Single-particle Energies of Superheavy Nuclei and Tests of Theory

T.L. Khoo; Paul Langacker; Paul Langacker; Paul Langacker

Single-particle Energies of Superheavy Nuclei and Tests of Theory

ORAL

Abstract

Superheavy nuclei (SHN) exist due to the stabilization from the shell-correction energy, which arises from gaps in the single-particle energies. Hence, knowledge of the single-particle energies is critical for understanding SHN. We have deduced the single-particle energies, which reproduce experimental 1-quasiparticle (qp) energies in odd-A Bk, Es, Cm and Cf nuclei, with corrections for the recoil term. Distinct shell gaps are evident at Z=100 and N=152. Comparisons with models reveal serious shortcomings in the single-particle energies of density functional theories, highlighting the need for improved effective interactions and questioning their predictions of magic gaps for SHN. In contrast, the single-particle spectrum from the ``universal'' Woods-Saxon potential gives fair agreement, provided deformation parameters (up to at least $\beta _{6})$ are chosen that minimize the total binding energy. Omission of $\beta _{6}$, for example, leads to diminution of the shell gaps and unreliable 1- and 2-qp energies. When properly defined, the Woods-Saxon potential applies for deformed shell-stabilized nuclei from Pu to Lr.

Nov. 4, 2010, 6:48 PM – Nov. 4, 2010, 7:00 PM

Authors

T.L. Khoo

Argonne National Laboratory
Paul Langacker

Drake University, University of Idaho, University of Kentucky, TUNL, TUD, Yale University/ TUD, Yale University, U. of Tennessee, Krakow, ANL, U. of Maryland, L.M.U. Munich, T.U. Munich, TRIUMF, Queens University, University of Guelph, Ursinus College, NSCL/MSU, The University of Tokyo, The Ohio State University, NSCL, Michigan State University, Univ. of Notre Dame, Govt. College, Kota, India, IUAC, India, Andhra Univ., India, G. Ghasidas Univ., India, UDC KC, India, Mississippi State Univ., JAEA, UNAM, UTK, ORNL, FSU, NSCL, University of Surrey, Tennessee Tech, University of Tennessee, Rutgers University, LSU, ORAU, Tennessee Tech., California Institute of Technology, King Abdul Aziz University, University of Colorado, U. Maryland, Tulane U., UNC-Wilmington, MIT, NIST, Argonne National Laboratory, Los Alamos National Laboratory, U. Mass. Lowell, U. Strasbourg, WNSL, Yale, CSNSM \& U.Jyvaskyla, Argonne \& U. Maryland, Argonne, Argonne \& CSNSM, Technische Universitat Munchen, UMass Lowell., Lawrence Livermore National Laboratory, LLNL, UNC/TUNL, Duke U/TUNL, NCSU/TUNL, NCA\&T, Duke/TUNL, UC Berkeley, JMU, UIUC, GWU, U. Sask, NGCSU, STYS, University of Warsaw, ORAU - ORNL, Col. Sch. Mines, U. Tenn., Ohio U., Rutgers, LBNL, U. Rochester, University of Edinburgh, INFN-Catania, Texas A\&M University, University of York, INL, LANL, UNC/CH, SJSU, Passport Systems, PNNL, GeorgiaTech, UC Berkeley and LBNL, Physics Division, Oak Ridge National Laboratory, A.W. Wright Nuclear Structure Laboratory, Yale University, Bonn University, Lawrence Berkeley National Laboratory, Western Michigan University, Michigan State University, WNSL Yale University, University Bonn, Department of Chemistry, WUSTL, Department of Physics and Astronomy, UT, Department of Physics and Astronomy, RU, Department of Chemistry, IU, Department of Physics, WMU, Department of Physics, University of Notre Dame, School of Earth and Space Exploration, Arizona State University, Los Alamos National Laboratory, Los Alamos, University of Notre Dame, University of Bochum, Khalifa University of Science, Technology \& Research, NSCL, JINA, Department of Physics and Astronomy, Michigan State University, Physics Department, Kalamazoo College, University of Minnesota, Twin Cities, Department of Physics and Astronomy, Ohio University, Department of Physics, University of California, San Diego, Oak Ridge National Laboratory, Tennessee Technological University, Louisiana State University, Rush University Medical Center, Colorado School of Mines, The University of South Dakota, Purdue University, University of South Dakota, Stanford University, University of Alabama, Variable Energy Cyclotron Centre, National Superconducting Cyclotron Laboratory, TN Tech. Univ., Rutgers Univ., Uppsala University, Kocaeli University, Ohio University, Yale, Daresbury, Oak Ridge, Cape Town, Georgia Tech, Guelph, Richmond, Florida State, Strasbourg, USNA, Tennessee, STARS-LIBERACE Collaboration, University of Richmond, Charles University, Prague, NC State University, Univ. of Richmond, Uni Koeln, TU Darmstadt, Radiation Monitoring Devices, University of Massachusetts, ESA/ESTEC, UMass, DFELL, Duke U/ TUNL, University of Maryland, Houghton College, NY, Massachusetts Institute of Technology, WNSL, Yale University, USA, IKP Cologne, Germany, IKP Cologne, Germany and WNSL, Yale University, USA, US Naval Academy, Univ. Mass. Lowell, Univ. of Sofia, U.S. Naval Academy, University of Cologne, Yale, Cologne, Yale , Cologne, Yale, Surrey, ANL., JAEA, Japan, Univ. of Maryland, Univ. of Massachusetts (Lowell), United States Naval Academy, Univ. of Tennessee, Univ. of Manchester, UK, Mississippi State University, Mississippi State, Massachusetts-Lowell, Argonne Nat.\ Lab, Notre Dame, Wright Nuclear Structure Laboratory, Yale Univ., Daresbury, UK, Institut Laue Langevin, Grenoble, France, Yale Univ., University of Notre Dame and Grinnell College, GANIL, France, Bruyeres-le-Chatel, France, Univ. Liverpool, INFN Napoli, Univ. Tennessee, Univ. Padua, INFN, Vanderbilt Univ., Univ. Milan, INFN, Univ. Tennessee, ORNL, UNIRIB, ORNL, UMaryland, UMaryland/ANL, GANIL, CENBG/CNRS/IN2P3, Mainz/ORAU, Tenn. Tech. Univ., Oak Ridge Associated Universities, WNSL, Yale University, New Haven CT, Department of Physics, University of Richmond, Richmond VA, Departamento de Fisica Teorica, Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Fermi National Accelerator Laboratory, Research Center Dresden-Rossendorf, Germany, NCSU and TUNL, Duke University and TUNL, Marietta College/NSCL, Westmont College, Wabash College, Rhodes College, Ohio Wesleyan University, Indiana University South Bend, Concordia College, Central Michigan University, Florida State University, Oak Ridge National Laboratories, Arizona State University, Cyclotron Institute, TAMU, University of Virginia, College of William \& Mary, Duke University, Morgan State University, Indiana University, Univ. of Birmingham, UK, Weizmann Institute of Science, Israel, Univ. of Wisconsin - La Crosse, McGill, Livermore, Northwestern, Manitoba, Hope College, Augustana College, University of Manitoba, University of WInnipeg, U. of Giessen, Germany, Joint Institute for Nuclear Research, Vanderbilt Univ. and Lawrence Berkeley Natl. Lab., Vanderbilt Univ. and Tsinghua Univ., Lawrence Berkeley Natl. Lab., Berkeley, Western Michigan, Manchester, Tsinghua University, Vanderbilt University, Universit\"at zu K\"oln, Simon Fraser University, Millsaps College, University of Arizona, IKS Leuven, University of Liverpool, University of Oslo, UNIRIB, Oak Ridge Associated Universities, UNC Chapel Hill, SJSU, LLNL, TUNL \& NCSU, TUNL \& Duke University, Duke University \& TUNL, NCSU \& TUNL, UNC \& TUNL, Univ. Richmond, WNSL, Yale Univ., WNSL/ University of Surrey, UK, WNSL / University of Caen Basse Normandie, France, WNSL / IKP Cologne, Germany, WNSL, RCNP, Osaka U, CRC, Tohuku U, TIT, Tokyo, ND, U. of Tokyo, CRC, Tohuku U,, KVI, U. of Groningen, Konan U, Notre Dame(ND), U. of Notre Dame, Lawrence Berkeley National Laboratory, Univ. of California, Berkeley, 94720, Dept. of Nuclear Engineering, and LBNL, JINR, U. Notre Dame, UNC and TUNL, Duke U. and TUNL, University of Kentucky, Department of Physics and Astronomy, Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506-0055, University of Illinois, University of north carolina, Fermilab, LLE, National Institute of Standards and Technology, The University of Tennessee - Knoxville / Oak Ridge National Laboratory, Brookhaven National Laboratory, INFN, Naples, Penn State University, University of Pennsylvania
Paul Langacker

Drake University, University of Idaho, University of Kentucky, TUNL, TUD, Yale University/ TUD, Yale University, U. of Tennessee, Krakow, ANL, U. of Maryland, L.M.U. Munich, T.U. Munich, TRIUMF, Queens University, University of Guelph, Ursinus College, NSCL/MSU, The University of Tokyo, The Ohio State University, NSCL, Michigan State University, Univ. of Notre Dame, Govt. College, Kota, India, IUAC, India, Andhra Univ., India, G. Ghasidas Univ., India, UDC KC, India, Mississippi State Univ., JAEA, UNAM, UTK, ORNL, FSU, NSCL, University of Surrey, Tennessee Tech, University of Tennessee, Rutgers University, LSU, ORAU, Tennessee Tech., California Institute of Technology, King Abdul Aziz University, University of Colorado, U. Maryland, Tulane U., UNC-Wilmington, MIT, NIST, Argonne National Laboratory, Los Alamos National Laboratory, U. Mass. Lowell, U. Strasbourg, WNSL, Yale, CSNSM \& U.Jyvaskyla, Argonne \& U. Maryland, Argonne, Argonne \& CSNSM, Technische Universitat Munchen, UMass Lowell., Lawrence Livermore National Laboratory, LLNL, UNC/TUNL, Duke U/TUNL, NCSU/TUNL, NCA\&T, Duke/TUNL, UC Berkeley, JMU, UIUC, GWU, U. Sask, NGCSU, STYS, University of Warsaw, ORAU - ORNL, Col. Sch. Mines, U. Tenn., Ohio U., Rutgers, LBNL, U. Rochester, University of Edinburgh, INFN-Catania, Texas A\&M University, University of York, INL, LANL, UNC/CH, SJSU, Passport Systems, PNNL, GeorgiaTech, UC Berkeley and LBNL, Physics Division, Oak Ridge National Laboratory, A.W. Wright Nuclear Structure Laboratory, Yale University, Bonn University, Lawrence Berkeley National Laboratory, Western Michigan University, Michigan State University, WNSL Yale University, University Bonn, Department of Chemistry, WUSTL, Department of Physics and Astronomy, UT, Department of Physics and Astronomy, RU, Department of Chemistry, IU, Department of Physics, WMU, Department of Physics, University of Notre Dame, School of Earth and Space Exploration, Arizona State University, Los Alamos National Laboratory, Los Alamos, University of Notre Dame, University of Bochum, Khalifa University of Science, Technology \& Research, NSCL, JINA, Department of Physics and Astronomy, Michigan State University, Physics Department, Kalamazoo College, University of Minnesota, Twin Cities, Department of Physics and Astronomy, Ohio University, Department of Physics, University of California, San Diego, Oak Ridge National Laboratory, Tennessee Technological University, Louisiana State University, Rush University Medical Center, Colorado School of Mines, The University of South Dakota, Purdue University, University of South Dakota, Stanford University, University of Alabama, Variable Energy Cyclotron Centre, National Superconducting Cyclotron Laboratory, TN Tech. Univ., Rutgers Univ., Uppsala University, Kocaeli University, Ohio University, Yale, Daresbury, Oak Ridge, Cape Town, Georgia Tech, Guelph, Richmond, Florida State, Strasbourg, USNA, Tennessee, STARS-LIBERACE Collaboration, University of Richmond, Charles University, Prague, NC State University, Univ. of Richmond, Uni Koeln, TU Darmstadt, Radiation Monitoring Devices, University of Massachusetts, ESA/ESTEC, UMass, DFELL, Duke U/ TUNL, University of Maryland, Houghton College, NY, Massachusetts Institute of Technology, WNSL, Yale University, USA, IKP Cologne, Germany, IKP Cologne, Germany and WNSL, Yale University, USA, US Naval Academy, Univ. Mass. Lowell, Univ. of Sofia, U.S. Naval Academy, University of Cologne, Yale, Cologne, Yale , Cologne, Yale, Surrey, ANL., JAEA, Japan, Univ. of Maryland, Univ. of Massachusetts (Lowell), United States Naval Academy, Univ. of Tennessee, Univ. of Manchester, UK, Mississippi State University, Mississippi State, Massachusetts-Lowell, Argonne Nat.\ Lab, Notre Dame, Wright Nuclear Structure Laboratory, Yale Univ., Daresbury, UK, Institut Laue Langevin, Grenoble, France, Yale Univ., University of Notre Dame and Grinnell College, GANIL, France, Bruyeres-le-Chatel, France, Univ. Liverpool, INFN Napoli, Univ. Tennessee, Univ. Padua, INFN, Vanderbilt Univ., Univ. Milan, INFN, Univ. Tennessee, ORNL, UNIRIB, ORNL, UMaryland, UMaryland/ANL, GANIL, CENBG/CNRS/IN2P3, Mainz/ORAU, Tenn. Tech. Univ., Oak Ridge Associated Universities, WNSL, Yale University, New Haven CT, Department of Physics, University of Richmond, Richmond VA, Departamento de Fisica Teorica, Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Fermi National Accelerator Laboratory, Research Center Dresden-Rossendorf, Germany, NCSU and TUNL, Duke University and TUNL, Marietta College/NSCL, Westmont College, Wabash College, Rhodes College, Ohio Wesleyan University, Indiana University South Bend, Concordia College, Central Michigan University, Florida State University, Oak Ridge National Laboratories, Arizona State University, Cyclotron Institute, TAMU, University of Virginia, College of William \& Mary, Duke University, Morgan State University, Indiana University, Univ. of Birmingham, UK, Weizmann Institute of Science, Israel, Univ. of Wisconsin - La Crosse, McGill, Livermore, Northwestern, Manitoba, Hope College, Augustana College, University of Manitoba, University of WInnipeg, U. of Giessen, Germany, Joint Institute for Nuclear Research, Vanderbilt Univ. and Lawrence Berkeley Natl. Lab., Vanderbilt Univ. and Tsinghua Univ., Lawrence Berkeley Natl. Lab., Berkeley, Western Michigan, Manchester, Tsinghua University, Vanderbilt University, Universit\"at zu K\"oln, Simon Fraser University, Millsaps College, University of Arizona, IKS Leuven, University of Liverpool, University of Oslo, UNIRIB, Oak Ridge Associated Universities, UNC Chapel Hill, SJSU, LLNL, TUNL \& NCSU, TUNL \& Duke University, Duke University \& TUNL, NCSU \& TUNL, UNC \& TUNL, Univ. Richmond, WNSL, Yale Univ., WNSL/ University of Surrey, UK, WNSL / University of Caen Basse Normandie, France, WNSL / IKP Cologne, Germany, WNSL, RCNP, Osaka U, CRC, Tohuku U, TIT, Tokyo, ND, U. of Tokyo, CRC, Tohuku U,, KVI, U. of Groningen, Konan U, Notre Dame(ND), U. of Notre Dame, Lawrence Berkeley National Laboratory, Univ. of California, Berkeley, 94720, Dept. of Nuclear Engineering, and LBNL, JINR, U. Notre Dame, UNC and TUNL, Duke U. and TUNL, University of Kentucky, Department of Physics and Astronomy, Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506-0055, University of Illinois, University of north carolina, Fermilab, LLE, National Institute of Standards and Technology, The University of Tennessee - Knoxville / Oak Ridge National Laboratory, Brookhaven National Laboratory, INFN, Naples, Penn State University, University of Pennsylvania
Paul Langacker

Drake University, University of Idaho, University of Kentucky, TUNL, TUD, Yale University/ TUD, Yale University, U. of Tennessee, Krakow, ANL, U. of Maryland, L.M.U. Munich, T.U. Munich, TRIUMF, Queens University, University of Guelph, Ursinus College, NSCL/MSU, The University of Tokyo, The Ohio State University, NSCL, Michigan State University, Univ. of Notre Dame, Govt. College, Kota, India, IUAC, India, Andhra Univ., India, G. Ghasidas Univ., India, UDC KC, India, Mississippi State Univ., JAEA, UNAM, UTK, ORNL, FSU, NSCL, University of Surrey, Tennessee Tech, University of Tennessee, Rutgers University, LSU, ORAU, Tennessee Tech., California Institute of Technology, King Abdul Aziz University, University of Colorado, U. Maryland, Tulane U., UNC-Wilmington, MIT, NIST, Argonne National Laboratory, Los Alamos National Laboratory, U. Mass. Lowell, U. Strasbourg, WNSL, Yale, CSNSM \& U.Jyvaskyla, Argonne \& U. Maryland, Argonne, Argonne \& CSNSM, Technische Universitat Munchen, UMass Lowell., Lawrence Livermore National Laboratory, LLNL, UNC/TUNL, Duke U/TUNL, NCSU/TUNL, NCA\&T, Duke/TUNL, UC Berkeley, JMU, UIUC, GWU, U. Sask, NGCSU, STYS, University of Warsaw, ORAU - ORNL, Col. Sch. Mines, U. Tenn., Ohio U., Rutgers, LBNL, U. Rochester, University of Edinburgh, INFN-Catania, Texas A\&M University, University of York, INL, LANL, UNC/CH, SJSU, Passport Systems, PNNL, GeorgiaTech, UC Berkeley and LBNL, Physics Division, Oak Ridge National Laboratory, A.W. Wright Nuclear Structure Laboratory, Yale University, Bonn University, Lawrence Berkeley National Laboratory, Western Michigan University, Michigan State University, WNSL Yale University, University Bonn, Department of Chemistry, WUSTL, Department of Physics and Astronomy, UT, Department of Physics and Astronomy, RU, Department of Chemistry, IU, Department of Physics, WMU, Department of Physics, University of Notre Dame, School of Earth and Space Exploration, Arizona State University, Los Alamos National Laboratory, Los Alamos, University of Notre Dame, University of Bochum, Khalifa University of Science, Technology \& Research, NSCL, JINA, Department of Physics and Astronomy, Michigan State University, Physics Department, Kalamazoo College, University of Minnesota, Twin Cities, Department of Physics and Astronomy, Ohio University, Department of Physics, University of California, San Diego, Oak Ridge National Laboratory, Tennessee Technological University, Louisiana State University, Rush University Medical Center, Colorado School of Mines, The University of South Dakota, Purdue University, University of South Dakota, Stanford University, University of Alabama, Variable Energy Cyclotron Centre, National Superconducting Cyclotron Laboratory, TN Tech. Univ., Rutgers Univ., Uppsala University, Kocaeli University, Ohio University, Yale, Daresbury, Oak Ridge, Cape Town, Georgia Tech, Guelph, Richmond, Florida State, Strasbourg, USNA, Tennessee, STARS-LIBERACE Collaboration, University of Richmond, Charles University, Prague, NC State University, Univ. of Richmond, Uni Koeln, TU Darmstadt, Radiation Monitoring Devices, University of Massachusetts, ESA/ESTEC, UMass, DFELL, Duke U/ TUNL, University of Maryland, Houghton College, NY, Massachusetts Institute of Technology, WNSL, Yale University, USA, IKP Cologne, Germany, IKP Cologne, Germany and WNSL, Yale University, USA, US Naval Academy, Univ. Mass. Lowell, Univ. of Sofia, U.S. Naval Academy, University of Cologne, Yale, Cologne, Yale , Cologne, Yale, Surrey, ANL., JAEA, Japan, Univ. of Maryland, Univ. of Massachusetts (Lowell), United States Naval Academy, Univ. of Tennessee, Univ. of Manchester, UK, Mississippi State University, Mississippi State, Massachusetts-Lowell, Argonne Nat.\ Lab, Notre Dame, Wright Nuclear Structure Laboratory, Yale Univ., Daresbury, UK, Institut Laue Langevin, Grenoble, France, Yale Univ., University of Notre Dame and Grinnell College, GANIL, France, Bruyeres-le-Chatel, France, Univ. Liverpool, INFN Napoli, Univ. Tennessee, Univ. Padua, INFN, Vanderbilt Univ., Univ. Milan, INFN, Univ. Tennessee, ORNL, UNIRIB, ORNL, UMaryland, UMaryland/ANL, GANIL, CENBG/CNRS/IN2P3, Mainz/ORAU, Tenn. Tech. Univ., Oak Ridge Associated Universities, WNSL, Yale University, New Haven CT, Department of Physics, University of Richmond, Richmond VA, Departamento de Fisica Teorica, Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Fermi National Accelerator Laboratory, Research Center Dresden-Rossendorf, Germany, NCSU and TUNL, Duke University and TUNL, Marietta College/NSCL, Westmont College, Wabash College, Rhodes College, Ohio Wesleyan University, Indiana University South Bend, Concordia College, Central Michigan University, Florida State University, Oak Ridge National Laboratories, Arizona State University, Cyclotron Institute, TAMU, University of Virginia, College of William \& Mary, Duke University, Morgan State University, Indiana University, Univ. of Birmingham, UK, Weizmann Institute of Science, Israel, Univ. of Wisconsin - La Crosse, McGill, Livermore, Northwestern, Manitoba, Hope College, Augustana College, University of Manitoba, University of WInnipeg, U. of Giessen, Germany, Joint Institute for Nuclear Research, Vanderbilt Univ. and Lawrence Berkeley Natl. Lab., Vanderbilt Univ. and Tsinghua Univ., Lawrence Berkeley Natl. Lab., Berkeley, Western Michigan, Manchester, Tsinghua University, Vanderbilt University, Universit\"at zu K\"oln, Simon Fraser University, Millsaps College, University of Arizona, IKS Leuven, University of Liverpool, University of Oslo, UNIRIB, Oak Ridge Associated Universities, UNC Chapel Hill, SJSU, LLNL, TUNL \& NCSU, TUNL \& Duke University, Duke University \& TUNL, NCSU \& TUNL, UNC \& TUNL, Univ. Richmond, WNSL, Yale Univ., WNSL/ University of Surrey, UK, WNSL / University of Caen Basse Normandie, France, WNSL / IKP Cologne, Germany, WNSL, RCNP, Osaka U, CRC, Tohuku U, TIT, Tokyo, ND, U. of Tokyo, CRC, Tohuku U,, KVI, U. of Groningen, Konan U, Notre Dame(ND), U. of Notre Dame, Lawrence Berkeley National Laboratory, Univ. of California, Berkeley, 94720, Dept. of Nuclear Engineering, and LBNL, JINR, U. Notre Dame, UNC and TUNL, Duke U. and TUNL, University of Kentucky, Department of Physics and Astronomy, Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506-0055, University of Illinois, University of north carolina, Fermilab, LLE, National Institute of Standards and Technology, The University of Tennessee - Knoxville / Oak Ridge National Laboratory, Brookhaven National Laboratory, INFN, Naples, Penn State University, University of Pennsylvania