Phaseshifts and elasticities
Phaseshifts
For several models you can obtain numerical values or figures of the phaseshifts. There are two commonly used parametrizations, which are the same for uncoupled waves, but different for coupled waves. These are the the bar-phaseshifts (Stapp, Ypsilantis and Metropolis) [1], and the eigen-phaseshifts (Blatt and Biedenharn)[2]. In NN-OnLine the bar-phaseshifts are used.
If you are requested to enter a phase, it must be given in spectral notation: (2S+1)LJ. You may use lowercase as well as uppercase letters. The table lists the phaseshifts and mixingparameters that are recognized:
1S0 3P0 1P1 3P1 3S1 E1 3D1 1D2 3D2 3P2 E2 3F2 1F3 3F3 3D3 E3 3G3 1G4 3G4 3F4 E4 3H4 1H5 3H5 3G5 E5 3I5 1I6 3I6 3H6 E6 3K6 1K7 3K7 3I7 E7 3L7 1L8 3L8 3K8 E8 3M8
Remember that for proton-proton scattering only the isovector phaseshifts are valid:
1S0 3P0 3P1 1D2 3P2 E2 3F2 3F3 1G4 3F4 E4 3H4 3H5 1I6 3H6 E6 3K6 3K7 1L8 3K8 E8 3M8
Inelasticities
Hoshizaki [8] proposed the first parametrization of the S matrix including inelasticities in 1968. During the eighties several people tried to the extend the bar-phaseshift parametrization to include inelasticities. Arndt [3] parametrized the K-matrix, while Bryan [4] Kermode [7], Klarsfeld [6] and Sprung [5] parametrized the S-matrix. A fierce discussion about the advantages and flaws of the proposed parametrizations followed. The final versions of these parametrizations are in principle equivalent and we have decided to follow Sprung's parametrization in NN-OnLine.
If you are asked for a phaseshift for a model that has inelasticities then, usually, if you give just the name e.g. 1D2 the programs will decide on their own what information to return. If you explicitly want only information on the elastic or the inelastic parts, add a trailing E (elastic, e.g. 1D2E) or I (inelastic, e.g. 1D2I) to the name of the phaseshift.
References:
- H.P. Stapp, T.J. Ypsilantis, and N. Metropolis, Phys. Rev. 105 (1957), 302
- J.M. Blatt and L.C. Biedenharn, Phys. Rev. 86 (1952), 399
- R.A. Arndt and L.D. Roper, Phys. Rev. D 25 (1982), 2011
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Ronald Bryan, Phys. Rev. C 24 (1981), 2657
Ronald Bryan, Phys. Rev. C 30 (1984), 305
Ronald A. Bryan, Phys. Rev. C 39 (1989), 783 -
D.W.L. Sprung and M.W. Kermode, Phys. Rev. C 26 (1982), 1327
D.W.L. Sprung, Phys. Rev. C 32 (1985), 699
D.W.L. Sprung, Phys. Rev. C 35 (1987), 869 -
Z. Melhem and M.W. Kermode, J. Phys. G 9 (1983), L267
M.W. Kermode and S.G. Cooper, J. Phys. G 11 (1985), 821 - S. Klarsfeld, Phys. Lett. 126B (1983), 148
- N. Hoshizaki, Prog. Theor. Phys. Suppl. 42 (1968), 1