Asymmetric angular distributions in two-frequency multiphoton ionization of hydrogen atoms

Summary We report on calculated angular distributions of electrons produced in the ionization of hydrogen atoms by a linearly polarized soft X-ray and a circularly polarized laser light, with both the electric fields vibrating on the same plane. Their shape exhibits asymmetries which are similar to those observed in multiphoton ionization of noble gases by singlefrequency elliptically polarized light. An explanation of these asymmetries is given in terms of lowering of symmetry caused by the simultaneous action of the two fields during the ionization of the atom. The case at hand is another example which allows a useful insight into a new class of physical situations which deserve to be further explored both experimentally and theoretically.

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Riassunto In questo lavoro si calcolano le distribuzioni angolari di elettroni prodotti nella ionizzazione di atomi di idrogeno da raggi X molli e da luce laser polarizzata circolarmente, i cui campi elettrici vibrano nello stesso punto piano. La loro forma mostra asimmetrie che sono simili a quelle osservate nella ionizzazione multifotonica di gas nobili prodotta da un laser polarizzato ellitticamente. La spiegazione di questa asimmetria è data in termini di riduzione di simmetria causata dalla simultanea azione dei due campi durante la ionizzazione dell'atomo. Il presente caso è un esempio di una nuova calsse di situazioni fisiche che meritano di essere esplorate sia sperimentalmente che teoricamente.

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Резюме Приводятся вычисленные угловые распределения электронов, образованных при ионизации водорода линейно поляризованным мягким рентгеновским излучением и диркулярно поляризованным лазерным излучением, причем оба электрических поля колеблются в той же плоскости. Форма распределения обнаруживает асимметрии, которые аналогичны асимметриям, обнаруженным при многофотонной ионизации инертных газов под действием монохроматического эллиптически поляризованного света. Предлагается объяяснение этих асимметрий в терминах понижения симметрии вследствие одновременного действия двух полей во время ионизации атома. Рассматривается другой пример, который позволяет правильно понять новый класс физических ситуаций, которые заслуживают дальнейшего теоретического и эксрериментального исследований.

     

On the Green's function technique for the study of multiphoton transitions in atoms

Summary The Green's function method for implicitly evaluating the sums over intermediate states occurring in the study of multiphoton processes is revisited. Partieular emphasis is given to bound-bound transitions and to the numerical techniques used to implement the method. This is also extended to the important case in which the sum over intermediate states must be performed with respect to an incomplete set. The accuracy of the method is tested against very precise results on atomic hydrogen obtained by direct summation over intermediate states.

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Riassunto Si riesamina il metodo della funzione di Green per calcolare implicitamente le somme di stati intermedi che compaiono nello studio dei processi a molti fotoni. L'enfasi é posta su transizioni discreto-discreto e sulle tecniche numeriche utilizzate. Il metodo é anche esteso al caso in cui si debba sommare su un insieme incompleto di stati intermedi. La precisione del metodo è verificata nel caso dell'idrogeno confrontandone i risultati con quelli otenuti mediante una somma accurata sugli stati intermedi.

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Резюме Заново исследуется метод функций Грина для явного вычисления сумм по промежуточным состояниям, которые появляются при рассмотрении многофотонных процессов. Особое внимание уделяется переходам из связаннного в связанное состояние и использованной вычислительной технике. Предложенный метод также обобщается на важный случай, в котором суммирование по промежуточным состояниям должно быть проведено по неполной системе состояний. Точность предложенного метода проверяется посредством сравнения с точными результатами для атома водорода, полученными прямым суммированием по промежуточным состояниям.

     

Laser-assisted particle-atom ionization. Analysis of triple and double differential cross-sections

Summary Based on a theoretical model worked out previously, an analysis is reported of triplet and double differential cross-section of hydrogen atom ionization by electron impact in the presence of a single-mode, homogeneous, linearly polarized, off-resonance laser field. In particular, calculations are carried out to investigatea) the dependence of the cross-sections on the field strength,b) the average number of exchanged photons,c) the limits of validity of a known sum rule. The reported results improve considerably the present knowledge of this kind of elementary stimulated atomic process. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

AbsoluteL-subshell ionization cross-sections ofZ∼50 targets by4He ion impact

Summary The X-radiation induced by⁴He ion impact on Ag, Cd, In, Sn, Sb, Te and I has been investigated for incident energies ranging from 0.6 to 0.5 MeV. Production cross-sections for various X-ray lines have been obtained by an internal normalization method, by means of simultaneous backscattering measurements. From the intensities on theL _α ,L _γ1,5 andL _γ2,3 lines theL-subshell ionization cross-sections have been extracted. Comparison with current theories shows systematic discrepancies for all the targets at incident energy below 2.0 MeV and, for Ag, Cd and In, even in the higher-energy region. These are attributed to deviations in the atomic parameters used in the data analysis as well as to a failure of the ionization theories employed.

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Riassunto Si sono effettuate misure di fluorescenza X indotta da bombardamento di ioni⁴He di energia compresa tra 0.6 e 5.0 MeV sugli elementi Ag, Cd, In, Sn, Sb, Te e I. Utilizzando un metodo di normalizzazione interna fondato su contemporanee misure di retrodiffusione Rutherford, si sono ottenute le sezioni d’urto assolute per un certo numero di righe X. Da quelle relative alle righeL _α ,L _γ1,5 eL _γ2,3 si sono poi ricavate le sezioni d’urto di ionizzazione per i diversi sottostratiL. Il confronto con le teorie disponibili ha evidenziato la presenza di sensibili disaccordi per tutti i bersagli al di sotto dell’energia incidente di 2.0 MeV e, per Ag, Cd ed In, anche per energie piú elevate, che sono stati attribuiti in parte ai parametri atomici disponibili per i calcoli delle sezioni d’urto ed in parte all’inadeguatezza delle teorie che descrivono il processo di ionizzazione.

     

Infra-red multiphoton dissociation

Summary Threshold processes and ideally focused, non attenuated beams areconsidered. The fractional dissociation per pulse ω is plainly related, through the local dissociation probabilityP, to a local primitive functionS depending only on the radiation frequency ν, the maximum ε of the local fluence, the state variables β as well as, possibly, the pulse temporal structure; ω is found to scale with regard to pulse energy focal length and cell volume in typical ways provided certain defined conditions are satisfied. ε₀ being the empirical threshold, it may be realistic and convenient to simply assumeS≡0 for ε⩽ε₀ andS=s ₁(ε−ε₀) for ε>ε₀,i.e. a step cross-section , with for ε⩽ε₀ and for ε>ε₀. Species like³²SF₆ and¹²CF₂Cl₂ comply with this step crosssection approximation within large limits. In addition,³² s ₁ turns out to be independent of the pulse tenporal structure and to be factorable:³² s ₁(ν, β)=ν(ν)·β(β).

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Riassunto Si considerano processi a soglia in fasci non attenuati e perfettamente focalizzati. Mediante la probabilità locale di dissociazione, la frazione di molecole dissociate per imulso ω è messa in relazione con una funzione primitiva localeS che dipende solo dalla frequenza della radiazione ν, dal massimo della fluenza locale ε, dalle variabili di stato β ed, eventualmente, dalla struttura temporale dell’impulso; si trova che ω varia con l’energia dell’impulso, la distanza focale ed il volume della cella in modi caratteristici purché siano soddisfatte alcune condizioni. Se ε₀ è la soglia empirica, può risultare realistico e conveniente semplicemente ammettere cheS≡0 per ε⩽ε₀ e cheS=s ₁(ε−ε₀) per ε>ε₀, cioè che la sezione d’urto sia a soglia, con per ε⩽ε₀ ed per ε>ε₀. Questa approssimazione è adeguata entro ampi limiti per specie come³²SF₆ e¹²CF₂Cl₂. Inoltre si osserva che³² s ₁ è indipendente dalla struttura temporale dell’impulso e fattorizzabile:³² s ₁(ν,β)=ν(ν)·β(β).

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Резюме Расаматриваются пороговые процессы и идеально сфокусированные, незатухающие пучки. Молярная диссоциация за импульс ω связана, через вероятность локальной диссоциацииP, с локальной функциейS, зависящей только от частоты излучения ν, от максимума локального потока ε, от переменных состояния β, а также может быть от временной структуры импульса. Получено, что ω изменяется с знергией импуляса, фокусным расстоянием и объемом ячейки обычным образом, при выполнении определенных условий, ε₀ является змпирическим порогом. Можно предположить, чтоS≡0 для ε⩽ε₀ иS=s ₁(ε−ε₀) для ε>ε₀, т.е. поперечное сечение является ступенчатым , с при ε⩽ε₀ и при ε>ε₀. Образцы типа³²SF₆ и¹²CF₂Cl₂ в широких пределах удовлетворяют зтому ступенчатому поперечному сечению. Кроме того, оказывается, что³² s ₁ не зависит от временной структуры импульса и факторизуется:³² s ₁(ν,β)=ν(ν)·β(β).

     

Quantum statistics of multiphoton unimolecular dissociation

Summary We suggest a statistical model for the process of multiphoton unimolecular dissociation which considers the energy levels of the vibrational active mode, a quasi-continuous heat bath constituted by the energy levels of the remaining modes of the molecule and an electronically excited fragment resulting from the dissociation. The master equation for the system and expressions for the moments are derived and discussed in the standard second-quantization formalism. From the master equation the diagonal and off-diagonal density matrix elements are evaluated and some discussion on their applications to establish the change of light statistics is given.

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Riassunto Si suggerisce un modello statistico per il processo di dissociazione unimolecolare multifotonico che considera i livelli di energia del modo attivo vibrazionale, un bagno di calore quasi continuo costituito dai livelli di energia dei restanti modi della molecola e di un frammento eccitato elettronicamente che risulta dalla dissociazione. L’equazione master del sistema e le espressioni degl’impulsi sono derivate e discusse nel formalismo standard della seconda quantizzazione. Per l’equazione master, gli elementi di matrice della densità diagonali e al di fuori della diagonale sono calcolati e si discute sulle loro applicazioni per stabilire il cambiamento della statistica della luce.

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Резюме Мя предлагаем статистическую модель для процесса многофотонной мономолекулярной диссоциации. Эта модель учитывает энергетические уровни колебательной активной моды, энергетические квазинепрерывные уровни термостата, которые состоят из знергетических уровней оставшихся мод молекулы, и электронных возбуюдений фрагментов, образованных при диссоциации. Выводится задаюЩее уравнение для системы и выражения для моментов. Проводится обсуждение в рамках стандартного формализма вторичного квантования. С помощью задающего уравнения вычисляются диагональные и недиагональные элементы матрицы плотности. Проводится обсуюдение статистики света.

     

Avoiding the opposite beams interaction in the He−Ne linear laser at 632.8 nm

Summary In the paper the role of the opposite beams in laser generations is discussed on the basis of experimental investigations performed on the He−Ne long linear laser. It is stated that standing waves do not interact with atoms in one-photon transitions. Laser oscillations always avoid generating standing waves inside the laser medium. The best way to avoid such standing waves is laser generation in the form of one short pulse travelling to and fro inside the resonator—the self-locking generation. Also discussed is the laser generation of two or more pulses inside the resonator. The work was supported by CPBR 8.14.     

The vibrational quasi-continuum in unimolecular multiphoton dissociation

Summary The vibrational quasi-continuum of the boron trifluoride molecule has been qualitatively studied and the formalism extended to treatN-normal-mode molecules. The anharmonic potential curves for the BF₃ normal modes have been calculated, and the computed anharmonicity constants have been tested against the fundamental frequencies. The potential curve of the wagging mode has been simulated by an internal rotation of one of the fluoride atoms. The vibrational-energy levels and wave functions have been calculated applying second-order perturbation theory. The quasi-continuum energy levels of BF₃ have been obtained by means of a method based in forming adequate linear combinations of wave functions belonging to theN-1 modes resulting from removing the i.r.-active mode; the associated energies have been minimized using a constrained minimization procedure. It has been found that the energy pattern of theN-1 vibrational modes possesses an energy density high enough for constituting a vibrational heat bath and, finally, it has been verified that the ?fictitious? pattern of the active mode is included in the pattern of theN-1 modes.

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Riassunto è stato studiato il quasi-continuo vibrazionale della molecola del trifluoruro di boro e il formalismo è stato esteso per trattare molecola conN modi normali. Sono state calcolate le curve anarmoniche del potenziale per i modi normali di BF₃ e sono state provate le costanti di anarmonicità calcolate rispetto alle frequenze fondamentali. La curva del potenziale del modo di scuotimento è stata simulata mediante una rotazione interna di uno degli atomi del fluoruro. Sono stati calcolati i livelli di energia vibrazionale e le funzioni d'onda, applicando la teoria di perturbazione di secondo ordine. Sono stati ottenuti i livelli di energia quasi continua del BF₃ mediante un metodo basato sulla formazione di adeguate combinazioni lineari di funzione d'onda che appartengono ai modiN-1 che risultano rimuovendo il modo i.r. attivo; le energie associate sono state minimizzate usando una procedura di minimizzazione vincolata. Si è trovato che il modello di energia degliN-1 modi vibrazionali una densità di energia alta abbastanza per costituire un bagno vibrazionale di calore e, infine, si è verificato che il modello ?fittizio? del modo attivo è incluso nel modello degliN-1 modi.

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Резюме Качественно исследуются колебательньій квазиконтиуум молекульі BF₃ и предлагается обобщенньій формализм для рассмотрения молекул сN-нормальньіми модами. Вьічисляются потенциальньіе кривьіе для нормальньіх мод BF₃. Вьічисленньіе константьі ангармоничности проверяются на фундаментальньіх частотах. Потенциальная кривая для модьі моделируется с помощью внутреннего вращения одного из атомов фтора. Вьічисляются уровни знергии колебательного движения и волновьіе функции, используя теорию возмущений второго порядка. Уровни энергии квазиконтинуума BF₃ получаются с помощью метода, основанного на образовании адекватньіх линейньіх комбинаций волновьіх функций, принадлежащихN-1, модам, которьіе возникают при удалении инфракрасной активной модьі. Ассоциированньіе энергии минимизируются, используя ограниченную процедуру минимизации. Получено, что спектр энергии дляN-1 колебательной модьі обладает достаточно вьісокой плотностью для образования колебательной тепловой бани. В заключение, проверяется, что ?фиктивньій? спектр активной модьі включается в спектр дляN-1 модьі.

     

Interaction of auto-decayed states in molecule photodissociation processes

Summary The process of molecule photodissociation (PD) in the vicinity of the ionization threshold is studied with direct transitions into the dissociative continuum being accompanied by occupation of pre-dissociative Rydberg and quasi-stationary valence (non-Rydberg) configuration states interacting with each other. Interaction with valence configuration of ≈XY is shown to result in major rearrangement of series of Rydberg resonances (whose width and profile indices turn out to depend greatly on the position of valence configuration levels, their own widths and configuration interaction constant). Possibilities of interference stabilization of individual resonances are shown and conditions for formation of bound states, with continuum serving as the background, are discussed. Calculation of the NO molecule photodissociation spectrum (in the (68600⋎71200) cm⁻¹ region) is given.

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Riassunto Si studia il processo di fotodissociazione delle molecole in vicinanza della soglia di ionizzazione con transizioni dirette nel continuo dissociativo accompagnato dall'occupazione di stati di configurazione di Rydberg pre-dissociativa ed a valenza quasi stazionaria (non di Rydberg) che interagiscono tra di loro. Si mostra che l'interazione con la configurazione di valenza di ≈XY risulta in una maggiore ridisposizione di serie di risonanze di Rydberg (i cui indici di ampiezza e profilo appaiono dipendere in gran parte dalla posizione dei livelli di configurazione di valenza, le loro ampiezze e interazione di configurazione costanti). Si mostrano le possibilità di stabilizzazione d'interferenza di risonanze individuali e si discutono le condizioni per la formazione di stati legati, con il continuo che funge da sfondo. Si dà il calcolo dello spettro di fotodissociazione della molecola di NO (nella regione (68600|71200) cm⁻¹).

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Реэиме Йсследуется процсс фотодиссоциации молекул вблизи порога ионизации в спуае ирямъх переходов в диссциативнъій континуум, которъіе сопобождиіотся заполненим пре-диццоциативнъіх ридберровских и квази-стаіциохарнъих валентнъіх (не-Ридберговских) конфигурагуацоннъіх состояний, которъіе взаимодействуіот друт с друтом. Показъівается, что взаимодействие с валентной конфигурацей ≈XY приводит к перегруппировке ряда Ридбергобских резнансов (у которъх џірина и индексъи профилх сущестбенно завият ояпложения уровней валентной конфигурации, их собственнъіх ширин и конфигурационной постоянной взаимодействия. Ппказывается возможность интерференционной стабилизации индивидуальнных резонансов. Обуждаются условия для образования связанных состояний. Проводится вычисление для спектра фотодиссоциации молекулы NO (в области (68600|71200) см⁻¹).

     

Intensity correlation as a means of manifesting coherent atomic excitation

Summary The excitation of atoms into a coherent linear superposition of states may not always be revealed by measurement of the spontaneous-emission intensity at a single detector. Correlation of the intensity at two detectors, however, can under specified circumstances reveal this coherent excitation. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.     

Generalized implicit-summation technique for multiquantum processes in systems containing continua

Summary Implicit-summation technique has been so far limited to the lowest-order term of the amplitude for multiphoton ionization. In this paper, a previosly derived result in which the higher-order terms are taken into account is considered. The implicit-summation technique is adapted for the treatment of the complete amplitude, resulting in a new set of differential equations. The solution procedure for this set of differential equations is discussed.

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Riassunto La tecnica di somma implicita è stata fino ad ora limitata al termine d'ordine piú basso dell'ampiezza per la ionizzazione multifotonica. In questo lavoro si considera un risultato derivato in precedenza nel quale termini di ordine piú alto sono presi in considerazione. La tecnica di somma implicita è adattata al trattamento dell'ampiezza completa, che risulta in una nuova serie di equazioni differenziali. Si discute la procedura di soluzione per questo gruppo di equazioni differenziali.

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Резюме Техника неявного суммирования до сих пор применялась к члену низшего порядка для амплитуды многофотонной В этой статье рассматривается ранее полученный результат, в котором учитываются члены более высоких порядков. Техника неявного сммирования применяется для рассмотрения полной амплитуды, получается новая система дифференцальных уравнений. Обсуждается процедура решемия этой системы дифференциальных уравнений.

     

Two-photon transitions between discretenS states in atomic He

Summary The two-photon transition probabilities from the ground state 1¹ S and from the metastable states 2¹ S and 2³ S to the lowest excited states are computed in He. A configuration interaction approach is used, and a detailed comparison between the ?length? and the ?velocity? gauges leads to an estimate of 1% accuracy. Correlation effects are found to account for about 20% of the transition probabilities. The life-time of the 2¹ S state is ≅19.6 ms. The two-photon transition probabilities display a dramatic dependence on frequency, characterized by resonances and transparencies. Based on work supported in part by the Gruppo Nazionale di Struttura della Materia of the C.N.R. and by the Frascati Synchrotron Radiation Contract (P.U.L.S.).     

The opposite beams in He−Ne ring laser at 632.8 nm

Summary In the paper the resonant interaction of the opposite beams in a He−Ne ring laser at 632.8 nm is discussed on the basis of experimental results. These results show that the stable laser generation is attained when no simultaneous interaction of the opposite beams exists in the laser system. In the experiment, the mode-locking generation was obtained by applying a combining mirror, reflecting some part of the output beam into the laser cavity.

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Riassunto Nel lavoro si discute sulla base dei risultati sperimentali l’interazione risonante degli sciami opposti in un laser ad anello He−Ne a 632.8 nm. Questi risultati mostrano che la generazione laser stabile è raggiunta quando nessuna interazione simultanea di raggi opposti esiste nel sistema laser. Nell’esperimento, la generazione di modi vincolati in fase è stata ottenuta applicando uno specchio combinante, che riflette qualche parte del raggio di output nella cavità laser.

     

Two-photon ionization by perturbation theory of a simple molecular model

Summary The two-photon ionization probability of a simple model of diatomic molecule has been exactly evaluated under the assumption that a perturbative treatment is valid. The model consists of a simple electron in one-dimensional motion in the field of two fixed Dirac delta wells. The exact results are compared with a number of approximations arising from simplifications introduced at the level of final state and/or the intermediate states involved in the evaluation of the relevant ionization amplitude.

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Riassunto è stata calcolata la probabilità di ionizzazione per assorbimento di due fotoni in un semplice modello di molecola biatomica omonucleare in condizioni nelle quali si può supporre valida una trattazione perturbativa. Il modello considerato consiste di un elettrone vincolato a muoversi di moto monodimensionale nel campo di due buche attrattive tipo delta di Dirac. Risultati esatti per il modello sono confrontati con approssimazioni ottenute semplificando la struttura dello stato finale dell'elettrone ionizzato e/o quella degli stati intermedi necessari per il calcolo dell'ampiezza di ionizzazione a due fotoni.

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Резюме В рамках применимости теории возмущений оценивается вероятность двух-фотонной ионизации в простой модели двухатомной молекулы. Модель состоит из электрона, участвующего в одно-мерном движении в поле двух фиксированных потенциальных ям в виде дельта-функций Дирака. Точные результаты сравниваются с рядом приближений, получающихся из упрощений, вводимых на уровне конечного состояния и/или промежуточных состояний, необходимых для вычисления соответствующей амплитуды двух-фотонной ионизации.

     

铅原子非共振多光子电离过程的研究

在激光波长为1064nm、532nm和355nm下,研究了铅原子的非共振多光子过程.通过改变激光脉冲的线宽研究了铅原子非共振7-光子电离速率和激光统计性的依赖关系.     

激光场中H原子多光子电离速率

建立了激光与原子相互作用的伪分立态模型,并用此模型计算了激光场中Ｈ原子的多光子电离速率。对于光子能量较小的激光,计算结果与其它理论计算结果相符合。     

用共振多光子电离技术测量分子动力学参数

理论上推导了央三光子共振四光子电离过程中，电离流与多光子动力学参数的关系。首次提出用共振多光子离技术获得三光子吸收截面，四光子电离截面以及无辐射弛豫速率参数法。实验测量了气相甲苯分子里德堡态的上述动力学参数。结果在理论预期的数量级范围内。     

Strong-field double ionization of Ar below the recollision threshold

Nonsequential double ionization of Ar by 45 fs laser pulses (800 nm) at (4-7)x10;{13} W/cm;{2} was explored in fully differential measurements. Well below the field-modified recollision threshold we enter the multiphoton regime. Strongly correlated back-to-back emission of the electrons along the polarization direction is observed to dominate in striking contrast to all previous data. No effect of Coulomb repulsion can be found, the predicted cutoff in the sum-energy spectra of two emitted electrons is confirmed, and the potential importance of multiple recollisions is discussed.     

Laser-Assisted particle-atom inelastic collisions. Role of the field polarization

Summary A theoretical treatment, of first order in the collision dynamics, is presented to analyse the role of electric polarization in offresonance laser-assisted atomic collisions. General expressions are presented for evaluating the modified spectrum and wave functions for anyn level of hydrogenic atoms in the presence of a laser, taken to be linearly and circularly polarized. Specific calculations are carried out for excitation of hydrogen atoms to the leveln=2 by electron impact. The two polarizations are found to yield large differences i) in the atomic-spectrum modifications, ii) in the structure of the cross-sections and iii) in the numerical results. In particular, only for linear polarization, the distribution in energy of the scattered electrons at a fixed scattering angle has the structure of a series of equally spaced lines of different height (the spacing being equal to the laser photon energy ℏw and the height of the line accounting for the number of final electrons with a given energy). For circular polarization no such a regular pattern is predicted. Since, among laser-assisted particle-atom collisions, at present energy gain-loss spectra of scattered electrons are most easily observed, it is hoped that the reported results may serve as a stimulus for new observations in this new class of atomic collisions. The theory to treat the multiphoton resonance case is outlined too. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Strong-field molecular ionization: determination of ionization probabilities calibrated with field-free alignment

We report an original optical method providing the probability of molecular ionization induced by femtosecond laser pulses. The approach consists of exploiting molecular alignment to extract reliable information about ionization. The cross defocusing technique implemented for this purpose reveals a sensitivity with respect to postpulse alignment, as well as to the free electron density induced by the ultrashort laser pulse. The analysis of the resulting signal thus gives access to absolute single-ionization probabilities calibrated through the degree of alignment, provided that free electrons are produced mainly by single ionization. The relevance of the method is assessed in N2.