No-core shell-model calculations with starting-energy-independent multivalued effective interactions

Abstract

Large-space no-core shell model calculations have been performed for 3 H, 4 He, 5 He, 6 Li, and 6 He, using a starting-energy-independent two-body effective interaction derived by application of the Lee-Suzuki similarity transformation. This transformation can be performed by direct calculation or by different iteration procedures, which are described. A possible way of reducing the auxiliary potential influence on the two-body effective interaction has also been introduced. The many-body effects have been partially taken into account by employing the recently introduced multi-valued effective interaction approach. Dependence of the 5 He energy levels on the harmonic-oscillator frequency as well as on the size of the model space has been studied. The Reid 93 nucleon-nucleon potential has been used in the study, but results have also been obtained using the Nijmegen II potential for comparison.

Large-basis shell-model calculations forp-shell nuclei

“…(3), the notation [ ] eff means that the quantity within the square brackets is the residual interaction to be used in the determination of the effective interaction within the model space P (see Ref. [9] for more details).…”

“…Large-basis no-core shell-model calculations have recently been performed [1][2][3][4][5][6][7][8][9][10][11]. In these calculations all nucleons are active, which simplifies the effective interaction as no hole states are present.…”

“…For A = 8, results were obtained for 8 He, 8 Li, 8 Be and 8 B in a 4hΩ model space. For A = 9 we calculated properties of 9 He, 9 Li, 9 Be, 9 B and 9 C also in a 4hΩ model space. As the A = 10 nuclides 10 C, 10 B, and partly 10 Be, were discussed in Ref.…”

Benchmark calculation of inclusive responses in the four-body nuclear system

“…In both techniques, one works in a finite subset of the Hilbert space, called the model space (or P -space). In order to account for many-body correlations left out by the truncation of the Hilbert space, one then builds an effective interaction by means of a unitary transformation [7] in the so-called cluster approximation [5]. The main differences between the NCSM and EIHH techniques originate from the choice of the localized A-body basis states: the harmonic oscillator (HO) basis function in the NCSM case, and the hyper-spherical-harmonics (HH) functions in the EIHH case.…”

“…The EIHH and NCSM [5] approaches are rather similar bound-state techniques. However, only the latter has made use of realistic interactions in calculations with A > 4.…”