<Emphasis Type="Italic">D</Emphasis>-Wave Resonances in Three-Body System Ps<Superscript>−</Superscript> with Pure Coulomb and Screened Coulomb (Yukawa) Potentials

We have investigated the doubly excited ¹ D ^e resonance states of Ps⁻ interacting with pure Coulomb and screened Coulomb (Yukawa) potentials employing highly correlated wavefunctions. For pure Coulomb interaction, in the framework of stabilization method and complex coordinate rotation method we have obtained two resonances below the n = 2 threshold of the Ps atom. For screened Coulomb interaction, we employ the stabilization method to extract resonance parameters. Resonance energies and widths for the ¹ D ^e resonance states of Ps⁻ for different screening parameter ranging from infinity (pure Coulomb case) to a small value are also reported.     

The ground state and doubly-excited <Superscript>1,3</Superscript>P° states of hot-dense plasma-embedded Li<Superscript>+</Superscript> ions

We have investigated the ground state and the doubly excited ^1,3P^○ resonance states of plasma-embedded Li⁺ ion. The plasma effect is taken care of by using a screened Coulomb potential obtained from the Debye model. A correlated wave function has been used to represent the correlation effect between the charged particles. The ground state of Li⁺ in plasmas for different screening parameters has been estimated in the framework of Rayleigh-Ritz variational principle. In addition, a total of 18 resonances (9 each for ¹P^○ and ³P^○ states) below the n=2 Li⁺ thresholds has been estimated by calculating the density of states using the stabilization method. For each spin state, this includes four members in the 2snp₊ (2≤n ≤5) series, three members in the 2snp_- (3≤n ≤5) series, and two members in the 2pnd (n=3, 4) series. The resonance energies and widths for various Debye parameters ranging from infinity to a small value for these ^1,3P^○ resonance states along with the ground state energies of Li⁺ and the Li²⁺ (1S), Li²⁺ (2S) threshold energies are reported. Furthermore, the wavelengths for the photo-absorption of lithium ion from its ground state to such ¹P^○ resonance states for different Debye lengths are also reported.     

Complex-scaling treatment for high-lying doubly excited resonances for screened Coulomb helium atom

This work presents an investigation on the doubly excited ¹S ^e autoionizing states of screened helium atom lying below the n = 4 threshold of the He⁺ ion. The potential generated in this system is represented by a Yukawa type potential. We have employed complex-coordinate rotation method, as it is a powerful scheme to study high lying resonances. Hylleraas type wave function is used to consider the correlation effect between all the charged particles. Our resonance parameters for the resonances lying below the He⁺ (n = 2) threshold agree well with those of the existing calculations by using the stabilization method. Resonances associated with higher thresholds are new calculations. All the present results are well converged with basis length N = 444.     

The <Superscript>1,3</Superscript>D<Superscript>○</Superscript> resonance states of positronium negative ion using exponential correlated wave functions

The doubly excited ^1,3D^○ resonance states of Ps^- associated with N=3, N=4 and N=5 Ps thresholds have been investigated using highly accurate correlated wave functions with exponents generated by a quasirandom process. Resonance parameters (both resonance positions and widths) are extracted in the framework of the stabilization method and the complex coordinate rotation method. In addition to many Feshbach resonances below the various Ps thresholds, we have identified two ¹ D^○ shape resonances with one each lying above the N=3 and N=4 thresholds, respectively, and two ³ D^○ shape resonances with one each lying above the N=3 and N=5 thresholds, respectively. The ¹ D^○ shape resonance associated with N=3 Ps threshold and some other Feshbach resonances are reported for the first time in the literature.     

Line shape parameters study of the 6p7p (<Superscript>1</Superscript>P<Subscript>1</Subscript>, <Superscript>3</Superscript>D<Subscript>1</Subscript> and <Superscript>3</Superscript>P<Subscript>1</Subscript>): Autoionizing resonances in barium

We report a systematic line shape analysis study of the 6p7p configuration based ¹P₁, ³D₁ and ³P₁ autoionizing resonances in barium using a Nd:YAG pumped dye laser system in conjunction with a thermionic diode ion detector. The even parity isolated autoionizing resonances have been approached via four intermediate states 6 snp ¹P₁ (6 ≤n ≤8) and 5d6p ¹P₁. A comparison of the Fano parameters of the resonance profiles reveals that the width of an autoionizing resonance is independent of the excitation path while the line profile parameter changes with the selection of different intermediate states.     

Structure of low-lying <Superscript>12</Superscript>C resonances

The hyperspherical adiabatic expansion is combined with complex scaling and used to calculate low-lying nuclear resonances of ¹²C in the 3α model. We use Ali-Bodmer potentials and compare results for other potentials α-α with similar ⁸Be properties. A three-body potential is used to adjust the ¹²C resonance positions to desired values extending the applicability of the method to many-body systems decaying into three α-particles. For natural choices of three-body potentials we find 14 resonances below the proton separation threshold, i.e. two 0⁺, three 2⁺, two 4⁺, one of each of 1^±, 2^-, 3^±, 4^-, and 6⁺. The partial-wave decomposition of each resonance is calculated as a function of the hyperradius. Strong variation is found from small to large distance. The connection to previous experimental and theoretical results is discussed and agreements as well as disagreements are emphasized.     

Triplet P states in Ps− using correlated exponential wave functions

We calculate the resonance parameters (energy and width) for the doubly excited ³P^o and ³P^e states in Ps⁻ using correlated exponential wave functions. The calculations are based on the method of complex-coordinate rotation. The resonance energies and widths for the triplet P-wave Feshbach and shape resonances with both even and odd parities in Ps⁻ ion associated with the N = 2, 3, 4, 5 Ps thresholds are reported. Our predications are in agreement with the available results. Few Feshbach and shape resonance parameters are reported for the first time in the literature. In view of a recent experiment on a singlet P-wave shape resonance state in Ps⁻, it is highly expected that the predications obtained from this study for the triplet P-wave resonance states will provide useful information for the future resonance experiments in Ps⁻. Furthermore, our findings could be found useful for the research communities of atomic physics, nuclear physics, and semiconductor quantum dots including excitons.     

Dielectron widths of the <Emphasis Type="Italic">S</Emphasis>-, <Emphasis Type="Italic">D</Emphasis>-vector bottomonium states

The dielectron widths of Y(nS)(n = 1, …, 7) and vector decay constants are calculated using the relativistic string Hamiltonian with a universal interaction. For Y(nS) (n = 1, 2, 3) the dielectron widths and their ratios are obtained in full agreement with the latest CLEO data. For Y(10580) and Y(11020) a good agreement with experiment is reached only if the 4S-3D mixing (with a mixing angle θ = 27°± 4°) and 6S-5D mixing (with θ = 40°±5°) are taken into account. The possibility to observe higher “mixed D-wave” resonances, $ \tilde \Upsilon $ \tilde \Upsilon (n ³ D ₁) with n = 3, 4, 5 is discussed. In particular, $ \tilde \Upsilon $ \tilde \Upsilon (≈11120), originating from the pure 5³ D ₁ state, can acquire a rather large dielectron width, ∼130 eV, so that this resonance may become manifest in the e ⁺ e ⁻ experiments. On the contrary, the widths of pure D-wave states are very small, Γ _ee (n ³ D ₁)≤ 2 eV.     

Doubly-Excited 1,3 P o States of H− Interacting with Screened Coulomb (Yukawa) Potentials

We have investigated the doubly excited 2s2p ³ P ^o and 2s3p ¹ P ^o resonance states of H⁻ embedded in a model plasma environment. Plasma effects are taken care of by using a screened Coulomb (Yukawa-type) potential. Correlated wave functions are used to represent the correlation effect between the charged particles. The density of resonance states has been calculated using the stabilization method. The calculated resonance energies and widths for various screening parameters are reported.     

Electron collisions with the BeH<Superscript>+</Superscript> molecular ion in the R-matrix approach

The R-matrix method is used to study electron collisions with the BeH⁺ molecular ion. The diatomic version of the UK Molecular R-matrix codes is used and a configuration-interaction calculation is first performed for the BeH⁺ target to obtain its potential energy curves for 19 lowest singlet and triplet states. Scattering calculations are then done to yield excitation and rotational excitation cross sections in the energy range 0 − 14 eV. Additionally we also obtain bound states of BeH and their quantum defects at the BeH equilibrium bond length 2.5369a ₀. Resonance positions and widths for Feshbach resonances in the e-BeH⁺ system are also obtained and presented at the equilibrium bond length 2.5369a ₀.     

Blackbody radiation shift of the Al<Superscript>+</Superscript> clock transition

The blackbody radiation shift of the Al⁺ 3s^{2 1}S^e ₀ ↦ 3s3p ³P^○ ₀ clock transition is evaluated. The polarizabilities of the two states are determined by means of configuration interaction calculations in conjunction with oscillator strength sum rules. The ground state polarizability was 24.14 ±0.12 a.u. while the metastable state polarizability was 24.62 ±0.25 a.u. The derived frequency shift at 300 K was Δν= -0.0042 ±0.0032 Hz. Some auxiliary sum rules are evaluated that allow for the conversion of a finite frequency polarizability difference to a static polarizability difference.     

Spin-orbit coupling in the ground and low-lying excited states of HF<Superscript>+</Superscript> and HF<Superscript>-</Superscript>

Electronic structure and spectroscopic properties B _e, ω_e, ω_e x _e, α_e, T _e of ground state and the low-lying excited states of HF⁺ and HF^- molecular ions were investigated within scalar relativistic multireference configuration interaction with single and double excitations framework using the GAMESS-US program package. All potential energy curves (PECs) were calculated using the relativistic complete active space self-consistent field/spin-orbit multi-configuration quasi-degenerate perturbation theory (CASSCF/SO-MCQDPT). The curves are all fitted to the analytical potential energy function (APEF), from which accurate spectroscopic constants are derived. The spin-orbit splitting was also been studied, the split value of X²P^{2}{\rm \Pi} state of HF⁺ is determined to be 288.38 cm^-1. The calculated properties are in good agreement with the available experimental value. Spectroscopic constants of the ground states of HF^- that have never been observed in experiment are obtained. These curves provide an interpretation of the known experimental observations on this system and suggest a number of further experiments which possible provide a critical test of this data.     

Saturation of Coulomb sum rules in the <Superscript>6</Superscript>Li case

The Coulomb sums S _L(q) of the ⁶Li nucleus have been obtained from electron scattering measurements at 3-momentum transfers q = 1.125–1.625 fm⁻¹. It is found that at q > 1.35 fm⁻¹ the Coulomb sum of the nucleus becomes saturated: S _L(q) = 1 .     

Theoretical study of photoionization of the isoelectronic sequence Rb<Superscript>+</Superscript>, Sr<Superscript>2+</Superscript>, and Y<Superscript>3+</Superscript>

The photoionization cross sections for the 4p shell of ions of the Kr isoelectronic sequence Rb⁺, Sr²⁺, and Y³⁺ are calculated. The configuration interaction theory and the perturbation theory are used to describe the many-electron effects. The relativistic effects are taken into account in the Pauli-Fock approximation. The calculated resonance structure of photoionization cross sections for the 4p shell in the region below the 4s threshold associated with the autoionization of the 4s-np singly excited states and the 4p4p-nln′l′ doubly excited states reproduces the results of recent measurements of total photoabsorption cross sections for the Rb⁺, Sr²⁺, and Y³⁺ ions. It is found that, as the nuclear charge in the isoelectronic sequence increases, the ratio between the direct and correlation parts of amplitudes of the 4s-(n/?)p transition changes and, as the consequence, the minimum of the photoionization cross section of the 4s shell shifts from the continuous spectrum to the region of states of discrete spectrum. This accounts for the strong changes in the shape of the 4s-np resonances in the photoionization cross sections for the 4p shell of Rb⁺, Sr²⁺, and Y³⁺, as well as the distinction between the shapes of the 4s-6p _1/2 mirror resonance in the partial 4p _1/2 and 4p _3/2 photoionization cross sections for the Y³⁺ ion which do not suppress each other in the total photoionization cross section, as is the case for similar resonances in Rb⁺ and Sr²⁺.     

Three-body analysis of<Superscript>11</Superscript>Li and its<Emphasis Type="Italic">β</Emphasis>-decay to deuteron channel and to halo analog state<Superscript>11</Superscript>Be* (18.3 MeV)

The ground state wave function of¹¹Li obtained in a three-body model proposed earlier (S Kumar and V S Bhasin,Phys. Rev. C65, 034007 (2002)) has been employed to study the probability distributions, momentum distributions and n−n correlation. Complex scaling method has been used to find the energy positions and widths of the three resonant states of¹¹Li above the breakup threshold. The formalism is extended further to study the β-decay of¹¹Li to two channels. One is the β-transition of¹¹Li into a high lying excited state of¹¹Be at 18.3 MeV, i.e.,¹¹Be* and the second is the decay to deuteron +⁹Li channel. The¹¹Be* state has been considered as a halo analog state identified as a bound three-body (⁹Li + n + p) system. The n-⁹Li interaction incorporates both the virtual state and the p-wave resonance observed experimentally. For p-⁹Li interaction, a Coulomb corrected separable interaction is constructed using charge indepedendence for strong interaction part. The n-p interaction is operative only in³S₁ state corresponding to the isotopic spin T^h =0. As a result the¹¹Be* state has the same isotopic spin as that of⁹Li core, i.e.,T = 3/2. Using these realistic parameters as input and without invoking any other free parameter, the model has been used to predict the strength of the Gamow-Teller β-decay of¹¹Li to¹¹Be*, i.e.,Bgt = 1.5 and the value of the branching ratio to⁹Li + deuteron channel to be 1.3 × 10^-4. These results are found to be in rather good agreement with the recent experimental findings.     

A three-step laser stabilization scheme for excitation to Rydberg levels in <Superscript>85</Superscript>Rb

We demonstrate a three-step laser stabilization scheme for excitation to nP and nF Rydberg states in ⁸⁵Rb, with all three lasers stabilized using active feedback to independent Rb vapor cells. The setup allows stabilization to the Rydberg states 36P_3/2–70P_3/2 and 33F_7/2–90F_7/2, with the only limiting factor being the available third step laser power. We study the scheme by monitoring the three laser frequencies simultaneously against a self-referenced optical frequency comb. The third step laser, locked to the Rydberg transition, displays an Allan deviation of 30 kHz over 1 second and <80 kHz over 1 hour. The scheme is very robust and affordable, and it would be ideal for carrying out a range of quantum information experiments.     

Indication for hyperdeformed cluster states in <Superscript>233</Superscript>Th

An activation technique was used to investigate relative yields of fission products from the reaction ²³²Th(n, f ) for neutron energies between 1.3 and 1.8MeV covering the region around the first hyperdeformed resonances. Intensities of characteristic γ-ray transitions were analyzed to search for changes in the mass distribution for neutron energies corresponding to the resonances and below the resonances. Relative increases in yield between 7 and 23% are observed for A ≈ 100 and 132 in the resonance region around 1.6MeV. It is proposed that the yield enhancement of daughter nuclei of the preformed fragments ¹³²Sn and ¹⁰¹Zr arises from cold fission of a di-cluster configuration. The experimental results support theoretical predictions for the existence of hyperdeformed octupole shapes based on the di-nuclear configuration ¹³²Sn + ¹⁰¹Zr.     

On the existence of <Emphasis Type="Bold">1, 3</Emphasis>P <Emphasis Type="Bold">o</Emphasis> resonances in H<Superscript>-</Superscript> between n = 2 and 3 H thresholds

We examine the influence of relativistic and QED effects on the existence of the ^1,3P ^o H^- resonances between n = 2 and 3 hydrogen thresholds, the relativistic and QED corrections and the coupling effects between the high singlet and triplet states are considered as first-order perturbations. We firstly obtain accurate non-relativistic resonant energies and widths of fifteen ¹P ^o resonances, and fifteen ³P ^o resonances. The fifteen ¹P ^o resonances are classified to be ₃ (2, 0) ^- _n ( 4 ? n ? 12) and ₃ (1, 1) ⁺ _n ( 3 ? n ? 8). The fifteen ³P ^o resonances are classified to be ₃ (2, 0) ⁺ _n ( 3 ? n ? 12) and ₃ (1, 1) ^- _n ( 4 ? n ? 8). We found there exist six Feshbach resonances for ₃ (2, 0) ^- _n (¹P ^o ) series, four Feshbach resonances for ₃ (1, 1) ⁺ _n (¹P ^o ) series, seven Feshbach resonances for ₃ (2, 0) ⁺ _n (³P ^o ) series, and three Feshbach resonances for ₃ (1, 1) ^- _n (¹P ^o ) series. Received 22 February 2002 Published online 24 September 2002     

K-matrix analysis of the (IJ<Superscript>PC</Superscript> = 00<Superscript>+ +</Superscript>)-wave in the mass region below 1900 MeV

We present the results of the current analysis of the partial wave IJ ^PC = 00^{+ +} based on the available data for meson spectra ( ππ, KˉK,ηη,η,ππππ). In the framework of the K-matrix approach, the analytical amplitude has been reconstructed in the mass region 280 MeV < < 1900 MeV. The following scalar-isoscalar states are seen: comparatively narrow resonances f ₀(980), f ₀(1300), f ₀(1500), f ₀(1750) and the broad state f₀(1200-1600). The positions of the amplitude poles (masses and total widths of the resonances) are determined as well as pole residues (partial widths to meson channels ππ, KˉK,ηη,η,ππππ). The fitted amplitude gives us the positions of the K-matrix poles (bare states) and the values of bare-state couplings to meson channels thus allowing the quark-antiquark nonet classification of bare states. On the basis of the obtained partial widths to the channels ππ, KˉK,ηη,η, we estimate the quark/gluonium content of f ₀(980), f ₀(1300), f ₀(1500), f ₀(1750), f₀(1200-1600). For f ₀(980), f ₀(1300), f ₀(1500) and f ₀(1750), their partial widths testify the qˉq origin of these mesons though being unable to provide precise evaluation of the possible admixture of the gluonium component in these resonances. The ratios of the decay coupling constants for the f₀(1200-1600) support the idea about the gluonium nature of this broad state. Received: 14 May 2002 / Accepted: 20 August 2002 / Published online: 11 February 2003 RID="a" ID="a"e-mail: anisovic@thd.pnpi.spb.ru Communicated by A. Sch?fer     

Autoionization states of the positronium negative ion in exponential cosine-screened Coulomb potentials

The 2s^2 1S^e2s^2~^1{\rm S}^e autoionization resonance states of the positronium negative ion (Ps^-) in exponential cosine-screened Coulomb potentials (ECSCP) are investigated using stabilization method. Highly correlated wave functions for Ps^- are used to take into account the correlation effect of the charged particles. Results for resonance energies and widths are reported for the screening parameter in the range 0.0-0.07 (in a₀ ^-1), to the best our knowledge, for the first time in the literature.