTiO3 for the comparison with other solid-state electronic structure approaches.

Spin-orbit interaction in relativistic nuclear structure models

Relativistic self-consistent mean-field (SCMF) models naturally account for the coupling of the nucleon spin to its orbital motion, whereas non-relativistic SCMF methods necessitate a phenomenological ansatz for the effective spin-orbit potential. Recent experimental studies aim to explore the isospin properties of the effective spin-orbit interaction in nuclei. SCMF models are very useful in the interpretation of the corresponding data, however standard relativistic mean-field and non-relativistic Hartree-Fock models use effective spin-orbit potentials with different isovector properties, mainly because exchange contributions are not treated explicitly in the former. The impact of exchange terms on the effective spin-orbit potential in relativistic mean-field models is analysed, and it is shown that it leads to an isovector structure similar to the one used in standard non-relativistic Hartree-Fock. Data on the isospin dependence of spin-orbit splittings in spherical nuclei could be used to constrain the isovector-scalar channel of relativistic mean-field models. The reproduction of the empirical kink in the isotope shifts of even Pb nuclei by relativistic effective interactions points to the occurrence of pseudospin symmetry in the single-neutron spectra in these nuclei.