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Title: An analytical solution of the time-independent Schrödinger equation for the Woods-Saxon potential for arbitrary angular momentum l states

The Woods-Saxon potential is probably the most studied and widely used short range potential in all of nuclear physics. For the angular momentum l= 0 case, Flügge had devised a method to obtain an analytical expression for the bound state energies of the radial time-independent Schrödinger equation for a neutron confined in a Woods-Saxon potential well. In this study, we extend Flügge's method to solve the radial Schrödinger equation for a neutron within the Woods-Saxon potential and the centrifugal potential for arbitrary values of l. Here, the Pekeris method is used to deal with the centrifugal term. We obtain an analytical expression for the bound states, valid for arbitrary angular momentum, and show that our expression reduces to that of Flügge, which applies to the l= 0 case. The numerical computations performed also show very good agreement with our analytical expression.
Authors:
 [1] ;  [2] ;  [3]
  1. Open University Malaysia, Lot G (7-06-01), Blok 7 Presint Alami, Pusat Perniagaan Worldwide 2, Jalan Tinju, Seksyen 13, 40100 Shah Alam, Selangor (Malaysia)
  2. International University of Malaya-Wales, Block A, City Campus, Jalan Tun Ismail, 50480 Kuala Lumpur (Malaysia)
  3. (Malaysia)
Publication Date:
OSTI Identifier:
22391560
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1657; Journal Issue: 1; Conference: PERFIK 2014: National Physics Conference 2014, Kuala Lumpur (Malaysia), 18-19 Nov 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; ANGULAR MOMENTUM; BOUND STATE; CALCULATION METHODS; INTERACTION RANGE; NEUTRONS; NUMERICAL SOLUTION; SCHROEDINGER EQUATION; WOODS-SAXON POTENTIAL