# Attosecond Time Delay in Photoionization of Noble-Gas and Halogen Atoms
## 1 Introduction  
Photoionization processes are traditionally studied using high-resolution synchrotron radiations [1; 2], which provides detailed information about the electronic structure of the target. A complete description of photoionization requires information on both the amplitude and phase of the dipole transition matrix elements, through the measurement of cross sections and asymmetry parameter. Thanks to the development of attosecond XUV-IR laser pump-probe technology [3; 4; 5], it is possible to observe and control ultrafast processes in matter on their natural time scale of attoseconds. In general, an electron is ionized from its parent target by absorbing a XUV photon, then the photoelectron's momentum and energy are shifted by the probing IR laser pulse. The time delay between the XUV and IR pulse can be tuned coherently to record the dynamics of electrons from different initial states. Experimentally, photoionization time delays have been measured for Helium [6], noble-gas atoms [7; 8; 9; 10; 11], negative ions [12], molecules [13; 14], and condensed matter systems [15; 16]. Theoretical description often requires an inclusion of many-electron effects for quantitatively accurate calculations [17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31]. Various aspects of the time delay in single photon ionization have been studied, such as angular dependence [32; 33; 34; 35], relativistic effects [36], Attochirp effect [37], and time delay in two photon ionization [38]. Only recently, a well-known discrepancy between theory and experiment on Ne \(2p\)-\(2s\) ionization time delay was resolved [39]. For more details on the attosecond physics of photoionization, a few recent reviews are available [40; 41; 42; 43]. Photoionization time delay can be measured using single attosecond XUV pulse in a streaking experiment [44; 45], or using attosecond XUV pulse train in a RABBIT experiment (Reconstruction of Attosecond Beating by Interference of Two-photon Transitions) [46]. In the frame of two-photonperturbation theory [25], both the streaking and RABBIT time delays are decomposed into two parts \(\tau=\tau_{W}+\tau_{CLC}\), where \(\tau_{W}\) and \(\tau_{CLC}\) are the Wigner time delay [47, 48] and Coulomb-laser coupling (CLC) time delay, respectively. The Wigner time delay measures the group delay of photoelectron after absorbing an XUV photon, and its accurate calculation frequently requires inclusion of many-electron effects. The CLC time delay is the energy derivative of free-free transition phase following single IR photon absorption. It can be estimated using an analytical formula [25] and does not contain any information about the target structure, as its name suggests. There has been a number of theoretical and experimental investigations of photoionization time delays from noble-gas atoms in the presence of a giant dipole resonance or a Cooper minimum. However, to the best of our knowledge, detailed theoretical time delay studies on halogen atoms, such as iodine, are not available. The giant dipole resonance is a well-known feature in many atomic photoionization spectra, which is a resonance-like broad peak that occurs above single-photon ionization threshold. It has been interpreted as originating from a potential barrier in a particular one-electron ionization channel [49, 50] or as originating from a many-electron, collective oscillation of the atomic electrons [51, 52]. Cooper minimum is another feature in many atomic photoionization spectra, which is a cross-section minimum and was explained as being due to a sign change of radial dipole matrix elements as a function of photon frequency [53, 54, 55]. In the vicinity of giant dipole resonance or Cooper minimum, the dipole transition matrix element usually undergoes \(\pi\) phase change and results in structured time delay. The giant dipole resonance comes from ionization of core electrons and is therefore known to persist even when the relevant atom becomes part of a larger molecule.