^{1, 2}

^{1}

^{1}

^{2}

The plasma screening effect is found to uncover a Cooper minimum in the photoionization cross sections from the ground state of the Li atom embedded in Debye plasma environment. The variation of the location of this minimum with Debye screening length is discussed and analyzed in terms of the instability of the ground state.

One of the features of the photoionization process which is most sensitive to the details of interaction, and on which we therefore focus in the present paper, is the plasma screening effect on the so-called Copper minimum. Quite a number of such minima have been found, both theoretically and experimentally [

In the non-relativistic dipole approximation, which is excellent for photoionization cross section below

Before presenting the plasma screening effect, however, it is useful to discuss the general characteristics of Cooper minima. Generally both discrete and continuum states have wave functions which are oscillatory. Thus the profile of the spectral distribution of the photoionization cross section hinges then on the dependence of the matrix element of the initial and final states. Increasing the principal quantum number, the number of nodes in the discrete state increases in accordance with its orbital quantum number. In addition, the continuum wave function becomes more compact with increasing energy, that is, its nodes move in towards the nucleus. In the complicated overlap of positive and negative amplitudes which go into the dipole matrix element, it may be that at some energy the positive and negative components just cancel giving a zero in the dipole matrix element [

Calculations have been performed by complex coordinate rotation method which employs square-integrable basis functions for computation of photoionization cross sections. Details regarding the basic theory and computational procedure have been discussed elsewhere [

The results of the plasma screening effect on the photoionization cross-sections of Li and Na ground state are depicted in Figures

Ground state energy (

Li | Na | ||||

2.0 | — | No bound state | 2.0 | — | No bound state |

3.0 | 0.101097 | −0.013282 | 3.0 | 0.295830 | −0.006226 |

4.0 | 0.079121 | −0.036019 | 4.0 | 0.235561 | −0.025245 |

5.0 | 0.059276 | −0.056043 | 5.0 | 0.204692 | −0. 043900 |

6.0 | 0.042996 | −0.072380 | 6.0 | 0.183378 | −0.059747 |

7.0 | 0.029767 | −0.085633 | 7.0 | 0.167208 | −0.072873 |

8.0 | 0.018962 | −0.096491 | 8.0 | 0.154713 | −0.083763 |

9.0 | 0.009959 | −0.105505 | 9.0 | 0.144056 | −0.092881 |

10.0 | 0.002425 | −0.113089 | 10.0 | 0.135604 | −0.100596 |

11.0 | No Min. | −0.119547 | 20.0 | 0.093342 | −0.140253 |

20.0 | No Min. | −0.178471 | 50.0 | 0.064678 | −0.168256 |

100.0 | No Min. | −0.188122 | 100.0 | 0.054388 | −0.178355 |

200.0 | No Min. | −0.193084 | 200.0 | 0.049244 | −0.183555 |

No Min. | −0.198141 | 0.044099 | −0.188857 |

Photoionization cross section (

Photoionization cross section of the sodium ground state for different Debye screening as a function of the ejected photoelectron energy.

For isolated Na, the relative phase difference between the bound 3 seconds state and the threshold function is just about _{D} is reduced to _{D} below

Location of Cooper minimum in photoionization cross section curve for Li ground state (in photoelectron energy in a.u.) and ground state energy (a.u.) versus Debye screening parameter (^{-1}).

Location of Cooper minimum in the photoionization cross section curve for Na ground state in photoelectron energy in a.u. and ground state energy (a.u.) versus Debye screening parameter (^{-1}).

Several important points have emerged from this study. The photoionization is very sensitive to the plasma screening near the ionization threshold. The location of Cooper minima in ground states of atom (Li and Na) in Debye plasma has been calculated over the entire range of _{D} (Debye screening length), and their behavior as a function of _{D}, has been explained primarily in terms of the instability of the bound states and the phase shifts of the discrete and the continuum states of the atom in the plasma environments. It is seen that a zero appears in the photoionization cross sections of Li in plasma environments when sufficient plasma screening effect modifies the core interaction in such a way that dipole matrix elements interfere destructively. It is also seen that with increasing plasma screening, the Cooper minima move further from thresholds owing to the increasing diffuseness of the ground states of the atoms. Since the screening effect, in one form or the other, is a common phenomenon in weakly coupled plasmas, the present results based strictly on the validity of the Debye model, exhibit some general and qualitative features.

The financial support by the National Science Council of Taiwan is gratefully acknowledged.