Pb Nuclei Research Articles

Effects of three-nucleon spin-orbit interaction on isotope shifts of Pb nuclei

We investigate effects of the $3N$ interaction, which effectively adds a density-dependent term to the LS channel, on the isotopes shifts of the Pb nuclei. With the strength so as to keep the $\ell s$ splitting of the single-nucleon orbits, the density-dependence in the LS channel tends to shrink the wave functions of the $j=\ell+1/2$ orbits while makes the $j=\ell-1/2$ functions distribute more broadly. Thereby the kink in the isotope shifts of the Pb nuclei at $N=126$ becomes stronger, owing to the attraction from neutrons occupying $0i_{11/2}$ in $N>126$. The density-dependence in the LS channel enables us to reproduce the data of the isotope shifts by the Hartree-Fock-Bogolyubov calculations in a long chain of neutron numbers, even without degeneracy between the $n1g_{9/2}$ and $n0i_{11/2}$ levels. We exemplify it by the semi-realistic M3Y-P6 interaction.

Error estimates for the Skyrme–Hartree–Fock model

There are many complementary strategies to estimate the extrapolation errors of a model calibrated in least-squares fits. We consider the Skyrme–Hartree–Fock model for nuclear structure and dynamics and exemplify the following five strategies: uncertainties from statistical analysis, covariances between observables, trends of residuals, variation of fit data, and dedicated variation of model parameters. This gives useful insight into the impact of the key fit data as they consist of binding energies, charge rms radii, and charge formfactor. Amongst others, we check in particular the predictive value for observables in the stable nucleus 208Pb, the super-heavy element 266Hs, r-process nuclei, and neutron stars.

Theoretical studies on the alpha decay of 178–220Pb isotopes

Abstract The α decay half lives for the isotopes of Pb ( Z = 82 ) nuclei in the range 178 ≤ A ≤ 220 have been studied systematically within the Coulomb and proximity potential model (CPPM) and also within CPPM with modified deformation dependent assault frequency. The half-lives have been evaluated using the experimental Q values. The computed half-lives are compared with the experimental data and also with the existing theoretical models and are found in good agreement. Using our model we could also demonstrate the influence of the neutron shell closure ( N = 126 ) in the alpha decay half lives through the Geiger–Nuttall (GN) plots of ln ⁡ λ vs. Z E − 1 / 2 , log 10 ⁡ T 1 / 2 vs. Q − 1 / 2 and − ln ⁡ P vs. Z Q − 1 / 2 . We have also studied the Universal curve of log 10 ⁡ T 1 / 2 vs. − ln ⁡ P , where all the alpha transitions could be plotted as a single line. The study on the various forms of GN plots, with various variables, enabled us in developing a new, simple relation for the alpha decay half lives of the Pb isotopes and our study also revealed that CPPM and CPPM with the modified assault frequency are appropriate for the alpha decay studies of Pb isotopes and thus can be successfully applied to other alpha emitter nuclides.

Exotica production with ALICE

The high collision energies reached at the LHC lead to significant production yields of light (anti-)nuclei and (hyper-)nuclei in proton–proton, proton–lead and, in particular, lead–lead collisions. The excellent particle identification capabilities of the ALICE apparatus, based on the specific energy loss in the Time Projection Chamber and the velocity information in the Time-Of-Flight detector, allow for the detection of these rarely produced particles. Further, the Inner Tracking System gives the possibility to separate primary nuclei from those coming from weak decay of heavier systems. One example of such a weak decay is the measurement of the (anti-)hypertriton decay to 3 He + π − (3 He + π + ). The aforementioned capabilities of the ALICE apparatus offer the unique opportunity to search for exotica, like the bound state of a Λ and a neutron which would decay into a deuteron and a pion, or the bound state of two Λ’s. Results on the production of stable nuclei in Pb–Pb collisions at √s NN = 2.76 TeV are presented, and compared with thermal model predictions. We further present the current status of the searches, by their upper limits on the production yields, and compare the results to thermal and coalescence model expectations.

Elastic proton-nucleus scattering in the Glauber-Sitenko approach and relativistic and nonrelativistic nuclear mean fields

The differential cross sections for elastic proton scattering on 40Ca and 208Pb nuclei at 800 MeV are analyzed along with respective spin observables on the basis of the Glauber-Sitenko approach with allowance for two-nucleon correlations, these correlations being taken into account via the inclusion of intermediate excitations of target nuclei and noneikonal corrections. The possibility of employing, in these calculations, realistic nucleon densities obtained in describing the structure of nuclei on the basis of the relativistic- and nonrelativistic-mean-field approximations with various versions of nucleon-interaction parameters is explored. It is shown that some of the nucleon-density versions considered here provide a reasonable description of experimental data, allowance for intermediate nuclear excitations and noneikonal corrections being substantial for ensuring agreement with these data.

Relativistic analysis of proton elastic scattering

The Dirac equation as the relevant wave equation, is used in modified DWUCK4 program to calculate the elastic scattering cross section throughout the energy range suitable for relativistic treatment of proton elastic scattering by nuclei 40Ca, 58Ni, 90Zr and 208Pb. A good fit to the experimental data is presented. The real and imaginary potentials are well determined and behave regularly with energy. The behaviour of the real central effective potential shows the development of a “wine-bottle” shape in the transition energy region and the persistence of a small attractive potential in the nuclear surface region, even at 800 MeV.

Recent STAR Results from U+U and Au+Au Collisions

Unlike Au or Pb nuclei which are more spherical, the uranium nuclei have a relatively large deformation on average. The prolate shape of uranium nuclei provides the feasibility to study how the initial geometry of the nuclei affects the azimuthal distributions of produced particles. It also provides a unique opportunity to understand the initial condition for particle production at mid-rapidity in heavy ion collisions as well as path length dependence of jet quenching and quarkonium in-medium effects.In this proceedings, the two- and four- particle cumulant, v2{2} and v2{4}, from U+U collisions at = 193 GeV and Au+Au collisions at = 200 GeV for inclusive charged hadrons at midrapidity will be presented. The STAR Zero Degree Calorimeter is used to subdivide the 0-1% centrality bin into even finer centralities. Differences were observed between the multiplicity dependence of v2{2} for most central Au+Au and U+U collisions. The observed v2{2} slope results were compared to Monte Carlo Glauber model predictions and it was seen that this model cannot explain the presented results on the multiplicity dependence of v2{2} in central collisions.

Spectroscopic factors of magic and semimagic nuclei within the self-consistent theory of finite Fermi systems

A scheme is presented to find single-particle spectroscopic factors (SF) of magic and semimagic nuclei within the self-consistent theory of finite Fermi systems (TFFS). In addition to the energy dependence of the mass operator Σ induced by the surface-phonon coupling effects which are commonly considered in this problem, the in-volume energy dependence of the operator Σ inherent in the self-consistent TFFS is also taken into account. This dependence arises due to the effect of high-lying particle-hole excitations and persists in nuclear matter. The self-consistent basis of the energy density functional method by Fayans et al. is used. Both the surface and in-volume contributions to the SFs turned out to be of comparable magnitude. The results for magic 40,48Ca and 208Pb nuclei and semimagic lead isotopes are presented.

Thermal photon v3 at LHC from fluctuating initial conditions

We calculate the triangular flow parameter $v_3$ of thermal photons for 0--40\% central collisions of Pb nuclei at LHC using an event-by-event hydrodynamic model with fluctuating initial conditions. Thermal photon $v_3$ with respect to the the participant plane angle is found to be positive and significant compared to the elliptic flow parameter $v_2$ of thermal photons. In addition, photon $v_3$ as a function of $p_T$ shows similar qualitative nature to photon $v_2$ in the region $1< p_T <6$ GeV/$c$. We argue that while $v_3$ originates from $\epsilon_3$ deformations of the initial state density distribution, fast buildup of radial flow due to fluctuations is the main driving mechanism for the observed large value.

Neutron-rich $^{208}$Pb nucleus with delta excitation under compression

The spherical Hartree-Fock approximation is applied to a no-core shell model with a realistic effective baryon-baryon interaction. The ground state properties of a heavy spherical neutron-rich doubly magic 208Pb nucleus under compression are investigated. It is found that the nucleus becomes more bound with the occurrence of Delta resonances. The creation of Delta increases as the compression is continuous. There is a considerable reduction in the compressibility when the Delta degree of freedom is activated. It is found that the Delta particle is the basic component of the 208Pb nucleus besides nucleons at the ground state without any compression. When the nucleus is compressed to about 4.31 times the ordinary density, the Delta component is sharply increased to about 14.4% of all baryons in the system. It is found that there is a radial density distribution for Delta at the ground state of 208Pb nucleus without any compression. The single particle energy levels are calculated and their behaviors are examined under compression too. A good agreement was obtained between the results of the effective Hamiltonian and the phenomenological shell model for the low lying single-particle spectra.

Neutron emission from electromagnetic dissociation of Pb nuclei at √sNN= 2.76 TeV measured with the ALICE ZDC

The ALICE Zero Degree Calorimeter system (ZDC) is composed of two identical sets of calorimeters, placed at opposite sides with respect to the interaction point, 114 meters away from it, complemented by two small forward electromagnetic calorimeters (ZEM). Each set of detectors consists of a neutron (ZN) and a proton (ZP) ZDC. They are placed at zero degrees with respect to the LHC axis and allow to detect particles emitted close to beam direction, in particular neutrons and protons emerging from hadronic heavy-ion collisions (spectator nucleons) and those emitted from electromagnetic processes. For neutrons emitted by these two processes, the ZN calorimeters have nearly 100% acceptance.

Nucleon size effects in the parity violating electron scattering asymmetry

We investigate isospin mixing e ects in the asymmetry as obtained in parity-violating electron scattering from 4 He, 12 C, 48 Ca, 90 Zr and 208 Pb nuclei. The scattering analysis is developed within the distorted wave Born approximation (DWBA) accounting for nucleon form factors. We use a relativistic mean field model, including the , !, and mesons, with density dependent couplings, as well as the electromagnetic interaction . Numerical results are presented for the asymmetry, charge and weak charge radius.

New data on (γ, n), (γ, 2n), and (γ, 3n) partial photoneutron reactions

Systematic discrepancies between the results of various experiments devoted to determining cross sections for total and partial photoneutron reactions are analyzed by using objective criteria of reliability of data in terms of the transitional photoneutron-multiplicity function Fi = σ(γ, in)/σ(γ, xn), whose values for i = 1, 2, 3, ... cannot exceed by definition 1.00, 0.50, 0.33, ..., respectively. It was found that the majority of experimental data on the cross sections obtained for (γ, n), (γ, 2n), and (γ, 3n) reactions with the aid of methods of photoneutron multiplicity sorting do not meet objective criteria (in particular, F2 > 0.50 for a vast body of data). New data on the cross sections for partial reactions on 181Ta and 208Pb nuclei were obtained within a new experimental-theoretical method that was proposed for the evaluation of cross sections for partial reactions and in which the experimental neutron yield cross section σexpt(γ, xn) = σ(γ, n) + 2σ(γ, 2n) + 3σ(γ, 3n) + ..., which is free from problems associated with determining neutron multiplicities, is used simultaneously with the functions Fitheor calculated within a combined model of photonuclear reactions.

Noncollective excitations in low-energy heavy-ion reactions: Applicability of the random-matrix model

We investigate the applicability of a random-matrix model to the description of noncollective excitations in heavy-ion reactions around the Coulomb barrier. To this end, we study fusion in the reaction ${}^{16}$O + ${}^{208}$Pb, taking account of the known noncollective excitations in the ${}^{208}$Pb nucleus. We show that the random-matrix model for the corresponding couplings reproduces reasonably well the exact calculations, obtained using empirical deformation parameters. This implies that the model may provide a powerful method for systems in which the noncollective couplings are not so well known.

INVESTIGATIONS OF THE DENSITY DISTRIBUTIONS OF 208Pb WITH THE THOMAS–FERMI METHOD

In this study, the neutron and proton density distributions of 208 Pb nucleus have been analytically calculated by using a new, simple and physically meaningful analytical expression obtained for the Fermi integral which is situated in the nucleon density distributions. The results obtained for 208 Pb have been compared with those of the other theoretical and experimental data and found in good agreement.

Few-nucleon transfers and weakly dissipative processes in the GRAZING model of low-energy nuclear reactions

The applicability of Winther’s semi-classical model in the GRAZING program to a representative set of low-energy nuclear reactions is examined. It is demonstrated that the model describes the processes of few-nucleon transfers with low dissipation of energy for spherical nuclei 40Ca, 96Zr, 208Pb, and others. Satisfactory agreement with experimental data is observed for transfers of no more than one proton and approximately 6–8 neutrons. The reactions in which the agreement with experimental data is poor at a standard set of parameters are indicated.

Fission and fragmentation of 208Pb nuclei in collisions with gold nuclei at an energy of 158 GeV per nucleon

The fission and fragmentation of ultrarelativistic 208Pb nuclei in collisionswith gold nuclei were studied by using a beam from the SPS accelerator at CERN at an energy of 158 GeV per nucleon. The detectors of the target area of the NA45/CERES spectrometer were used in respective measurements. The value obtained for the fission cross section is 301 ± 44 mb, where about 77% of events stem from the electromagnetic interaction of colliding nuclei, while the remaining part is the contribution of peripheral nuclear interactions. The spallation of lead nuclei that involves the formation of heavy fragments occurs only in collisions where the impact parameter satisfies the condition b > 10 fm. A complete disintegration of lead nuclei to intermediate-mass fragments and light particles is observed in some peripheral collisions.

W and Z in heavy ion collisions with CMS

Abstract Electroweak W and Z boson measurements in PbPb collisions at nucleon–nucleon center of mass energy s = 2.76 TeV at the LHC using the CMS detector are presented. The W analysis is based on 2010 PbPb data corresponding to an integrated luminosity of 7.3 μ b − 1 and also on 2011 pp data corresponding to an integrated luminosity of 231 n b − 1 . The Z analysis is based on 2011 PbPb data with an integrated luminosity of 150 μ b − 1 . The dependence of W and Z production as a function of PbPb collision centrality is studied and shown to scale with the number of NN binary collisions. W + and W − yields in PbPb and pp collisions are in agreement once we take into account the proton and neutron composition in Pb nuclei. The muon charge asymmetry is measured as a function of pseudo-rapidity and is in agreement with next-to-leading order perturbative QCD calculations.

Photon and electroweak boson production in PbPb collisions

The production of electroweak bosons (photons, W and Z particles) in PbPb collisions at a centre-of-mass energy per nucleon pair of 2.76 TeV has been measured with the CMS detector at the LHC. Direct photons are selected by applying isolation criteria, while W and Z bosons are reconstructed through their muonic decay. The production rates in PbPb data are studied as a function of the collision centrality and compared to that in pp interactions (or next-to-leading-order calculations), once normalised by the number of binary nucleon–nucleon interactions. Apart from an expected asymmetry between W + and W − due to the different quark content of protons and Pb nuclei, no deviation from binary-scaled production is observed. The isolated-photon energy is further used as a reference for away-side jets, which are found to be less energetic in PbPb than in pp collisions.

Low-lying dipole response in stable and unstable nuclei

The presence of some low-lying (pygmy) strength in the dipole spectrum, at excitation energy well below the isovector giant dipole energy, has been confirmed in several nuclei. The microscopic structure and the nature of these states, in particular the possible collective nature and the isospin character, are currently under strong debate. In addition, a relation with the isovector properties of the equation of state of nuclear matter, such as the symmetry energy or its slope, has been proposed. We present a detailed analysis of Skyrme Hartree–Fock plus random phase approximation (RPA) predictions for both the isoscalar and isovector dipole responses, of different neutron-rich nuclei (68Ni, 132Sn and 208Pb). All of them show a low-energy peak that increases in magnitude with increasing values of the slope of the symmetry energy at saturation. Eventually, the collectivity associated with the RPA states contributing to this peak is more pronounced in the isoscalar than in the isovector channel.