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Methods	
  of	
  Extrac/ng	
  Op/cal	
  
Poten/als	
  
Sean	
  Brudney	
  
2015	
  REU	
  
Chart	
  of	
  Nuclides	
  
hCp://www.nndc.bnl.gov/chart/reCenter.jsp?z=74&n=105	
  
FRIB:	
  
Facility	
  for	
  Rare	
  Isotope	
  Beams	
  
•  Short-­‐lived	
  nuclei	
  
•  Never	
  before	
  seen	
  	
  
hCp://www.frib.msu.edu/about	
  
Many-­‐Body	
  Systems	
  
Why?	
  
•  Op/cal	
  Poten/als	
  are	
  useful	
  in	
  Many-­‐Body	
  
systems	
  
•  My	
  methods	
  test	
  theory	
  and	
  limita/ons	
  
•  Applicable	
  to	
  study	
  of	
  interac/ons	
  of	
  nuclei	
  
and	
  par/cles	
  in	
  unstable	
  systems	
  
Poten/al	
  Wells	
  
•  Interac/on	
  of	
  nucleus	
  and	
  par/cle	
  looks	
  like	
  a	
  
well	
  
•  Several	
  types	
  of	
  wells	
  
– Square	
  Well	
  
– Wood-­‐Saxon	
  Curve	
  
Quantum	
  System	
  
•  Nuclei	
  studied	
  by	
  crea/ng	
  reac/ons	
  
•  Reac/ons	
  in	
  quantum	
  systems	
  
•  Schrodinger	
  Equa/on	
  essen/al	
  	
  
•  Eigenvalue	
  Problem	
  
Finding	
  a	
  Poten/al	
  
•  Create	
  a	
  truncated	
  basis	
  
•  Calculate	
  a	
  Hamiltonian	
  
•  Expand	
  solu/on	
  of	
  well	
  in	
  created	
  basis	
  
•  Used:	
  Harmonic	
  Oscillator	
  in	
  poten/al	
  well	
  
hCp://hyperphysics.phy-­‐astr.gsu.edu/	
  
Green’s	
  Func/on	
  &	
  Dyson	
  Equa/on	
  
•  Poten/al	
  is	
  extracted	
  from	
  rearranging	
  
the	
  Dyson	
  Equa/on	
  
Dickhoff,	
  Willem	
  Hendrik.,	
  and	
  Dimitri	
  Van.	
  Neck.	
  Many-­‐body	
  Theory	
  Exposed!:	
  Propagator	
  Descrip:on	
  of	
  Quantum	
  Mechanics	
  in	
  Many-­‐body	
  
Systems.	
  Hackensack,	
  NJ:	
  World	
  Scien/fic,	
  2008.	
  
Thank	
  You	
  
•  Filomena	
  Nunes,	
  Jimmy	
  Rotureau,	
  Pawel	
  
Danielewicz,	
  and	
  the	
  Few	
  Body	
  group	
  
•  Michigan	
  State	
  University	
  
•  Na/onal	
  Superconduc/ng	
  Cyclotron	
  
Laboratory	
  
•  Na/onal	
  Science	
  Founda/on	
  

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methods of extracting opitcal potentials presentation

  • 1. Methods  of  Extrac/ng  Op/cal   Poten/als   Sean  Brudney   2015  REU  
  • 2. Chart  of  Nuclides   hCp://www.nndc.bnl.gov/chart/reCenter.jsp?z=74&n=105  
  • 3. FRIB:   Facility  for  Rare  Isotope  Beams   •  Short-­‐lived  nuclei   •  Never  before  seen     hCp://www.frib.msu.edu/about  
  • 5. Why?   •  Op/cal  Poten/als  are  useful  in  Many-­‐Body   systems   •  My  methods  test  theory  and  limita/ons   •  Applicable  to  study  of  interac/ons  of  nuclei   and  par/cles  in  unstable  systems  
  • 6. Poten/al  Wells   •  Interac/on  of  nucleus  and  par/cle  looks  like  a   well   •  Several  types  of  wells   – Square  Well   – Wood-­‐Saxon  Curve  
  • 7. Quantum  System   •  Nuclei  studied  by  crea/ng  reac/ons   •  Reac/ons  in  quantum  systems   •  Schrodinger  Equa/on  essen/al     •  Eigenvalue  Problem  
  • 8. Finding  a  Poten/al   •  Create  a  truncated  basis   •  Calculate  a  Hamiltonian   •  Expand  solu/on  of  well  in  created  basis   •  Used:  Harmonic  Oscillator  in  poten/al  well   hCp://hyperphysics.phy-­‐astr.gsu.edu/  
  • 9. Green’s  Func/on  &  Dyson  Equa/on   •  Poten/al  is  extracted  from  rearranging   the  Dyson  Equa/on   Dickhoff,  Willem  Hendrik.,  and  Dimitri  Van.  Neck.  Many-­‐body  Theory  Exposed!:  Propagator  Descrip:on  of  Quantum  Mechanics  in  Many-­‐body   Systems.  Hackensack,  NJ:  World  Scien/fic,  2008.  
  • 10.
  • 11.
  • 12. Thank  You   •  Filomena  Nunes,  Jimmy  Rotureau,  Pawel   Danielewicz,  and  the  Few  Body  group   •  Michigan  State  University   •  Na/onal  Superconduc/ng  Cyclotron   Laboratory   •  Na/onal  Science  Founda/on