Electric dipole response of ${}^6\mathrm{He}$: Halo-neutron and core excitations

Electric dipole ($E1$) response of ${}^6\mathrm{He}$ is studied with a fully microscopic six-body calculation. The wave functions for the ground and excited states are expressed as a superposition of explicitly correlated Gaussians. Final state interactions of three-body decay channels are explicitly taken into account. The ground state properties and the low-energy $E1$ strength are obtained consistently with observations. Two main peaks as well as several small peaks are found in the $E1$ strength function. The peak at the high-energy region indicates a typical macroscopic picture of the giant dipole resonance, the out-of-phase proton-neutron motion. The transition densities of the lower-lying peaks exhibit in-phase proton-neutron motion in the internal region, out-of-phase motion near the surface region, and spatially extended neutron oscillation, indicating a soft-dipole mode and its vibrationally excited mode. The compressional dipole strength is also examined in relation to the soft-dipole mode.

Figure 1

Schematic diagrams of three patterns for the $E1$ excitations of ${}^6\mathrm{He}$. Small circles and shaded ones denote neutron and proton, respectively. Thick solid lines denote the coordinates on which the $E1$ operator acts.

Figure 2

Energy convergence of ${}^6\mathrm{He}$ as a function of basis dimension. The parameter $u$ of the MN potential is set to be unity.

Figure 3

Proton and neutron density distributions of ${}^{4,6}$He.

Figure 4

Electric dipole strength of ${}^6\mathrm{He}$ calculated with each basis set of the excitation diagram. Full indicates the result of calculation including all the basis sets. Note the different scale of the sp $B\left(E1\right)$ value.

Figure 5

Electric dipole strength of ${}^4\mathrm{He}$.

Figure 6

Electric dipole strength functions of ${}^6\mathrm{He}$ measured from the threshold energy $E_{\mathrm{th}}$. A hatched area denotes theoretical uncertainly due to a choice of the smearing width ranging from 0.75 to 2.0 MeV in the Lorentzian function (18). Experimental data taken from Ref. [5] are multiplied by $\frac{4\pi }{3}$ to be consistently with the $E1$ operator of Eq. (6).

Figure 7

The same as Fig. 6 but for a wider energy region. The results with different $u$ parameters of the MN potential are also plotted. The smearing width of the Lorentzian function is set to be 2.0 MeV.

Figure 8

Electric dipole transition densities for proton and neutron of the states with the excitation energy of (a) 3.0, (b) 7.2, (c) 17.7, and (d) 32.9 MeV, respectively.

Figure 9

Electric dipole transition densities for proton and neutron of ${}^4\mathrm{He}$ at the excitation energy of 31.8 MeV.

Figure 10

Ratio of the proton-proton ($pp$) distance of ${}^6\mathrm{He}$ to that of the ground state of ${}^4\mathrm{He}$ as a function of $E1$ excitation energy.

Figure 11

Compressional electric dipole strength of ${}^6\mathrm{He}$ as a function of the excitation energy.

Figure 12

Isoscalar compressional dipole strength of ${}^6\mathrm{He}$ as a function of the excitation energy.