arXiv subjects
Publications and source records attributed to A. M. Shirokov.
A technique for describing scattering states within the nuclear shell model is proposed. This technique is applied to scattering of nucleons by $α$ particles based on ab initio No-Core Shell Model calculations of $^5$He and $^5$Li nuclei with JISP16 NN interaction.
We perform \textit{ab initio} no-core shell-model calculations for $A=18$ and $19$ nuclei in a $4\hbarΩ$, or $N_{\rm max}=4$, model space by using the effective JISP16 and chiral N3LO nucleon-nucleon potentials and transform the many-body effective Hamiltonians into the $0\hbarΩ$ model space to construct the $A$-body effective Hamiltonians in the $sd$-shell. We separate the $A$-body effective Hamiltonians with $A=18$ and $A=19$ into inert core, one-, and two-body components. Then, we use these core, one-, and two-body components to perform standard shell-model calculations for the $A=18$ and $A=19$ systems with valence nucleons restricted to the $sd$ shell. Finally, we compare the standard shell-model results in the $0\hbarΩ$ model space with the exact no-core shell model results in the $4\hbarΩ$ model space for the $A=18$ and $A=19$ systems and find good agreement.
Saturation properties of the JISP16 NN interaction are studied in symmetric nuclear matter calculations, with special attention paid to the convergence properties with respect to the number of partial waves. We also present results of pure neutron matter calculations with the JISP16 interaction.
Background: Phase-equivalent transformations (PETs) are well-known in quantum scattering and inverse scattering theory. PETs do not affect scattering phase shifts and bound state energies of two-body system but are conventionally supposed to modify two-body bound state observables such as the rms radius and electromagnetic moments. Purpose: In order to preserve all bound state observables, we propose a new particular case of PETs, a deuteron-equivalent transformation (DET-PET), which leaves unchanged not only scattering phase shifts and bound state (deuteron) binding energy but also the bound state wave function. Methods: The construction of DET-PET is discussed; equations defining the simplest DET-PETs are derived. We apply these simplest DET-PETs to the JISP16 $NN$ interaction and use the transformed $NN$ interactions in calculations of $^3$H and $^4$He binding energies in the No-core Full Configuration (NCFC) approach based on extrapolations of the No-core Shell Model (NCSM) basis space results to the infinite basis space. Results: We demonstrate the DET-PET modification of the $np$ scattering wave functions and study the DET-PET manifestation in the binding energies of $^3$H and $^4$He nuclei and their correlation (Tjon line). Conclusions: It is shown that some DET-PETs generate modifications of the central component while the others modify the tensor component of the $NN$ interaction. DET-PETs are able to modify significantly the $np$ scattering wave functions and hence the off-shell properties of the $NN$ interaction. DET-PETs give rise to significant changes in the binding energies of $^3$H (in the range of approximately 1.5 MeV) and $^4$He (in the range of more than 9 MeV) and are able to modify the correlation patterns of binding energies of these nuclei.
We discuss the studies of light nuclei in ab initio No-core Full Configuration approach based on extrapolations to the infinite model space of large-scale No-core Shell Model calculations on supercomputers. The convergence at the end of p shell and beginning of the sd shell can be achieved if only reasonable soft enough NN interactions are used. In particular, good predictions are obtained with a realistic JISP16 NN interaction obtained in J-matrix inverse scattering approach and fitted to reproduce light nuclei observables without three-nucleon forces. We discuss the current status of this NN interaction and its recent development.
We present results from ab initio No-Core Full Configuration simulations of the exotic proton-rich nucleus $^{14}$F whose first experimental observation is expected soon. The calculations with JISP16 NN interaction are performed up to the $N_{\max}=8$ basis space. The binding energy is evaluated using an extrapolation technique. This technique is generalized to excitation energies, verified in calculations of $^6$Li and applied to $^{14}$B, the $^{14}$F mirror, for which some data are available.
We discuss realistic nonlocal NN interactions of a new type - J-matrix Inverse Scattering Potential (JISP). In an ab exitu approach, these interactions are fitted to not only two-nucleon data (NN scattering data and deuteron properties) but also to the properties of light nuclei without referring to three-nucleon forces. We discuss recent progress with the ab initio No-core Shell Model (NCSM) approach and respective progress in developing ab exitu JISP-type NN-interactions together with plans of their forthcoming improvements.
We perform no-core full configuration calculations for a set of light nuclei including $^{16}$O with a realistic NN interaction, JISP16. We obtain ground state energies and their uncertainties through exponential extrapolations that we demonstrate are reliable in $^2$H, $^3$H and $^4$He test cases where fully converged results are obtained directly. We find that $^6$He, $^6$Li and $^8$He are underbound by about 600 keV, 560 keV and 1.7 MeV, respectively. $^{12}$C is overbound by about 1.7 MeV and $^{16}$O is overbound by about 16 MeV. The first excited $0^+$ states in $^{12}$C and $^{16}$O are also evaluated but their uncertainties are significantly larger than the uncertainties for the ground states.
We introduce the no-core full configuration (NCFC) approach and present results for $^4$He, $^{12}$C and $^{14}$F with the realistic NN interaction, JISP16. We obtain ground state energies and their uncertainties through exponential extrapolations that we demonstrate are reliable in $^4$He where fully converged results are obtained. We find $^{12}$C is overbound by 1.7 MeV and we predict the yet-to-be-measured binding energy of $^{14}$F to be $70.2\pm 3.5$ MeV. The extrapolated spectrum of $^{14}$F is in reasonable agreement with known features of the $^{14}$B spectrum.
The $J$-matrix inverse scattering approach can be used as an alternative to a conventional $R$-matrix in analyzing scattering phase shifts and extracting resonance energies and widths from experimental data. A great advantage of the $J$-matrix is that it provides eigenstates directly related to the ones obtained in the shell model in a given model space and with a given value of the oscillator spacing $\hbarΩ$. This relationship is of a particular interest in the cases when a many-body system does not have a resonant state or the resonance is broad and its energy can differ significantly from the shell model eigenstate. We discuss the $J$-matrix inverse scattering technique, extend it for the case of charged colliding particles and apply it to the analysis of $nα$ and $pα$ scattering. The results are compared with the No-core Shell Model calculations of $^5$He and $^5$Li.
We introduce the no-core full configuration (NCFC) approach and present results for $^4$He, $^{12}$C and $^{14}$F with the realistic NN interaction, JISP16. We obtain ground state energies and their uncertainties through exponential extrapolations that we demonstrate are reliable in $^4$He where fully converged results are obtained. We find $^{12}$C is overbound by 1.7 MeV and we predict the yet-to-be-measured binding energy of $^{14}$F to be $68.1 \pm 2.7$ MeV. The extrapolated spectrum of $^{14}$F is in reasonable agreement with known features of the $^{14}$B spectrum.
Fully-microscopic No-core Shell Model (NCSM) calculations of all stable $s$ and $p$ shell nuclei are used to determine realistic $NN$ interaction JISP16 describing not only the two-nucleon data but the binding energies and spectra of nuclei with $A\leq 16$ as well. The JISP16 interaction, providing rapid convergence of the NCSM calculations, is obtained in an {\em ab exitu} approach by phase-equivalent transformations of the JISP6 $NN$ interaction.
Projection operators for the use within ab initio no-core shell model, are suggested.
Nucleon-nucleon (NN) phase shifts and the spectroscopy of $A \le 6$ nuclei are successfully described by an inverse scattering potential that is separable with oscillator form factors.
The nucleon-nucleon interaction is constructed by means of the $J$-matrix version of inverse scattering theory. Ambiguities of the interaction are eliminated by postulating tridiagonal and quasi-tridiagonal forms of the potential matrix in the oscillator basis in uncoupled and coupled waves, respectively. The obtained interaction is very accurate in reproducing the $NN$ scattering data and deuteron properties. The interaction is used in the no-core shell model calculations of $^3$H and $^4$He nuclei. The resulting binding energies of $^3$H and $^4$He are very close to experimental values.
We show that a quantum system with nonlocal interaction can have bound states of unusual type -- Isolated States (IS). IS is a bound state that is not in correspondence with the $S$-matrix pole. IS can have a positive as well as a negative energy and can be treated as a generalization of the bound states embedded in continuum on the case of discrete spectrum states. The formation of IS in the spectrum of a quantum system is studied using a simple rank--2 separable potential with harmonic oscillator form factors. Some physical applications are discussed, in particular, we propose a separable $NN$ potential supporting IS that describes the deuteron binding energy and the s-wave triplet and singlet scattering phase shifts. We use this potential to examine the so-called problem of the three-body bound state collapse discussed in literature. We show that the variation of the two-body IS energy causes drastic changes of the binding energy and of the spectrum of excited states of the three-nucleon system.
We discuss the extension of the oscillator-basis $J$-matrix formalism on the case of true $A$-body scattering. The formalism is applied to loosely-bound $^{11}$Li and $^6$He nuclei within three-body cluster models ${\rm {^9Li}}+n+n$ and $α+n+n$. The $J$-matrix formalism is used not only for the calculation of the three-body continuum spectrum wave functions but also for the calculation of the $S$-matrix poles associated with the $^{11}$Li and $^6$He ground states to improve the description of the binding energies and ground state properties. The effect of the phase equivalent transformation of the $n{-}α$ interaction on the properties of the $^6$He nucleus is examined.
Phase-equivalent transformation of local interaction is generalized to the multi-channel case. Generally, the transformation does not change the number of the bound states in the system and their energies. However, with a special choice of the parameters, the transformation removes one of the bound states and is equivalent to the multi-channel supersymmetry transformation recently suggested by Sparenberg and Baye. Using the transformation, it is also possible to add a bound state to the discrete spectrum of the system at a given energy $E<0$ if the angular momentum at least in one of the coupled channels $l\ge 2$.