In order to extract the response functions from the measured spin observables one must choose a set of nn amplitudes which can be compared to the nuclear responses. As mentioned in the previous section, amplitudes calculated using the Argonne potential [WSA84] were chosen for this data. This means that the calculation of the response functions is, in fact, model dependent, but this is unavoidable. Again, as previously mentioned, several different models were investigated and the results seem, within the levels of uncertainty present, fairly robust.

In order to make the results only as model dependent as necessary the response functions are presented as the ratio of the longitudinal response function to the transverse response function. This technique will cancel out the effects of distortion assuming that the distortion factors are spin independent.

From equations to , in the optimal frame the ratio of the longitudinal to transverse spin observables will be

where , , , and are the optimal frame amplitudes for nn scattering. A calculation of those amplitudes using the Argonne potential indicates that for all values of energy loss in these experiments, at all angles measured the ratios of and are less than 0.1%. Therefore, it is possible to ignore the terms which include the amplitudes and write

or,

Figure shows the ratio for both deuterium and carbon at . Also included is from the Faddeev calculations (short-dashed line) and from free scattering (long-dashed line).

**Figure:** versus energy loss for both deuterium and carbon at
. The short-dashed line are the results from the
Faddeev calculations and the long-dashed line is the free scattering result
from the Argonne potential. The vertical dotted line indicates the energy
loss for free np scattering.

This ratio appears to be more consistent with the free np scattering than with the Faddeev calculations. Also the difference between the deuterium and carbon data seem negligible. Figure shows the ratio . In this case the data seems consistently high compared to both the Faddeev calculations and the free scattering calculations except, perhaps, in the tail region where statistics are poor.

**Figure:** versus energy loss for both deuterium and carbon at
. The short-dashed line are the results from the
Faddeev calculations and the long-dashed line is the free scattering result
from the Argonne potential. The vertical dotted line indicates the energy
loss for free np scattering.

Finally, to get the ratio of the longitudinal response to the transverse response is divided by . This result is shown in figure .

**Figure:** Response function ratio versus energy loss showing
both the deuterium and carbon data at . The
dashed line indicates the results
of Faddeev calculations. Also shown are the results from
[Pan94] at (double line) and
(thick solid line).

Also shown on figure are the results from the Faddeev calculations and some results from [Pan94] obtained by the methods described in section . The results from [Pan94] are not completely representative of the experimental data. The two sets of calculations were done at a constant momentum transfer, fm and 1.5 fm, whereas the data were taken at a constant scattering angle. At this means that momentum transfer will vary over the range of energy loss from fm to fm. In other words the best that can presently be said is that the data should ideally behave in a similar manner as the results from [Pan94]. That being the case, the results shown in figure are striking in that the data does agree better with the [Pan94] results than with the Faddeev calculations. Figure shows the same plot as figure except that the three data points at the high momentum transfer have been grouped into one 30 MeV bin to try to improve the statistics.

**Figure:** Response function ratio versus energy loss showing
both the deuterium and carbon data at . The
dashed line indicates the results
of Faddeev calculations. Also shown are the results from
[Pan94] at (double line) and
(thick solid line). The data at high energy loss
have all been binned together to improve statistics.

The data seem even more consistent with the predictions from [Pan94].

Typically the ratio, , is derived using the transverse spin observable because, as mentioned above, the small values of the and amplitudes decouple the equations for and in terms of and . can still be determined as a function of both and , but usually the results are considerably more uncertain. This is shown in figure .

**Figure:** Response function ratio versus energy loss showing
both the deuterium and carbon data at . The
dashed line indicates the results
of Faddeev calculations. Also shown are the results from
[Pan94] at (double line) and
(thick solid line). The data at high energy loss
have all been binned together to improve statistics.

The huge uncertainties make it impossible to draw any conclusions from the ratio .

For the data the two ratios of spin longitudinal c.m. spin observables to transverse c.m. spin observables are show in figures and .

**Figure:** versus energy loss for both deuterium and carbon at
. The short-dashed line are the results from the
Faddeev calculations and the long-dashed line is the free scattering result
from the Argonne potential. The vertical dotted line indicates the energy
loss for free np scattering.

**Figure:** versus energy loss for both deuterium and carbon at
. The short-dashed line are the results from the
Faddeev calculations and the long-dashed line is the free scattering result
from the Argonne potential. The vertical dotted line indicates the energy
loss for free np scattering.

From figure one can see that has become very small, and this is revealed again in figure (notice the scale). In dividing by such a small number it is difficult to say much about . is a little easier to follow in figure . The deuterium data seems to agree better here with the free scattering calculations than the Faddeev results.

The response ratio, , is shown in figure along with Faddeev calculations for and the same computational results from [Pan94] as were shown with the response function ratios.

**Figure:** Response function ratio versus energy loss showing
both the deuterium and carbon data at . The
dashed line indicates the results
of Faddeev calculations. Also shown are the results from
[Pan94] at (double line) and
(thick solid line).

The deuterium data can be said to be consistent with both the Faddeev calculations and the results from [Pan94] near the quasifree peak where the statistics are good enough to still make a statement. The momentum transfer in this region will be about fm. Interestingly, the response ratio for the carbon data has fallen significantly at and seems to be substantially different than the deuterium, which it was not at .

Tue Apr 1 08:52:10 EST 1997