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Title: Nuclear Theory. Final Technical Report for DOE Grant DE-FG02-91ER40608

Abstract

We summarize our main research achievements under DOE grant DE-FG02-91ER40608. Task A: An important question in physics is the extent to which physical systems display ordered structures, which can be interpreted as underlying symmetries of dynamic origin. Our research, from early days until to date, has been devoted to unraveling these symmetries. The language to describe symmetries is mathematics, especially algebras. We have developed models based on algebraic structures to describe the regularities observed in atomic nuclei (interacting boson model and interacting boson-fermion model), in molecules (vibron model and electron-vibron model), in hadrons (algebraic string model) and in clusters of alpha particles in atomic nuclei (algebraic cluster model). We have further introduced an even more complex type of symmetry, called supersymmetry, to describe regularities in the spectra of nuclei with an odd number of particles. Our models have provided tools to analyze spectral properties of medium-mass and heavy nuclei with unprecedented accuracy, and have led to the discovery of several types of symmetries in atomic nuclei, including in recent years (2000-2001) the discovery of symmetries at the critical point of phase transitions between spherical and ellipsoidal shapes, the so-called critical symmetries. One of the most important questions in physics todaymore » is the nature of an elusive particle, called neutrino. Originally thought to be mass-less, it has now been found to have a mass. This discovery has led to the 2015 Nobel Prize in Physics. However, the actual value of the mass is unknown, as well as whether or not the neutrino is its own antiparticle. A way to answer this question is through the observation of a rare process, called neutrino-less double beta decay in which two neutrons inside the nucleus are transformed into two protons with the emission of two electrons. Our research in recent years (2009-to date) has been focused on a calculation of the expected half-life for this process as a function of the neutrino mass in order to determine precisely the average neutrino mass, if neutrino-less double beta decay is observed. The calculation includes both the phase space factors, which depend on atomic structure, and the nuclear matrix elements, which depend on the nuclear structure of the decaying nucleus. This calculation is of importance in guiding the experimental searches, for which major investments are being made both in the U.S. and Worldwide. Task B: Our research program spans three major topics in nuclear physics and related areas: nuclear many-body theory, mesoscopic physics and nanoscience, and cold atom physics. To understand these subjects, we have developed sophisticated methods that take advantage of advances in high-performance computing and novel many-body methods, enabling studies that were not possible previously. In nuclear many-body theory, our research program has focused on understanding how the properties of atomic nuclei emerge from the underlying correlations among their constituents. In particular, we have developed auxiliary-field quantum Monte Carlo (AFMC) methods for the configuration-interaction shell model, allowing calculations in model spaces that are many orders of magnitude larger than those that can be treated in conventional methods. AFMC has become the state-of-the-art method for calculating statistical properties of nuclei such as level densities in the presence of correlation, and we found excellent agreement with experiments. Knowledge of such properties is important for deciphering the astrophysical processes that generate the chemical elements in stars and the design of next-generation nuclear reactors with increased efficiency and minimal nuclear waste. We demonstrated the microscopic emergence of collectivity and developed a unified approach to quantum and thermal shape phase transitions in nuclei. In mesoscopic physics and nanoscience, we made important contributions at the interface of nuclear physics and finite-size quantum many-body systems such as quantum dots and ultra-small metallic grains (nanoparticles). We pioneered a statistical theory that describes the universal fluctuations of the transport properties of almost-isolated quantum dots, and whose predictions were confirmed in subsequent experiments. We developed methods to study the effects of pairing correlations in nanoparticles in the regime where the conventional theory of superconductivity breaks down and identified signatures of the competition between pairing and spin exchange correlations. In cold atom physics, we made important breakthroughs in our understanding of the thermodynamics of the unitary Fermi gas, which describes the limit of strongest short-range interactions in a fermionic many-body system, and whose physics is relevant to other strongly correlated systems such as nuclei, quark matter and neutron stars. In particular, we developed AFMC methods that enabled the accurate calculation of pairing correlations across the superfluid phase transition in the unitary Fermi gas. Our results for a fundamental property known as the contact were in excellent agreement with the most recent precision ultracold atomic gas experiments.« less

Authors:
 [1];  [1]
  1. Yale University
Publication Date:
Research Org.:
Yale Univ., New Haven, CT (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1605421
Report Number(s):
DOE-YALE-40608
DOE Contract Number:  
FG02-91ER40608
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 97 MATHEMATICS AND COMPUTING

Citation Formats

Iachello, Francesco, and Alhassid, Yoram. Nuclear Theory. Final Technical Report for DOE Grant DE-FG02-91ER40608. United States: N. p., 2020. Web. doi:10.2172/1605421.
Iachello, Francesco, & Alhassid, Yoram. Nuclear Theory. Final Technical Report for DOE Grant DE-FG02-91ER40608. United States. doi:10.2172/1605421.
Iachello, Francesco, and Alhassid, Yoram. Thu . "Nuclear Theory. Final Technical Report for DOE Grant DE-FG02-91ER40608". United States. doi:10.2172/1605421. https://www.osti.gov/servlets/purl/1605421.
@article{osti_1605421,
title = {Nuclear Theory. Final Technical Report for DOE Grant DE-FG02-91ER40608},
author = {Iachello, Francesco and Alhassid, Yoram},
abstractNote = {We summarize our main research achievements under DOE grant DE-FG02-91ER40608. Task A: An important question in physics is the extent to which physical systems display ordered structures, which can be interpreted as underlying symmetries of dynamic origin. Our research, from early days until to date, has been devoted to unraveling these symmetries. The language to describe symmetries is mathematics, especially algebras. We have developed models based on algebraic structures to describe the regularities observed in atomic nuclei (interacting boson model and interacting boson-fermion model), in molecules (vibron model and electron-vibron model), in hadrons (algebraic string model) and in clusters of alpha particles in atomic nuclei (algebraic cluster model). We have further introduced an even more complex type of symmetry, called supersymmetry, to describe regularities in the spectra of nuclei with an odd number of particles. Our models have provided tools to analyze spectral properties of medium-mass and heavy nuclei with unprecedented accuracy, and have led to the discovery of several types of symmetries in atomic nuclei, including in recent years (2000-2001) the discovery of symmetries at the critical point of phase transitions between spherical and ellipsoidal shapes, the so-called critical symmetries. One of the most important questions in physics today is the nature of an elusive particle, called neutrino. Originally thought to be mass-less, it has now been found to have a mass. This discovery has led to the 2015 Nobel Prize in Physics. However, the actual value of the mass is unknown, as well as whether or not the neutrino is its own antiparticle. A way to answer this question is through the observation of a rare process, called neutrino-less double beta decay in which two neutrons inside the nucleus are transformed into two protons with the emission of two electrons. Our research in recent years (2009-to date) has been focused on a calculation of the expected half-life for this process as a function of the neutrino mass in order to determine precisely the average neutrino mass, if neutrino-less double beta decay is observed. The calculation includes both the phase space factors, which depend on atomic structure, and the nuclear matrix elements, which depend on the nuclear structure of the decaying nucleus. This calculation is of importance in guiding the experimental searches, for which major investments are being made both in the U.S. and Worldwide. Task B: Our research program spans three major topics in nuclear physics and related areas: nuclear many-body theory, mesoscopic physics and nanoscience, and cold atom physics. To understand these subjects, we have developed sophisticated methods that take advantage of advances in high-performance computing and novel many-body methods, enabling studies that were not possible previously. In nuclear many-body theory, our research program has focused on understanding how the properties of atomic nuclei emerge from the underlying correlations among their constituents. In particular, we have developed auxiliary-field quantum Monte Carlo (AFMC) methods for the configuration-interaction shell model, allowing calculations in model spaces that are many orders of magnitude larger than those that can be treated in conventional methods. AFMC has become the state-of-the-art method for calculating statistical properties of nuclei such as level densities in the presence of correlation, and we found excellent agreement with experiments. Knowledge of such properties is important for deciphering the astrophysical processes that generate the chemical elements in stars and the design of next-generation nuclear reactors with increased efficiency and minimal nuclear waste. We demonstrated the microscopic emergence of collectivity and developed a unified approach to quantum and thermal shape phase transitions in nuclei. In mesoscopic physics and nanoscience, we made important contributions at the interface of nuclear physics and finite-size quantum many-body systems such as quantum dots and ultra-small metallic grains (nanoparticles). We pioneered a statistical theory that describes the universal fluctuations of the transport properties of almost-isolated quantum dots, and whose predictions were confirmed in subsequent experiments. We developed methods to study the effects of pairing correlations in nanoparticles in the regime where the conventional theory of superconductivity breaks down and identified signatures of the competition between pairing and spin exchange correlations. In cold atom physics, we made important breakthroughs in our understanding of the thermodynamics of the unitary Fermi gas, which describes the limit of strongest short-range interactions in a fermionic many-body system, and whose physics is relevant to other strongly correlated systems such as nuclei, quark matter and neutron stars. In particular, we developed AFMC methods that enabled the accurate calculation of pairing correlations across the superfluid phase transition in the unitary Fermi gas. Our results for a fundamental property known as the contact were in excellent agreement with the most recent precision ultracold atomic gas experiments.},
doi = {10.2172/1605421},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2020},
month = {3}
}