Coulomb dynamical polarization potential and the electric dipole polarizability for weakly bound and neutron-rich light nuclei

In this paper, we present a method to determine the dipole polarizability of light exotic nuclei with a two-body deuteronlike cluster structure. Using the adiabatic approximation, we solve the Schrödinger equation for the internal motion of the exotic projectile incident on a heavy target nucleus and express the resulting Coulomb dynamical polarization potential (CDPP) in terms of regular and irregular Coulomb functions. We then obtain a new expression for the dipole polarizability (${\alpha }_0$) by equating the real part of this CDPP to the classical expression for the polarization potential. The ${\alpha }_0$ values for many weakly bound light nuclei are calculated and where values are available were found to be in good agreement with those obtained in previous studies using various other methods.

Figure 1

Coordinates describing the elastic scattering of a projectile ($P$) in the Coulomb field of a target ($T$). The weakly bound projectile is considered to have a two-body cluster structure with a charged core ($C$) and weakly bound neutron(s) ($\nu$). See text for further details.

Figure 2

(a) The real and imaginary CDPP for ${}^6\mathrm{He}+{}^{208}\mathrm{Pb}$ at 14 MeV compared with the TELP extracted from a CDCC calculation. (b) Angular distribution of ${}^6\mathrm{He}+{}^{208}\mathrm{Pb}$ elastic scattering at 14 MeV calculated with CDCC and the optical model using the CDPP compared with the data of Ref. [27].

Figure 3

The polarizability functions ${\alpha }_0\left(R\right)$ for ${}^2\mathrm{H},{}^6\mathrm{He},{}^8\mathrm{He},{}^{11}\mathrm{Li}$, and ${}^{11}\mathrm{Be}+{}^{208}\mathrm{Pb}$ at energies near the Coulomb barrier, calculated using Eq. (44). ${\alpha }_0^{\max }=0.43,1.5,0.22,5.76,2.5{\mathrm{fm}}^3$ located at 15.5, 28.6, 12.9, 52.4, 39.7 fm for ${}^2\mathrm{H},{}^6\mathrm{He},{}^8\mathrm{He},{}^{11}\mathrm{Li}$, and ${}^{11}\mathrm{Be}$, respectively.

Figure 4

CDPPs for ${}^2\mathrm{H},{}^6\mathrm{He},{}^{11}\mathrm{Li}$, and ${}^{11}\mathrm{Be}+{}^{208}\mathrm{Pb}$ on linear and logarithmic scales. The solid lines denote the real CDPP calculated in this paper [Eq. (39)] and the dashed lines represent the CDPP calculated using the semiclassical formula (2) with ${\alpha }_0$ tuned to give the best match to our CDPP.

Figure 5

The dependence of the dipole polarizability on ${\varepsilon }_0$ for different weakly bound light nuclei taken from Table 1.

Figure 6

The dependence of the root-mean-square radius of the real part of the CDPP and $R_0$ on the dipole polarizability for different weakly bound light nuclei considered in Table 1.