An s—d-Shell-Model Study for A = 18–22

Halbert, E.C.; McGrory, J.B.; Wildenthal, B. H.; Pandya, S.P.

doi:10.1007/978-1-4615-8228-1_6

Cited by 59 publications

(26 citation statements)

References 92 publications

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“…These efforts, which to a large extent have been concentrated on (sd)-shell nuclei, were rewarded by quite some success in reproducing experimental energy spectra, electromagnetic transition probabilities and moments, ft-values, and spectroscopic factors [1]. The main criticism against this kind of calculations -with the exceptions of the ones performed with an SU(3)-classified basis-is that the physical structure of the states can hardly be understood from the resulting eigenvectors.…”

Section: Introductionmentioning

confidence: 98%

Perturbation theory instead of large scale shell model calculations?

Feldmeier

Manakos

1977

Z Physik A

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Results of large scale shell model calculations for (sd)-shell nuclei are compared with a perturbation theory treatment. It is shown that second order perturbation theory provides an excellent approximation when the SU(3)-basis is used as a starting point. The results indicate that perturbation theory treatment in an SU(3)-basis including 2hco excitations should be preferable to a full diagonalization within the (sd)-shell.

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Section: Introductionmentioning

confidence: 98%

Perturbation theory instead of large scale shell model calculations?

Feldmeier

Manakos

1977

Z Physik A

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“…Calculations for up to five particles in the sd shell gave very satisfactory results, but the spectrum of 22 Na (i.e., (sd) 6 T = 0) was very bad [7]. (Note that 10 B is (p) 6 T = 0).…”

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confidence: 99%

Three-Body Monopole Corrections to Realistic Interactions

2003

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It is shown that a very simple three-body monopole term can solve practically all the spectroscopic problems-in the p, sd and pf shells-that were hitherto assumed to need drastic revisions of the realistic potentials.PACS numbers: 21.60. Cs, 21.30.+y, The first exact Green's function Monte Carlo (GFMC) solutions for A > 4 nuclei confirmed that two-body (2b) interactions fell short of perfectly reproducing experimental data [1]. The inclusion of a three-body (3b) force lead to excellent spectroscopy, but some problems remained for the binding and symmetry energies and spin orbit splittings. No core shell model calculations (NCSM) [2] have recently developped to the point of approximating the exact solutions with sufficient accuracy to provide a very important-though apparently negative-result in 10 B [3]: While in the lighter systems the spectra given by a strict two-body potential are not always good-but always acceptable-in 10 B, the spectrum is simply very bad.My purpose is to show the striking analogy between this situation and what occurs in conventional (0 ω) shell model calculations with realistic G-matrices, and then explain how a very simple 3b term can solve practically all the spectroscopic problems-in the p, sd and pf shells-that were hitherto assumed to need drastic revisions of the realistic (R) 2b potentials.The first realistic matrix elements [5], and the first large scale shell model codes [6] appeared almost simultaneously. Calculations for up to five particles in the sd shell gave very satisfactory results, but the spectrum of 22 Na (i.e., (sd) 6 T = 0) was very bad [7]. (Note that 10 B is (p) 6 T = 0). At the time nobody thought of 3b forces, and naturally the blame was put on the 2b matrix elements (V JT stuv , stuv are subshells). The proposed phenomenological cures amounted to fit them to the experimental levels. Two "schools" emerged: One proposed to fit them all (63 in the sd shell), and lead eventually to the famous USD interaction [8,9]. The alternative was to fit only the centroids, given in Eqs. (1,2).They are associated to the 2b quadratics in number (n s ) and isospin operators (T s ), Eqs. (3,4), and they define the monopole Hamiltonian, Eq. (5), in which we have added the single particle (1b) term. The idea originated in Ref.[10], where it was found that the Kuo Brown (KB) interaction in the pf shell [11] could yield excellent spectroscopy through the modificationsThe validity of this prescription was checked in perturbative calculations [12], and convincingly confirmed for A = 47 − 52 once exact diagonalizations became feasible [13,14,15,16, 17].In what follows f will stand generically for (p 3/2 , d 5/2 , f 7/2 ) in the (p, sd, pf ) shells respectively. Obviously r = p 1/2 and r ≡ d 3/2 , s 1/2 for the p and sd shells.Nowadays the 2b N N potentials are nearly perfect, and the calculations are exact. Therefore, the blame for bad spectroscopy must be put on the absence of 3b terms. Which means that the monopole corrections must be 3b and Eq. (5) must be supplemented bywhere n stu ...

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“…Figures 4, 5 and 6 show the results of a shell model calculation for A = 18, 19 and 20 respectively using these five sets of renormalized matrix elements. We also present the associated experimental spectra and results using the Kuo-Brown matrix elements [21] for purposes of comparison. It is interesting to compare the spectra which result without the DWBA correction and when it is included i.e.…”

Section: Results and Conclusionmentioning

confidence: 99%

Renormalized shell model matrix elements derived from nucleon-nucleon phase shifts

1978

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We apply the G matrix elements calculated by Singh et al. (using the DWBA approach) to some spectra calculations for A=18, 19, 20 after first renormalizing the matrix elements by including second-order processes in G. The corrections introduced by the Distorted-Wave-Born-Correction Term are attractive for both the H.J. and Reid potentials. The magnitude and uncertainties in these corrections are discussed. Differences between these potentials are attributed chiefly to their different off-the-energy-shell behaviour. The results are compared to calculations with the Kuo matrix elements and with experiment.

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An s—d-Shell-Model Study for A = 18–22

Cited by 59 publications

References 92 publications

Perturbation theory instead of large scale shell model calculations?

Perturbation theory instead of large scale shell model calculations?

Three-Body Monopole Corrections to Realistic Interactions

Renormalized shell model matrix elements derived from nucleon-nucleon phase shifts

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