The mass distributions of baryon resonances populated in near-central collisions of Au on Au and Ni on Ni are deduced by defolding the $p_t$ spectra of charged pions by a method which does not depend on a specific resonance shape. In addition the mass distributions of resonances are obtained from the invariant masses of $(p, \pi^{\pm})$ pairs. With both methods the deduced mass distributions are shifted by an average value of -60 MeV/c$^2$ relative to the mass distribution of the free $\Delta(1232)$ resonance, the distributions descent almost exponentially towards mass values of 2000 MeV/c^2. The observed differences between $(p, \pi^-)$ and $(p, \pi^+)$ pairs indicate a contribution of isospin $I = 1/2$ resonances. The attempt to consistently describe the deduced mass distributions and the reconstructed kinetic energy spectra of the resonances leads to new insights about the freeze out conditions, i.e. to rather low temperatures and large expansion velocities
The relativistic coupled-cluster method is applied to calculate the magnetic dipole hyperfine constant ''A'' of the 6s 1/2 , 6p 1/2 , 6p 3/2 , and 5d 3/2 states of singly ionized barium. After the inclusion of two-body correlation effects into the computation of the hyperfine matrix elements, the accuracy of the obtained values was significantly increased compared to earlier computations. Based on these numbers and earlier calculations of the electric dipole transitions and excitation energies, an estimate for the accuracy of the ͉͓5 p 6 ͔6s 1/2 ͘ →͉͓5p 6 ͔5d 3/2 ͘ parity-nonconserving electric dipole transition amplitude is carried out. The results suggest that for the first time, to our knowledge, a precision of better than 1% is feasible for this transition amplitude.An experiment to observe parity nonconservation ͑PNC͒ in a single trapped and laser cooled ion was proposed by Fortson about a decade ago ͓1͔. Initial steps towards the realization of such an experiment on Ba ϩ have been taken and the results were reported recently ͓2͔.Relativistic many-body calculations have been performed for the parity-nonconserving electric dipole amplitude for the ͉͓5 p 6 ͔6s 1/2 ͘→͉͓5p 6 ͔5d 3/2 ͘ transition in 137 Ba ϩ ͓3,4͔.
Electric dipole transition amplitudes of certain low-lying states of Pb+ have been calculated using the relativistic coupled-cluster theory and compared with previous calculations. The role of electron correlation is found to be important. Some of the results we have obtained would be useful in estimating the size of the parity non-conserving amplitude for the 6p2P1/2 → 6p2P3/2 transition.
This work presents a first time accurate calculation of the magnetic dipole hyperfine structure constants for the ground state and some low-lying excited states of Pb + . By comparing different levels of approximation with experimental results, we demonstrate the importance of correlation effects which reach beyond lower order relativistic many body perturbation theory. Employing relativistic coupled-cluster theory we obtain a quantitative understanding of the core-polarization and correlation effects inherent in this system and observe completely different trends compared to Ba + .Coupled-cluster theory has been used to study a wide range of many-body systems [1]. Although the non-relativistic version of this theory has been very successfully applied to a variety of light atoms and molecules [2], its extension to the relativistic regime is rather recent [3,4]. There have been relatively few theoretical studies of properties of heavy atomic systems based on the relativistic coupled-cluster (RCC) theory. Pb + (Z=82) is the heaviest atomic ion that has been trapped and cooled so far [5,6]. The magnetic dipole hyperfine constants have been measured for the 6p 2 P 1/2 and 6p 2 P 3/2 states of this ion [7] and these data can be compared with calculations of the corresponding quantities using RCC theory. Such comparisons would indeed constitute an important test of this theory. The non-linear RCC in the singles and doubles approximation with partial triples added in some cases has yielded results to an accuracy of about one percent for atoms and ions with a single s valence electron [8,9,10]. However, the correlation effects in Pb + are expected to be much stronger as it has a 6p valence electron and two 6s electrons in its outermost core orbital.The hyperfine structure constant (A)for the atomic state |JM can be expressed in terms of a reduced expectation value where r j is the radial position of the j th electron, α j is the Dirac matrix and Y10 is a vector spherical harmonic.We have used the RCC theory in to obtain the atomic wavefunctions. As pointed out in our earlier work [12] coupled-cluster theory is equivalent to all order manybody perturbation theory (MBPT). In the open-shell coupled-cluster theory [13,14] the many-body wavefunction for a system with single valence electron can be written aswhere a † v is the creation operator corresponding to a valence orbital 'v' and |Φ 0 is a closed-shell determinantal state built from occupied Dirac-Fock (DF) orbitals. T-and S v -are the closed and open shell excitation operators respectively. In this work both T-and S voperators are truncated beyond double excitations and triple excitations are added on the leading order MBPT level.Explicitly, the T-operator is defined as
The relativistic coupled cluster theory is employed to calculate the hyperfine structure of the 2S
1/2, 2P
1/2, 2P
3/2, 2D
3/2 and
2D
5/2
states of singly ionized calcium. The importance of correlation effects is
highlighted. Our results are compared with other theoretical calculations and
experiments.
Ionization potentials and excitation energies of rubidium and cesium atoms are computed using the relativistic coupled cluster ͑CC͒ method. The effect of electron correlations on the ground and excited state properties is investigated using different levels of CC approximations and truncation schemes. The present work demonstrates that the even-parity channel truncation scheme produces results almost as accurate as obtained from the all-parity channel approximation scheme at a reduced computational cost. The present study also indicates that for a given basis the linearized CC method tends to overestimate the ground and excited state properties compared to the full CC method.
We report the results of our relativistic coupled cluster singles, doubles, and partial triples calculations of the ionization potentials ͑IP͒ and excitation energies ͑EE͒ for different low-lying levels of Ba ϩ . The accuracies of the IP's and EE's are approximately 0.2% and 1%, respectively. The inclusion of the triple excitations were crucial to achieve this degree of precision.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.