Slow cross-symmetry phase relaxation in complex collisions

We discuss the effect of slow phase relaxation and the spin off-diagonal S-matrix correlations on the cross-section energy oscillations and the time evolution of the highly excited intermediate systems formed in complex collisions. Such deformed intermediate complexes with strongly overlapping resonances can be formed in heavy-ion collisions, bimolecular chemical reactions, and atomic cluster collisions. The effects of quasiperiodic energy dependence of the cross sections, coherent rotation of the hyperdeformed ?(3 : 1) intermediate complex, Schrödinger cat states, and quantum-classical transition are studied for ²⁴Mg + ²⁸Si heavy-ion scattering.     

Properties of some resonances of the 55Mn(p,γ)56Fe reaction in the E p = (1.3−1.8) MeV region

Radiative decay of 21 resonances in the ⁵⁵Mn(p, )⁵⁶Fe reaction was studied in the proton beam energy region E _p = (1.3–1.8) MeV. Branching of decay to many low lying bound states up to excitation energy E _x 8 MeV was measured. Exact energy of all resonances has been established, what pointed out that five of the resonances are very close doublets. For all studied resonances their spin-parity characteristics were determined. Assignment of some resonances as isobaric analogues of the states in the ⁵⁶Mn nucleus was discussed and short note about energy systematics of isobaric analogue resonances was given.     

Near threshold neutron-fission cross section

The formal theory of intermediate structure in nuclear reactions is applied to the problem of sub-threshold fission processes induced by a neutron beam in a region of overlapping resonances. An explicit expression is obtained for the energy-averaged cross section also in the presence of a fission vibration in the second well. A method is shown for computing heights and curvatures of the two fission barriers from a knowledge of the slope of the cross section near the threshold, using also information from low-energy intermediate structures and from g.s. isomers. The method is applied to ²³⁵U, ²³⁸Np and ²⁴³Pu. The existence of a new isomer in ²³⁸Np is also predicted.     

S-wave inverse problem and sum rules for potentials with a simple pole at the origin

In a previous paper (F. Calogero and A. Degasperis, J. Math. Phys.9 (1968), 90) an approach to the inverse problem for the nonrelativistic S-wave potential scattering has been developed with the aim of obtaining explicit and exact expressions of the potential in terms of the phase shift and of the bound states parameters. Since this method, based on the high energy asymptotic expansion, yields the expression of the potential and of all its derivative at the origin only if these quantities are bounded, physically interesting interactions such as the Yukawa potential could not be considered. In this paper this approach has been generalized to potentials with a simple pole at the origin and the expression of the Laurent coefficients of the potential in a neighborhood of the origin has been obtained as an explicit functional of the experimental data. Furthermore the general structure of the high energy expansion of the phase shift has been derived and discussed. The requirement that the potential has only a simple pole at the origin turns out to imply strong constraints on the experimental data. These conditions on the experimental data have been explicitely expressed as a set of infinitely many nonlinear sum rules involving only the phase shift and the energies of the bound states.     

Spectral properties and bound-state scattering for weakly coupled λP(ϕ)2 models

We analyze the particle structure in weakly coupled λP(?)₂ models. Topics include existence of bound states and resonances, asymptotic expansions for bound-state masses, low-energy asymptotic completeness, and perturbation theory for scattering events involving bound states. The analysis is based on analyticity properties and perturbation theory for the Bethe-Salpeter kernel.     

A study of the excited states of23Na from the22Ne(p, γ)23Na reaction

The gamma decays of 19²²Ne(p, γ)²³Na resonances in the range ofE _p =400?1300 keV have been investigated by means of a 38 cm³ Ge(Li) detector. Branching ratios of the resonances and bound states were determined. Gamma-ray energy measurements yield the energies of 19 bound states and the value of 8794.0±1.5 keV forQ. The existence of the 3913 keV doublet state was studied through the (p, γ) reaction. No evidence for such a doublet was found.     

Resonances in Three-Body Systems Studied by a Full Angular-Momentum, Smooth-Exterior Complex-Scaling Finite-Element Method

 The development of a tool for calculating resonances and bound states in three-body systems described by a single-potential energy surface is reported. The method has been applied to the antiprotonic helium, doubly excited states in helium, the ¹¹Li nuclear halo, the NeICl van der Waals molecule, and the recently found FHD reaction complex. Received November 26, 2001; accepted for publication November 28, 2001     

Electroreflectance of bound excitonic states in semiconductors

While first-derivative spectroscopy (thermoreflectance, piezoreflectance, wavelength derivative modulation) has a general validity, no matter whether one is studying interband or excitonic transitions (involving also bound states), things are more complex in the case of electroreflectance (ER). As a matter of fact, Aspnes and Rowe's third-derivative theory does not include bound excitonic states. Using a phenomenological approach one can see that only in the case of a strong mixing between d³ε_r/dE³ and d³ε₁/dE³ it is possible to observe a qualitative agreement between Δε and d³ε/dE³ in some particular cases where Wannier excitonic series gives a predominant contribution to the optical spectra.     

How does the Entropy/Information Bound Work?

According to the universal entropy bound, the entropy (and hence information capacity) of a complete weakly self-gravitating physical system can be bounded exclusively in terms of its circumscribing radius and total gravitating energy. The bound’s correctness is supported by explicit statistical calculations of entropy, gedanken experiments involving the generalized second law, and Bousso’s covariant holographic bound. On the other hand, it is not always obvious in a particular example how the system avoids having too many states for given energy, and hence violating the bound. We analyze in detail several purported counterexamples of this type, and exhibit in each case the mechanism behind the bound’s efficacy. In memoriam Asher Peres.     

Three body resonances in a coupled channel ND approach

Assuming a three body channel to be dominated by the formation of bound states and resonances, the three body problem is reduced to an effective two body coupled channel problem in which pairs of particles, either bound states or resonances, scatter from the remaining third particle. We treat this effective two body problem by the partial wave matrix $\text{N}\text{D}$ method. We study in particular a coupled two channel problem, one channel consisting of one resonance plus one particle, the other of one bound state plus one particle. Our main purpose is to investigate in a full coupled channel situation the possible generation of three particle resonances. With single particle exchange forces forming the dynamical input to the $\text{N}\text{D}$ integral equations, enhancements are generated in a spinless model which correspond to three-particle resonances. The model is then applied, with spin included, to the $\text{p + p +}{}^{12}\text{C}$ system at low energy, in which ($\text{p +}{}^{12}\text{C}$) can form either the bound state ¹³N (G.S.) or the resonance ¹³N¹ (1.944 Mev); the two channels are then $\text{p +}{}^{13}\text{N(G.S.)}$ and $\text{p +}{}^{13}\text{N}{}^1$. The p-p interaction is neglected. It is found that the main effect in this case is the force arising from the coupling of the channels, which is sufficiently strong to generate a three particle level in the composite system ¹⁴O.     

Resonance scattering with modified continuum states: (II). Application of the unified model with one particle in the continuum to the 12C + n system

Starting from the conventional shell model, different methods for the treatment of the continuum are given. Using the modified continuum states of part I together with the reaction operator formalism, the present approach unifies the numerical features of the R-matrix theory and the physical picture of the shell model. As it treats the bound states and the scattering states in the same basis we calculated both for the ¹²C + n system as a test case. It is found that the results resemble the experimental data quite well, including for the first time the negative-parity resonances.     

Investigation of auto-ionizing states in xenon by resonantly enhanced multi-photon ionization

We have examined the autoionization spectrum of xenon by resonantly enhanced three-photon ionization (2 + 1 REMPI) involving intermediate states 5p ⁵6p[J = 0, 2]. The properties of the observed autoionization resonances change significantly with the choice of the intermediate state. For ionization via an intermediate state with predominantly 5p ⁵(²P_3/2) core character, a strong continuum with embedded window-type 5p ⁵(²P _1/2)nd'-autoionization resonances is observed. For intermediate states, predominantly with 5p ⁵(²P_1/2) core character, both 5p ⁵(²P _1/2)nd'- as well as 5p ⁵(²P _1/2)ns'-resonances are present in the spectrum as overlapping, nearly symmetric peaks on a rather weak continuum. Calculations confirm the significant dependence of the spectral lineshapes upon the excitation pathway to the autoionizing state. The ionization data are compared with spectra obtained by monitoring third-harmonic generation via autoionizing states without resonant excitation of intermediate states. These spectra also exhibit the signature of both the nd'- and ns'-resonances. Received 30 September 2002 Published online 28 January 2003 RID="a" ID="a"Permanent address: Rostov State University of Transport Communication, 344038, Rostov-on-Don, Russia. RID="b" ID="b"e-mail: halfmann@physik.uni-kl.de     

Breakup and electromagnetic response of light weakly-bound dicluster systems

This study is focused on the breakup and electromagnetic response of light weakly-bound dicluster nuclei. The cluster picture in the case of ⁷Li is shown to be a very good approximation and in this framework we calculate nuclear structure observables. We solve the Schrödinger equation for the relative motion both for discrete and continuum states and this automatically takes the role of resonances into proper account. A concentration of strength in the low energy continuum, solely due to the weakly-bound nature of the bound states is seen and explained as a favorable matching between the wavelengths of the initial and final states. Finally, preliminary results on form factors are briefly outlined and their microscopic derivation as well as utilization in reaction studies are discussed.     

Efimov effect in 2-neutron halo nuclei

This paper presents an overview of our theoretical investigations in search of Efimov states in light 2-neutron halo nuclei. The calculations have been carried out within a three-body formalism, assuming a compact core and two valence neutrons forming the halo. The calculations provide strong evidence for the occurrence of at least two Efimov states in ²⁰C nucleus. These excited states move into the continuum as the two-body (core-neutron) binding energy is increased and show up as asymmetric resonances in the elastic scattering cross-section of the n-¹⁹C system. The Fano mechanism is invoked to explain the asymmetry. The calculations have been extended to ³⁸Mg, ³²Ne and a hypothetical case of a very heavy core (A = 100) with two valence neutrons. In all these cases the Efimov states show up as resonances as the two-body energy is increased. However, in sharp contrast, the Efimov states, for a system of three equal masses, show up as virtual states beyond a certain value of the two-body interaction.     

A generalized r-matrix interpretation of the 89Y + n total cross section at low incident energies

The resonance structure observed in the ⁸⁹Y(n, n)⁸⁹Y total cross-section measurements in the range of 0.9 to 1.2 MeV neutron energy is investigated using a comprehensive theory of nuclear reactions. A shell-model calculation which formed the initial stage of this study predicts satisfactorily the energies of the negative-parity states that contribute to the observed anomalies. The neutron decay widths for these resonances are evaluated using the model wave functions. The general trends in the energy dependence of the total cross section are satisfactorily reproduced by the theory. The factors that could contribute to the discrepancies between theory and experiment are discussed. The theoretical estimates of the damping widths for the two 1^? anomalies that occur in this region were within 20 to 25% of the experimental values and support the view that these are intermediate-type resonances. Their configurational structure as predicted by the model calculation suggests that they are the parent states of the T_> components of the giant dipole resonance near 21.0 MeV in ⁹⁰Zr. The distribution of E1 widths calculated for a proposed 1^? → 2⁺ (at 0.78 MeV) transition in ⁹⁰Y indicates that an anomaly corresponding to these 1^? states can also be expected in the (n, γ) reaction.     

Structure of doorway states in the40Ca+n reaction

A model including 2p-1h and collective states in⁴¹Ca is used to investigate the intermediate structure resonances seen in then+⁴⁰Ca reaction. With potential well parameters determined by a calculation of the bound states it is found that most of thes-wave strength can be accounted for by the inclusion of one main doorway state component.     

Étude des états excités du noyau 34Cl: (I). Courbe d'excitation de la réaction 33S(p, γ)34Cl, énergies,rapports d'embranchement et vies moyennes des niveaux du 34Cl

Resonance energies and strengths are reported for forty-five ³³S(p, γ)³⁴Cl resonances in the range E_p = 1.0–2.0 MeV. Analysis of the γ-ray spectra by means of two Ge(Li) detectors leads to precise excitation energies of bound states and branching ratios of resonant levels and bound states. New bound levels are found. The reaction Q-value is 5140.3 ± 1.5 keV. Mean lives (or limits) of twelve bound states of ³⁴Cl have been obtained from DSA measurements at seven of the studied ³³S(p, γ)³⁴Cl resonances.     

A microscopic approach to the multipole resonances in 20Ne

A fully microscopic study of the proton radiative capture on ¹⁹F with excitation of the multipole resonances in ²⁰Ne is presented. The calculation makes use of a version of the Feshbach formalism of nuclear reactions. The bound states are described as linear combinations of angular momentum projected one particle — one hole configurations in a deformed Hartree-Fock basis. The agreement for the 90° yields with the experimental data is excellent. Gross features as well as intermediate structures are nicely reproduced.     

Isobaric analogue resonances in71As through proton elastic scattering on70Ge

The analogues of the low-lying levels in⁷¹Ge have been observed as resonances in the compound nucleus⁷¹As through proton elastic scattering on⁷⁰Ge in the energy rangeE _p=3.5 to 5.3 MeV. The excitation functions cover the analogue resonances corresponding to states upto 2.3 MeV excitation in⁷¹Ge. The sub-structures in the 5.06 MeV resonance, first observed by Temmer and co-workers have been confirmed in the present experiment. The present investigation reveals similar sub-structures in the 4.13 MeV resonance lending further support to the existence of intermediate structure near an isobaric analogue resonance. The resonance parameters and the spectroscopic factors (for the corresponding parent states) have been extracted. The results are compared with the information available from the⁷⁰Ge(d, p)⁷¹Ge reaction.     

Kurzlebige Compoundzustände in der niederenergetischen Elektron-Helium-Streuung

Electron scattering measurements have been made of the energy dependences of the excitation of the Helium 2³ S, 2¹ S, 2³ p, and 2¹ P states at different scattering angles in the range from 20 to 145°. In the energy range from 22 to 23 eV five overlapping resonances of the (e-He)-system have been determined, one of which (22.42 eV) is identified to be a 3² S, another (22.60 eV) a 3² P-state. The energy values of the other resonances are resp. 22.55, 22.75, and 22.85 eV. The half-widths are below approximately 40 meV. In the 2³ P-channel three peaks vanish at the same scattering angle, a fact, which seems not understandable in terms of first order resonance poles.