Backward scattering of low-energy antiprotons by highly charged and neutral uranium: Coulomb glory

Collisions of antiprotons with He-, Ne-, Ni-like, bare, and neutral uranium are studied theoretically for scattering angles close to $180°$ and antiproton energies in the interval from $100\mathrm{eV}$ to $10\mathrm{keV}$. We investigate the Coulomb glory effect which is caused by a screening of the Coulomb potential of the nucleus and results in a prominent maximum of the differential cross section in the backward direction at some energies of the incident particle. We found that for larger numbers of electrons in the ion the effect becomes more pronounced and shifts to higher energies of the antiproton. On the other hand, a maximum of the differential cross section in the backward direction can also be found in the scattering of antiprotons on a bare uranium nucleus. The latter case can be regarded as a manifestation of the screening property of the vacuum-polarization potential in nonrelativistic collisions of heavy particles.

Figure 1

(Color online) Scaled differential cross section $d\tilde{\sigma }∕d\Omega$, defined by Eq. (16), on He-like uranium for different energies of the incident antiproton: (a) $E=100\mathrm{eV}$, (b) $E=20\mathrm{eV}$, (c) $E=500\mathrm{eV}$, (d) $E=5\mathrm{eV}$, and (e) $E=1\mathrm{keV}$. The dashed line represents the scaled Rutherford cross section.

Figure 2

(Color online) Scaled differential cross section $d\tilde{\sigma }∕d\Omega$, defined by Eq. (16), on Ne-like uranium for different energies of the incident antiproton: (a) $E=300\mathrm{eV}$, (b) $E=500\mathrm{eV}$, (c) $E=200\mathrm{eV}$, (d) $E=100\mathrm{eV}$, and (e) $E=1\mathrm{keV}$. The dashed line represents the scaled Rutherford cross section.

Figure 3

(Color online) Scaled differential cross section $d\tilde{\sigma }∕d\Omega$, defined by Eq. (16), on Ni-like uranium for different energies of the incident antiproton: (a) $E=2\mathrm{keV}$, (b) $E=1.5\mathrm{keV}$, (c) $E=1\mathrm{keV}$, (d) $E=2.5\mathrm{keV}$, and (e) $E=3\mathrm{keV}$. The dashed line represents the scaled Rutherford cross section.

Figure 4

(Color online) Scaled differential cross section $d\tilde{\sigma }∕d\Omega$, defined by Eq. (18), on neutral uranium for different energies of the incident antiproton: (a) $E=7\mathrm{keV}$, (b) $E=5\mathrm{keV}$, (c) $E=8\mathrm{keV}$, (d) $E=2\mathrm{keV}$, and (e) $E=9\mathrm{keV}$.

Figure 5

(Color online) Scaled differential cross section $d\tilde{\sigma }∕d\Omega$, defined by Eq. (16), on bare uranium nucleus for different energies of the incident antiproton: (a) $E=400\mathrm{eV}$, (b) $E=800\mathrm{eV}$, and (c) $E=100\mathrm{eV}$. The dashed line represents the scaled Rutherford cross section.