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)L_J. 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:

1. H.P. Stapp, T.J. Ypsilantis, and N. Metropolis, Phys. Rev. 105 (1957), 302
2. J.M. Blatt and L.C. Biedenharn, Phys. Rev. 86 (1952), 399
3. R.A. Arndt and L.D. Roper, Phys. Rev. D 25 (1982), 2011
4. 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
5. 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
6. 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
7. S. Klarsfeld, Phys. Lett. 126B (1983), 148
8. N. Hoshizaki, Prog. Theor. Phys. Suppl. 42 (1968), 1