Elastic proton scattering at intermediate energies as a probe of the ${}^{6,8}\mathrm{He}$ nuclear matter densities

The Glauber model analysis of the elastic ${}^{6,8}\mathrm{He}+p$ scattering data at energies around 700 MeV/nucleon, measured in two separate experiments at GSI-Darmstadt, has been carried out using several phenomenological parametrizations of the nuclear matter density. By taking into account the new data points measured at high-momentum transfer, the nuclear matter radii of ${}^{6,8}\text{He}$ have been accurately determined from the Glauber model analysis of the data, with the spin-orbital interaction explicitly taken into account. The well-known geometry for the core and dineutron halo has been used with the new parametrizations of the ${}^6\text{He}$ density to extract the detailed information on the structure of ${}^6\text{He}$ in terms of the core and dineutron halo radii. An enhanced sensitivity of the data measured at high-momentum transfer to the core part of the ${}^{6,8}\text{He}$ densities has been found.

Figure 1

Elastic ${}^{6,8}\mathrm{He}+p$ scattering data at energies around 700 MeV/nucleon measured by Neumaier et al. [8] and by Kiselev et al. [12] at the low- and high-momentum transfers, respectively.

Figure 2

Elastic $p+{}^4\mathrm{He}$ scattering data measured at proton energies around 700 MeV (circles [8] and squares [17]) in comparison with the elastic scattering cross section given by the GMSM calculation (solid line), taking into account the s-o term and using a Gaussian density for ${}^4\mathrm{He}$ that gives $R_{\mathrm{m}}=1.47$ fm.

Figure 3

Elastic ${}^6\mathrm{He}+p$ scattering cross sections (divided by Rutherford cross section) obtained with the GMSM calculation (solid curve) using the best-fit parameters of the GG (a) and GO (b) models of the nuclear density, in comparison with the data measured by Neumaier et al. [8] and by Kiselev et al. [12] at low- and high-momentum transfers, respectively. The dash-dotted curves were obtained with the best-fit parameters of the GG and GO density models taken from Ref. [10], and the dashed curves were obtained with the ${}^6\mathrm{He}$ density given by the cluster-orbital shell-model approximation (COSMA) [21].

Figure 4

The same as Fig. 3 but for the ${}^8\mathrm{He}+p$ scattering.

Figure 5

The average nuclear matter density distribution of ${}^6\mathrm{He}$ (a) deduced from the GMSM fit to the data using the present SF, GH, WS, GG, and GO parametrizations, with the uncertainty band determined by the statistical errors of the best-fit parameters of the density models. The same density is plotted in logarithmic scale (b) to illustrate the uncertainty at large radii.

Figure 6

The same as Fig. 5 but for the matter distribution of ${}^8\mathrm{He}$.

Figure 7

The sensitivity of the elastic ${}^8\mathrm{He}+p$ data to the core (a) and halo (b) parts of the GG density of ${}^8\text{He}$ being used in the GMSM calculation. See text for more details.

Figure 8

Results of the GMSM calculation of the elastic ${}^{6,8}\mathrm{He}+p$ scattering using the GO density models, with or without the inclusion of the s-o term.

Figure 9

The nuclear geometry for a two-neutron halo nucleus. See text for more details.