Onset of intruder ground state in exotic $\mathrm{Na}$ isotopes and evolution of the $N=20$ shell gap

Onset of intruder ground state in exotic $Na$ isotopes and evolution of the $N = 20$ shell gap

Yutaka Utsuno, Takaharu Otsuka, Thomas Glasmacher, Takahiro Mizusaki, and Michio Honma

Phys. Rev. C 70, 044307 – Published 18 October 2004

Abstract

The onset of intruder ground states in $Na$ isotopes is investigated by comparing experimental data and shell-model calculations. This onset is one of the consequences of the disappearance of the $N = 20$ magic structure, and the $Na$ isotopes are shown to play a special role in clarifying the change of this magic structure. Both the electromagnetic moments and the energy levels clearly indicate an onset of ground state intruder configurations at neutron number $N = 19$ already, which arises only with a narrow $N = 20$ shell gap in $Na$ isotopes resulting from the spin-isospin dependence of the nucleon-nucleon interaction (as compared to a wider gap in stable nuclei like ${}^{40}{Ca}$ ). It is shown why the previous report based on the mass led to a wrong conclusion.

Received 24 June 2004

DOI:https://doi.org/10.1103/PhysRevC.70.044307

Authors & Affiliations

Yutaka Utsuno¹, Takaharu Otsuka^2,3,4, Thomas Glasmacher⁵, Takahiro Mizusaki⁶, and Michio Honma⁷

¹Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-1195, Japan
²Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan
³Center for Nuclear Study, University of Tokyo, Hongo, Tokyo 113-0033, Japan
⁴RIKEN, Hirosawa, Wako-shi, Saitama 351-0198, Japan
⁵National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
⁶Institute of Natural Sciences, Senshu University, Higashimita, Tama, Kawasaki, Kanagawa 214-8580, Japan
⁷Center for Mathematical Sciences, University of Aizu, Tsuruga, Ikki-machi Aizu-Wakamatsu, Fukushima 965-8580, Japan

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Vol. 70, Iss. 4 — October 2004

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Figure 1
(a) Electric quadrupole moments, (b) magnetic dipole moments, and (c) $n p n h (n = 0, 2, 4)$ probabilities of the ground states of neutron-rich $Na$ isotopes, as a function of the neutron number, $N$ . In (a) and (b), the circles are experimental values taken from Refs. 22, 23, while the solid and the dashed lines denote, respectively, the MCSM calculation with the SDPF-M interaction and USD-model calculation.Reuse & Permissions
Figure 2
Two-neutron separation energies of $Na$ isotopes, as a function of the neutron number, $N$ . The circles and the crosses are the experimental values taken from the mass table by Audi et al. [34] and a new measurement by Lunney et al. [21], respectively. The solid line denotes the MCSM calculation with the SDPF-M interaction, while the dashed line the USD-model calculation.Reuse & Permissions
Figure 3
(a) $S_{2 n}$ of ${}^{30}{Na}$ compared among the shell-model calculations (with the USD interaction and the SDPF-M one) and experiment. For the SDPF-M interaction, a truncated calculation within the $s d$ shell and the full one by the MCSM are compared, too. The circle and the cross are experimental data taken from Refs. 34 and [21], respectively. (b) Corresponding dominant neutron configurations of the ground state and the ESPE’s obtained from each interaction. All the ESPE’s are obtained by assuming the filling configuration.Reuse & Permissions
Figure 4
Comparison of the energy levels of ${}^{27 - 30}{Na}$ relative to the experimental ground state among the experiment (Exp.) and the shell-model calculations by the SDPF-M and the USD interactions. The $E 2$ strength from the ground state is illustrated by the width of the arrow. The experimental $B (E 2)$ values of ${}^{28, 30}{Na}$ and the energy levels of ${}^{27}{Na}$ are taken from Refs. 25 and 36, respectively. For ${}^{30}{Na}$ , the levels calculated from SDPF-M interaction are grouped into four columns; the first (second) one is $K = 2 (1)$ rotational band dominated by intruder configurations, the third one represents spherical states which are basically of normal configurations, and negative-parity states are shown in the fourth column.Reuse & Permissions
Figure 5
Schematic sketch of the sources of the correlation energy of the intruder and the normal states of semimagic [(a) and (b)] and open-shell [(c) and (d)] nuclei. Typical configurations for these states are shown. The proton-neutron interaction is illustrated by thick wavy lines, while the proton-proton and neutron-neutron interactions are drawn by thin wavy lines.Reuse & Permissions
Figure 6
(a) Quadrupole moment and (b) magnetic moment of ${}^{30}{Na}$ as a function of the $N = 20$ shell gap [controlled by a parameter $x$ in Eq. (1)]. The experimental [22, 23] and USD-model ones are denoted by the squares and crosses, respectively. (c) $2 p 2 h$ probabilities in the (positive-parity) ground states of ${}^{29 - 31}{Na}$ . (d) Energies of the $2 p 2 h$ - and $1 p 1 h$ -dominant lowest states of ${}^{30}{Na}$ (denoted by “ $2 p 2 h$ ” and “ $1 p 1 h$ ,” respectively) measured from that of the $0 p 0 h$ -dominant lowest state. The range of the shell gap giving the $n p n h$ ground state $(n = 0, 1, 2)$ is indicated by $n$ ex. Note that the corresponding shell gaps of ${}^{29, 31}{Na}$ are, respectively, smaller and larger by $0.24 MeV$ than the one of ${}^{30}{Na}$ .Reuse & Permissions

Physical Review C

covering nuclear physics

Onset of intruder ground state in exotic $Na$ isotopes and evolution of the $N = 20$ shell gap

Yutaka Utsuno, Takaharu Otsuka, Thomas Glasmacher, Takahiro Mizusaki, and Michio Honma

Phys. Rev. C 70, 044307 – Published 18 October 2004

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Physical Review C

covering nuclear physics

Onset of intruder ground state in exotic Na isotopes and evolution of the N=20 shell gap

Yutaka Utsuno, Takaharu Otsuka, Thomas Glasmacher, Takahiro Mizusaki, and Michio Honma

Phys. Rev. C 70, 044307 – Published 18 October 2004

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Onset of intruder ground state in exotic $Na$ isotopes and evolution of the $N = 20$ shell gap