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 Mesgun Sebhatu
 Winthrop University
 Rock Hill, SC 29733
 sebhatum@winthrop.edu

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 Historical background :
 The Yukawa Potential and OPEP (1935)
 Phenomenological potentials:
 e.g. The Reid Softcore potential(1968)
 One Boson Exchange Potentials (OBEPs ):
 e.g. Bonn Potential (1970 – Present)
 QCD and/or Effective field theory
inspired potentials ( present)
 Solitary Wave Exchange Potentials (SWEPs):
 e.g. lF^{4} SWEP and SG SWEP (1975?)

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 The field equations for spinzero meson fields used in the derivation of
SWEPs are nonlinear generalization of the well known KleinGordon equation. They are of the
form^{1}:

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 A Pair of Quantized Solitary Wave Solution for the SGE from which
the SG SWEP is derived are :

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 Once the SG solution is expressed as
a tan^{1} series (as shown below).

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 The lowest order NN interaction is represented by the 2^{nd}
order Feynman diagrams shown below. Using Feynman rules an expression
for an NN scattering amplitude is written down. [See e.g. Bjorken and
Drell, Relativistic Quantum Mechanics (1964) ] The only change is that
the Feynman propagator is replaced by the SG propagator.

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 The momentum space SG SWEP obtained from the diagrams shown earlier with
leading non static terms is^{3}:

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 In general, V_{NN}(x) = V_{C}
+ V_{T}+ V_{LS} + V_{LL}

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 L= O, 1, 2, 3, 4, 5,…
 = S, P, D, F, G, H,…
 J = L+S; S= O or 1
 ^{2S+1}L_{J}
 When S =0, 2S+1 =1, Singlet States
 When S=1, 2S+1=3, triplet States
 L= 0, 2, 4, … Even States
 L= 1, 3, 5, … Odd States
 ^{1}S_{0 }, ^{1}D_{2 }, ^{1}G_{4},
…are leading even singlet states
 ^{1}P1 , ^{1}F_{3} , ^{1}H_{5}
, …are leading odd singlet states
 ^{3}S_{1}^{3}D_{1 }is the most interesting example
of a coupled triple state. It has the only bound NN State—the deuteron.

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 SWEPs yield good results with just the leading four terms n=0,1,2,3,
&4

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 For singlet NN states (S=0, T=1)
S_{12}=0, V_{LS}=0 and <(t_{1} ¢
t_{2})(s_{1} ¢ s_{2})>=3

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 CNS @ George Washington U.
 CNS maintains the world data base for experimental NN
etc. Phase shifts
 NN Online from Netherlands
 They maintain NN Nijmegen Potentials, Phase shifts, Deuteron
Properties.
 U of Hamburg from Germany
 They have potentials obtained by inverting experimental phase shifts.
 The have also greatly extended my work on SWEPs they call them One
Solitary Boson Wave Exchange
Potentials (OSBEPs).
 Some general references:
 Derivation of OPEP
 Radial Schrödinger equation and Phase Shifts
 Deuteron Wave Functions and
Properties
 M. Sebhatu and E. W. Gettys, A
Least Squares Method for the Extraction of Phase Shifts, Computers in
Physics 3(5), 65 (1989)

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