Toward a unified realistic shell-model Hamiltonian with the monopole-based universal force

Abstract

We propose a unified realistic shell-model Hamiltonian employing the pairing plus multipole Hamiltonian combined with the monopole interaction constructed starting from the monopole-based universal force by Otsuka et al. (Phys. Rev. Lett. 104, 012501 (2010)). It is demonstrated that the proposed PMMU model can consistently describe a large amount of spectroscopic data as well as binding energies in the p f and p f 5/2 g 9/2 shell spaces, and could serve as a practical shell model for even heavier mass regions. PACS numbers: 21.30.Fe, 21.60.Cs, 21.10.Dr, 27.50.+e The nuclear shell-model interaction can in principle be derived microscopically from the free nucleon-nucleon force. In fact, such attempts were made in the early years for the beginning of the shell [1,2]. However, it was soon after realized that such an interaction fail to describe binding energies, excitation spectra, and transitions if many valence nucleons were considered. To reproduce experimental data, considerable efforts have been put forward to construct the so-called effective interactions, such as USD [3] and USDA/B [4] for the sd shell, KB3G [5] and GXPF1A [6] for the p f shell, and JUN45 [7] and jj4b [8] for the p f 5/2 g 9/2 model space. Each of these interactions is applicable to a given model space while mutual relations among them are obscure. On the other hand, it has been shown [9] that realistic effective interactions are dominated by the pairing plus quadrupole-quadrupole (P + QQ) terms with the monopole interaction. This finding not only makes the understanding of effective interactions in nuclei intuitive, but may also be used to unify effective interactions for different model spaces. In particular, one may begin to talk about universality for shell models.Along the lines of this thought, we have carried out shellmodel calculations using the extended P + QQ Hamiltonian combined with the monopole terms (EPQQM), which are regarded as corrections for the average monopole interaction. It has been demonstrated that despite of its simplicity, this EPQQM model works surprisingly well for different mass regions, for example, the proton-rich p f shell [10] and the p f 5/2 g 9/2 shell [11], the neutron-rich f pg shell [12], and the sd-p f shell region [13]. It has also been successfully applied to the neutron-rich nuclei around 132 Sn [14,15]. However, these calculations rely heavily on phenomenological adjustments on the monopole corrections. Consequently, the EPQQM model cannot describe binding energies or unusual structures such as the first excited 0 + state of Zn and Ge isotopes around N = 40 [16], and it essentially provides no information about the unconventional shell evolution in neutronrich nuclei.The monopole interaction is a crucial ingredient for successful shell-model calculations. It is defined as [17]where V JT ab,ab are the interaction matrix elements. The connection between the monopole interaction and the tensor force [18] was confirmed, which explains the shell evolution [19]. It was shown [20,21] shown by open and ...

Transition strengths in the neutron-rich Ni73,74,75 isotopes

“…Here the sign ≈ is related to the expected anharmonicities coming from the "blocking" of the odd neutron. Shell-model calculations performed using the V low-k approach [34] or a unified realistic Hamilto-nian with a monopole based universal force [35] show that almost 90% of the strength is exhausted by the 5/2 + , 13/2 + , and 11/2 + members of the multiplet, with the 13/2 + state giving the dominant contribution (see below for shell-model calculations).…”

“…Shell-model calculations have been performed using SM1, a unified realistic interaction employing the pairing plus multipole Hamiltonian combined with the monopole interaction constructed starting from the monopole-based universal force from Refs. [35,36], or SM2, an effective Hamiltonian derived from the CD-Bonn potential, renormalized by way of the V low-k approach [37], within the framework of the timedependent perturbation theory [34].…”

“…The large-scale shell-model calculations are performed under the truncation that protons and neutrons are not excited from the f 7/2 and the p 3/2 orbitals. The interaction matrix elements and the single-particle energies are given in the same way as the derivation of the Hamiltonian in the previous papers [35,38], where the effective charges for proton and neutron are taken as e p = 1.50e and e n = 0.75e. In model (2), SM2, a different valence space was considered, TABLE II.…”

IBM-1 Model ile çift-çift Fe İzotoplarının Nükleer Özelliklerinin İncelenmesi

“…Deneysel sonuçlar [1] incelendiğinde, bu farklılıklar kararlılık eğrisinde bölgelere göre ve izotop, izoton, izobar çizgileri boyunca gözlenebilmektedir. Son yıllarda, A~50 bölgesinde yer alan orta kütleli çift-çift Fe izotopları için ile yapılan deneysel çalışmaların yanında, kabuk modeli, QRPN, etkileşen bozon modeli (IBM) gibi bazı modeller ile çalışmalar gerçekleştirilmiştir [2][3][4][5][6][7][8][9]. Çift-çift 50,52,54,56,58,60 Fe izotoplarının kuantum şekil faz geçişleri teorik olarak incelenmiştir [2].…”

Isospin Properties of Nuclear Pair Correlations from the Level Structure of the Self-Conjugate Nucleus Ru88

“…[47] predicted a delay in the band crossing frequency in the N ¼ Z nuclei 84 42 Mo 42 and 88 44 Ru 44 as an effect of enhanced neutron-proton interactions. Kaneko et al [48] employed LSSM calculations using a "pairing-plus-multipole" Hamiltonian [49] in the ð1p 1=2 ; p 3=2 ; f 5=2 ; g 9=2 ; d 5=2 Þ (often denoted as fpgd) model space for studying 88 44 Ru 44 , 90 44 Ru 46 , and 92 44 Ru 48 and concluded that T ¼ 0 np pairing is responsible for the distinct difference in rotational behavior between the N ¼ Z and N > Z nuclei. These calculations also predicted a significant delay in the band crossing frequency for N ¼ Z and their prediction for the J ð1Þ moment of inertia of 88 44 Ru 44 revealed a sharp irregularity at a rotational frequency ℏω c ≈ 0.65 MeV [48].…”