Nuclear Mass Number Research Articles

CRPropa 2.0 – A public framework for propagating high energy nuclei, secondary gamma rays and neutrinos

Version 2.0 of CRPropa [CRPropa is published under the 3rd version of the GNU General Public License (GPLv3). It is available, together with a detailed documentation of the code, at https://crpropa.desy.de.] is public software to model the extra-galactic propagation of ultra-high energy nuclei of atomic number Z⩽26 through structured magnetic fields and ambient photon backgrounds taking into account all relevant particle interactions. CRPropa covers the energy range 7×1016<E/eV<A×1022 where A is the nuclear mass number. CRPropa can also be used to track secondary γ-rays and neutrinos which allows the study of their link with the charged primary nuclei – the so called multi-messenger connection. After a general introduction we present several sample applications of current interest concerning the physics of extragalactic ultra-high energy radiation.

Helium nuclei, deuteron, and dineutron in2+1flavor lattice QCD

We calculate the binding energies for multinucleon bound states with the nuclear mass number less than or equal to 4 in $2+1$ flavor QCD at the lattice spacing of $a=0.09\text{ }\text{ }\mathrm{fm}$ employing a relatively heavy quark mass corresponding to ${m}_{\ensuremath{\pi}}=0.51\text{ }\text{ }\mathrm{GeV}$. To distinguish a bound state from attractive scattering states, we investigate the volume dependence of the energy shift between the ground state and the state of free nucleons by changing the spatial extent of the lattice from 2.9 to 5.8 fm. We conclude that $^{4}\mathrm{He}$, $^{3}\mathrm{He}$, deuteron and dineutron are bound at ${m}_{\ensuremath{\pi}}=0.51\text{ }\text{ }\mathrm{GeV}$. We compare their binding energies with those in our quenched studies and also with several previous investigations.

Momentum dependence of hadronic production of the ϕ-meson and its width in nuclear matter

Information on the properties of the ϕ meson in the nuclear environment has been derived from its production in proton collisions with C, Cu, Al, and Au nuclear targets. The experiment was carried out with 2.83 GeV protons at the Cooler Synchrotron COSY, with the ϕ being detected via its K + K − decay using the ANKE magnetic spectrometer. The measured dependence of the production cross section on the nuclear mass number has been compared with calculations within three different nuclear models. These suggest a significant broadening of the width of the ϕ in medium relative to its vacuum value. The ANKE results obtained in the momentum range 0.6 < p ϕ < 1.6 GeV/c are compared with data from photoproduction experiments at slightly higher momenta.

Fragment mass distributions for heavy nuclei fission induced by intermediate energy probes

Recent experiments have shown that the multimode approach for describing the fission process leads to some compatibility with the observed results. A systematic analysis of the parameters obtained by fitting the fission-fragment mass distribution to the spontaneous and low-energy data has shown that the values for those parameters present a smooth dependence upon the nuclear mass number. In the present work it is shown that the same parameter-values obtained for low-energy fission can be used to describe intermediate-energy fission results of fragment-mass distributions if one takes into account the appropriate distribution of the fissioning system. To calculate the fission-fragment mass distributions, Monte Carlo simulations are used. This simulation considers a two-step reaction mechanism, namely, an intranuclear cascade providing the compound nucleus followed by a mechanism of competition between particle evaporation and fission. The fission-fragment masses are obtained according to the multimode approach following the Statistical Scission Model. Simulations for fission induced by 660 MeV protons on 241Am and 237Np, and for fission of 238U induced by photons from Bremsstrahlung with end-point energy of 50 MeV have been performed, and the results have been compared with recent experimental data.

Total Cross Sections for Neutron Nucleus Scattering

Systematics of neutron scattering cross sections on various materials for neutron energies up to several hundred MeV are important for ADSS applications. Ramsauer model is well known and widely applied to understand systematics of neutron nucleus total cross sections. In this work, we examined the role of nuclear effective radius parameter (r$_0$) on Ramsauer model fits of neutron total cross sections. We performed Ramsauer model global analysis of the experimental neutron total cross sections reported by W. P. Abfalterer, F. B. Bateman, {\it et. al.,}, from 20MeV to 550MeV for nuclei ranging from Be to U . The global fit functions which can fit total cross section data over periodic table are provided along with the required global set of parameters. The global fits predict within $\pm 8%$ deviation to data, showing the scope for improvement. It has been observed that a finer adjustment of r$_0$ parameter alone can give very good Ramsauer model description of neutron total scattering data within $\pm 4%$ deviation. The required r$_0$ values for Ramsauer model fits are shown as a function of nuclear mass number and an empirical formula is suggested for r$_0$ values as a function of mass number. In optical model approach for neutron scattering, we have modified the real part of Koning-Deleroche potentails to fit the neutron total cross sections using SCAT2 code. The modified potentails have a different energy dependence beyond 200MeV of neutron energy and fit the total cross sections from Al to Pb.

Fragment mass distributions in the fission of heavy nuclei by intermediate- and high-energy probes

Recent experiments have shown that the multimode approach for describing the fission process is compatible with the observed results. A systematic analysis of the parameters obtained by fitting the fission-fragment mass distribution to the spontaneous and low-energy data has shown that the values for those parameters present a smooth dependence upon the nuclear mass number. In this work, a new methodology is introduced for studying fragment mass distributions through the multimode approach. It is shown that for fission induced by energetic probes (E > 30 MeV) the mass distribution of the fissioning nuclei produced during the intranuclear cascade and evaporation processes must be considered in order to have a realistic description of the fission process. The method is applied to study 208Pb, 238U, 239Np and 241Am fission induced by protons or photons.

Ground state properties of La isotopes in reflection asymmetric relativistic mean field theory

The ground state properties of La isotopes are investigated with the reflection asymmetric relativistic mean field (RAS-RMF) model. The calculation results of binding energies and the quadrupole moments are in good agreements with the experiment. The calculation results indicate the change of the quadrupole deformation with the nuclear mass number. The “kink” on the isotope shifts is observed at A = 139 where the neutron number is the magic number N = 82. It is also found that the octupole deformations may exist in the La isotopes with mass number A ∼ 145–155.

PARTIAL DECAY WIDTHS OF THE ϕ INTO e+e− AND K+K− PAIRS IN 12 GeV p + A REACTIONS AT KEK-PS E325

The experiment KEK-PS E325 measured e+e− and K+K− pairs produced in 12 GeV p + A reactions, in order to search for in-medium modification of vector mesons. In the e+e− spectra, a significant excess on the low-mass side of the ϕ-meson peak is observed in the very low βγ (= p/m) region of the copper target data. On the other hand when the velocity of ϕ mesons is higher or a smaller target, carbon, is employed, the observed ϕ-meson shapes are consistent with the expected shape in vacuum, both in the e+e− and K+K− spectra. We have also compared the nuclear mass number dependence of ϕ-meson production between the e+e− and K+K− decay channels. Using these results, the first experimental limits are obtained for in-medium broadening of the partial decay widths.

Modification of theω-Meson Lifetime in Nuclear Matter

Information on hadron properties in the nuclear medium has been derived from the photoproduction of omega mesons on the nuclei C, Ca, Nb, and Pb using the Crystal Barrel/TAPS detector at the ELSA tagged photon facility in Bonn. The dependence of the omega-meson cross section on the nuclear mass number has been compared with three different types of models: a Glauber analysis, a Boltzmann-Uehling-Uhlenbeck analysis of the Giessen theory group, and a calculation by the Valencia theory group. In all three cases, the inelastic omega width is found to be 130-150 MeV/c(2) at normal nuclear matter density for an average 3-momentum of 1.1 GeV/c. In the rest frame of the omega meson, this inelastic omega width corresponds to a reduction of the omega lifetime by a factor approximately 30. For the first time, the momentum dependent omegaN cross section has been extracted from the experiment and is in the range of 70 mb.

Core Polarization and Tensor Coupling Effects on Magnetic Moments of Hypernuclei

Effects of core polarization and tensor coupling on the magnetic moments in Λ13C, Λ17O, and Λ41Ca Λ-hypernuclei are studied by employing the Dirac equation with scalar, vector and tensor potentials. It is found that the effect of core polarization on the magnetic moments is suppressed by Λ tensor coupling. The Λ tensor potential reduces the spin-orbit splitting of pΛ states considerably. However, almost the same magnetic moments are obtained using the hyperon wavefunction obtained via the Dirac equation either with or without the A tensor potential in the electromagnetic current vertex. The deviations of magnetic moments for pΛ states from the Schmidt values are found to increase with nuclear mass number.

Relativistic chiral mean-field model with parity and charge projection for finite nuclei

We study the role of pions on the ground states of finite nuclei with explicit treatment of pions by variation after charge and parity projection based on the relativistic chiral mean-field (CPPCMF) model. This CPPCMF model has been applied to $^{4}\mathrm{He}$ and demonstrated to provide good ground-state properties within a spherical pion field ansazt. We further apply this model to heavier nuclei up to $^{56}\mathrm{Ni}$ in this article. We find that pions play dominant role also for properties of $^{12}\mathrm{C}$. However, this pionic effect is significantly suppressed in $^{16}\mathrm{O}$ due to the Pauli blocking effect. We find that pionic correlations reflect largely the particle configurations in the shell structure. As for the heavier nuclei, the pionic energy systematics as a function of nuclear mass number are clearly separated into two groups, the LS and $\mathit{jj}$ closed-shell nuclei. The large amount of pionic contributions are obtained for $\mathit{jj}$ closed-shell nuclei as compared with those for LS closed-shell nuclei. This fact may indicate that the pion plays an important role on the formation of the $\mathit{jj}$ magic numbers. The pionic contributions are reduced approximately as ${A}^{\ensuremath{-}2/3}$ with the nuclear mass number. We discuss the reason of this reduction of the pionic energy with the nuclear mass and propose to improve our present ansatz of dealing with pions for heavier nuclei.

Pion-induced double-charge exchange reactions in the Δ resonance region

We have applied the Giessen BUU (GiBUU) transport model to the description of the double-charge exchange (DCX) reaction of pions with different nuclear targets at incident kinetic energies of 120--180 MeV. The DCX process is highly sensitive to details of the interactions of pions with the nuclear medium and, therefore, represents a major benchmark for any model of pion scattering off nuclei at low and intermediate energies. The impact of surface effects, such as the neutron skins of heavy nuclei, is investigated. The dependence of the total cross section on the nuclear mass number is also discussed. We achieve a good quantitative agreement with the extensive data set obtained at LAMPF. Furthermore, we compare the solutions of the transport equations obtained in the test-particle ansatz using two different schemes: the full and the parallel ensemble methods.

Isospin dependence of pseudospin symmetry in nuclear resonant states

The relativistic mean field theory in combination with the analytic continuation in the coupling constant method is used to determine the energies and widths of single-particle resonant states in Sn isotopes. It is shown that there exists clear shell structure in the resonant levels as appearing in the bound levels. In particular, the isospin dependence of pseudospin symmetry is clearly shown in the resonant states, is consistent with that in the bound states, where the splittings of energies and widths between pseudospin doublets are found in correlation with the quantum numbers of single-particle states, as well as the nuclear mass number. The similar phenomenon also emerges in the spin partners.

Nuclear mass number dependence of inclusive production of ω and ϕ mesons in 12 GeVp+Acollisions

The inclusive production of {omega} and {phi} mesons is studied in the backward region of the interaction of 12 GeV protons with polyethylene, carbon, and copper targets. The mesons are measured in e{sup +}e{sup -} decay channels. The production cross sections of the mesons are presented as functions of rapidity y and transverse momentum p{sub T}. The nuclear mass number dependences (A dependences) are found to be A{sup 0.710{+-}}{sup 0.021(stat){+-}}{sup 0.037(syst)} for {omega} mesons and A{sup 0.937{+-}}{sup 0.049(stat){+-}}{sup 0.018(syst)} for {phi} mesons in the region of 0.9<y<1.7 and p{sub T}<0.75 GeV/c.

Flavor changing supersymmetry interactions in a supernova

We consider for the first time flavor changing neutral currents (FCNC’s) in the infall stage of stellar collapse. We take as an example R-Parity violating interactions of the minimal standard supersymmetric model involving neutrinos and quarks. However, our considerations extend to other kinds of flavor changing neutrino reactions as well. We examine non-forward neutrino scattering processes on heavy nuclei and free nucleons in the supernova core. This investigation has led to four principal original discoveries/products: (1) first calculation of neutrino flavor changing cross sections for spin 1/2 (e.g., free nucleon) and spin 0 nuclear targets; (2) discovery of nuclear mass number squared ( A 2) coherent amplification of neutrino-quark FCNC’s; (3) analysis of FCNC-induced alteration of electron capture and weak/nuclear equilibrium in the collapsing core; and (4) generalization of the calculated cross sections (mentioned in 1) for the case of hot heavy nuclei to be used in collapse/supernova and neutrino transport simulations. The scattering processes that we consider allow electron neutrinos to change flavor during core collapse, thereby opening holes in the ν e sea, which allows electron capture to proceed and results in a lower core electron fraction Y e. A lower Y e implies a lower homologous core mass, a lower shock energy, and a greater nuclear photo-disintegration burden for the shock. In addition, unlike the standard supernova model, the core now could have net muon and/or tau lepton numbers. These effects could be significant even for supersymmetric couplings below current experimental bounds.

Nuclear effects in the Drell-Yan process at very high energies

We study Drell-Yan (DY) dilepton production in proton(deuterium)-nucleus and in nucleus-nucleus collisions within the light-cone color-dipole formalism. This approach is especially suitable for predicting nuclear effects in the DY cross section for heavy-ion collisions, as it provides the impact parameter dependence of nuclear shadowing and transverse momentum broadening, quantities that are not available from the standard parton model. For $p(D)+A$ collisions we calculate nuclear shadowing and investigate nuclear modification of the DY transverse momentum distribution at the Relativistic Heavy Ion Collider and the Large Hadron Collider for kinematics corresponding to coherence length much longer than the nuclear size. Calculations are performed separately for transversely and longitudinally polarized DY photons, and predictions are presented for the dilepton angular distribution. Furthermore, we calculate nuclear broadening of the mean transverse momentum squared of DY dileptons as function of the nuclear mass number and energy. We also predict nuclear effects for the cross section of the DY process in heavy-ion collisions. We found a substantial nuclear shadowing for valence quarks, stronger than for the sea.

Are the J/ ψ and χcA dependencies the same?

It has been empirically observed that the dependence of J/ ψ and ψ′ production on nuclear mass number A is very similar. This has been postulated to be due to the predominance of color-octet preresonant states in charmonium production and absorption. Two new experiments, NA60 at CERN and HERA-B at DESY, will measure the χ c A dependence for the first time. These measurements should shed new light on the charmonium production and absorption mechanisms.

Charge-exchange spin monopole modes

Using the self-consistent Hartree-Fock plus Tamm-Dancoff approximation with Skyrme interactions, the response of some $\ensuremath{\beta}$ stable closed-shell nuclei to charge-exchange ${(t}_{\ifmmode\pm\else\textpm\fi{}})$ spin monopole fields is estimated in the coordinate space. Both the isoscalar and isovector spin-correlation are included simultaneously. The excitation energy of ${t}_{+}$ giant resonance decreases considerably as the neutron excess (and consequently the nuclear mass number) increases, while that of ${t}_{\ensuremath{-}}$ giant resonance remains nearly constant. We have tried to separate out the Gamow-Teller strength from the present charge-exchange spin monopole strength, both of which have the same quantum numbers, ${J}^{\ensuremath{\pi}}{=1}^{+}.$

Application of a Simple Ramsauer Model for Neutron Total Cross Sections for Nuclear Mass Numbers A < 40

A recent paper discussed fits of the nuclear Ramsauer model to total neutron cross sections for mass numbers A > 40 and for neutron energies between 6 and 60 MeV. These results are extended to nuclei of mass <40. A reasonably simple parameterization is found that gives a good representation of a recent set of precision data in this mass range. Particular emphasis is placed on the elements of biological importance: carbon, nitrogen, and oxygen.

Relativistic radioactive beams: A new access to nuclear-fission studies

The secondary-beam facility of GSI Darmstadt was used to study the fission properties of 70 short-lived radioactive nuclei. Most of them have not been accessible so far in conventional fission experiments. Relativistic secondary projectiles were produced by fragmentation of a 1 A GeV 238 U primary beam and identified in nuclear charge and mass number. Using these reaction products as secondary beams, the giant resonances, mostly the giant dipole resonance, were excited by electromagnetic interactions in a secondary lead target, and fission from excitation energies around 11 MeV was induced. The fission fragments were identified in nuclear charge, and their velocity vectors were determined. Elemental yields and total kinetic energies have been obtained for a number of neutron-deficient actinides and preactinides. The characteristics of multimodal fission of nuclei around 227 Th were systematically investigated. The proton even–odd effect was determined for all systems.