Neutron Transfer Reactions for Deformed Nuclei Using Sturmian Basis States

ORAL

Abstract

Transfer reactions leading to nuclear excitations of several MeV are of interest to indirect measurements of cross sections. The spin-parity distribution P(J$\pi $,E) of $^{\mathrm{156}}$Gd excited states above the neutron separation energy Sn $=$ 8.536 MeV expected to be populated via a 1-step neutron pickup reaction $^{\mathrm{157}}$Gd($^{\mathrm{3}}$He,$^{\mathrm{4}}$He)$^{\mathrm{156}}$Gd are studied. Excited states in $^{\mathrm{156}}$Gd are viewed as rotational excitations built on intrinsic states consisting of a neutron hole in the $^{\mathrm{157}}$Gd core; that is, a neutron removal from a deformed Woods-Saxon type single-particle states. The reaction cross section to each excited state is calculated as coherent contribution using a standard reaction code based on spherical basis states. The spectroscopic factor associated with each state is the expansion coefficient of the deformed neutron state in a spherical Sturmian basis along with the spherical form factors. The total cross section is generated using Lorentzian smearing distribution function. Our calculations show that, within the assumptions and computational modeling, the reaction has a smooth formation probability P(J$\pi $,E) within the energy range relevant to the desired reaction. The formation probability P(J$\pi $,E) resembles a Gaussian distribution with centroids and widths that differ for positive and negative parity states.

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Authors

  • Vesselin G. Gueorguiev

    Ronin Institute, Montclair, NJ 07043, USA

  • Michael Schmitt

    Old Dominion University, Thomas Jefferson National Accelerator Facility, KAIST , CAPP/IBS, CAPP/IBS, New Mexico State University, Goddard Space Flight Center, Caltech, Cornell University, Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy Northwestern University, Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Perimeter Institute for Theoretical Physics, Max Planck Institute for Gravitational Physics (Albert Einstein Institute), University of Ottawa, Northwestern University, Universitat Autonoma de Barcelona, Chinesse Academy of Sciences, Zentrum fur Astronomie und Astrophysik, TechSource Inc., Purdue Univ, KAIST, CAPP/IBS, CAPP, IBS, IBS/CAPP, KAIST, KAIST, IBS/CAPP, Cal Poly, Ohio State University, Kenyon College, Embry-Riddle (Prescott), Univ of California - Berkeley, Lawrence Berkeley Natl Lab, Univ of Toronto, Montana State University, NASA Marshall Space Flight Center, Heidelberger Institut für Theoretische Studien, Georgia Institute of Technology, Canadian Institute for Theoretical Astrophysics, Universit\'a di Parma, Istituto Nazionale di Fisica Nucleare, University of Mount Union, Univ of Florida - Gainesville, DESY, Vinca Institute, University of Belgrade, Fermilab, Ohio State Univ - Columbus, Indiana Univ - Bloomington, FUZZYICS, Interactive Research Institute for Science and Education, Western Michigan University, West Virginia University, Morgantown, Marshall University, Huntington, Jordan University of Science and Technology, Instituto de Fisica, Universidade de Sao Paulo, Departamento de Ciencias da Natureza, Matematica e Educacao, Universidade Federal de Sao Carlos, UVA, University of Virginia, Brown University, Central Michigan University, U. S. Army Research Laboratory, U. S. Army Research Laboratory/ORAU, The Australian National University, Air Force Institute of Tech - WPAFB, IMPU, Pennsylvania State University, Pennsylvania State Univ, University of North Carolina Chapel Hill, University of California, Berkeley, Princeton University, Michigan State University, North Carolina State University, University of Manitoba, University of Notre Dame, Argonne National Laboratory/University of Chicago, Argonne National Laboratory/University of Manitoba, McGill University, Ohio University, Technical University Dortmund, Czech Technical University, Lancaster University, University of Tennessee, Tennessee Technical University, Max-Planck Institute, Oak Ridge National Lab, South Dakota School of Mines and Technology, Univ of South Carolina, Stanford University, Univ of Wisconsin, Madison, Harvard, Universidade do Estado do Rio de Janeiro, Universitat de les Illes Balears, Long Island University, Brigham Young University, Radboud University, University College Dublin, Louisiana State University, University of Chicago, University of California, Irvine, Soreq NRC, Yavne 81800, Israel, Lawrence Livermore National Laboratory, Argonne National Laboratory, University of Chicago, Argonne National Laboratory, University of Kentucky, Retired, Lawrence Livermore National Laboratory L-414, Livermore, CA 94551, USA, California State University, University of Illinois, Urbana-Champaign, University of Texas at San Antonio, California Institute of Technology, Vanderbilt University and Fisk University, Instituto de Astronomy UNAM, CIERA and NorthWestern University, Hillsdale College, Spitzer Science Center, California Institute of Technology, Jet Propulsion Laboratory, California Institute of Technology, Oberlin College, West Virginia University, National Radio Astronomy Observatory, KU, MIT, LANL, Univ. of Chicago, Leiden University, Albert Einstein Institute, University of Amsterdam, Montana State Univ, CIERA-Northwestern University, MIT, Rochester Inst of Tech, Princeton University, Institute for Advanced Study, None, Department of Physics, Florida State University, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA, Department of Physics, Florida A\&M University, University of Florida, Gainesville, Washington Univ, Los Alamos Natl Lab, Shahid Beheshti University Tehran Iran, NIST, U. Waterloo, Tulane U., NCState, Institute for Quantum Computing, RIKEN, Nagoya Univ, Tulane Univ, North Carolina State Univ, The University of Manitoba, Jefferson Laboratory, Yerevan Physics Institute, North Carolina Central University, Massachusetts Inst of Tech-MIT, Tel Aviv University, International Institute of Physics - UFRN, University of Houston, Rutgers University, University of Sao Paulo, UC Berkeley, UMass Amherst, Indian Institute of Technology, University of Michigan - Ann Arbor, Max Planck Institute, Hannover, INAF Padova, Univ of Pisa, Univ of Trento, Hampton University, University of South Carolina, Ohio Univ, Ohio University, CLAS Collaboration, Lamar University, University of Texas, Rio Grande Valley, Franklin and Marshall College, NASA/GSFC, NASA/GSFC & CRESST, University of Arkansas, University of Utah, Johns Hopkins University, Universidad de la Republica, Uruguay, Department of Physics, Missouri University of Science and Technology, Rolla, MO, 65409, University of Glasgow, GANIL, Dept. of Chemistry and Physics, Washington University, St. Louis MO 63130, Facility for Rare Isotope Beams (FRIB), Michigan State University, East Lansing MI 48824, National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing MI 48824, Lawrence Berkeley Laboratory, Washington University, U Minnesota, NASA/GSFC $\&$ CRESST, Washington University, St. Louis, University of Minnesota, Jet Propulsion Laboratory, NASA Goddard Space Flight Center, Jet Propulsion Laboratory, Pasadena, California Institute of Technology, NASA/Goddard Space Flight Center, Indian Institute of Science Education and Research, Kolkata, Sapienza University Rome, Institut d'Astrophysique de Paris, University of Mississippi, Instituto Superior Tecnico, Lisbon, Albert Einstein Institute Golm, Salisbury U., Ohio State U., Ohio U., Ernst-Moritz-Arndt-Universit\"at, National Superconducting Cyclotron Laboratory, Facility for Rare Isotope Beams, UW-Madison, Eureka Scientific, Cambridge University, Wayne State University, Indian Institute of Technology, Indore, Michigan State Univ, Binghamton Univ, Youngstown State Univ, Institute of Physics, Czech Academy of Sciences, Boyce Research Initiatives and Educational Foundation, Brilliant Sky Observatory, San Diego Mesa College, Indiana Univ, Columbia University, UCLA, Univ. of Kentucky, Air Force Research Lab., Argonne Nat'l Lab., Michigan State Univ., Michigan State University, USA, TRIUMF, Canada, Technische Universitat Munchen, Germany, Institut Laue-Langevin, France, Physikalisch-Technische Bundenstalt, Germany, Julich Centre for Neutron Science, Germany, University of Michigan, USA, Syracuse University, Syracuse, Center for Astrophysics and Planetary Science, Cornell University, Budapest Neutron Centre, Defense Threat Reduction Agency, Osaka University, University of Groningen, University of Tokyo, Kyoto University, Tohoku University, Konan University, Ankara University, University of Michigan, Lawrence Berkeley National Laboratory, Univ of Washington, Aichi University of Education, eXtreme Gravity Institute - Montana State University, The Ohio State University, Universidade Federal Fluminese, Brookhaven National Laboratory, Frankfurt Institute of Advanced Studies, Duke University, Univ of Texas, Arlington, Magdalena Ridge Observatory, New Mexico Tech, Florida State Univ, Univ of Maryland-College Park, Univ of Cincinnati, Radboud University Nijmegen, University of Pisa, ICTS-TIFR, AEI, Hannover, University of Connecticut, Storrs, ANL, Louisiana State University - Baton Rouge, Brigham Young University - Idaho, Fermi National Accelerator Lab, University of Colorado Boulder, Northwestern Univ

  • Michael Schmitt

    Old Dominion University, Thomas Jefferson National Accelerator Facility, KAIST , CAPP/IBS, CAPP/IBS, New Mexico State University, Goddard Space Flight Center, Caltech, Cornell University, Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy Northwestern University, Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Perimeter Institute for Theoretical Physics, Max Planck Institute for Gravitational Physics (Albert Einstein Institute), University of Ottawa, Northwestern University, Universitat Autonoma de Barcelona, Chinesse Academy of Sciences, Zentrum fur Astronomie und Astrophysik, TechSource Inc., Purdue Univ, KAIST, CAPP/IBS, CAPP, IBS, IBS/CAPP, KAIST, KAIST, IBS/CAPP, Cal Poly, Ohio State University, Kenyon College, Embry-Riddle (Prescott), Univ of California - Berkeley, Lawrence Berkeley Natl Lab, Univ of Toronto, Montana State University, NASA Marshall Space Flight Center, Heidelberger Institut für Theoretische Studien, Georgia Institute of Technology, Canadian Institute for Theoretical Astrophysics, Universit\'a di Parma, Istituto Nazionale di Fisica Nucleare, University of Mount Union, Univ of Florida - Gainesville, DESY, Vinca Institute, University of Belgrade, Fermilab, Ohio State Univ - Columbus, Indiana Univ - Bloomington, FUZZYICS, Interactive Research Institute for Science and Education, Western Michigan University, West Virginia University, Morgantown, Marshall University, Huntington, Jordan University of Science and Technology, Instituto de Fisica, Universidade de Sao Paulo, Departamento de Ciencias da Natureza, Matematica e Educacao, Universidade Federal de Sao Carlos, UVA, University of Virginia, Brown University, Central Michigan University, U. S. Army Research Laboratory, U. S. Army Research Laboratory/ORAU, The Australian National University, Air Force Institute of Tech - WPAFB, IMPU, Pennsylvania State University, Pennsylvania State Univ, University of North Carolina Chapel Hill, University of California, Berkeley, Princeton University, Michigan State University, North Carolina State University, University of Manitoba, University of Notre Dame, Argonne National Laboratory/University of Chicago, Argonne National Laboratory/University of Manitoba, McGill University, Ohio University, Technical University Dortmund, Czech Technical University, Lancaster University, University of Tennessee, Tennessee Technical University, Max-Planck Institute, Oak Ridge National Lab, South Dakota School of Mines and Technology, Univ of South Carolina, Stanford University, Univ of Wisconsin, Madison, Harvard, Universidade do Estado do Rio de Janeiro, Universitat de les Illes Balears, Long Island University, Brigham Young University, Radboud University, University College Dublin, Louisiana State University, University of Chicago, University of California, Irvine, Soreq NRC, Yavne 81800, Israel, Lawrence Livermore National Laboratory, Argonne National Laboratory, University of Chicago, Argonne National Laboratory, University of Kentucky, Retired, Lawrence Livermore National Laboratory L-414, Livermore, CA 94551, USA, California State University, University of Illinois, Urbana-Champaign, University of Texas at San Antonio, California Institute of Technology, Vanderbilt University and Fisk University, Instituto de Astronomy UNAM, CIERA and NorthWestern University, Hillsdale College, Spitzer Science Center, California Institute of Technology, Jet Propulsion Laboratory, California Institute of Technology, Oberlin College, West Virginia University, National Radio Astronomy Observatory, KU, MIT, LANL, Univ. of Chicago, Leiden University, Albert Einstein Institute, University of Amsterdam, Montana State Univ, CIERA-Northwestern University, MIT, Rochester Inst of Tech, Princeton University, Institute for Advanced Study, None, Department of Physics, Florida State University, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA, Department of Physics, Florida A\&M University, University of Florida, Gainesville, Washington Univ, Los Alamos Natl Lab, Shahid Beheshti University Tehran Iran, NIST, U. Waterloo, Tulane U., NCState, Institute for Quantum Computing, RIKEN, Nagoya Univ, Tulane Univ, North Carolina State Univ, The University of Manitoba, Jefferson Laboratory, Yerevan Physics Institute, North Carolina Central University, Massachusetts Inst of Tech-MIT, Tel Aviv University, International Institute of Physics - UFRN, University of Houston, Rutgers University, University of Sao Paulo, UC Berkeley, UMass Amherst, Indian Institute of Technology, University of Michigan - Ann Arbor, Max Planck Institute, Hannover, INAF Padova, Univ of Pisa, Univ of Trento, Hampton University, University of South Carolina, Ohio Univ, Ohio University, CLAS Collaboration, Lamar University, University of Texas, Rio Grande Valley, Franklin and Marshall College, NASA/GSFC, NASA/GSFC & CRESST, University of Arkansas, University of Utah, Johns Hopkins University, Universidad de la Republica, Uruguay, Department of Physics, Missouri University of Science and Technology, Rolla, MO, 65409, University of Glasgow, GANIL, Dept. of Chemistry and Physics, Washington University, St. Louis MO 63130, Facility for Rare Isotope Beams (FRIB), Michigan State University, East Lansing MI 48824, National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing MI 48824, Lawrence Berkeley Laboratory, Washington University, U Minnesota, NASA/GSFC $\&$ CRESST, Washington University, St. Louis, University of Minnesota, Jet Propulsion Laboratory, NASA Goddard Space Flight Center, Jet Propulsion Laboratory, Pasadena, California Institute of Technology, NASA/Goddard Space Flight Center, Indian Institute of Science Education and Research, Kolkata, Sapienza University Rome, Institut d'Astrophysique de Paris, University of Mississippi, Instituto Superior Tecnico, Lisbon, Albert Einstein Institute Golm, Salisbury U., Ohio State U., Ohio U., Ernst-Moritz-Arndt-Universit\"at, National Superconducting Cyclotron Laboratory, Facility for Rare Isotope Beams, UW-Madison, Eureka Scientific, Cambridge University, Wayne State University, Indian Institute of Technology, Indore, Michigan State Univ, Binghamton Univ, Youngstown State Univ, Institute of Physics, Czech Academy of Sciences, Boyce Research Initiatives and Educational Foundation, Brilliant Sky Observatory, San Diego Mesa College, Indiana Univ, Columbia University, UCLA, Univ. of Kentucky, Air Force Research Lab., Argonne Nat'l Lab., Michigan State Univ., Michigan State University, USA, TRIUMF, Canada, Technische Universitat Munchen, Germany, Institut Laue-Langevin, France, Physikalisch-Technische Bundenstalt, Germany, Julich Centre for Neutron Science, Germany, University of Michigan, USA, Syracuse University, Syracuse, Center for Astrophysics and Planetary Science, Cornell University, Budapest Neutron Centre, Defense Threat Reduction Agency, Osaka University, University of Groningen, University of Tokyo, Kyoto University, Tohoku University, Konan University, Ankara University, University of Michigan, Lawrence Berkeley National Laboratory, Univ of Washington, Aichi University of Education, eXtreme Gravity Institute - Montana State University, The Ohio State University, Universidade Federal Fluminese, Brookhaven National Laboratory, Frankfurt Institute of Advanced Studies, Duke University, Univ of Texas, Arlington, Magdalena Ridge Observatory, New Mexico Tech, Florida State Univ, Univ of Maryland-College Park, Univ of Cincinnati, Radboud University Nijmegen, University of Pisa, ICTS-TIFR, AEI, Hannover, University of Connecticut, Storrs, ANL, Louisiana State University - Baton Rouge, Brigham Young University - Idaho, Fermi National Accelerator Lab, University of Colorado Boulder, Northwestern Univ

  • Michael Schmitt

    Old Dominion University, Thomas Jefferson National Accelerator Facility, KAIST , CAPP/IBS, CAPP/IBS, New Mexico State University, Goddard Space Flight Center, Caltech, Cornell University, Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy Northwestern University, Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Perimeter Institute for Theoretical Physics, Max Planck Institute for Gravitational Physics (Albert Einstein Institute), University of Ottawa, Northwestern University, Universitat Autonoma de Barcelona, Chinesse Academy of Sciences, Zentrum fur Astronomie und Astrophysik, TechSource Inc., Purdue Univ, KAIST, CAPP/IBS, CAPP, IBS, IBS/CAPP, KAIST, KAIST, IBS/CAPP, Cal Poly, Ohio State University, Kenyon College, Embry-Riddle (Prescott), Univ of California - Berkeley, Lawrence Berkeley Natl Lab, Univ of Toronto, Montana State University, NASA Marshall Space Flight Center, Heidelberger Institut für Theoretische Studien, Georgia Institute of Technology, Canadian Institute for Theoretical Astrophysics, Universit\'a di Parma, Istituto Nazionale di Fisica Nucleare, University of Mount Union, Univ of Florida - Gainesville, DESY, Vinca Institute, University of Belgrade, Fermilab, Ohio State Univ - Columbus, Indiana Univ - Bloomington, FUZZYICS, Interactive Research Institute for Science and Education, Western Michigan University, West Virginia University, Morgantown, Marshall University, Huntington, Jordan University of Science and Technology, Instituto de Fisica, Universidade de Sao Paulo, Departamento de Ciencias da Natureza, Matematica e Educacao, Universidade Federal de Sao Carlos, UVA, University of Virginia, Brown University, Central Michigan University, U. S. Army Research Laboratory, U. S. Army Research Laboratory/ORAU, The Australian National University, Air Force Institute of Tech - WPAFB, IMPU, Pennsylvania State University, Pennsylvania State Univ, University of North Carolina Chapel Hill, University of California, Berkeley, Princeton University, Michigan State University, North Carolina State University, University of Manitoba, University of Notre Dame, Argonne National Laboratory/University of Chicago, Argonne National Laboratory/University of Manitoba, McGill University, Ohio University, Technical University Dortmund, Czech Technical University, Lancaster University, University of Tennessee, Tennessee Technical University, Max-Planck Institute, Oak Ridge National Lab, South Dakota School of Mines and Technology, Univ of South Carolina, Stanford University, Univ of Wisconsin, Madison, Harvard, Universidade do Estado do Rio de Janeiro, Universitat de les Illes Balears, Long Island University, Brigham Young University, Radboud University, University College Dublin, Louisiana State University, University of Chicago, University of California, Irvine, Soreq NRC, Yavne 81800, Israel, Lawrence Livermore National Laboratory, Argonne National Laboratory, University of Chicago, Argonne National Laboratory, University of Kentucky, Retired, Lawrence Livermore National Laboratory L-414, Livermore, CA 94551, USA, California State University, University of Illinois, Urbana-Champaign, University of Texas at San Antonio, California Institute of Technology, Vanderbilt University and Fisk University, Instituto de Astronomy UNAM, CIERA and NorthWestern University, Hillsdale College, Spitzer Science Center, California Institute of Technology, Jet Propulsion Laboratory, California Institute of Technology, Oberlin College, West Virginia University, National Radio Astronomy Observatory, KU, MIT, LANL, Univ. of Chicago, Leiden University, Albert Einstein Institute, University of Amsterdam, Montana State Univ, CIERA-Northwestern University, MIT, Rochester Inst of Tech, Princeton University, Institute for Advanced Study, None, Department of Physics, Florida State University, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA, Department of Physics, Florida A\&M University, University of Florida, Gainesville, Washington Univ, Los Alamos Natl Lab, Shahid Beheshti University Tehran Iran, NIST, U. Waterloo, Tulane U., NCState, Institute for Quantum Computing, RIKEN, Nagoya Univ, Tulane Univ, North Carolina State Univ, The University of Manitoba, Jefferson Laboratory, Yerevan Physics Institute, North Carolina Central University, Massachusetts Inst of Tech-MIT, Tel Aviv University, International Institute of Physics - UFRN, University of Houston, Rutgers University, University of Sao Paulo, UC Berkeley, UMass Amherst, Indian Institute of Technology, University of Michigan - Ann Arbor, Max Planck Institute, Hannover, INAF Padova, Univ of Pisa, Univ of Trento, Hampton University, University of South Carolina, Ohio Univ, Ohio University, CLAS Collaboration, Lamar University, University of Texas, Rio Grande Valley, Franklin and Marshall College, NASA/GSFC, NASA/GSFC & CRESST, University of Arkansas, University of Utah, Johns Hopkins University, Universidad de la Republica, Uruguay, Department of Physics, Missouri University of Science and Technology, Rolla, MO, 65409, University of Glasgow, GANIL, Dept. of Chemistry and Physics, Washington University, St. Louis MO 63130, Facility for Rare Isotope Beams (FRIB), Michigan State University, East Lansing MI 48824, National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing MI 48824, Lawrence Berkeley Laboratory, Washington University, U Minnesota, NASA/GSFC $\&$ CRESST, Washington University, St. Louis, University of Minnesota, Jet Propulsion Laboratory, NASA Goddard Space Flight Center, Jet Propulsion Laboratory, Pasadena, California Institute of Technology, NASA/Goddard Space Flight Center, Indian Institute of Science Education and Research, Kolkata, Sapienza University Rome, Institut d'Astrophysique de Paris, University of Mississippi, Instituto Superior Tecnico, Lisbon, Albert Einstein Institute Golm, Salisbury U., Ohio State U., Ohio U., Ernst-Moritz-Arndt-Universit\"at, National Superconducting Cyclotron Laboratory, Facility for Rare Isotope Beams, UW-Madison, Eureka Scientific, Cambridge University, Wayne State University, Indian Institute of Technology, Indore, Michigan State Univ, Binghamton Univ, Youngstown State Univ, Institute of Physics, Czech Academy of Sciences, Boyce Research Initiatives and Educational Foundation, Brilliant Sky Observatory, San Diego Mesa College, Indiana Univ, Columbia University, UCLA, Univ. of Kentucky, Air Force Research Lab., Argonne Nat'l Lab., Michigan State Univ., Michigan State University, USA, TRIUMF, Canada, Technische Universitat Munchen, Germany, Institut Laue-Langevin, France, Physikalisch-Technische Bundenstalt, Germany, Julich Centre for Neutron Science, Germany, University of Michigan, USA, Syracuse University, Syracuse, Center for Astrophysics and Planetary Science, Cornell University, Budapest Neutron Centre, Defense Threat Reduction Agency, Osaka University, University of Groningen, University of Tokyo, Kyoto University, Tohoku University, Konan University, Ankara University, University of Michigan, Lawrence Berkeley National Laboratory, Univ of Washington, Aichi University of Education, eXtreme Gravity Institute - Montana State University, The Ohio State University, Universidade Federal Fluminese, Brookhaven National Laboratory, Frankfurt Institute of Advanced Studies, Duke University, Univ of Texas, Arlington, Magdalena Ridge Observatory, New Mexico Tech, Florida State Univ, Univ of Maryland-College Park, Univ of Cincinnati, Radboud University Nijmegen, University of Pisa, ICTS-TIFR, AEI, Hannover, University of Connecticut, Storrs, ANL, Louisiana State University - Baton Rouge, Brigham Young University - Idaho, Fermi National Accelerator Lab, University of Colorado Boulder, Northwestern Univ