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If the Lord Almighty had consulted me before embarking on the Creation, I should have recommended something simpler.


Possibly apocryphal remark attributed to Alfonso X ``The Wise''.

Measurement of spin isospin responses in nucleon-nucleus scattering in the quasifree region has generated a good deal of interest in recent years. Theoretical work was done [AEM82] which predicted that the spin longitudinal nuclear response should be enhanced over the spin transverse nuclear response for momentum transfers between and , primarily due to the low pion mass. Several experiments including both scattering [Car84] and scattering [Lut93] [Che93] [Tad94] were conducted at the Los Alamos Meson Physics Facility (LAMPF) with MeV to investigate this phenomenon. No evidence for the predicted enhancement in the ratio of spin longitudinal to spin transverse responses was found. The lack of enhancement generated a good deal of theoretical work including different techniques for making ``exact'' calculations of the responses of light nuclei [Glo96] [Wit96] [Pan94]. Motivated by the new theoretical work, this thesis presents the results of measurements made on and quasifree reaction at the Indiana University Cyclotron Facility (IUCF) with MeV.

The primary interest in this experiment was in the deuterium results because light nuclei were the subject of both the Faddeev calculations [Wit96] and the Green's function Monte Carlo calculations [Pan94]. The laboratory frame spin observables ('s) are, for the most part, consistent with the results of Faddeev calculations at all three angles reported () with the obvious exceptions at and (figures gif and gif). The individual 's were not reported in [Pan94]. The center-of-mass spin observables ('s), calculated using the laboratory frame spin observables, did not agree as well with Faddeev results. Generally, the 's are in qualitative agreement with the predicted Faddeev curves, but in several case the deuterium data seem to be more in agreement with the values expected from free np scattering, calculated using the Argonne potential [WSA84].

The final goal of these experiments was to obtain the ratio of the spin longitudinal isospin nuclear response to the spin transverse isospin nuclear response (). These results are shown in figure gif for and in figure gif for and are compared with predictions made using the Green's function Monte Carlo calculations and the Faddeev calculations. In the case the [Pan94] calculations do a better job of predicting experimental results. However, direct comparison is not possible at this time because the [Pan94] calculations are done at constant momentum transfer whereas the experiment was done at a constant scattering angle. At the momentum transfer for these data will be around fm, so the data would be expected to fall between the two curves presented, which they do. In addition the deuterium data are consistent with the prediction by Pandharipande et al. in that any enhancement in is pushed out to higher excitation energies in the tail of the quasifree distribution although statistical uncertainties prevent an unambiguous conclusion. The agreement of the data with the [Pan94] calculations is, perhaps, a little surprising since those calculations do not include any distortions. In fact, if the inclusion of distortions has the same effect on as it did in the RPA calculations ( suppressed compared to [IcK92]) then the curves given by the GFMC calculations will move in the direction which may improve the agreement. By what amount the curves will move, if at all, is currently impossible to say. These results may indicate that, as predicted, even the is subject to the effects of two-body mechanisms in which the transferred momentum, q, is shared by two nucleons. It has been suggested that such processes are responsible for measurements of enhancement in the transverse channel [Pro96] which could mask any enhancement in the longitudinal channel. This interpretation would be consistent with measurements of the spin transverse response in quasifree electron scattering [CaS92].

The most interesting feature of the data is that they clearly indicate that the [Pan94] predictions could potentially do a much better job of representing the data than do the Faddeev calculations. While the Faddeev calculations consistently do a good job of predicting cross sections [And96] and some of the spin observables they seem to do a worse job of predicting the overall nuclear spin response in charge exchange reactions.

The measurement of using the spin observable from the other transverse direction is complicated by the fact that it is coupled to the spin-0 response, but these results are shown in figure gif. Due to the calculational difficulties the results are more uncertain, but they are still consistent with the results in figure gif. However, in this case the data do not provide a differentiation of the models.

The deuterium longitudinal to transverse response ratios measured at are consistent with both the [Pan94] results and the Faddeev results. In this case the momentum transfer of the data is about fm. However, the large uncertainties for the case make it impossible for one to differentiate between the models.

While the primary focus of this work is to determine the response ratio from the deuterium charge exchange reaction, it is worth mentioning that the carbon results are consistent with previous work. was previously measured in a quasifree charge exchange reaction on carbon at MeV, and the results, reported in [Tad94] are reproduced in figure gif. The data were collected at momentum transfers of fm (), fm (), and fm (). The [Tad94] results show that for the lower momentum transfers at and are approximately unity and, perhaps, falling in the tail region around fm. A similar trend can be seen in the carbon data from this experiment for which fm. At ( fm) has dropped to in the peak region which also seems to have happened in the [Tad94] data by the time the momentum transfer is fm (). Therefore, at least qualitatively the carbon data agree with previous work done at 500 MeV. In fact, the current data perhaps indicate that the response ratio in carbon is falling more quickly at MeV as a function of momentum transfer than at MeV.

Along the same lines, some comparison can be made between the data collected at and those reported on here at . Spin-observable data from [Lut93], taken at at LAMPF, has been used to calculate and this has been compared to the data from this experiment in figure gif.

Figure: A comparison of as a function of energy loss between two different experiments. , data are shown in open squares, and , data (from LAMPF) are shown with closed squares.

These data do not use the Argonne potential to calculate the free response since that model is only valid up to 350 MeV. Rather the Bugg and Bryan phase shifts [BuB91] were used to extract the nuclear responses for both sets of data. The data aren't precisely comparable since the IUCF data has a momentum transfer range from 1.32 fm to 1.43 fm and the LAMPF data goes from 1.18 fm to 1.23 fm. However, these ranges are close and it is, therefore, reassuring that the results seem consistent within the uncertainties.

In light of the results from the deuterium data, it would now be interesting to see more complete calculations done using the Green's function Monte Carlo techniques that would reflect data taken at a constant scattering angle as well as predictions for the individual spin observables and the possible inclusion of distortions. These data indicate that this technique is a potentially useful method for calculating the spin-isospin responses of light nuclei excited by hadronic probes. However, the large uncertainty associated with measurement of the deuterium responses makes it impossible to use these results to constrain the model any further. Currently data are being analyzed from the quasifree reaction and, if the predictions in [Pan94] prove correct, the enhancement of in the tail of the distribution should be even more pronounced. Additionally, [Pan94] also makes predictions for the quasifree charge-exchange reaction, which is currently an approved experiment at IUCF awaiting beam time. If these other experiments also support the conclusions of Pandharipande et al., it would be exciting to see if their calculational techniques can in the future be extended to heavier targets, such as carbon, and give insight into the persistent question of the effect of the nuclear medium on the NN interaction.

next up previous contents
Next: References Up: Measurement of Polarization Observables Previous: Response Functions

Michael A. Lisa
Tue Apr 1 08:52:10 EST 1997