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Precision study of the d+p->3He+eta reaction for excess energies between 20 and 60 MeV

The differential and total cross sections for the d+p->3He+eta reaction have been measured at COSY-ANKE at excess energies of 19.5, 39.4, and 59.4 MeV over the full angular range. The results are in line with trends apparent from the detailed near-threshold studies and also agree with those from CELSIUS, though the present data have higher precision. While at 19.5 MeV the results can be described in terms of s- and p-wave production, by 59.4 MeV higher partial waves are required. Including the 19.5 MeV point together with the near-threshold data in a global s- and p-wave fit gives a poorer overall description of the data though the position of the pole in the 3He scattering amplitude, corresponding to the quasi-bound or virtual state, is hardly changed.

The differential and total cross sections for the dp → 3 He η reaction have been measured at COSY-ANKE at excess energies of 19. 5, 39.4, and 59.4 MeV over the full angular range. The results are in line with trends apparent from the detailed near-threshold studies and also agree with those from CELSIUS, though the present data have higher precision. While at 19. 5 MeV the results can be described in terms of s-and p-wave production, by 59. 4 MeV higher partial waves are required. Including the 19. 5 MeV point together with the near-threshold data in a global s-and p-wave fit gives a poorer overall description of the data though the position of the pole in the η 3 He scattering amplitude, corresponding to the quasi-bound or virtual state, is hardly changed. We have recently provided results on the dp → 3 He η reaction very near threshold in fine energy steps. These show that the total cross section reaches a plateau for an excess energy Q that is less than 1 MeV [1] and this behavior was confirmed by an independent measurement [2]. The abrupt variation of the cross section can be understood [3] as being due to a final state interaction (FSI) that is enhanced through the presence of a quasibound or virtual state pole in the η 3 He elastic scattering amplitude for |Q| < 1 MeV, though its location in the complex planes is ambiguous.
Further evidence for the pole hypothesis is to be found from the study of the angular distribution [4]. For Q < 11 MeV a linear dependence on the cosine of the η production angle is seen, which suggests that only the η s-wave and s-p interference are important in this region. However, the energy dependence of the angular slope shows that the phase of the interference changes rapidly with Q, presumably due to the pole in the swave production amplitude. It is therefore of interest to investigate how this behavior extends to higher energies and this we have done through measurements at Q = 19.5, 39.4, and 59.4 MeV. The first two energies overlap with results obtained by a CELSIUS collaboration [5] and, while the data sets are largely consistent, the present ones allow firmer conclusions to be drawn. The energy range 10 -60 MeV seems to be a transition region going from one where there is s + p dominance to a regime where higher partial waves become important.
The experiment was carried out using the ANKE spectrometer [6] in combination with a hydrogen cluster target [7] at an internal station of the Cooler Synchrotron COSY-Jülich. The conditions were identical to those of our near-threshold work [1] with the exception that, instead of using a beam that was continuously ramped in energy, three fixed values of the beam momentum were requested, viz 3.223, 3.306, and 3.389 GeV/c. The produced 3 He were detected in the ANKE forward detection system, which consists of one drift chamber, two multiwire proportional chambers, and three layers of scintillation hodoscopes. The trigger used demanded hits in the first two layers. The tracks of charged particles could be traced back through the precisely known magnetic field to the interaction point, leading to a momentum reconstruction for registered particles. The 3 He were then identified by making a cut in the energy loss versus momentum plot using the information from all the hodoscope layers.
The missing-mass distribution for all dp → 3 He X events measured at Q = 19.5 MeV is presented in Fig. 1. This shows a prominent η peak sitting on a background that is rather similar to that observed in the belowthreshold data taken under identical conditions to the ones used here [1]. The spectrum has been modeled in a phase-space Monte Carlo simulation of two-, three-, and four-pion production plus a small component arising from misidentified protons from the intense deuteron breakup reaction. These simulations were fitted together with that for the dp → 3 He η reaction to the data. Af- Missing-mass distribution for the dp → 3 He X reaction at an excess energy of 19.5 MeV with respect to the η threshold. Contributions of simulated reactions to the background fit and their sum (Σ) are shown. After subtracting these from the data, the difference histogram shows a clean η peak (shaded) that agrees very well with the simulation (solid histogram) of the dp → 3 He η reaction.
ter subtracting the sum of the background reactions from the measured points, a clean η peak was found.
In order to determine the differential cross section for each excess energy, the whole range of the 3 He c.m. production angles was divided into 20 bins and a missingmass distribution constructed for each of them. The η content was determined in a similar manner to that shown in Fig. 1.
In the near-threshold experiment the value of Q could be determined directly from the data by studying the size of the momentum ellipse [1]. This leads to significant errors as Q gets larger and the ellipse expands. Therefore, the excess energy was calculated from the preset COSY beam momentum. This leads to an uncertainty of 0.8 MeV, which is consistent with the precision of 0.1% in the COSY beam momentum. For excess energies in the 20 -60 MeV range this uncertainty is of minor importance.
Just as in the earlier work [1], the luminosity L needed to convert counts to cross sections was found through the simultaneous measurement in the forward detector of the deuteron from dp elastic scattering. The cross section varies very fast with the deuteron angle in this region [9] and it is the systematic uncertainty in the determination of this angle that dominates the error in L of about ±15%. However, it is important to stress that this generally affects all three energies in the same way, as it does also the near-threshold data [1]. Figure 2 shows the angular distributions obtained at the three different energies. Also presented are the points  Table I.   TABLE I: Results for the dp → 3 He η differential and total cross sections. In addition to the statistical errors, there is a common systematic uncertainty of 15% in the total cross sections, due mainly to the luminosity determination. The fit parameters an of Eq. (1)   Ref. [2] Ref. [5] Ref. [10] Ref. [11] Ref. [12] Ref. [13] [

ANKE points
with the values of the parameters a n being given in Ta The values obtained for the total dp → 3 He η cross sections are also reported in Table I and compared with other published results in Fig. 3. Not shown there is the 15% uncertainty in the ANKE data that arises mainly from the luminosity determination. As discussed earlier, this is largely a common factor that does not affect the discussion of the energy dependence. The rise apparent between 20 and 40 MeV in both our data and those of CELSIUS [5] possibly reflects the increased influence of the higher partial waves that are needed to describe the angular dependence of Fig. 2.
The strong forward/backward asymmetry shown by the data of Fig. 2 arises from the interference between odd and even partial waves and at low energies this can be summarized by a slope parameter, defined by The values of α deduced at 19.5 MeV and from our previous measurements are shown in Fig. 4. The results presented in Ref. [2] show a very similar behavior, as do those of Ref. [11], though with much lower precision.

[MeV/c]
Since the 19.5 MeV differential cross section can be fit by a quadratic in cos θ η , these data might be described in terms of s-and p-wave production amplitudes. It is therefore of interest to try to include these values together with our near-threshold measurements of the reaction [1] in a global energy-dependent fit to see if the s+p hypothesis holds up to this energy. As pointed out in Ref. [4], due to the spin complexity, there are two independent s-wave production amplitudes and five p-wave terms. The FSI should affect the two swave terms in similar ways and some support for this is to be found in the weak energy dependence of the deuteron tensor analyzing powers of the reaction [10]. The ansatz of Ref. [4] therefore assumes average s-and p-wave amplitudes, f s and p η f p , in terms of which the total cross section and slope parameter are expressed as where p p is the initial proton c.m momentum. The rapid rise in the total cross section from threshold is due to the pole in the s-wave amplitude f s and this is also responsible for the non-linear behavior of the slope parameter α with the η c.m. momentum shown in Fig. 4. This comes about because of the variation of the phase of the interference Re(f * s f p ) with p η in Eq. (4). The s-wave amplitude was taken as the product of a near and distant pole, where the distant one is an effective pole that absorbs any residual momentum dependence so that f B is taken as constant [1], as is the reduced p-wave amplitude f p . Before the ansatz can be compared to the experimental data, it has to be smeared over the spread in the initial deuteron beam momentum inside COSY [1]. Fitting the resulting formulae to the total cross section and asymmetry data leads to the dashed curves in Figs. 3 and 4 if the 19.5 MeV point is not included in the fit, as it was not in our near-threshold work [1]. Including this point leads to the solid curves, which gives a much poorer description of the asymmetry at low p η , though the differences are much harder to see for the total cross section in the near-threshold region.
Despite the poorer overall description of the low energy data, the position of the nearby pole in the complex energy plane is only changed from |Q| ≈ 0.4 MeV to ≈ 0.9 MeV through the inclusion of the 19.5 MeV point. This shows that the position of the η 3 He pole is robustly fixed in magnitude, though the data cannot determine whether it is a quasi-bound or virtual state. The data also indicate that the s-wave amplitude carries on decreasing with energy until at least 19.5 MeV with the p-waves becoming steadily more important. However, the higher χ 2 /ndf obtained when including the 19.5 MeV point (1.61 versus 1.42) and the systematically poorer description of the asymmetry data in Fig. 4 suggest that the modelling of in terms of only spin-averaged s-and p-wave amplitudes is insufficient at this energy.
In summary, we have extended the measurements of the dp → 3 He η differential and total cross sections to higher excess energies. Although the angular distribution at 19.5 MeV might be described in terms of just s and p waves, a global fit of the data using the methodology of Ref. [4] gives unsatisfactory results and this suggests that higher partial waves are probably already significant at this energy. The negative value of the a 4 parameter in Table I is a sign that at least f waves are important at 59.4 MeV. On the other hand, even if the fit is forced to describe a data set that includes the 19.5 MeV point, the position of the η 3 He pole hardly moves.
The analysis of Ref. [4] assumed that the energy dependence of the two s waves was identical. This can only be tested through precise measurements of the deuteron tensor analyzing powers of the reaction in finer energy steps than are currently available [10]. Data on this observable will be provided by the COSY-ANKE collaboration [14].