Session KJ: Physics Opportunities and Theory in Heavier Nuclei

The Jefferson Science Fellows (JSF) program at the US Department of State

In 2004 the US Department of State and the National Academies established the Jefferson Science Fellows program, to bring tenured faculty in sciences, engineering, and medicine to the Department of State or USAID for a year in residence, with continuing connections. Over twenty physical scientists have been Fellows, working in a wide variety of offices on a broad range of topics. The main advantage to Fellows is the opportunity to make an impact on important national and international issues, applying skills and judgments gained through their research, teaching, and service. The JSF experience can also create broader horizons for physicists, especially beyond the laboratory. The selection process and examples, including my own, will be described. Information can be found at //sites.nationalacademies.org/PGA/Jefferson/.   

Excited state energies in the shell model Monte Carlo approach

The configuration-interaction shell model approach has been successful in describing the spectroscopic properties of nuclei. However, its application to medium-mass and heavy nuclei has been hampered by the combinatorial increase of the dimension of the many-particle model space as a function of the number of valence orbitals and the number of valence nucleons. The shell model Monte Carlo (SMMC) method is a powerful technique for calculating the ground state and thermal properties of nuclei in model spaces that are many orders of magnitude larger than those that can be treated by direct diagonalization methods~[1,2]. However, it is generally difficult to access specific energy levels in SMMC. We are investigating a method within the SMMC approach to extract the excitation energy of certain states. We discuss preliminary applications of the method.\\[4pt] [1] Y. Alhassid, A. Mukherjee, H. Nakada and C. \"Ozen, Journal of Physics: Conference Series {\bf 403}, 012012 (2012).\\[0pt] [2] Y. Alhassid, M. Bonett-Matiz, S. Liu, and H. Nakada, arXiv:1304.7258.   

Finite amplitude method for discrete collective excited states and sum rules

The finite amplitude method (FAM) is one of the new efficient iterative methods for solving the QRPA problem, based on the linear response theory. The original FAM equations are solved with a small imaginary width introduced to the QRPA energy, and, up to present, its direct application to discrete excitations has not been fully accomplished. To this end we proposed a new formulation of the FAM using the contour integration technique. We show that the discrete QRPA amplitudes and energies can be expressed by means of contour integration around the QRPA poles in a complex-energy plane. We then discuss the contour integral formulation for the QRPA sum rules needed to constrain modern energy density functionals.   

Isospin transfer modes in exotic nuclei

This work presents a self-consistent approach to nuclear spin-isospin response, which attempts to describe simultaneously the overall strength distribution up to high excitation energy, quenching and the fine structure of the low-lying strength. The approach is based on the extension of the covariant energy density functional (CEDF) theory. The effective one-boson exchange interaction spans effective mesons and emergent collective modes. While heavy mesons are treated as classical fields, the low-lying collective phonons are included within non-perturbative quantum field theory schemes in the time-blocking approximation. Thus, the covariant spin-isospin response theory has been advanced to the inclusion of temporal and spatial non-localities [1,2] while pairing correlations of the superfluid type are included on the equal footing by means of the Gorkov's Green functions. The approach based on a few parameters of the CEDF provides a high-quality description of nuclear excitation spectra in both neutral and charge-exchange channels. Results of the recent calculations for spin-isospin response of exotic medium-mass nuclei studied at NSCL and RIKEN are presented and discussed. \\[4pt] [1] T. Marketin, E. Litvinova, D. Vretenar, P. Ring, Phys. Lett. B 706, 477 (2012).\\[0pt] [2] E. Litvinova, B.A. Brown, D.-L. Fang, T. Marketin, R.G.T. Zegers, Phys. Lett. B 730, 307 (2014).   

Spin-orbit decomposition of ab initio nuclear wavefunctions

Although the modern shell-model picture of atomic nuclei is built from single-particle orbitgs with good total angular momentum $j$ leading to $j$-$j$ coupling schemes, phenomenological models decades ago suggested for $0p$ nuclei a simpler picture can be realized by coupling of total orbital angular momentum $L$ and total spin $S$. I revisit this idea with large-basis, no-core shell model (NCSM) calculations using modern \textit{ab initio} two-body interactions and dissect the resulting NCSM wavefunctions into their $L$- and $S$-components. Remarkably, despite a gap of nearly fifty years and six orders of magnitude in the basis dimension, there is broad agreement between NCSM and phenomenological wavefunctions computed with the Cohen-Kurath force.   

The competition of particle-vibration coupling and tensor interaction in spherical nuclei

The search for missing terms in the energy density functionals (EDF) is one of the leading directions in the development of nuclear density functional theory (DFT). Tensor force is one of possible candidates [1]. However, despite extensive studies [1] the questions about its effective strength and unambiguous signals still remain open. One of the main experimental benchmarks for the studies of tensor interaction is provided by the data on the single-particle states in the $N=82$ and $Z=50$ isotopes. The energy splittings of the proton $h_{11/2}$ and $g_{7/2}$ states in the $Z=50$ isotopes and neutron $1i_{13/2}$ and $1h_{9/2}$ states in the $N=82$ isotones are used in the definition of tensor force in the Skyrme DFT [1]. However, in experiment these states are not ``mean-field'' states because of coupling with vibrations. Employing relativistic particle-vibration coupling (PVC) model [2] we show that many features of these splittings can be reproduced when PVC is taken into account. This suggests the competition of PVC and tensor interaction and that tensor interaction should be weaker as compared with previous estimates.\\[4pt] [1] H. Sagawa and G. Colo, Prog. Part. Nucl. Phys. 76, 76 (2014).\\[0pt] [2] E. Litvinova, Phys. Rev. C 85, 021303(R) (2012).   

Damping of Quantum Vibrations Revealed in Deep Sub-barrier Fusion

We demonstrate that when two colliding nuclei approach each other, their quantum vibrations are damped near the touching point. To show those, we for the first time apply the random-phase-approximation (RPA) method to the two-body $^{16}$O + $^{16}$O and $^{40}$Ca + $^{40}$Ca systems. We show that this damping is responsible for the fusion hindrance phenomena measured in the deep sub-barrier fusion reactions. We calculate the octupole transition strengths for the two nuclei adiabatically approaching each other. The calculated transition strength drastically decreases near the touching point, strongly suggesting the vanishing of the quantum couplings between the relative motion and the vibrational intrinsic degrees of freedom of each nucleus. Based on this picture, we also calculate the fusion cross section for the $^{40}$Ca + $^{40}$Ca system using the coupled-channel method with the damping factor simulating the vanishing of the couplings. The calculated results reproduce well the experimental data, indicating that the smooth transition from the sudden to adiabatic processes indeed occurs in the deep sub-barrier fusion reactions.   

Ab initio Bogoliubov coupled cluster theory

Coupled cluster (CC) theory has become a standard method in nuclear theory for realistic ab initio calculations of medium mass nuclei, but remains limited by its requirement of a Slater determinant reference state which reasonably approximates the nuclear system of interest. Extensions of the method, such as equation-of-motion CC, permit the calculation of nuclei with one or two nucleons added or removed from a doubly magic core, yet still only a few dozen nuclei are accessible with modern computational restrictions. In order to extend the applicability of ab initio methods to open-shell systems, the superfluid nature of nuclei must be taken into account. By utilizing Bogoliubov algebra and employing spontaneous symmetry breaking with respect to particle number conservation, superfluid systems can be treated by a single reference state. An ab initio theory to include correlations on top of a Bogoliubov reference state has been developed in the guise of standard CC theory. The formalism and first results of this Bogoliubov coupled cluster theory will be presented to demonstrate the applicability of the method.   

Reformulation of a chiral random matrix model in the thermodynamic limit

The chiral random matrix theory provides a universal framework to study the low-lying Dirac eigenmodes and describes chiral phase transition suitably. In this theory, we had considered distributions of topological zero modes to incorporate effects of the axial anomaly and obtained thereby well defined topological susceptibility as a function of temperature. In this talk, we propose a reformulation of the chiral random matrix model with the proper distribution of the topological zero modes in the thermodynamic limit by means of the sectional measurement and report the temperature dependence of physical quantities associated with the chiral phase transition.   

Monte-Carlo Hauser-Feshbach simulations of prompt fission gamma-ray properties

Properties of prompt fission neutrons and $\gamma$ rays, emitted before the weak decays of the fission fragments toward stability, are important for both nuclear technologies and a better understanding of the fission process. In the present work, we use the Hauser-Feshbach model to simulate the de-excitation of the fully accelerated fission fragments treated as compound nuclei. Our Monte-Carlo implementation of the Hauser-Feshbach statistical model, which takes into account the competition between the neutron and $\gamma$ emissions, allows the description of both average quantities, like in the Los Alamos model, and correlations between the emitted particles. Our simulations will be compared against available experimental data and current evaluations. In particular, we will compare our average $\gamma$-ray spectrum with recent measurements at the research reactor KFKI in Budapest for the $^{235}$U($n_{\mathrm{th}},f$) and $^{252}$Cf(sf) reactions, as well as multiplicity-dependent distributions obtained at the DANCE facility at LANSCE.   

Order-by-order predictions for nuclear and neutron matter

We report on {\it ab initio} predictions of nuclear and neutron matter obtained within the BHF approach together with chiral forces. The parameters of the two- and many-body forces are constrained by the properties of the two- and the few-nucleon systems and not readjusted when such forces are applied in nuclear matter. Chiral effective field theories are based on a low-momentum expansion (ChPT) valid for momenta less than the chiral symmetry breaking scale, $\Lambda$. Therefore, nucleon-nucleon potentials based on ChPT are usually multiplied by a regulator function $f(p',p) = exp[-(p'/\Lambda)^{2n}-(p/\Lambda)^{2n}]$, where 0.5 GeV is a typical choice for the cutoff $\Lambda$. Together with power counting, ChPT allows for a systematic development of nuclear forces, where two- and many-body forces emerge on an equal footing at each order. The question we wish to explore is: how good is the rate of convergence of the chiral expansion? Better and better convergence with increasing order should be seen as improved cutoff independence. We will be concerned with the energy per particle in nuclear and neutron matter as well as the symmetry energy. The purpose is to determine the accuracy with which these quantities can be predicted in ChPT, order by order.   

Hydrodynamic Models for Nuclear Systems

In this talk I will discuss applications of hydrodynamic models to nuclear systems for studying dynamic processes including vortex pinning in neutron stars and nuclear fission.   

Chiral Spirals from Discontinuous Chiral Symmetry

Recently phases of the inhomongeneous chiral condensates (IChC) attract renewed attentions in quark matter context. A number of theoretical studies have suggested that in some domain of moderate quark density the IChC phases are energetically more favored than the normal, chiral symmetric phase. In particular, the NJL-type model studies indicate that the phase of IChCs may mask the usual 1st order chiral phase transition line and its critical end point, and might change the conventional wisdom. In this talk, I will discuss characteristic features of the IChC phases and their potential impacts on the compact star physics. In particular, some of the IChC phases open gaps near the quark Fermi surface, suppressing back-reaction from the quark to gluon sectors. This mechanism delays the chiral restoration in the strange quark sector, forbids the emergence of the large bag constant, and as a consequence, makes the quark matter EOS very stiff.