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Register a new userNonsymmetrized Hyperspherical Harmonics approach to A=6 system
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The Hyperspherical Harmonics basis, without a previous symmetrization step, is used to calculate binding energies of the nuclear A=6 systems using a version of the Volkov potential acting only on s-wave. The aim of this work is to illustrate the use of the nonsymmetrized basis to deal with permutational-symmetry-breaking term in the Hamiltonian, in the present case the Coulomb interaction.
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The Schroedinger equation is solved for an A-nucleon system using an expansion of the wave function in nonsymmetrized hyperspherical harmonics. Our approach is both an extension and a modification of the formalism developed by Gattobigio et al.. The extension consists in the inclusion of spin and isospin degrees of freedom such that a calculation with more realistic NN potential models becomes possible, whereas the modification allows a much simpler determination of the fermionic ground state. The approach is applied to four- and six-body nuclei (4He, 6Li) with various NN potential models. It is shown that the results for ground-state energy and radius agree well with those from the literature.
A different formulation of the effective interaction hyperspherical harmonics (EIHH) method, suitable for non-local potentials, is presented. The EIHH method for local interactions is first shortly reviewed to point out the problems of an extension to non-local potentials. A viable solution is proposed and, as an application, results on the ground-state properties of 4- and 6-nucleon systems are presented. One finds a substantial acceleration in the convergence rate of the hyperspherical harmonics series. Perspectives for an application to scattering cross sections, via the Lorentz transform method are discussed.
We demonstrate the ability to calculate electromagnetic sum rules with the textit{ab initio} symmetry-adapted no-core shell model. By implementing the Lanczos algorithm, we compute non-energy weighted, energy weighted, and inverse energy weighted sum rules for electric monopole, dipole, and quadrupole transitions in $^4$He using realistic interactions. We benchmark the results with the hyperspherical harmonics method and show agreement within $2sigma$, where the uncertainties are estimated from the use of the many-body technique. We investigate the dependence of the results on three different interactions, including chiral potentials, and we report on the $^4$He electric dipole polarizability calculated in the SA-NCSM that reproduces the experimental data and earlier theoretical outcomes. We also detail a novel use of the Lawson procedure to remove the spurious center-of-mass contribution to the sum rules that arises from using laboratory-frame coordinates. We further show that this same technique can be applied in the Lorentz integral transform method, with a view toward studies of electromagnetic reactions for light through medium-mass nuclei.
The non-symmetrized hyperspherical harmonics method for a three-body system, composed by two particles having equal masses, but different from the mass of the third particle, is reviewed and applied to the $^3$H, $^3$He nuclei and $^3_{Lambda}$H hyper-nucleus, seen respectively as $nnp$, $ppn$ and $NNLambda$ three-body systems. The convergence of the method is first tested in order to estimate its accuracy. Then, the difference of binding energy between $^3$H and $^3$He due to the difference of the proton and the neutron masses is studied using several central spin-independent and spin-dependent potentials. Finally, the $^3_{Lambda}$H hypernucleus binding energy is calculated using different $NN$ and $Lambda N$ potential models. The results have been compared with those present in the literature, finding a very nice agreement.
A program to calculate the three-particle hyperspherical brackets is presented. Test results are listed and it is seen that the program is well applicable up to very high values of the hypermomentum and orbital momenta. The listed runs show that it is also very fast. Applications of the brackets to calculating interaction matrix elements and constructing hyperspherical bases for identical particles are described. Comparisons are done with the programs published previously.
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