The nuclear monopole Hamiltonian

Duflo, J.; Zuker, A. P.

doi:10.1103/physrevc.59.r2347

Cited by 110 publications

(120 citation statements)

References 14 publications

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“…Perhaps the most significant is the following: The monopole centroids V T f 7/2 (sd) must be such that when f 7/2 fills the d, (l = 2) orbits are depressed with respect to the s, (l = 0) one [18]. However, it is clear from the spectrum and the spectroscopic factors in 29 Si that the filling of d 5/2 favours the p, (l = 1) orbit(s) over the f, (l = 3) ones [29].…”

Section: The Story Repeats Itself Formentioning

confidence: 99%

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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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Section: The Story Repeats Itself Formentioning

confidence: 99%

“…H m can be characterized by demanding correct single particle and single hole spectra around closed shell nuclei [18]. This set (cs ± 1) is taken to include the differences in binding energies (gaps) 2BE(cs) − BE(cs + 1)−BE(cs−1).…”

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Three-Body Monopole Corrections to Realistic Interactions

2003

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“…The modified aspect of another effective interaction FPD6 [22] refers also to the monopole terms [23]. These indicate the importance of the monopole terms in spectroscopy [15,18,19,23,24]. Our interaction has the most important term V 0 πν as the average monopole field but does not include the monopole terms which affect spectroscopy.…”

Section: Introductionmentioning

confidence: 99%

Improvement of the extended interaction by modifying the monopole field

2001

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The extended pairing plus QQ interaction with the J-independent isoscalar protonneutron force as an average monopole field, which has succeeded in describing collective yrast states of N ≈ Z even-A nuclei, is improved. The improvement is accomplished by adding small monopole terms (relevant to spectroscopy) to the average monopole field (indispensable to the binding energy). This modification extends the applicability of the interaction to nuclei with N ≈ 28 such as 48 Ca, and moreover improves energy levels of noncollective states. The modified interaction successfully describes not only even-A but also odd-A nuclei in the f 7/2 shell region. Results of exact shell model calculations in the model space (f 7/2 , p 3/2 , p 1/2 ) (its usefulness has been demonstrated previously) are shown for A=47, 48, 49, 50 and 51 nuclei.

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“…[19] assume that the N = 50 shell gap evolves in a similar manner as observed in the Zr isotopes [25] in combination with an estimated N = 50 g 9/2 -s 1/2 gap size of 5 MeV in 78 Ni. Experimental input on the size of the N = 50 shell gap near 68 Ni would provide valuable information for these large-scale shell-model calculations as it can serve as an anchor point for the gap-size evolution [19].…”

Section: Introductionmentioning

confidence: 99%

“…Experimental input on the size of the N = 50 shell gap near 68 Ni would provide valuable information for these large-scale shell-model calculations as it can serve as an anchor point for the gap-size evolution [19]. Calculations using three-body forces and information from the Zr chain resulted in an estimated N = 50 gap size of 1.5-2 MeV near N = 40 [19,24,25].…”

Section: Introductionmentioning

confidence: 99%

Experimental study of theNi66(d,p) Ni67
Diriken¹,
Raabe²,
Eberth³
et al. 2015
Phys. Rev. C
9
1
5
0
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The quasi-SU(3) sequence of the positive parity νg 9/2 ,d 5/2 ,s 1/2 orbitals above the N = 40 shell gap are assumed to induce strong quadrupole collectivity in the neutron-rich Fe (Z = 26) and Cr (Z = 24) isotopes below the nickel region. In this paper the position and strength of these single-particle orbitals are characterized in the neighborhood of 68 Ni (Z = 28, N = 40) through the 66 Ni(d,p) 67 Ni one-neutron transfer reaction at 2.95 MeV/nucleon in inverse kinematics, performed at the REX-ISOLDE facility in CERN. A combination of the Miniball γ -array and T-REX particle-detection setup was used and a delayed coincidence technique was employed to investigate the 13.3-μs isomer at 1007 keV in 67 Ni. Excited states up to an excitation energy of 5.8 MeV have been populated. Feeding of the νg 9/2 (1007 keV) and νd 5/2 (2207 keV and 3277 keV) positive-parity neutron states and negative parity (νpf ) states have been observed at low excitation energy. The extracted relative spectroscopic factors, based on a distorted-wave Born approximation analysis, show that the νd 5/2 single-particle strength is mostly split over these two excited states. The results are also compared to the distribution of the proton single-particle strength in the 90 Zr region (Z = 40,N = 50).

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The nuclear monopole Hamiltonian

Cited by 110 publications

References 14 publications

Three-Body Monopole Corrections to Realistic Interactions

Three-Body Monopole Corrections to Realistic Interactions

Improvement of the extended interaction by modifying the monopole field

Experimental study of theNi66(d,p) Ni67
Diriken¹,
Raabe²,
Eberth³
et al. 2015
Phys. Rev. C
9
1
5
0
View full text Add to dashboard Cite

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The nuclear monopole Hamiltonian

Cited by 110 publications

References 14 publications

Three-Body Monopole Corrections to Realistic Interactions

Three-Body Monopole Corrections to Realistic Interactions

Improvement of the extended interaction by modifying the monopole field

Experimental study of theNi66(d,p) Ni67Diriken1, Raabe2, Eberth3 et al. 2015Phys. Rev. C9150View full textAdd to dashboardCite

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Experimental study of theNi66(d,p) Ni67
Diriken¹,
Raabe²,
Eberth³
et al. 2015
Phys. Rev. C
9
1
5
0
View full text Add to dashboard Cite