L. Fonda

Decay Theory of Unstable Quantum Systems

The present review article is aimed at a clear formulation of the basic problematics of the decay and at a description of the various recent attempts to solve this delicate problem, illustrating both their successes and limitations. The organisation of the article is as follows. After a short summary of the classical description of the decay, a detailed study of the quantum non-decay probability is given. Then the peculiar dynamical situation leading to the formation of an unstable system is identified and the formal and physical aspects of the process are discussed. A detailed analysis is then made of the preparation procedure of an unstable system which is shown to amount to a localisation of the decay fragments within a distance of the order of the range of the forces acting between them. After this the discussion of the general properties of the non-decay probability at all times is completed.

Theory of resonance reactions

Abstract A general formal theory of resonance reactions and scattering is developed without the use of channel radii. The approach employed allows a simple physical interpretation of the two energies, one of which must be kept fixed while the other one is varied in order for a Breit-Wigner denominator to vanish. A new result, obtained without a weak channel coupling hypothesis, is that a sharp resonance may be caused by forces which, if slightly different, would lead to a stable bound state even in the presence of strong coupling to open channels. The possibility of shapes other than the usual Breit-Wigner type is also discussed. A special formula is derived for resonances near a threshold caused by bound states just below that threshold in the same channels where the peak is seen.

On the quantum foundations of the exponential decay law

SummaryBy assuming that in every actual decay process the unstable system is subject to repeated processes of measurement which ascertain whether the system is decayed or not, we prove that the decay law is exponential, obtaining a consistent reconciliation of the quantum and the classical statistical descriptions of decay experiments. We also show that the measurement process is a localization of the decay products and that, consequently, the unstable system is reduced to a unique quantum state. We are able to give, within the framework of ordinary quantum mechanics, a natural definition of the wave function of the unstable system.RiassuntoNell’ipotesi che in ogni effettivo processo di decadimento il sistema instabile sia soggetto a ripetuti processi di misura che accertano se il sistema è decaduto o no, si dimostra che la legge di decadimento è esponenziale, giungendo ad una coerente riconciliazione delle descrizioni statistica e quantistica degli esperimenti di decadimento. Si mostra inoltre che il processo di misura è una localizzazione dei prodotti di decadimento e che, conseguentemente, il sistema instabile viene ridotto ad un unico stato quantistico. Nel quadro della meccanica quantistica ordinaria si dà una definizione naturale della funzione d’onda del sistema instabile.РеэюмеПредполагая, что в каждом реальном процессе распада нестабильная система подвергается повторным процессам иэмерения, которые устанавливают распалась ли система или нет, мы докаэываем, что эакон распада является зкспоненциальным, что приводит непротиворечивому примирению квантового и классического статистического описаний зкспериментов по распаду. Мы также покаэываем, что процесс иэмерения представляет локалиэацию продуктов распада и, следовательно, нестабильная система приводится к единственной квантовой системе. В рамках обычной квантовой механики мы можем дать естественное определение волновой функции нестабильной частицы.

Does the lifetime of an unstable system depend on the measuring apparatus

SummaryWithin the description of the experimental determination of the decay law recently proposed we investigate the possibility that the experimentally determined lifetime τ be different from the theoretical lifetime 1/γ for undisturbed evolution of the unstable quantum system. It is shown that in some specific examples the deviation of τ from 1/γ is competitive with the accuracy of the experiment. It is made plausible that such a difference, together with a variation of τ with the different experimental set-ups, could be revealed by properly choosing some specific unstable systems and properly devised measuring apparatuses.RiassuntoSeguendo lo schema teorico recentemente proposto per la descrizione della determinazione sperimentale della legge di decadimento, si investiga la possibilità che la vita media τ determinata sperimentalmente risulti diversa da quella teorica 1/γ ottenuta supponendo che il sistema instabile evolva indisturbato. Si mostra che in alcuni casi specifici la deviazione di τ da 1/γ è dello stesso ordine della precisione sperimentale. Diventa pertanto plausibile che una siffatta deviazione, come pure una variazione di τ al mutare degli apparati sperimentali, possa essere rivelata scegliendo opportuni sistemi instabili e utilizzando apparati di misura adatti.РеэюмеВ рамках недавно предложенного описания зкспериментального опре-деления эакона распада мы исследуем воэможность, что зкспериментально опре-деленное время жиэни т отличается от теоретического времени жиэни 1/γ по причине невоэмушенной зволюции нестабильной квантовой системы. Покаэывается, что в некоторых специальных случаях отклонениеτ от 1/γ конкурирует с точностью зксперимента. Окаэывается правдоподобным, что такая раэница вместе с иэмене-ниемτ в эависимости от раэличной зкспериментальной аппаратуры может быть обнаружена с помошью соответствуюшего выбора некоторых специальных неста-бильных систем и соответствуюшей иэмерительной аппаратуры.

Multiple-scattering theory of X-ray absorption: a review

The author reviews the basic elements of the theory of X-ray absorption using the tools provided by the theory of multiple scattering. He first uses an approximate momentum space approach which gives a very clear physical insight where the final formulas expressing EXAFS and XANES, i.e. the structures appearing in the absorption coefficient above the edge of a deep core-level threshold, are given in terms of eigenstates of the photoelectron momentum. He then reviews the correct formalism, the curved-wave theory for which he needs to work in angular momentum space. Simple graphic representations are given for the multiple-scattering function.

Threshold behavior of cross sections of charged particles

Abstract The energy dependence of scattering and reaction cross sections at the threshold of a new channel with Coulomb forces is investigated. In the case of opposite charges an anomaly is found in which the average over the Coulomb bound state resonances below the threshold energy is discontinuously different from the limit from above. The resolution and precision necessary, however, make it very difficult to measure the phenomenon.

Coherent rotational states: Their formation and detection

Abstract In this paper, we describe molecules and nuclei, with energy spectrum close to that of an ideal rotator, and therefore capable of being pushed into a coherent rotational state. The formation of a coherent rotational state is obtained by means of a strong electromagnetic pulse. In the case of a molecule, resort is made to a laser pulse, while for a nucleus use is made of the Coulomb excitation in a heavy-ion collision. The latter is a thought experiment in that the “coherence” period obtained in the evolution of typical observables is out of reach of experimental detection. For the molecular case, the experiment is feasible and has been done.

Bound states embedded in the continuum and the formal theory of scattering

Abstract The formal theory of scattering is developed when bound states embedded in the continuum are present. It is shown that it is still possible to define the scattering matrix due to the vanishing of the matrix element connecting the state vector describing the generic bound state embedded in the continuum with the unperturbed state pertaining to the same energy. The scattering matrix does not exhibit a polar singularity, or could even be not singular, at the energies of these bound states.

The stimulated decay of the lambda hyperon - I

SummaryIn order to interpret a recent experimental result regarding the stimulated decay of Λ-hyperons bound in hyperfragments, a model has been considered in which the decay of the Λ-hyperon may also occur when in the virtual gS-state. The consequences of the non-conservation of parity are also considered.RiassuntoPer interpretare un recente risultato sperimentale riguardante il decadimento degli iperoni Λ legati in iperframmenti è stato preso in esame un modello nel quale il decadimento dell’iperone Λ può accadere anche nello stato gS virtuale. Si considerano anche le conseguenze della non conservazione della parità.

On proton decay

Abstract The problem of proton decay is considered taking into account that in actual experiments there is an interaction of the proton with its environment which could imply an increase of its theoretical lifetime. It is seen that, by application of the time-energy uncertainly relation, no prolongement of the lifetime is obtained in this case.