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

^{†} For
a discussion of the methods used and earlier results, see G.M. Hale and D.C. Dodder, Proc.
Int. Conf. on Nuclear Cross Sections for Technology, Knoxville, TN 1979, Eds. J.L. Fowler,
C.H. Johnson and C.D. Bowman (NBS Special Publication 594) p.650.).

These analyses
include data from all possible reactions for the two-body channels d + t (or d +
^{3}He in the case of ^{5}Li) and N + ^{4}He at cm energies
corresponding to E_{x} < 23 MeV. In addition, N + ^{4}He* 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
^{5}He analysis, for example, the χ^{2} per
degree of freedom for the fit is 1.6, and it includes more than 2600 data points. Similar
results were obtained for the ^{5}Li 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 ^{5}He and in
5.3 (in PDF or PS) for ^{5}Li. Positions and widths
for the lowest two A = 5 states have already been given in (1997CS01), and for the
second excited state of ^{5}He (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.