FermiGasy. W. Udo Schröder, 2005 Pairing Energy 2 1 Nucleon Pair Outside Closed Shells 2 s/1 d 1 p 1 s 2 6 2/10 18 O neutrons 18 O: 2 neutrons outside.

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Presentation transcript:

FermiGasy

W. Udo Schröder, 2005 Pairing Energy 2 1 Nucleon Pair Outside Closed Shells 2 s/1 d 1 p 1 s 2 6 2/10 18 O neutrons 18 O: 2 neutrons outside closed shells Residual (Pairing) interaction mixes SM states  6 pair states in sd shell = 12 s.p. states Equal amplitudes for |j,± m> Shell Model states

W. Udo Schröder, 2005 Pairing Energy 3 Schrödinger Equation 3 pair states  i, i =1,2,3 ortho- normalized Search for eigen states  i of H project on

W. Udo Schröder, 2005 Pairing Energy 4 Matrix Eigen Value Equation Approximation: Eigen value equ. solve for (Actually a difficult problem!) Solution 1: symmetric c 11 = c 21 = c 31

W. Udo Schröder, 2005 Pairing Energy 5 Pairing Energies and Components Solutions i= 2, 3: Symmetric solution i=1: c 11 = c 21 = c 31 i=2 i=3 i=3 similar

W. Udo Schröder, 2005 Pairing Energy 6 18 O Pairing Eigen Functions and Energies 2:=3G 18 O g.s. = 16 O g.s. x 1 n-pair 12 s.p. sd particle states ( ) possible 2N pairs V R  populates 3 I =0 states

W. Udo Schröder, 2005 Pairing Energy 7 Occupation Numbers Heavy nuclei: many SM states close in energy, contribute to pairing  high dimensionality of wave function  occupation numbers for s.p. states  18 O:  1 :2 neutrons in 6 states for fraction c 11 2 of time.  FF