Session R11: Nuclear Theory

Not Participating

The microscopic description of nuclear collectivity in heavy nuclei within the framework of the configuration-interaction shell model is a major challenge due to the combinatorial increase of the model space dimension with the number of valence nucleons and/or orbitals. The shell model Monte Carlo (SMMC) method is a powerful technique for overcoming this limitation, allowing the calculation of thermal and ground-state properties of nuclei in model spaces that are many orders of magnitude larger than those that can be treated by conventional shell model methods. Previous SMMC calculations have provided only indirect evidence of collectivity in heavy nuclei. Recently, a method has been developed to extract the energies of several excited states for each spin and parity through the calculation of imaginary-time response matrices of one-body densities [1]. We apply this method to chains of lanthanide isotopes and obtain direct spectral signatures of the crossover from vibrational to rotational collectivity. \newline [1] Y. Alhassid, M. Bonett-Matiz and C.N. Gilbreth, to be published.   

Towards analog quantum simulations of lattice gauge theories with trapped ions

Gauge field theories play a central role in nuclear physics and are at the heart of the Standard Model. Despite significant progress in applying classical computational techniques to perform Euclidean simulation of gauge theories, it has remained a challenging task to compute the real-time dynamics of these theories, which describe processes such as the evolution of matter after heavy ion collisions. An exciting possibility that has been explored in recent years is the use of highly-controlled quantum systems to simulate, in an analog fashion, properties of a target system whose dynamics are difficult to compute. Engineered atom-laser interactions in a linear crystal of trapped ions offer a wide range of possibilities for quantum simulations of complex physical systems. Here, we present practical proposals for analog simulation of lattice gauge theories whose dynamics can be mapped into spin-spin interactions in any dimension. In addition, the evolution of the Schwinger model (1+1 QED) is simulated using the effective Hamiltonian describing the interactions of the ions and phonons in a Paul trap. Future possibilities to extend such a mapping to a larger class of gauge field theories include devising higher-order spin interactions and taking advantage of phononic excitations.   

On Demand

Nuclear state densities are important inputs to the Hauser-Feshbach theory of compound-nucleus reactions. We benchmark the static-path plus random-phase approximation (SPA+RPA) to state densities in a chain of heavy samarium isotopes ($^{148,150,152,154}$Sm), in which the collectivity changes from vibrational to rotational with increasing neutron number. We use a pairing-plus-quadrupole interaction in the configuration-interaction shell model framework. The SPA+RPA includes large-amplitude static fluctuations and small-amplitude quantal fluctuations around each static fluctuation. We have developed a Monte Carlo method for calculating the SPA+RPA thermal energy and heat capacity, which are necessary for the calculation of the state density. We compare the SPA+RPA with the self-consistent mean-field approximation and exact shell-model Monte Carlo results obtained with the same model space and interaction. The SPA+RPA describes pairing and rotational correlations beyond the mean-field approximation. In particular, the SPA+RPA in deformed nuclei reproduces the enhancement of the state density with respect to the mean-field density due to rotational collectivity. We study the evolution of this rotational enhancement with increasing neutron number.   

Not Participating

Real time simulations of quantum systems hold the key to modeling and understanding the dynamics and responses of strongly interacting many-body systems such as atomic nuclei and their interactions with other matter. Classical calculations of such systems are plagued by an exponential growth of particle configurations and aggressively more difficult to handle sign problems. Quantum computing offers a pathway to directly simulate the real time evolution of these systems with polynomial scaling and no sign problem. However, current quantum computation is too noisy to implement and execute the formal quantum computing algorithms that have been proposed to compute such real time dynamics. This limitation often manifests itself as a limit in the number of quantum gates that can be applied before the QPU enters a decoherent state and all information about the simulated dynamics is lost. We demonstrate an alternative efficient high-fidelity encoding of the nuclear dynamics onto a QPU and apply it to the real-time simulation of neutron scattering using a Hamiltonian derived from chiral effective field. We will present both simulated data and real data taken on the Lawrence Livermore National Lab’s quantum testbed   

Not Participating

The No-Core Shell Model with Continuum (NCSMC) is a recently developed approach capable of describing both bound and scattering states in light nuclei simultaneously. This technique represents a state-of-the-art ab initio method and combines the No-Core Shell Model description of short-range correlations with the clustering and scattering properties of the Resonating Group Method. Recent NCSMC calculations of $^7$Be and $^7$Li will be presented. The properties of these nuclei were investigated by analyzing the continuum of all the binary mass partitions involved in the creation of these systems, using chiral interactions as the only input. Our calculations reproduce all the experimentally known states in the correct order and predict new possible resonances with negative and positive parity. A positive-parity $S$ wave resonance is found analyzing the continuum of p + $^6$He at a very low energy above the threshold, which produces a very pronounced peak in the astrophysical $S$ factor of the $^6$He(p,$\gamma$) $^7$Li radiative capture. Possible implications for astrophysics have still to be investigated.   

Constructing an Exactly Solvable Model to test Many-body theories

We deal with the construction of a simple many-body model that can be solved exactly. This model serves as a reliable tool for testing the validity and accuracy of many-body approximation methods such as mean field approximations in nuclear collective motion. The model consists of a system of two distinguishable sets of fermions interacting via a schematic two-body force. We construct the Hamiltonian of the model by means of vector operators that satisfy a Lie algebra and which are the generators of an SO(3,1) group. The Hamiltonian depends on an adjustable parameter that regulates the strength of the two-body interaction. The size of the Hamiltonian's matrix is rendered finite by means of a built-in symmetry. By diagonalizing this matrix, we obtain exact energy eigenvalues. Using this model, we test the accuracy of several many-body approximation methods by comparing their energy spectra with those obtained from the model.   

On Demand

In this work we use Bayesian analysis to estimate the parameters of radiative capture reactions~$^{\mathrm{3}}$He($\alpha $,$\gamma )^{\mathrm{7}}$Be and~$^{\mathrm{3}}$H($\alpha $,$\gamma )^{\mathrm{7}}$Li using effective field theory (EFT). EFT provides a model independent framework to describe physical systems as an expansion of low momentum scale over a high momentum scale. Here we consider two competing effective field theory power countings for the model comparison. In the first power counting, two-body currents contribute at leading order, and in the second power counting they contribute at higher orders. We estimate the parameters for the two power countings using most recent capture data and scattering data. For $^{\mathrm{3}}$He($\alpha $,$\gamma )^{\mathrm{7}}$Be, the first power counting is favored if elastic scattering data in the incoming channel is considered in the analysis. Without constraints from elastic scattering data, both the power countings are equally favored. For $^{\mathrm{3}}$H($\alpha $,$\gamma )^{\mathrm{7}}$Li, the first power counting is favored with or without constraints from elastic scattering data.   

Variable Nuclear Barrier Heights Due To Nuclear Vibrations Thereby Allowing Some Low Energy Nuclear Reactions Without The Artifice of Tunneling

Nuclear barrier heights are often thought to be static repulsive forces repelling an incoming positive charge such as a proton from contacting the positive nucleus generating a nuclear reaction unless the coming charge has sufficient kinetic energy to overcome the positive repulsive nuclear potential energy. Some low energy nuclear occurred which could not be explained by classical physics. "tunneling" was invented in order to explain phenomenon. All nuclei are vibrating changing their position in relation to the incoming positive charge. The barrier height-incoming charge value is position dependent therefore the barrier height is repeatedly changing, If the barrier height is lower, some previously thought impossible nuclear reactions may take place obviating the need for the "tunneling" explanation.If the nucleus is a three dimensional oscillator where $r = ((AcosX)^2 + (AcosY)^2 + (AcosZ)^2)^(1/2)$. If $cos=0$,$ r= 0$ and V= infinitely high. If $cos=RMScos, r= 1.22A $ average. If $cos= 1, r = 1.707A$ max. Thus, if $V =k(q_1)(q_2)/r$, the barrier height ranges from infinitely high, to $V = 0.816q_1q_2/A$ on average,to a low of $V=0.577(q_1)(q_2)/A$ where A = average amplitude of nuclear vibration, $(q_1)$ is the nuclear charge, $(q_2)$ is the incoming particle charge.