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Intermediate Energy Nuclear Physics Program

The originally proposed and funded research activities followed two major areas of study: semileptonic probes of the hadronic neutral current and charm production. The charm production work revolved around the Jefferson Lab experiment E03-008, 'Sub-threshold $J/\psi$ Photoprouction', which ran in late 2004. The PI was a co-spokesperson for the experiment. For the three year renewal proposal starting in 2007, the scope and size of the research project changed and increased. In addition to the parity violating studies, the PI had well defined lead roles in a series experiments nucleon spin-structure functions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Nuclear Science References Database

The Nuclear Science References (NSR) database together with its associated Web interface, is the world's only comprehensive source of easily accessible low- and intermediate-energy nuclear physics bibliographic information for more than 210,000 articles since the beginning of nuclear science. The weekly-updated NSR database provides essential support for nuclear data evaluation, compilation and research activities. The principles of the database and Web application development and maintenance are described. Examples of nuclear structure, reaction and decay applications are specifically included. The complete NSR database is freely available at the websites of the National Nuclear Data Center (http://www.nndc.bnl.gov/nsr) and the International Atomic Energy Agency (http://www-nds.iaea.org/nsr)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Experimental Program Final Technical Progress Report: 15 February 2007 to 30 September 2012

This is the final technical report of the grant DE-FG02-04ER41301 to the University of Colorado at Boulder entitled "Intermediate Energy Nuclear Physics" and describes the results of our funded activities during the period 15 February 2007 to 30 September 2012. These activities were primarily carried out at Fermilab, RHIC, and the German lab DESY. Significant advances in these experiments were carried out by members of the Colorado group and are described in detail.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The experimental nuclear reaction data (EXFOR): Extended computer database and Web retrieval system

The EXchange FORmat (EXFOR) experimental nuclear reaction database and the associated Web interface provide access to the wealth of low- and intermediate-energy nuclear reaction physics data. This resource is based on numerical data sets and bibliographical information of ~22,000 experiments since the beginning of nuclear science. The principles of the computer database organization, its extended contents and Web applications development are described. New capabilities for the data sets uploads, renormalization, covariance matrix, and inverse reaction calculations are presented in this paper. The EXFOR database, updated monthly, provides an essential support for nuclear data evaluation, application development, and research activities. Finally, it is publicly available at the websites of the International Atomic Energy Agency Nuclear Data Section, http://www-nds.iaea.org/exfor, the U.S. National Nuclear Data Center, http://www.nndc.bnl.gov/exfor, and the mirror sites in China, India and Russian Federation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Intermediate/High Energy Nuclear Physics

Our primary goals are fundamental descriptions of nuclear phenomena relevant to experiment. Our balanced program consists of developing and applying (1) QCD for high-energy nuclear collisions, and (2) non-perturbative many-body theory for strong interactions. We are developing first principles treatments of physical observables for present and future experiments at FRIB, RHIC, JLab, LHC and EIC. We are also developing and applying a non-perturbative framework for strongly interacting many-body systems including a covariant Hamiltonian framework for solving quantum field theory in non-perturbative domains. We continue close interactions with the Iowa State University relativisitic heavy-ion collider and electron-ion collider experimental group.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Calculation of the C 12 + C 12 sub-barrier fusion cross section in an imaginary-time-dependent mean field theory

The 12 C + 12 C sub-barrier fusion cross section is calculated within the framework of a time-dependent Hartree-Fock-based classical model using the Feynman path-integral method. The modified astrophysical S* factor is compared to direct and indirect experimental results. A good agreement with the direct data is found. In the lower-energy region where recent analyses of experimental data obtained with the Trojan horse method (THM) lead to contrasting results, the model predicts a nonresonant S* factor half-way between those results. Low-energy resonances revealed in the THM data are added to the calculation, and the relative reaction rate in the Gamow region is calculated. In particular, including 0 + resonances result in some agreement with the THM data. Here, the role of different resonances is discussed in detail, and their influence on the reaction rate at temperatures relevant to stellar evolution is investigated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Astrophysical factors of C 12 + C 12 fusion extracted using the Trojan horse method

Carbon-carbon burning plays an important role in many stellar environments. Recently, Tumino et al. reported a sharp rise of the astrophysical S factor for carbon-carbon fusion determined using the indirect Trojan horse method. We demonstrate that the rise at low energies seen in the aforementioned work is an artifact of using an invalid plane-wave approximation that neglects the Coulomb interactions between charged particles. Our analysis shows that such a rise disappears if the Coulomb (or Coulomb-nuclear) interactions in the initial and final states are included.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Reaction dynamics and in-medium nucleon-nucleon cross section with 12 C+ 1 H at 95 MeV/nucleon

Reaction dynamics and effective in-medium nucleon-nucleon (NN) cross section are studied, using the antisymmetrized molecular dynamics (AMD) model with one of the simplest heavy ion collisions, 12 C+ ⁢1 H. The roles of different stochastic processes are studied, which are installed in the original AMD. One is the diffusion process as a part of the quantum fluctuation originated from the Fermi motion during the time evolution of the wave packets in the mean field (AMD/D). The second is a coalescence treatment for light clusters with A ≤ 8 (AMD/D-COALS). The third is the collision process, installed in AMD with different form of the in-medium NN cross sections. These different processes are examined, using the experimental angular distributions and energy spectra of light charged particles and intermediate mass fragments. The effective in-medium NN cross sections are evaluated from the simulated AMD events and compared with the experimentally extracted values. A good agreement is obtained between the AMD values from the 12 C + 1 H reaction at 95 MeV/nucleon and the experimental results for nuclear matter.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Pion production in a transport model based on mean fields from chiral effective field theory

We develop a Boltzmann-Uehling-Uhlenbeck (BUU) transport model based on the Sk χm* energy density functional, which is constructed from fitting the nuclear equation of state and nucleon effective masses in asymmetric nuclear matter predicted by the two- and three-body chiral interactions as well as the binding energies of finite nuclei. This new χBUU transport model is then used to study how baryon mean-field potentials affect the kinematics of a scattering or decay process and the equilibrium properties of a hot N–Δ–π system in a box with periodic boundary conditions. We find that the inclusion of mean-field potentials in the energy conservation condition for scattering and decay processes is necessary to maintain the equilibrium numbers of N,Δ, and π. Although the baryon mean-field potentials have significant effects on the total Δ and π numbers, they only slightly affect the ratio of effective negatively to positively charged pions. We also study pion production in central 197 Au + 197 Au collisions at the incident energy of E/A = 400 MeV and compare the results with the experimental data from the Four Pi (FOPI) Collaboration at the Gesellschaft für Schwerionenforschung mbH (GSI) in Germany. We find that our model can well describe the experimental results and the threshold effect due to baryon mean-field potentials does not affect much the charged pion ratio in this model. Here, we further make predictions on pion production for the ongoing experiments of 132 Sn + 124 Sn and 108 Sn + 112 Sn at the incident energy of E/A = 270 MeV by the SAMURAI Pion-Reconstruction and Ion-Tracker (SπRIT) Collaboration at the Institute of Physical and Chemical Research (RIKEN) in Japan.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Experimental liquid-gas phase transition signals and reaction dynamics

The experimental liquid-gas phase transition signals are examined for the quasiprojectile (QP) reconstructed from the reactions of 40 Ar + 27 Al, 48 Ti, 58 Ni at 47 MeV/nucleon, using measures of caloric curve, multiplicity derivative, moment parameters, and fluctuation of maximum fragment charge number (NVZ). The QP source is reconstructed, using moving source parametrizations on an event-by-event basis. For the determination of the temperature, a quadrupole fluctuation thermometer is used. Deuterons are chosen for the thermometer to minimize the Coulomb and secondary sequential decay effects. Here, a new event-by-event method is proposed for the thermometer to determine the temperature. All measures show a characteristic signature around the temperature T = 9.0 ± 0.4 MeV, which may suggest that the QP system goes into the liquid-gas phase transition at T c = 8.3 ± 0.4 MeV after the Coulomb correction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Absence of hindrance in a microscopic 12 C + 12 C fusion study

Studies of low-energy fusion of light nuclei are important in astrophysical modeling, with small variations in reaction rates having a large impact on nucleosynthesis yields. Due to the lack of experimental data at astrophysical energies, extrapolation and microscopic methods are needed to model fusion probabilities. To investigate deep sub-barrier 12 C+ 12 C fusion cross sections and establish trends for the S factor. Microscopic methods based on static Hartree-Fock and time-dependent Hartree-Fock (TDHF) mean-field theory are used to obtain 12 C+ 12 C ion-ion fusion potentials. Fusion cross sections and astrophysical S factors are then calculated using the incoming wave boundary condition method. Both density-constrained frozen Hartree-Fock (DCFHF) and density-constrained TDHF (DC-TDHF) predict a rising S factor at low energies, with DC-TDHF predicting a slight damping in the deep sub-barrier region (≈1 MeV). Comparison between DC-TDHF calculations and maximum experimental cross sections in the resonance peaks are good. However, the discrepancy in experimental low-energy results inhibits interpretation of the trend. Using the fully microscopic DCFHF and DC-TDHF methods, no S factor maximum is observed in the 12 C+ 12 C fusion reaction. In addition, no extreme sub-barrier hindrance is predicted at low energies. Furthermore, the development of a microscopic theory of fusion including resonance effects, as well as further experiments at lower energies must be done before the deep sub-barrier behavior of the reaction can be established.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Transport model comparison studies of intermediate-energy heavy-ion collisions

Transport models are the main method to obtain physics information on the nuclear equation of state and in-medium properties of particles from low to relativistic-energy heavy-ion collisions. The Transport Model Evaluation Project (TMEP) has been pursued to test the robustness of transport model predictions in reaching consistent conclusions from the same type of physical model. To this end, calculations under controlled conditions of physical input and set-up were performed with various participating codes. These included both calculations of nuclear matter in a box with periodic boundary conditions, which test separately selected ingredients of a transport code, and more realistic calculations of heavy-ion collisions. Over the years, six studies have been performed within this project. In this intermediate review, we summarize and discuss the present status of the project. We also provide condensed descriptions of the 26 participating codes, which contributed to some part of the project. These include the major codes in use today. After a compact description of the underlying transport approaches, we review the main results of the studies completed so far. They show, that in box calculations the differences between the codes can be well understood and a convergence of the results can be reached. These studies also highlight the systematic differences between the two families of transport codes, known under the names of Boltzmann–Uehling–Uhlenbeck (BUU) and Quantum Molecular Dynamics (QMD) type codes. However, when the codes were compared in full heavy-ion collisions using different physical models, as recently for pion production, they still yielded substantially different results. This calls for further comparisons of heavy-ion collisions with controlled models and of box comparisons of important ingredients, like momentum-dependent fields, which are currently underway. Furthermore, our evaluation studies often indicate improved strategies in performing transport simulations and thus can provide guidance to code developers. Results of transport simulations of heavy-ion collisions from a given code will have more significance if the code can be validated against benchmark calculations such as the ones summarized in this review.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Effect of internal magnetic field on collective flow in heavy ion collisions at intermediate energies

The properties of nuclear matter under extreme conditions of high temperature, density, and isospin asymmetry have attracted wide attention in recent years. At present, heavy ion reactions in combination with corresponding model simulations are one of the most important ways to investigate this subject. It is known that a strong magnetic field can be created in heavy ion collisions. However, its effect on the motion of charged particles is usually neglected in previous transport model simulations. In this work, within the ultrarelativistic quantum molecular dynamics (UrQMD) model, the temporal evolution and spatial distribution of the internal magnetic field are calculated. The magnetic field strength is found to reach about eB ≈ 470 MeV 2 (B ≈ 8 × 10 16 G) for Au + Au collisions at E lab = 1 GeV/nucleon with impact parameter of 7 fm. The magnetic field in Cu + Au collisions exhibits somewhat different spatial distribution from that in Au + Au collisions. The magnetic field is found to affect the directed flow of pions at forward and backward rapidities to some extent, dependent of the impact parameter and beam energy while the effect on the elliptic flow is small. In addition, the effects of the magnetic field on the π – /π + ratio over the whole rapidity range and the elliptic flow difference $v$$^{n}_{2}$–$v$$^{p}_{2}$ between neutrons and protons at forward and backward rapidities are on the same order as those from the nuclear symmetry energy. Here, the $v$$^{n}_{2}$–$v$$^{p}_{2}$ difference in the midrapidity region is not strongly affected by the magnetic field, and the total π – /π + yield ratio is immune to it. It is advisable to include the magnetic field effects in future studies using pion flow, pion yield ratio, and nucleon elliptic flow difference to probe the symmetry energy at super saturation densities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Influence of the tensor force on the microscopic heavy-ion interaction potential

The tensor interaction is known to play an important role in the nuclear structure studies of exotic nuclei. However, most microscopic studies of low-energy nuclear reactions neglect the tensor force, resulting in a lack of knowledge concerning the effect of the tensor force on heavy-ion collisions. An accurate description of the heavy-ion interaction potential is crucial for understanding the microscopic mechanisms of heavy-ion fusion dynamics. Furthermore, the building blocks of the heavy-ion interaction potential in terms of the ingredients of the effective nucleon-nucleon interaction provides the physical underpinnings for connecting the theoretical results with experiment. The tensor force has never been incorporated for calculating the nucleus-nucleus interaction potential. The theoretical study of the influence of the tensor force on heavy-ion interaction potentials is required to further our understanding of the microscopic mechanisms entailed in fusion dynamics. The full Skyrme tensor force is implemented into the static Hartree-Fock and dynamic density-constrained time-dependent Hartree-Fock (DC-TDHF) theory to calculate both static (frozen density) and dynamic microscopic interaction potentials for reactions involving exotic and stable nuclei. The static potentials are found to be systematically higher than the dynamical results, which are attributed to the microscopic dynamical effects included in TDHF. We also show that the dynamical potential barriers vary more significantly by the inclusion of tensor force than the static barriers. The influence of isoscalar and isovector tensor terms is also investigated with the TIJ set of forces. For light systems, the tensor force is found to have an imperceptible effect on the nucleus-nucleus potential. However, for medium and heavy spin-unsaturated reactions, the potentials may change from a fraction of an MeV to almost 2 MeV by the inclusion of tensor force, indicating a strong impact of the tensor force on subbarrier fusion. The tensor force could indeed play a large role in the fusion of nuclei, with spin-unsaturated systems seeing a systematic increase in ion-ion barrier height and width. Furthermore, this fusion hindrance is partly due to static, ground-state effects from the inclusion of the tensor force, though additional hindrance appears when studying nuclear dynamics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Neutron skins as laboratory constraints on properties of neutron stars and on what we can learn from heavy ion fragmentation reactions

The equation of state (EOS) of infinite nuclear matter with a small proton or neutron fraction is a crucial input to determine the properties of neutron stars and compare model predictions to astronomical observations. The so-called symmetry energy is the part of the EOS accounting for the difference in the number of neutrons and protons. Numerous experiments have been devised to assess the symmetry energy and constrain its functional dependence with the nucleon density. Further constraints follow from a stellar modeling using the EOS to reproduce astronomical observations such as neutron star masses and radii. Here, the recent detection of gravitational waves emitted from neutron star mergers and the nucleosynthesis ensuing from these events caused a surge of interest for such studies. Several types of nuclear reactions have been proposed to study the symmetry energy part of the EOS. Some of them consist in determining the neutron skin in nuclei and exploit its correlation with the slope parameter of the symmetry energy. In this article, we explore a particular set of reactions using high-energy (E lab ~ 1 GeV/nucleon) neutron-rich projectiles. We explore measurements of all reaction fragments (a) in the same isotopic chain, i.e., only by removal of neutrons, (b) in all charge-changing channels, and (c) total interaction cross sections. Using Hartree-Fock-Bogoliubov (HBF) predictions for neutron and proton densities with Skyrme interactions, we explore the sensitivity of these cross sections with the neutron skin in nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Ionization yield measurement in a germanium CDMSlite detector using photo-neutron sources

Two photo-neutron sources, Y 88 Be 9 and Sb 124 Be 9 , have been used to investigate the ionization yield of nuclear recoils in the CDMSlite germanium detectors by the SuperCDMS collaboration. In this study, we evaluate the yield for nuclear recoil energies between 1 and 7 keV at a temperature of ~ 50 mK . We use a geant4 simulation to model the neutron spectrum assuming a charge yield model that is a generalization of the standard Lindhard model and consists of two energy dependent parameters. We perform a likelihood analysis using the simulated neutron spectrum, modeled background, and experimental data to obtain the best fit values of the yield model. The ionization yield between recoil energies of 1 and 7 keV is shown to be significantly lower than predicted by the standard Lindhard model for germanium. There is a general lack of agreement among different experiments using a variety of techniques studying the low energy range of the nuclear recoil yield, which is most critical for interpretation of direct dark matter searches. This suggests complexity in the physical process that many direct detection experiments use to model their primary signal detection mechanism and highlights the need for further studies to clarify underlying systematic effects that have not been well understood up to this point.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Single-nucleon knockout cross sections for reactions producing resonance states at or beyond the drip line

Single-nucleon knockout cross sections from fast secondary beams of the proton-drip-line nuclei 9 C, 13 O, and 17 Ne on a 9 Be target have been studied with emphasis on the production of resonance states. These states were identified by their invariant mass, and resonances with two-, three-, and five-body exit channels were examined. The measured cross sections for these states were compared with eikonal-model predictions using shell-model or variational Monte Carlo spectroscopic factors. The experimental yields were found to be suppressed relative to the model predictions, especially when a well-bound neutron or proton is removed. This suppression exceeds that found systematically in measured inclusive cross sections to particle-bound final states. In neutron knockout from 9 C and 13 O projectiles, this suppression of the unbound ground-state residuals yield is a factor of two to three times larger than that found in the bound final-state studies. Modifications to the structure of these systems due to coupling of the shell-model configurations to the continuum is expected to contribute to this extra suppression, especially when the final state is a near-threshold resonance. Furthermore, other considerations including the role of nuclear dynamics may be required to explain all the observed trends.

6 ≤ A ≤ 19↗

Kinetic approach of light-nuclei production in intermediate-energy heavy-ion collisions

We develop a kinetic approach to the production of light nuclei up to mass number A ≤ 4 in intermediate-energy heavy-ion collisions by including them as dynamic degrees of freedom. The conversions between nucleons and light nuclei during the collisions are incorporated dynamically via the breakup of light nuclei by a nucleon and their reverse reactions. We also include the Mott effect on light nuclei; i.e., a light nucleus will no longer be bound if the phase-space density of its surrounding nucleons is too large. With this kinetic approach, we obtain a reasonable description of the measured yields of light nuclei in central Au+Au collisions at energies of 0.25⁢A GeV–1.0⁢A GeV by the FOPI Collaboration. Our study also indicates that the observed enhancement of the α-particle yield at low incident energies can be attributed to a weaker Mott effect on the α particle, which makes it more difficult to dissolve in nuclear medium, as a result of its much larger binding energy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗