Angle-resolved non-resonant two-photon single ionization of argon using 9.3 eV photons produced via high harmonic generation
AAngle-resolved non-resonant two-photon single ionization of argon using 9.3 eVphotons produced via high harmonic generation
Kirk A. Larsen,
1, 2, ∗ Daniel S. Slaughter, and Thorsten Weber Graduate Group in Applied Science and Technology,University of California, Berkeley, CA 94720, USA Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA (Dated: April 14, 2020)We present an experimental study on the photoionization dynamics of non-resonant one-color two-photon single valence ionization of neutral argon atoms. Using 9.3 eV photons produced via highharmonic generation and a 3-D momentum imaging spectrometer, we detect the photoelectrons andions produced from non-resonant two-photon ionization in coincidence. Photoionization from the 3 p orbital produces a photoelectron scattering wave function with p and f partial wave components,which interfere and result in a photoelectron angular distribution with peak amplitude perpendicularto the VUV polarization. The comparison between the present results and two previous sets oftheoretical calculations [Pan, C. & Starace, A. F. (1991). Physical Review A , 44(1), 324., andMoccia, R., Rahman, N. K., & Rizzo, A. (1983).
Journal of Physics B: Atomic and MolecularPhysics , 16(15), 2737.] indicates that electron-electron correlation contributes appreciably to thetwo-photon ionization dynamics.
The photoionization dynamics of multi-electron atomicand molecular systems are influenced by electron-electroncorrelation. Non-resonant two-photon ionization canprobe such correlation effects in both the initial and finalstates of the target. A particularly sensitive observable isthe photoelectron angular distribution (PAD), which canprovide a detailed view of the underlying mechanisms in-volved in the photoionization process and its correlatednature, e.g. information on the role of continuum statesand interchannel coupling [1–12]. The PAD emergesfrom a coherent summation over a set of final continuumstates. The sensitivity of the PAD to electron-electroncorrelation arises from its dependence on the amplitudesand phases of the different partial wave components ofthe coherent sum. These distinct angular momentumcomponents can interfere to create nodes and antinodesin the PAD.PADs are uniquely characterized by their energy-dependent anisotropy parameters, or β parameters. Thenumber of β terms used to describe the PAD increaseswith the photon order. As such, a two-photon PAD canexhibit more anisotropy and structure than the corre-sponding one-photon PAD. Previous two-photon inves-tigations of the anisotropy parameters in neon and ar-gon have been realized using two-color two-photon above-threshold ionization (ATI) schemes [13–15], where ioniza-tion was performed with a VUV field in the presence ofa strong NIR dressing field that generated photoelectronsidebands. This can make comparison with theory verychallenging. Measurements that lie within the pertur-bative limit and target non-resonant bound-continuumtransitions, driven by the second photon (rather thancontinuum-continuum transitions), are highly sensitiveto electron-electron correlation and can be achieved in ∗ [email protected] a one-color two-photon ionization scheme by exclusivelyusing a VUV field with a photon energy in a non-resonant region below the ionization threshold. How-ever, measuring a PAD from n on-resonant o ne-color t wo- p hoton s ingle i onization (NOTPSI) in an atomic gas re-quires sufficiently high VUV intensities to enable nonlin-ear processes. Since high intensity ultrashort VUV lightsources are limited to a small number of free electronlasers (FELs) and tabletop high-order harmonic gener-ation (HHG) systems, angle-resolved measurements onNOTPSI in rare gases are scarce.Over the years, a few studies have investigated one-color two-photon ionization in helium and krypton usingVUV FELs [16–18]. PADs were measured in helium atseveral photon energies, across both the resonant andnon-resonant regions, in Ref. [18]. Here, anisotropy pa-rameters as well as amplitude ratios and phase differencesof the partial wave components of the scattering wavefunction could be extracted, due to the simple nature ofthe target. By moving to more complex many-electronsystems, more terms and higher angular momentum com-ponents contribute to the photoelectron scattering wavefunction, and many-electron effects become more signifi-cant. This increase in complexity represents a great chal-lenge for experiment and theory alike.Previous theoretical studies on angle-resolved two-photon ionization in helium have indicated that a single-active-electron picture appears to be a valid approach indescribing the photoionization dynamics for photon ener-gies below the ionization threshold (and even in the abovethreshold region) [1]. It is unlikely that this is true formore complex core targets. This compels angle-resolvedmeasurements in more complicated systems, where manyactive and correlated electrons are required to describethe photoionization dynamics. To our knowledge, noangle-resolved measurements exist for complex multi-electron systems such as argon, were electron-electroncorrelation is expected to play a more significant role a r X i v : . [ phy s i c s . a t o m - ph ] A p r in the photoionization dynamics than in simple systemslike helium. The aim of this experimental investigationis to reveal, for the first time, clear contributions fromelectron-electron correlation in the PADs emerging fromNOTPSI of argon.Despite the paucity of experimental data, the problemhas not escaped theoretical treatment. Over a quarter ofa century ago, the β parameters for one-color two-photonsingle ionization (including NOTPSI) were calculated forargon using a Hartree-Fock approach [19] providing un-correlated and Coulomb correlated results, and a randomphase approximation calculation [20], which neglectedelectron-electron correlation. The uncorrelated resultsof Ref. [19, 20] are somewhat ambiguous due to discrep-ancies between the calculations performed in the lengthand velocity gauge at various photon energies. The cor-related results of Ref. [19] show better gauge invariancein both the resonant and non-resonant two-photon ion-ization regions and the computed β parameters suggestmaximum photoelectron emission perpendicular to theionizing field at 9.3 eV. However, to our knowledge, thesecalculations have for decades remained unverified by anyexperimental measurement.In this work, we present results on angle-resolvedNOTPSI of argon from the 3 p orbital using 3-D momen-tum imaging, where the photoelectron and ion are mea-sured in coincidence. Using a 400 nm driving field, weproduce and select VUV photons with an energy of 9.3eV via HHG, which are then used to perform NOTPSI.Interference between different angular momentum com-ponents of the photoelectron wave function results in aPAD exhibiting maximum intensity perpendicular to theionizing VUV field. These experimental results are com-pared against previous calculations, which suggest thatelectron-electron correlation considerably influences thephotoionization dynamics.The valence photoionization dynamics in neutral ar-gon were investigated using the cold target recoil ion mo-mentum imaging [21–24] (COLTRIMS) technique. Here,the photoelectron-ion pair produced by NOTPSI are col-lected with full 4 π solid angle, and their 3-D momentaare measured in coincidence, on an event-by-event basis.The charged particles are guided by parallel DC elec-tric and magnetic fields (15.55 V/cm, 3.72 G) towardsposition- and time-sensitive detectors at opposite endsof the spectrometer. The detectors consist of a multi-channel plate (MCP) chevron stack with a delay-line an-ode readout [25, 26]. The electron and ion detectors area three layer hex-anode with a 80 mm MCP, and a twolayer quad-anode with a 120 mm MCP, respectively. The3-D momentum of each charge carrier is encoded into itshit position on the detector and its time-of-flight relativeto the laser trigger.The laser system has been described previously [24],but we briefly highlight a few modifications made to thesystem below. A Ti:sapphire near-infrared (NIR) lasersystem produces 12 mJ, 45 fs pulses at 50 Hz, which arefrequency doubled using a 0.25 mm thick beta-barium borate (BBO) crystal, where the copropagating 800 nmNIR and 400 nm blue fields are then separated using twodichroic mirrors. The reflected blue photons ( ∼ ∼
50 fs) are focused (f = 6 m) into a 10 cm long gascell containing 3 Torr of krypton to generate VUV oddharmonics via HHG. The resulting VUV frequency combis then separated from the 400 nm fundamental by re-flection from three silicon mirrors near Brewster’s anglefor the 400 nm field, resulting in a suppression of thefundamental by a factor of < − . The 3 rd harmonic(133 nm, 9.3 eV) is isolated by transmission through a0.25 mm thick MgF window, which totally suppressesthe 5 th harmonic and above. The femtosecond pulse du-ration of the 3 rd harmonic is also maintained, while theresidual 400 nm pulse is temporally separated from the3 rd harmonic pulse by ∼
700 fs, due to the difference inthe group velocity dispersion (GVD) of the window at ω and 3 ω [27, 28]. After transmission through the window,we estimate the pulse duration of the 3 rd harmonic to be ∼
30 fs, based on its spectral bandwidth, its estimatedattochirp, and the thickness and GVD of the MgF win-dow [29, 30]. The femtosecond 9.3 eV pulses are thenback-focused (f = 15 cm) into the 3-D momentum imag-ing spectrometer using a protected aluminium mirror, thereflectance of which has been measured to be 43% at 9.3eV [31]. The pulse energy of the 3 rd harmonic on targetis approximately 10 nJ, which was measured using a pairof broadband VUV filters (Acton Optics FB130-B-1D.3)and a calibrated photodiode.A beam of argon atoms is prepared from an adiabaticexpansion through a 0.03 mm nozzle, which is then colli-mated by a pair of skimmers. This atomic jet propagatesperpendicular to the focusing VUV beam, where the twointersect in the interaction region (approximately 0.01 × × ∼ s s p s p ( S ). Ionization from the 3 p orbital re-sults in the ground electronic state of the cation Ar + ,a P state. From two-photon selection rules, the finalstates must have either S or D total symmetry, whilethe photoelectron wave function must be either a p - oran f -wave. It follows that we can express the allowedfinal states in the three forms listed below: S : 3 p P + (cid:15)p (1) D : 3 p P + (cid:15)p (2) D : 3 p P + (cid:15)f (3)In (2) and (3) above, we see that the D final statecontains contributions from two different photoelectronangular momentum components, p - and f -waves. Thecoherent sum of these two partial waves can create an in-terference pattern in the PAD. Since the initial state hastotal magnetic quantum number M = 0, so too must thefinal states. Hence the m value of the photoelectron andion wave functions must sum to 0. From this restriction,we see that only m = 0 , ± f -wave com-ponent can contribute, while all m values of the p -wavesmay contribute. These photoelectron states are pairedto states of the core with the appropriate m value.A diagram depicting the NOTPSI pathway in thepresent experiment is shown in Fig 1. The grey box in-dicates the region containing the bound excited statesof argon, beginning at 11.55 eV. The ionization poten-tial of argon is 15.76 eV, while the two-photon energy is ∼ Ar: 3p6 (1 S)Ar+ : 3p5 (2 P) ωω e − FIG. 1. An energy level diagram depicting the NOTPSI path-way from the 3 p orbital of Ar at 9.3 eV. The grey box indicatesthe region containing bound excited states, the first appear-ing at 11.55 eV. The ionization potential of Ar is 15.76 eV,hence the red double-arrow corresponds with a photoelectronkinetic energy of 2.84 eV. The measured photoelectron kinetic energy spectrumis presented in Fig 2 (a). Here, we observe a single peakcentered at 2.8 eV, with a full width at half maximum(FWHM) of ∼
400 meV, indicative of the two-photonspectral bandwidth of the 3 rd harmonic (convolved withthe electron energy resolution of the spectrometer). Thephotoelectron momentum distribution transverse versusparallel to the VUV polarization vector is shown in Fig 2(b), where we observe electron emission peaking towardshigh transverse momentum and low longitudinal momen-tum. To gain more insight into the photoelectron emis-sion pattern, we turn to the angle-differential photoion-ization cross section.For two-photon ionization of a target atom by lin- Electron Energy (eV) C oun t s (a) p (a.u.) p ( a . u . ) (b) FIG. 2. (a) The photoelectron energy spectrum and (b)momentum distribution parallel versus perpendicular to theVUV polarization. early polarized light, the angle-differential photoioniza-tion cross section is given by dσd
Ω = σ π [1 + β P (cos θ ) + β P (cos θ )] (4)where σ is the total photoionization cross section, θ is the angle between the photoelectron momentum vec-tor and the polarization vector of the light, β and β are the second and fourth order anisotropy parameters,and P and P are the second and fourth order Legendrepolynomials in variable cos θ [32]. The measured angle-differential photoionization amplitude is presented in Fig3. Equation 4 has been applied to fit the data (solid redline) using the projection method discussed in [33], wherethe error on the β parameters is determined via statisti-cal bootstrapping [34]. The β parameters retrieved fromthe fit are β = -0.93 ± β = 0.25 ± (radians) C oun t s = -0.93 ± = 0.25 ± FIG. 3. The angle-differential photoionization cross sectionfor NOTPSI of Ar at 9.3 eV. The experimental data is fit usingEquation 4, where the retrieved β parameters are displayedabove the plot. The PAD exhibits peak intensity at angles near π/ π . We attribute these features to the interferencebetween the different p - and f -wave components of thephotoelectron scattering wave function. These two angu-lar momentum components destructively interfere alongthe polarization direction, yielding an angle-differentialamplitude that peaks perpendicular to the field. Thisinterference is analogous to the interference between thephotoelectron s and d partial waves in photodetachmentof I − and O − [35–37].We compare our retrieved β parameters with those ex-tracted from Ref. [19] at a photon energy of 9.3 eV andRef. [20] at a photon energy of 8.6 eV, presented in Ta-ble I and Fig. 4. In Ref. [19], the calculations wereperformed using a 2 nd order time-independent perturba-tion theory method, in both a Hartree-Fock (HF) ap-proach and a Coulomb correlated HF approach. In theuncorrelated HF calculation, there is significant disagree-ment between the length and velocity gauges, while theCoulomb correlated HF approach exhibits much bettergauge invariance. We find that the Coulomb correlatedHF calculations show good qualitative agreement withthe present measurements (seen in Fig. 4 (b)), specifi-cally in the direction of maximum photoelectron emis-sion. There are, however, significant quantitative dis-crepancies in the magnitude of β and the sign of β (seeTable I). The uncorrelated HF calculations of Ref. [19], in either the length or velocity gauge, compare less fa-vorably with the present measurements (seen in Fig. 4(a)).In Ref. [20], the two-photon ionization cross sectionswere calculated using a random phase approximationmethod with HF wave functions for the initial, interme-diate, and target states, neglecting electron-electron cor-relation. There is reasonable agreement at this photonenergy between the calculations in length and velocitygauge (seen in Fig. 4 (c)). They both resemble the un-correlated results in the velocity gauge of Ref. [19] shownin Fig. 4 (a). However, there is poor qualitative andquantitative agreement between the uncorrelated theo-ries and the measurement. Despite the quantitative dis-agreements, the correlated HF results of Ref. [19] suggestthat electron-electron correlation is essential in the accu-rate description of the NOTPSI dynamics of argon. β β HF Length [19] -0.62 -0.18HF Velocity [19] -0.13 -0.48Correlated Length [19] -0.54 -0.05Correlated Velocity [19] -0.48 -0.01Random Phase Approx. Length [20] 0.03 -0.62Random Phase Approx. Velocity [20] 0.04 -0.58Experiment -0.93 0.25TABLE I. The β parameters extracted from the calculationsin [19] at a photon energy of 9.3 eV and in [20] at a pho-ton energy of 8.6 eV, and those retrieved from the presentmeasurement. The discrepancies between the theory in Refs. [19, 20]and the present measurements may be attributed to aninadequate treatment of electron-electron correlation inthe calculations. The level of correlation accounted forin the Coulomb correlated HF approach of Ref. [19] ledto better gauge invariance and a PAD with greater sim-ilarity to the present measurements. This suggests thata higher level of electron-electron correlation must be in-cluded for a more accurate description of NOTPSI inargon.In conclusion, we have reported results on NOTPSIof argon using 3-D momentum imaging and an intense9.3 eV femtosecond pulse. We find that the observedphotoelectron emission pattern can be explained by theinterference between the different p and f partial wavecomponents of the photoelectron scattering wave func-tion, which add destructively along the polarization di-rection of the ionizing VUV field. Our measurements arecompared against a previous set of calculations, whichreveal that the photoionization dynamics are evidentlyinfluenced by electron-electron correlation effects. It ap-pears that the level of electron-electron correlation ac-counted for in the Coulomb correlated HF calculationsin Ref. [19] is not sufficient to reach complete agreementwith the present results. Our measurements can serve asa benchmark for future ab initio theoretical treatments ofNOTPSI dynamics in multi-electron systems. A particu- (a)(b)(c) FIG. 4. The photoelectron angular distribution for NOTPSIof Ar at 9.3 eV for the experimentally retrieved β parameters(solid red curve in (a), (b), and (c)) and those extracted from[19, 20]. The blue curves in (a) correspond with the uncorre-lated HF calculation of [19], the blue curves in (b) correspondwith the Coulomb correlated calculation of [19], and the bluecurves in (c) correspond with the random phase approxima-tion calculation of [20] (dashed: velocity gauge, solid: lengthgauge). The orientation the VUV polarization is indicated bythe horizontal double arrow. lar challenge may be incorporating continuum-continuumcoupling in the calculations, which is expected to be im-portant in reproducing the PAD in non-resonant regions[38]. In addition to further development of theoreticalmethods, there is a clear need for follow-up experimentsto investigate the photon energy dependence of electron-electron correlation effects by angle-resolved photoioniza-tion of multi-electron atoms and small molecules, usingintense VUV, XUV, and soft X-rays, preferably at pho-ton energies where calculated anisotropy parameters aregauge invariant, and correlated and uncorrelated resultsdiffer markedly.Work at Lawrence Berkeley National Laboratory wasperformed under the auspices of the U.S. Departmentof Energy under Contract No. DE-AC02-05CH11231,and was supported by the U.S. Department of EnergyOffice of Basic Energy Sciences, Division of ChemicalSciences, Biosciences and Geosciences. This researchused resources of the National Energy Research ScientificComputing Center (NERSC), a U.S. Department of En-ergy Office of Science User Facilities under Contract No.DE-AC02-05CH11231. We are indebted to the Roent-Dek Company for long-term support with detector soft-ware and hardware. We thank Roger Y. Bello, Robert R.Lucchese, and C. William McCurdy for the many helpfuldiscussions. [1] Diego I. R. Boll, Omar A. Foj´on, C. W. McCurdy,and Alicia Palacios. Angularly resolved two-photonabove-threshold ionization of helium. Phys. Rev. A ,99:023416, Feb 2019. doi:10.1103/PhysRevA.99.023416.URL https://link.aps.org/doi/10.1103/PhysRevA.99.023416 .[2] F. L. Yip, T. N. Rescigno, C. W. McCurdy, andF. Mart´ın. Fully differential single-photon double ion-ization of neon and argon.
Phys. Rev. Lett. , 110:173001,Apr 2013. doi:10.1103/PhysRevLett.110.173001. URL https://link.aps.org/doi/10.1103/PhysRevLett.110.173001 .[3] Robert R. Lucchese. Effects of interchannel coupling on the photoionization cross sections of carbon dioxide.
TheJournal of Chemical Physics , 92(7):4203–4211, 1990. doi:10.1063/1.457778. URL https://doi.org/10.1063/1.457778 .[4] Bryan Basden and Robert R. Lucchese. Vibrationallyresolved cross sections and asymmetry parameters for thephotoionization of n with coupling between the (3 σ g ) − and the (2 σ u ) − channels. Phys. Rev. A , 37:89–97, Jan1988. doi:10.1103/PhysRevA.37.89. URL https://link.aps.org/doi/10.1103/PhysRevA.37.89 .[5] J. Jose, R. R. Lucchese, and T. N. Rescigno. Interchannelcoupling effects in the valence photoionization of sf6.
TheJournal of Chemical Physics , 140(20):204305, 2014. doi: https://doi.org/10.1063/1.4876576 .[6] R. E. Stratmann and Robert R. Lucchese. Resonancesand the effects of interchannel coupling in the photoion-ization of cs2.
The Journal of Chemical Physics , 97(9):6384–6395, 1992. doi:10.1063/1.463699. URL https://doi.org/10.1063/1.463699 .[7] T. N. Rescigno, B. H. Lengsfield, and A. E. Orel. In-terchannel coupling and ground state correlation effectsin the photoionization of co.
The Journal of ChemicalPhysics , 99(7):5097–5103, 1993. doi:10.1063/1.466010.URL https://doi.org/10.1063/1.466010 .[8] R G Houlgate, K Codling, G V Marr, and J BWest. Angular distribution and photoionizationcross section measurements on the 3p and 3s sub-shells of argon.
Journal of Physics B: Atomic andMolecular Physics , 7(17):L470–L473, dec 1974. doi:10.1088/0022-3700/7/17/003. URL https://doi.org/10.1088%2F0022-3700%2F7%2F17%2F003 .[9] Zikri Altun and Steven T. Manson. Photoelectron an-gular distributions of ns subshells of open-shell atomsas indicators of interchannel coupling: Sc4 s photoion-ization. Phys. Rev. A , 61:030702, Feb 2000. doi:10.1103/PhysRevA.61.030702. URL https://link.aps.org/doi/10.1103/PhysRevA.61.030702 .[10] S. H. Southworth, A. C. Parr, J. E. Hardis, and J. L.Dehmer. Channel coupling and shape resonance effectsin the photoelectron angular distributions of the 3 σ − g and 2 σ − u channels of n . Phys. Rev. A , 33:1020–1023,Feb 1986. doi:10.1103/PhysRevA.33.1020. URL https://link.aps.org/doi/10.1103/PhysRevA.33.1020 .[11] C. D. Lin. Channel interaction and threshold behaviorof photoionization.
Phys. Rev. A , 9:171–180, Jan 1974.doi:10.1103/PhysRevA.9.171. URL https://link.aps.org/doi/10.1103/PhysRevA.9.171 .[12] David J. Kennedy and Steven Trent Manson. Photoion-ization of the noble gases: Cross sections and angulardistributions.
Phys. Rev. A , 5:227–247, Jan 1972. doi:10.1103/PhysRevA.5.227. URL https://link.aps.org/doi/10.1103/PhysRevA.5.227 .[13] Louis H Haber, Benjamin Doughty, and Stephen RLeone. Photoelectron angular distributions and cross sec-tion ratios of two-color two-photon above threshold ion-ization of argon.
The Journal of Physical Chemistry A ,113(47):13152–13158, 2009.[14] S. Mondal, H. Fukuzawa, K. Motomura, T. Tachibana,K. Nagaya, T. Sakai, K. Matsunami, S. Yase, M. Yao,S. Wada, H. Hayashita, N. Saito, C. Callegari, K. C.Prince, C. Miron, M. Nagasono, T. Togashi, M. Yabashi,K. L. Ishikawa, A. K. Kazansky, N. M. Kabachnik,and K. Ueda. Pulse-delay effects in the angular dis-tribution of near-threshold euv + ir two-photon ioniza-tion of ne.
Phys. Rev. A , 89:013415, Jan 2014. doi:10.1103/PhysRevA.89.013415. URL https://link.aps.org/doi/10.1103/PhysRevA.89.013415 .[15] Stefan D¨usterer, G Hartmann, C Bomme, R Boll,JT Costello, B Erk, A De Fanis, M Ilchen, P Johnsson,TJ Kelly, et al. Two-color xuv+ nir femtosecond pho-toionization of neon in the near-threshold region.
NewJournal of Physics , 21(6):063034, 2019.[16] Takahiro Sato, Atsushi Iwasaki, Kazuki Ishibashi, To-moya Okino, Kaoru Yamanouchi, Junichi Adachi, AkiraYagishita, Hiroki Yazawa, Fumihiko Kannari, MakotoAoyma, et al. Determination of the absolute two-photon ionization cross section of he by an xuv free electronlaser.
Journal of Physics B: Atomic, Molecular and Op-tical Physics , 44(16):161001, 2011.[17] M. Meyer, D. Cubaynes, V. Richardson, J. T. Costello,P. Radcliffe, W. B. Li, S. D¨usterer, S. Fritzsche, A. Mi-helic, K. G. Papamihail, and P. Lambropoulos. Two-photon excitation and relaxation of the 3 d − d resonancein atomic kr. Phys. Rev. Lett. , 104:213001, May 2010. doi:10.1103/PhysRevLett.104.213001. URL https://link.aps.org/doi/10.1103/PhysRevLett.104.213001 .[18] R Ma, K Motomura, KL Ishikawa, S Mondal,H Fukuzawa, A Yamada, K Ueda, K Nagaya, S Yase,Y Mizoguchi, et al. Photoelectron angular distributionsfor the two-photon ionization of helium by ultrashort ex-treme ultraviolet free-electron laser pulses.
Journal ofPhysics B: Atomic, Molecular and Optical Physics , 46(16):164018, 2013.[19] Cheng Pan and Anthony F. Starace. Angular dis-tribution of electrons following two-photon ionizationof the ar atom and two-photon detachment of thef − ion. Phys. Rev. A , 44:324–329, Jul 1991. doi:10.1103/PhysRevA.44.324. URL https://link.aps.org/doi/10.1103/PhysRevA.44.324 .[20] R Moccia, N K Rahman, and A Rizzo. Two-photonionisation cross section calculations of noble gases: re-sults for ne and ar.
Journal of Physics B: Atomic andMolecular Physics , 16(15):2737–2751, aug 1983. doi:10.1088/0022-3700/16/15/016. URL https://doi.org/10.1088%2F0022-3700%2F16%2F15%2F016 .[21] R. Drner, V. Mergel, O. Jagutzki, L. Spielberger,J. Ullrich, R. Moshammer, and H. Schmidt-Bcking.Cold Target Recoil Ion Momentum Spectroscopy:a ’momentum microscope’ to view atomic collisiondynamics.
Physics Reports , 330(2-3):95–192, June2000. ISSN 0370-1573. doi:doi: DOI: 10.1016/S0370-1573(99)00109-X. URL .[22] Joachim Ullrich, Robert Moshammer, Alexander Dorn,Reinhard D¨orner, L Ph H Schmidt, and H Schmidt-B¨ocking. Recoil-ion and electron momentum spec-troscopy: reaction-microscopes.
Reports on Progress inPhysics , 66(9):1463, 2003.[23] T Jahnke, Th Weber, T Osipov, AL Landers, O Jagutzki,L Ph H Schmidt, CL Cocke, MH Prior, H Schmidt-B¨ocking, and R D¨orner. Multicoincidence studies ofphoto and auger electrons from fixed-in-space moleculesusing the coltrims technique.
Journal of ElectronSpectroscopy and Related Phenomena , 141(2-3):229–238,2004.[24] F. P. Sturm, T. W. Wright, D. Ray, I. Zalyubovskaya,N. Shivaram, D. S. Slaughter, P. Ranitovic, A. Belkacem,and Th. Weber. Time resolved 3d momentum imaging ofultrafast dynamics by coherent vuv-xuv radiation.
Re-view of Scientific Instruments , 87(6):063110, 2016. doi:10.1063/1.4953441. URL https://doi.org/10.1063/1.4953441 .[25] Roentdek. Roentdek delayline detectors. URL .[26] Ottmar Jagutzki, Alfred Cerezo, Achim Czasch,R Dorner, M Hattas, Min Huang, Volker Mergel, UweSpillmann, Klaus Ullmann-Pfleger, Thorsten Weber,et al. Multiple hit readout of a microchannel plate de-tector with a three-layer delay-line anode.
IEEE Trans- actions on Nuclear Science , 49(5):2477–2483, 2002.[27] T. K. Allison, J. van Tilborg, T. W. Wright,M. P. Hertlein, R. W. Falcone, and A. Belka-cem. Separation of high order harmonics withfluoride windows.
Opt. Express , 17(11):8941–8946, May 2009. doi:10.1364/OE.17.008941. URL .[28] H. H. Li. Refractive index of alkaline earth halidesand its wavelength and temperature derivatives.
Journalof Physical and Chemical Reference Data , 9(1):161–290,1980. doi:10.1063/1.555616. URL https://doi.org/10.1063/1.555616 .[29] Taro Sekikawa, Tomotaka Katsura, Satoshi Miura,and Shuntaro Watanabe. Measurement of theintensity-dependent atomic dipole phase of ahigh harmonic by frequency-resolved optical gat-ing.
Phys. Rev. Lett. , 88:193902, Apr 2002. doi:10.1103/PhysRevLett.88.193902. URL https://link.aps.org/doi/10.1103/PhysRevLett.88.193902 .[30] Taro Sekikawa, Tomoki Ohno, Tomohiro Yamazaki, Ya-suo Nabekawa, and Shuntaro Watanabe. Pulse com-pression of a high-order harmonic by compensating theatomic dipole phase.
Phys. Rev. Lett. , 83:2564–2567, Sep1999. doi:10.1103/PhysRevLett.83.2564. URL https://link.aps.org/doi/10.1103/PhysRevLett.83.2564 .[31] K. A. Larsen, J. P. Cryan, N. Shivaram, E. G.Champenois, T. W. Wright, D. Ray, O. Kostko,M. Ahmed, A. Belkacem, and D. S. Slaughter. Vuvand xuv reflectance of optically coated mirrors forselection of high harmonics.
Opt. Express , 24(16):18209–18216, Aug 2016. doi:10.1364/OE.24.018209. URL .[32] Katharine L Reid. Photoelectron angular distribu-tions.
Annual review of physical chemistry , 54(1):397–424, 2003.[33] X-J Liu, R R Lucchese, A N Grum-Grzhimailo, Y Mor-ishita, N Saito, G Prmper, and K Ueda. Molecular-framephotoelectron and electron-frame photoion angular dis-tributions and their interrelation.
Journal of Physics B:Atomic, Molecular and Optical Physics , 40(3):485–496,jan 2007. doi:10.1088/0953-4075/40/3/004. URL https://doi.org/10.1088%2F0953-4075%2F40%2F3%2F004 .[34] Bradley Efron. Bootstrap methods: another look at thejackknife. In
Breakthroughs in statistics , pages 569–593.Springer, 1992.[35] Richard Mabbs, Emily R. Grumbling, KostyantynPichugin, and Andrei Sanov. Photoelectron imaging: anexperimental window into electronic structure.
Chem.Soc. Rev. , 38:2169–2177, 2009. doi:10.1039/B815748K.URL http://dx.doi.org/10.1039/B815748K .[36] J. L. Hall and M. W. Siegel. Angular dependence ofthe laser photodetachment of the negative ions of car-bon, oxygen, and hydrogen.
The Journal of Chemi-cal Physics , 48(2):943–945, 1968. doi:10.1063/1.1668743.URL https://doi.org/10.1063/1.1668743 .[37] J. Cooper and R. N. Zare. Angular distribution of pho-toelectrons.
The Journal of Chemical Physics , 48(2):942–943, 1968. doi:10.1063/1.1668742. URL https://doi.org/10.1063/1.1668742https://doi.org/10.1063/1.1668742