Adiabatically coupled systems and fractional monodromy

We present a 1-parameter family of systems with fractional monodromy and adiabatic separation of motion. We relate the presence of monodromy to a redistribution of states both in the quantum and semi-quantum spectrum. We show how the fractional monodromy arises from the non diagonal action of the dynamical symmetry of the system and manifests itself as a generic property of an important subclass of adiabatically coupled systems

Doorway states in nuclear reactions as a manifestation of the "super-radiant" mechanism

A mechanism is considered for generating doorway states and intermediate structure in low-energy nuclear reactions as a result of collectivization of widths of unstable intrinsic states coupled to common decay channels. At the limit of strong continuum coupling, the segregation of broad (''super-radiating") and narrow (''trapped") states occurs revealing the separation of direct and compound processes. We discuss the conditions for the appearance of intermediate structure in this process and doorways related to certain decay channels.Comment: 16 page

Interfering Doorway States and Giant Resonances. I: Resonance Spectrum and Multipole Strengths

A phenomenological schematic model of multipole giant resonances (GR) is considered which treats the external interaction via common decay channels on the same footing as the coherent part of the internal residual interaction. The damping due to the coupling to the sea of complicated states is neglected. As a result, the formation of GR is governed by the interplay and competition of two kinds of collectivity, the internal and the external one. The mixing of the doorway components of a GR due to the external interaction influences significantly their multipole strengths, widths and positions in energy. In particular, a narrow resonance state with an appreciable multipole strength is formed when the doorway components strongly overlap.Comment: 20 pages, LaTeX, 3 ps-figures, to appear in PRC (July 1997

Resonance trapping and saturation of decay widths

Resonance trapping appears in open many-particle quantum systems at high level density when the coupling to the continuum of decay channels reaches a critical strength. Here a reorganization of the system takes place and a separation of different time scales appears. We investigate it under the influence of additional weakly coupled channels as well as by taking into account the real part of the coupling term between system and continuum. We observe a saturation of the mean width of the trapped states. Also the decay rates saturate as a function of the coupling strength. The mechanism of the saturation is studied in detail. In any case, the critical region of reorganization is enlarged. When the transmission coefficients for the different channels are different, the width distribution is broadened as compared to a chi_K^2 distribution where K is the number of channels. Resonance trapping takes place before the broad state overlaps regions beyond the extension of the spectrum of the closed system.Comment: 18 pages, 8 figures, accepted by Phys. Rev.

Helium in superstrong magnetic fields

We investigate the helium atom embedded in a superstrong magnetic field gamma=100-10000 au. All effects due to the finite nuclear mass for vanishing pseudomomentum are taken into account. The influence and the magnitude of the different finite mass effects are analyzed and discussed. Within our full configuration interaction approach calculations are performed for the magnetic quantum numbers M=0,-1,-2,-3, singlet and triplet states, as well as positive and negative z parities. Up to six excited states for each symmetry are studied. With increasing field strength the number of bound states decreases rapidly and we remain with a comparatively small number of bound states for gamma=10^4 au within the symmetries investigated here.Comment: 16 pages, including 14 eps figures, submitted to Phys. Rev.

Intramolecular vibrational energy relaxation seen as expansion in phase space. I. Some experimental results for H2O+(X̃ 2B1), C2H4 +(X̃ 2B3), and HCN+(B̃2Σ +)

It has been shown by Heller that a nonstationary wave packet resulting from a Franck-Condon transition evolves on the potential energy surface of the final electronic state and propagates through phase space at a rate which can be determined from the autocorrelation function \C(t)\2 = | 〈∅(0) |∅(t) ) |2. Since C(t) can be obtained by Fourier transformation of an optical spectrum S(E), i.e., from an observable quantity, it is possible to derive from an experimental measurement information concerning the density operator of a so-called dynamical statistical ensemble (DSE). This density operator, denoted ρav, represents a statistical mixture of the eigenstates of the system with weights determined by the dynamics of the system. It becomes diagonal after a so-called break time Script T sign;B. Its measure, according to a definition due to Stechel, can be interpreted as an effective number of states (denoted script N) that significantly contribute to the dynamics. The break time Script T sign;B represents the finite period of time allowed to expand in the phase space and after which no further progress can be made. Therefore, the number script N∞ of phase space cells which are accessed after a very long interval of time (or in practice after the break time) remains limited. Information on the validity of statistical theories of unimolecular reactions is contained in the fraction ℱ of the available phase space which is eventually explored. In order to assess the representativity of the sampling, it is necessary to account for the selection rule which requires all the states counted in script N ∞ to belong to the totally symmetric representation. It is also appropriate to estimate the role played by Fermi resonances and similar vibrational interactions which bring about energy flow into zero-order antisymmetric modes. A method to carry out the necessary partitionings is suggested. The functions script N T and ℛ T, and the quantities Script T signB, script N ∞, t script N, and ℱ have been determined from experimental data in three cases. In each case, the rate ℛT = d script N r/dT starts from an initial value of zero, increases up to a maximum which is reached after a time of the order of 10-14 s, and then exhibits an overall decrease upon which oscillations are superimposed. For state X̃ 2B1 of H2O+, Script T signB ≃a 2.4×10-14 s and Script T sign ≃ 0.3. The wave packet never accesses that part of the phase space that corresponds to the excitation of antisymmetric vibrations. For state X̃ 2B3u of C2 H4 +, Script T signB ≃1.6 × 10-13 s and Script T sign ≃ * 5×10-4. This fraction raises to 6 × 10 -3 if measured with respect to the effectively available phase space. When the spectrum consists of a discrete part followed by a dissociation continuum, the method can be extended to study the behavior of the bound part of the wave packet only. This has been applied to state B̃ 2Σ+ of HCN+ which is characterized by a very irregular spectrum. This case offers an example of complete occupation of phase space after a break time which is of the order of 2 ×10 -13 s. © 1990 American Institute of Physics

Intramolecular vibrational relaxation seen as expansion in phase space. III. The long-time limit

Asymptotic formulas that describe the behavior of the function N(T) measuring the phase space volume sampled by a nonstationary wave packet during its time evolution are derived. It is shown that, in the long-time limit, N(T)∼T-1 when the dynamics is regular, whereas N(T)∼T-2 In T for the chaotic case. © 1997 American Institute of Physics

Intramolecular vibrational relaxation seen as expansion in phase space. 4. Generic relaxation laws for a spectroscopic clump profile

We examine the volume of phase space sampled by a nonstationary wave packet when the spectral function consists of a single clump or of a series of them. The relaxation laws are expressed in terms of reduced time variables tau, whose definition involves either the average density of states (for a single clump) or appropriately weighted average densities of states (when the spectrum consists of many clumps). Introducing reasonable approximations, very simple generic relaxation laws are derived for the ratio N(tau)/N-infinity which measures the fraction of available phase space that has been sampled by time tau. Under certain assumptions, these laws are found to depend neither on the number nor on the individual features (shapes and widths) of the clumps. However, they strongly depend on the nature (regular or chaotic) of the underlying dynamics. When the dynamics is regular, the relaxation law is expressed in terms of tau(-1), whereas the corresponding equation in the chaotic limit is slightly more complicated and involves terms in tau(-2) and tau(-2) ln tau. Phase space is thus explored according to essentially different relaxation laws in the regular and chaotic limits, the difference being appreciable during the entire relaxation. These laws reflect in the time domain the difference in the distribution of nearest-neighbor level spacings observed in the energy domain (Poisson or Wigner statistics)

Couplages entre modes normaux étudiés par la fonction de corrélation. Effet Duschinsky et résonance de Fermi.

The dynamical information contained in a correlation function obtained by the Fourier transform of an electronic spectrum can be used to study strong intermode couplings, such as the Duschinsky effect (DE) and the Fermi resonance (FR). Both of them complicate the calculation of the correlation function by destroying its factorisability. In some particular cases, the DE can greatly simplify the form of the correlation function by concealing one of its inherent frequencies. The DE never leads to a beat or to a systematic decrease of the correlation function. A simple classical approximation for the correlation function which takes into account the Lissajous motion of the center of the wave packet, but does not allow for its deformation or spreading is found to be useful in a harmonic model. The FR leads to a beat in the correlation function which results from a periodic energy transfer from the active to the inactive mode. A practical method is given to extract the perturbed and unperturbed energies as well as the coupling matrix element of a FR from a low-resolution spectrum by Fourier transformation of just that part of the spectrum which corresponds to the quasidegenerate interacting states. The case of the B2Sigma+u state of CS2+ is treated as an example