Doorway States Research Articles

The dynamics of predissociating high Rydberg states of NO

In this paper we present a theoretical study of the predissociation dynamics of the nf(N+=2) (with the principal quantum numbers n=40–95) and the np(N+=0) (n=70–125) Rydberg series of NO, which exhibit a marked lifetime dilution (lengthening) at n≳65 for the f series and at n≳116 for the p series [M.J.J. Vrakking and Y. T. Lee, J. Chem. Phys. 102, 8818 (1995)]. The multichannel effective Hamiltonian with several doorway (for excitation) and escape (for decay) states was constructed using experimental information on the quantum defects and on the decay width constants incorporating both intramolecular coupling and exterior electric field coupling between high Rydbergs. The analysis of the intramolecular Rydberg electron–core dipole long range coupling (HR-D) in conjunction with the energy gaps between proximal pairs of energy levels, which are subjected to appropriate selection rules, reveals that (i) for low l(≤3) core-penetrating Rydbergs only a small number of accidental near-resonances are exhibited, and (ii) for high l(≳3) nonpenetrating Rydbergs the electron-core dipole coupling decreases fast with increasing l, i.e., (HR-D)∝l−7. The general characteristics of the high l(≳3) manifold establish a bottleneck effect, which precludes intramolecular l mixing, implying that high Rydberg lifetime dilution effects can be induced only by exterior electric field coupling (HSTARK). Parameter-free multichannel effective Hamiltonian calculations were conducted under narrow-band excitation conditions, which interrogate the electric field induced mixing in the energetic vicinity of the doorway state. The electric field induced l mixing model accounts semiquantitatively for the electric field dependence of the energy-resolved line shapes of the nf(N+=2) series and for the n and electric field dependence of the lifetimes of the nf(N+=2) and the np(N+=0) series. Accidental near-resonant simultaneous intramolecular and electric field coupling np(N+=0)↔HR-Dn′d(N+=1)↔HSTARKn′ l(≥3)(N+=1) for two sets of proximal states n=92, n′=80 and n=95, n′=82, result in mediated-sequential mixing, which is manifested by slow decay times below the onset of effective electric field mixing by weak (F0≂0.04–0.08 V/cm) stray electric fields.

Where is the non-spin-flip isovector monopole resonance in 208Tl?

The experimental study of the \ensuremath{\Delta}${\mathit{T}}_{\mathit{z}}$=+1 component of the isovector monopole resonance of $^{208}\mathrm{Pb}$ has revealed itself as an experimental puzzle. We present in this work a theoretical calculation of the strength distribution of this resonance and of its neutron decay properties, within the framework of a model in which random phase approximation states are coupled with continuum configurations and with a set of ``doorway states'' in order to describe the basic escape and damping mechanisms of the nuclear vibration. Our results are compared with existing measurements and with other theoretical analyses. \textcopyright{} 1996 The American Physical Society.

On description of the direct nucleon decay of giant resonances

A semimicroscopical approach is formulated to describe the direct nucleon decay of various giant resonances in intermediate and heavy mass spherical nuclei. The approach consists in: (i) the exact continuum-RPA calculations for amplitudes of the reactions accompanied by excitation and the nucleon decay of the collective particle-hole states (doorway states); (ii) the Breit-Wigner parametrization of the RPA reaction-amplitudes in the vicinity of the giant giant-resonance energy and evaluation of the doorway-state parameter (the energy, entrance and partial nucleon, escape widths); (iii) the phenomenological consideration for the doorway-state coupling to many-particle configurations with the use of reasonable statistical assumptions and derivation on this base the expressions for the energy-averaged reaction amplitudes. The nuclear mean field and quasiparticle interaction are the input quantities for calculations. Examples of description for the direct nucleon decay of a number of giant resonances in the $^{208}Pb$ parent nucleus are given together with the comparison with corresponding experimental data.

PNC effects in neutron-232Th scattering: a window to class II or new states of nuclei?

Abstract The sign correlation of parity-non-conserving ( pnc ) asymmetries observed in neutron 232 Th scattering at the peak of p-wave resonances is examined. Assuming that it is a real effect, the conditions that this implies for a theoretical explanation are determined. It is shown that it has to rely on the existence of two states of opposite parity, which act as “doorway states”, different from those recently considered in the present field. The location of these states, their energy difference and their spreading width are estimated. It is shown that experimental data on 232 Th favor the location of both “doorway states” in the low energy region ( E s 0 , E p 0 ∼0–1 keV). In this case, the asymmetry exhibits a different sign depending on whether the energy of the p-wave resonance is below or above E s 0 . Candidates for such states are then considered, including the well known parity doublet built on a pear-shape nucleus, a more exotic one based on a structure where spins of nucleons align along their momentum ( σ · p correlation), and finally an accidental one in the second well of the potential energy surface. The evidence for a sign correlation in a limited energy range partly depends on the size of the random contribution to the observed pnc effects. The examination of the root mean square value of the pnc matrix element between states of the compound nucleus shows that the range of predictions is quite large and does not provide any constraint at present.

Selection rule for fragmentations of doorway s-hole states in light nuclei.

A selection rule for fragmentations of doorway {ital s}-hole states in light nuclei is given. In the two-body fragmentation process of the doorway {ital s}-hole states in light nuclei, smaller fragments than the {alpha} particle ({ital p}, {ital n}, {ital d}, {ital t}, and {sup 3}He) are allowed, while the fragments such as the {alpha} particle and the larger particles are forbidden, in spite of the fact that the {ital Q} value for the {alpha} fragment is similar to or even larger than those for the {ital p}, {ital n}, and {ital d} fragments. The selection rule comes from the spatial symmetry of the doorway {ital s}-hole states. The spectroscopic factors and partial widths for the two-body fragmentations of the {ital s}-hole state of {sup 11}B and {sup 15}N are calculated to show the selection rule. The calculated escape widths for the {sup 11}B({ital s}-hole) and {sup 15}N({ital s}-hole) doorway states are in good correspondence with the experimental widths. This may suggest that the following scenario is realized; in light nuclei the fragmentation process of the {ital s}-hole state in the doorway stage is superior or competitive to that in the compound nuclear stage. {copyright} {ital 1996 The American Physicalmore » Society.}« less

Nuclear Dicke states and the direct-semidirect model

Abstract The structure of the doorway state assumed in the direct-semidirect model was addressed by Sokolov and Zelevinsky. Modifications of the model due to the nuclear Dicke state in the presence of two open channels has been considered. The results of calculations for neutron capture to the single particle states in Pb and Ca are presented.

The dynamics of high autoionizing Rydberg states of Ar

In this paper we present a theoretical study of the autoionization dynamics of high 2P1/2np′[3/2]1 Rydbergs (with the principal quantum numbers n=100–280) of Ar in weak homogeneous electric fields (F=0.01–1.0 V/cm), which were experimentally interrogated by time-resolved zero-electron kinetic energy (ZEKE) spectroscopy [M. Mühlpfordt and U. Even, J. Chem. Phys. 103, 4427 (1995)], and which exhibit a marked dilution (i.e., ∼2 orders of magnitude lengthening) of the lifetimes relative to those inferred on the basis of the n3 scaling law for the spectral linewidths of the np′ (n=12–24) Rydbergs. The multichannel effective Hamiltonian (Heff) with several doorway state(s) (for excitation and decay) and pure escape states (for decay) was advanced and utilized to treat the dynamics of the mixed Stark manifold of the ZEKE Rydbergs. Heff of dimension 2n−1 is then constructed for a n Rydberg manifold using independent experimental information on the (l dependent) quantum defects δ(l) and the (l, K, J dependent) decay widths, which are of the form Γ0(lKJ)/(n−δ(l))3, with Γ0(lKJ) being the decay widths constants. Here, l, K, and J are the azimuthal, the electronic and the total electronic angular momentum quantum numbers, respectively. Two coupling ranges are distinguished according to the strength of the reduced electric field F̄(n,p′)=(F/V cm−1)n5/ 3.4×109[δ(p′)(mod1)]. Range (A); The onset of the effective coupling of the doorway and escape states, i.e., 0.7≤F̄(n,p′)≤2. Range (B); The strong mixing domain F̄(n,p′)≥3. The lifetimes in range (B) can be well represented by a nearly democratic mixing of all the doorway and escape states (lKJ), with the average value 〈τ(n)〉≂〈τSM(n)〉= 2n4ℏ/[𝒥(lJK)Γ0(lJK)]. In range (B) 〈τ(n)〉 increases with increasing n and is only weakly F dependent. Range (A) is characterized by a hierarchy of two time scales for the decay, with a short decay component, which manifests the residue of the doorway state, and a distribution of very long lifetimes with an average value 〈τLONG(n)〉≂η(n)〈τSM(n)〉, where η(n)≂2–5. In range (A), 〈τLONG(n)〉 decreases with increasing n and decreases with increasing F, manifesting the enhancement of mixing. We identified range (B) for n=150–280, where a semiquantitative agreement between the experimental ZEKE lifetimes and spectra and our theory was obtained. A tentative identification of range (A) for lower n (=100–150) values was accomplished. We have also performed a theoretical study of the Ar autoionization dynamics via the 2P1/2nd′[3/2]1 doorway state, which was experimentally studied by Merkt [J. Chem. Phys. 100, 2623 (1994)]. The onset of range (A) was identified in the region n=70–80, with the estimated lifetimes near the onset being in agreement with experiment. Our analysis explains the higher n onset for the np′ doorway state mixing (n≂100 and F≂0.1 V/cm) than for the np′ doorway state mixing (n′=70–80 for F≂0.1 V/cm). Experimental values of 〈τLONG(n)〉 (around n≂90) in range (A), excited via the 2P1/2nd′[3/2]1 doorway state, are considerably longer than those predicted by our theory for l mixing. The discrepancy may be due to (lml) mixing, which presumably originates from Rydberg–ion collisions.

On direct nucleon decay of the giant dipole resonance and photonucleon reactions

A semimicroscopical approach is proposed to describe the partial cross sections of the photonucleon reactions proceeding via the giant dipole resonance and the branching ratios for the direct nucleon decay of this resonance. The approach is formulated in two steps. The first (microscopical) one consists in the use of the continuum-RPA for calculating the energy, partial nucleon and radiative widths of those 1 − collective particle-hole states (doorway states), which exhaust most of the classical sum rule. The second step concerns the coupling of the doorway state to complex configurations. It is phenomenologically taken into consideration with the use of a statistical assumption. Applications of the approach are given.

Extraction of dynamics from the resonance structure of HeH2+ spectra

For the reaction of He with H2+, starting with accurate theoretically computed reactive, elastic, and inelastic scattering data that reveals many complex unassignable narrow resonances, the detailed motions governing the dynamics of the tight transition state are extracted. Methods ranging from scattering theory, the stabilization theory of dynamics, nonlinear dynamic periodic orbit theory, and hierarchical smoothing theory which was developed to study complex ‘‘chaotic’’ spectra, are all used in the analysis. Relationships between the doorway model of nuclear physics, aspects of transition state theory, and models of nonlinear chaotic dynamics are pointed out and used to shed light on the fact that the complex resonance structure observed is one quantum manifestation of classical transient chaos in scattering processes. The transition (or doorway) state corresponds to the only populous and robust periodic orbit or set of similar periodic orbits whose motion allows the types of energy transfers necessary to go from reactants to products. Wave packet motion and quantum eigenfunctions are influenced by these periodic orbits.

On the application of probability absorbers and doorway states in atomic collisions

The properties of absorber and doorway states are briefly reviewed and related, and the performance of the method to improve atomic and molecular bases at lower and higher intermediate energies, respectively, is illustrated.

Dynamics of Ultrahigh Molecular Rydbergs in Weak Electric Fields

In this paper we explore the dynamics of the mixed Stark manifold of ultrahigh Rydberg states (principal quantum number n = 50-250) of the large molecules interrogated by time-resolved ZEKE (zero-electron kinetic energy) spectroscopy. We pursue the formal analogy between the coupling, accessibility, and decay of ultrahigh Rydbergs in an external weak (F = 0.01 -1.0 Vkm) electric field and intramolecular (interstate and intrastate) relaxation in a bound level structure. The effective Hamiltonian formalism with several doorway and escape states was advanced to treat the dynamics. The theory accounts for the dilution effect, Le., the dramatic lengthening of the lifetimes of ultrahigh Rydbergs, relative to that expected on the basis of the n-3 scaling law for the decay widths. Model calculations for the field-induced (I> mixing reveal that the Rydberg time-resolved population probability is characterized by two distinct (-ns and -ps) time scales. To date, long time-resolved (10 ps-100 ns time scales) nonexponential decay of ZEKE Rydbergs was experimentally documented, in accord with our analysis. The predicted existence of the short decay times (1 - 10 ns) was not yet subjected to an experimental test. Next, we extend the model calculations to treat the mixing of several n manifolds, demonstrating that in the strong mixing limit the overall features of the temporal decay are similar to that of a single n manifold.

On the dynamics of high Rydberg states of large molecules

In this paper we explore the level structure, the optical excitation modes and the dynamics of a mixed Stark manifold of very high Rydberg states (with principal quantum numbers n=80–250) of large molecules, e.g., 1,4 diaza bicyclo [2,2,2] octane (DABCO) and bis (benzene) chromium (BBC) [U. Even, R. D. Levine, and R. Bersohn, J. Phys. Chem. 98, 3472 (1994)] and of autoionizing Rydbergs of atoms [F. Merkt, J. Chem. Phys. 100, 2623 (1994)], interrogated by time-resolved zero-electron kinetic energy (ZEKE) spectroscopy. We pursue the formal analogy between the level structure, accessibility and decay of very high Rydbergs in an external weak (F≂0.1–1 V cm−1) electric field and intramolecular (interstate and intrastate) relaxation in a bound molecular level structure. The onset n=nM of the strong mixing (in an external field F and in the field exerted by static ions) of a doorway state, which is characterized by a low azimuthal quantum number l, a finite quantum defect δ, and a total nonradiative width Γs≂Γ0/n3, with the inactive high l manifold is specified by nM≂80.6δ1/5(F/V cm−1)−1/5. At n≥nM the level structure and dynamics are characterized by the product γρ, where ρ is the density of states and γ=ΓsD(n) is the average decay width of the eigenstates, with the dilution factor D(n)≊n−2 for (lml) mixing and D(n)≂n−1 for (l) mixing, whereupon γρ=(Γ0/4δR)(nM/n)5, being independent of D(n). The sparse level structure is realized for γρ≪1, while the dense level structure prevails for γρ≳1, resulting in two limiting situations; (a) a dense limit for n≥nM and a sparse limit for n≫nM, and (b) a sparse limit for all n≥nM. The experimental information currently available on the decay dynamics of molecular (DABCO and BBC) and atomic (Ar) Rydbergs for n≥nM corresponds to case (b). The time-resolved dynamics was characterized in terms of the excited state total population probability P(t) and the population probability I(t) of the doorway state. P(t), which is interrogated by time-resolved ZEKE spectroscopy, will exhibit for both the sparse and dense level structures and for all excitation conditions a superposition of exponential temporal decay terms with an average lifetime of ∼ℏ/γ. I(t) can be used to interrogate coherence effects, which in case (b) are manifested in quantum beats, while case (a) corresponds to a giant resonance with a molecular time characterized by the reciprocal energetic spread of the Stark manifold. The experimental data for the onset of strong mixing and for the diluted lifetimes [ℏ/ΓsD(n) with D(n)∼n−1] of the high Rydbergs (n∼100–200) of BBC and of DABCO are in accord with the predictions of the theory for the limit of strong (l) mixing. While strong mixing is realized for F̄=Fn5/3.4×109δ≳1, we expect that for the weak mixing regime (F̄<1) the dynamics of ultrahigh Rydbergs will be characterized by two distinct (∼ns and ∼μs) time scales. Finally, we emphasize the universality of the model, which provides a unified description of the level structure and dynamics of high Rydbergs of molecules and of autoionizing atoms.

Nearby Doorway States, Parity Doublets, and Parity Mixing in Compound Nuclear States.

We discuss the implications of a doorway state model for parity mixing in compound nuclear states. We argue that in order to explain the tendency of parity violating asymmetries measured in ${}^{233}\mathrm{Th}$ to have a common sign, doorway states that contribute to parity mixing must be found in the same energy neighborhood of the measured resonance. The work concentrates on novel nuclear structure input, namely, that in the region of interest ( ${}^{233}\mathrm{Th}$) nuclei exhibit octupole deformations which leads to the existence of nearby parity doublets. These parity doublets are then used as doorway states in a model for parity mixing.

Fragmentation and splitting of Gamow-Teller resonances in Sn(3He,t)Sb charge-exchange reactions, A=112-124.

Fragmentation and splitting of the Gamow-Teller (GT) strength has been observed in a systematic study of the ${(}^{3}$He,t) charge-exchange reaction at E${(}^{3}$He)=200 MeV over the entire range of stable Sn isotopes. Triton energy spectra were observed with a high-resolution magnetic spectrometer at angles near \ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{} where \ensuremath{\Delta}L=0 transitions are enhanced. Excitation energies, widths, 0\ifmmode^\circ\else\textdegree\fi{} cross sections, and strengths B(GT) were determined. A theoretically predicted configuration splitting of the main Gamow-Teller component into two components, expected to be dominant near A=118 at the onset of the filling of the 1${\mathit{h}}_{11/2}$ neutron orbital, could not be observed. This may be due to the fact that the total widths of the resonances of 5--6 MeV exceed the predicted splitting. A comparison of the 0\ifmmode^\circ\else\textdegree\fi{} cross sections for the transitions to the Gamow-Teller resonances and the isobaric analog states leads to strengths B(GT) for the main Gamow-Teller components of typically 65% of the sum-rule value of 3(N-Z). Three to four additional Gamow-Teller fragments (``pygmy resonances'') were observed in all final nuclei at lower excitation energies. The excellent energy resolution of the experiment made it possible to observe a pronounced fine structure in these low-lying resonances which is believed to be due to coupling to two-particle--two-hole doorway states. Also seen with all target nuclei was a systematic sequence of strong ${\mathit{J}}^{\mathrm{\ensuremath{\pi}}}$=${1}^{+}$ states near the ground states in all Sb isotopes (${\mathit{E}}_{\mathit{x}}$=0 to 220 keV). In addition, strong \ensuremath{\Delta}L=1 resonances were observed in all nuclei at excitation energies of typically 20 MeV. Furthermore, nonresonant background from quasifree charge exchange was observed. An average of \ensuremath{\sim}85% of all excess neutrons seems to contribute to this background in approximate agreement with results from (e,e'p) experiments.

The dynamics of one-dimensional excitons in liquids

The properties of excitons in one-dimensional molecular aggregates, dissolved at room temperature in a liquid, were studied by means of femtosecond nonlinear optical experiments. Both the one-exciton band (i.e., Frenkel-excitons) and multiexciton bands contribute to the observed nonlinear optical response. The rapid motions in the liquid lead to ultrafast perturbations of the molecular energy levels. This localizes the excitons on limited sections of the chains of aggregated molecules. Ultrafast frequency-resolved pump–probe spectroscopy on the lowest two exciton bands was employed to determine the delocalization length of the optical excitations. The kinetics of the exciton populations was measured by ultrafast grating scattering experiments and time-resolved single photon counting. A model is described in which the multiexciton bands act as doorway states in the exciton–exciton annihilation process. These bands thereby determine the population decay of the Frenkel excitons at high excitation densities. Room temperature photon echo experiments show that stochastic perturbations of the exciton transition frequencies occur on two distinct time scales. In particular the slow components of the fluctuations are affected by motional narrowing, associated with the exciton delocalization length. It is therefore argued that the optical dephasing of excitons is directly related to the spatial extent of the excitation on the aggregate chain.

Intramolecular vibrational dynamics of diacetylene and diacetylene-d1 via eigenstate-resolved overtone spectroscopy

Abstract The high resolution spectra of several CH overtone bands in diacetylene and diacetylene-d1 were measured using optothermally detected excitation of a collimated molecular beam. The first overtone of the acetylenic CH stretches in these two molecules were recorded in a single resonance scheme using a 1.5 μm color center laser. The second overtone spectra were taken using sequential infrared/infrared double resonance with a 3.0 and a 1.5 μm color center lasers. The perturbations in the spectra have been analyzed to obtain information about the nature and timescales of the underlying intramolecular vibrational redistribution processes. The uncovered dynamical features appear to be dominated by anharmonic couplings and exhibit regular, not chaotic, behavior. The first and second overtone spectra of diacetylene-d1 are consistent with a coupling model which involves coupling through a doorway state and then subsequent coupling to the bath. In diacetylene, a combination band was also recorded which, in the local mode picture, is equivalent to putting two quanta in one acetylenic CH stretch and one quanta at the other end of the molecule. Comparison of this spectrum with the spectrum obtained by putting three quanta in the same CH stretch, is consistent with earlier observations that delocalized combination bands are less perturbed than nearly isoenergetic pure overtone states.

The intramolecular dynamics of allene in the region around 6000 cm−1 via eigenstate resolved IR spectroscopy

We have recorded and analyzed the molecular beam spectra of allene in the regions of the ν 1 + ν 5 and 2 ν 8 bands around 5947.5 and 6135.5 cm −1 , respectively. The ν 1 + ν 5 band only shows minor perturbations and we suspect the presence of a doorway state that causes parallel Coriolis coupling to the bath states. Perpendicular Coriolis interactions do not seem to play an important role since the size of the matrix elements does not increase systematically with J ′. The spectrum in the region of the 2 ν 8 band is more complicated; a total of six sub-bands has been identified with K = 0–2. Based on the lack of any systematic dependence on J ′ and an inverse dependence of the coupling on K , we expect that neither parallel nor perpendicular Coriolis coupling is present in this band. The effective lifetime for both bands is calculated to be about 200 ps, which is very similar to the lifetimes of an acetylenic CH stretch overtone.

The spin-dipole resonance and parity mixing in compound nuclear states

We examine the role of the giant spin-dipole resonance (both isoscalar and isovector) in parity mixing in compound nuclear states. We consider its contribution to the longitudinal asymmetry measured in recent experiments with epithermal polarized neutrons on unpolarized medium and heavy mass nuclei. Empolying the doorway state approximation we calculate the contribution of the spin-dipole to the parity nonconserving spreading width and average asymmetry.

Theory of parity violation in compound nuclear states: One particle aspects.

In this work we formulate the reaction theory of parity violation in compound nuclear states using Feshbach's projection operator formalism. We derive in this framework a complete set of terms that contribute to the longitudinal asymmetry measured in experiments with polarized epithermal neutrons. We also discuss the parity violating spreading width resulting from this formalism. We then use the above formalism to derive expressions which hold in the case when the doorway state approximation is introduced. In applying the theory we limit ourselves in this work to the case when the parity violating potential and the strong interaction are one-body. In this approximation, using as the doorway the giant spin-dipole resonance and employing well known optical potentials and a time-reversal even, parity odd one-body interaction we calculate or estimate the terms we derived. In our calculations we explicitly orthogonalize the continuum and bound wave functions. We find the effects of orthogonalization to be very important. Our conclusion is that the present one-body theory cannot explain the average longitudinal asymmetry found in the recent polarized neutron experiments. We also confirm the discrepancy, first pointed out by Auerbach and Bowman, that emerges, between the calculated average asymmetry and the parity violating spreading width, when distant doorways are used in the theory.

Application of regularized probability absorber states to He++H+ collisions

To improve on the behaviour of usual close coupling expansions at intermediate energies it has been recently proposed to enlarge the basis with the addition of probability absorbers or doorway states. Application to atomic expansions requires the regularization of the Coulomb potential interactions, either by using model potentials or projection techniques. A preliminary application of the latter method to the benchmark He+(1s)+H+ collisional system is presented, using a one-centre atomic expansion, in the range of 10-500 KeV impact energies. Use of different regularizations, together with an analysis on the shape of the probability absorber functions, permits electron loss, ionization, charge exchange and excitation cross sections to be obtained.