Calculation of vector analyzing power in the p + 6 , 8 H е elastic scattering at intermediate energies Е

A calculations of the analyzing power (Ay) of the elastic proton scattering on He and He are presented in the framework of the Glauber multiple diffraction scattering at E = 71 and 1000 MeV/nucleon. The wave functions obtained in the three-body α-n-nmodel for He and the density distribution function in the no-core shell model for He are used. Our calculations qualitatively reproduced the data of Ay for pHe and pHe scattering and compare with the calculations’ results in the other approaches.


Introduction
The first reliable measurements of the vector analyzing power in elastic р 6 Не and р 8 Не-scattering at 71 MeV/nucleon have been made recently at the RIKEN accelerator [1][2][3].An appearance of such type of date makes it possible to test different model calculations that take into account the spin-orbit interaction, because the spin-orbit coupling in nuclei manifests itself in the polarization phenomena in nuclear elastic scattering. 1  The 6 Не and 8 Не nuclei are neutron-excess β-radioactive with the dominant α + 2n and α + 4n structure.The facts justifying the α-n-n-model of 6 Не and the α-2n-2n-model of 8 Не are the fellowing low binding energies in the channel α-2n (Е α-2n = 0.973 MeV [4]) and α-4n (Е α-4n = 3.1 MeV [4]), spectroscopic factors of α-2n and α-4n channels close to one.Also the measurement of the differential cross sections of high-energy proton scattering on 6 Не and 8 Не in inverse kinematics [5][6][7][8] shows the evidence of the well-defined clustering of these nuclei on α-partial core and valence nucleons, which form halo or skin with the radius about 0.9 fm.The analysis of the differential cross sections of р 6 Не and р 8 Не-scattering carried out in the full microscopic folding-model [9] with wave function in (0+2+4) ħω model space concluded that 6 He is a typical halo nucleus, while 8 He has no halo, but can have a neutron skin.The newest analyses of the analyzing power data for the 6 He and 8 He scattering from hydrogen at E = 71 MeV/nucleon has been presented in [10].The g-folding approach based on the multi-ħω no-core shell model wave functions (WFs), agrees with analyzing power data.
We calculated the analyzing power (A y ) of the elastic scattering of protons on the 6 He and 8 He isotopes made in the framework of the Glauber multiple diffraction scattering at E = 71 and 1000 MeV/nucleon.We use the WFs obtained in the three-body α-n-n-model for 6 He [11,12] and the density distribution function in the large scale shell model for 8 He [9].These are three-body α-n-n functions for 6 He calculated by the variational method with different intercluster interaction potentials.The n-n potential is the same for both models.The α-n potential is the Sack-Biedenharn-Breit potential in model 1 [11] and the potential split in orbital-angular momentum parity in model 2 [12].The details of calculation were presented in [13].
Our calculations (see Figs. 1a and 1b) show that А у has approximately the same behavior at small angles for all model WFs, despite significant differences of three-body and oscillator WFs of 6 He.The fact that the calculated curves have the same behavior at small angles (corresponds to small momentum transfer), suggests a weak influence of the peripheral region of the nucleus (scattering on neutron skin or halo) on А у .This is explained by a small contribution of the spin-orbit interaction to the valence neutrons near zero at small momentum transfers.
Increase of the amplitude of А у with angle increasing (and momentum transfer) indicates of significant sensitivity of the analyzing power to the distribution of nucleons in the central region of the nucleus.Essentially different from each other in oscillations size, all calculated curves reach their maximum and minimum values at the same angles.As the energy increases from 71 to 1000 MeV/nucleon, the number of oscillations increases.
Comparison of our calculations with the data [1,2] in Fig. 1a shows only qualitative agreement; in particular, all the curves change the sign from positive to negative at θ ~ 40°.
For comparison, Fig. 1a shows the results of calculation with this characteristic from [2] (curves 4, 5, 6).The results obtained in [2] were analyzed in the optical model with several potentials: phenomenological, folding (cluster and nucleon) and non-local one in full microscopic model with three sets of single-particle WFs (Woods-Saxon with halo, without halo and with oscillator one).The authors were able to provide a quantitative description of the data only with the phenomenological optical potential with special fitting of the parameters (curve 4).The calculation in the cluster foldingmodel with increased values r 0 and a is in only qualitative agreement with the experiment (curve 5).Other calculations (curve 6) do not result in satisfactory description of А у .The example is curve 6, calculated in the microscopic model with the Woods-Saxon WF with the halo.
Figures 2a and 2b show a comparison of А у for the р 6 Не (curve 1 is the same as the curve 1 in Figs.1a and 1b) and for the р 8 Не (curve 2) scattering at 70 (a) and 1000 (b) MeV/nucleon.Figures show that the analyzing powers for р 6 Не and р 8 Не are very similar.However, the mass effect of 8 He valence neutrons is that А у for р 8 Не is slightly shifted to the region of smaller angles compared to р 6 Не scattering at both energies.The last calculations of this characteristic were carried out in [10] using distorted wave approximation (DWA).The wave function of 8 He specified from a no-core shell model used a complete (0+2+4)~ħω basis.In Fig. 2a we show the curve 3 [10], which is in better agreement with the data in this case.The DWA describes А у at such low energy more realistically, because there are no energetic or angular limitations, that exist in the Glauber approximation.
Comparison of the analyzing powers of p 4,6,8 Не and p 6 Li scattering, made in [2], revealed interesting features of their behavior.The vector analyzing powers for р 6 Не and р 4 Не have the same behavior (changing the sign from positive to negative at θ ~ 60°), whereas А у for р 6 Li scattering is positive and increases smoothly without changing the sign.As we mentioned above it was much more complicated to reproduce the analyzing power for р 6 Не scattering.Thus, the negative values of this characteristics contradict to the majority of predictions based on the optical model.And only the special adjustment of the optical potential parameters provides А у qualitative description.The upgrade of the RIKEN facility will in principle allow the measurement of the A y angular distribution for the protons elastic scattering on the He isotopes at somewhat higher energies.Thus we investigated the predictions for the А у at Е = 1000 МeV/nucleon which better correspond to Glauber approach.

Fig. 1b .
Fig. 1b.The same as in Fig. 1а but at Е = 1000 MeV/nucleon.Explanations are given in the text.