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A = 5 resonance parameters:

The resonance parameters tabulated here are based on comprehensive multichannel R-matrix analyses of reactions in the ⁵He and ⁵Li systems (Hale, Dodder and Witte, private communication^†

These analyses include data from all possible reactions for the two-body channels d + t (or d + ³He in the case of ⁵Li) and N + ⁴He at cm energies corresponding to E_x < 23 MeV. In addition, N + ⁴He* channels are included to approximate the effects of three-body breakup processes. The fits obtained to the measurements for the two-body reactions are generally quite good. In the ⁵He analysis, for example, the χ² per degree of freedom for the fit is 1.6, and it includes more than 2600 data points. Similar results were obtained for the ⁵Li analysis, which includes even more data.

The level information has been obtained from the A = 5 R-matrix parameters using two different prescriptions, given in separate tables. The recommended prescription, called the "extended" R-matrix method (1987HA20, 1997CS01), comes from the complex poles and residues of the S matrix. This prescription has been found to give resonance parameters that are free, both formally and practically, of all dependence on the "geometric" parameters of R-matrix theory, such as boundary conditions and channel radii. The parameters are listed in 5.1 (in PDF or PS) for ⁵He and in 5.3 (in PDF or PS) for ⁵Li. Positions and widths for the lowest two A = 5 states have already been given in (1997CS01), and for the second excited state of ⁵He (3/2⁺) in (1987HA20), using this prescription.

For comparison, we also list in 5.2 (in PDF or PS) and 5.4 (in PDF or PS) the more standard R-matrix resonance parameters that were used in the A = 4 level compilation (1992TI02), as defined in the Appendix there. This multi-level generalization of the single-level resonance prescription given by Lane and Thomas (1958LA73) is based on the real poles and residues of the "resonant" reactance matrix (K_R), which, because it is not truly an asymptotic quantity as is the S matrix, retains dependence on the channel radii, and on the specification of the "non-resonant" phase shift. Our prescription is based on the usual assumption that the non-resonant phase shifts are the "hard-sphere" phases associated with the complete reflection of ingoing waves at the nuclear surface.

The single-level prescription of Lane and Thomas was used recently by Barker (1997BA72) to obtain an interpretation of the behavior of the cross sections near the J^π = 3/2⁺ resonance in A = 5 equivalent to that of the complex S-matrix pole and shadow pole description of (1987HA20).

A comparison of the tables for a given system shows that the resonance parameters from the two prescriptions can be quite different, however. The widths for the resonant reactance-matrix pole prescription tend to be much larger than those of the S-matrix pole prescription, and they do not usually correspond with the experimental values. For that reason, reaction numbers were not given in the 5.2 (in PDF or PS) and 5.4 (in PDF or PS) listing the K_R-based parameters, as defined in (1992TI02).

In some cases, resonances seen using the recommended method are not present in the usual prescription, even though the input R-matrix parameters are identically the same. These differences, which are most evident for light systems having broad resonances, stem from the fact that the resonant K-matrix prescription is based on the apparent positions of the S-matrix poles as seen from the real axis of the physical sheet. For broad resonances, as is known from the complex-eigenvalue expansion of the level matrix (1958LA73), the apparent pole positions can change rapidly (or even disappear entirely) as the vantage point is varied, causing significant differences with the actual positions (and residues) of the poles in the complex energy plane.