Alpha cluster states and molecular orbitals in sd-shell nuclei

M. Kimuraa, N. Furutachib and Y. Kanada-En’yoc

aCreative Research Institution Sousei Research Department, Hokkaido University,Sapporo 001-0021, Japan

bMeme Media Laboratory, Hokkaido University, Sapporo 060-8628, Japan

cYukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan

The α-clustering and molecular-orbitals of 22Ne and F isotopes are investigated based onantisymmetrized molecular dynamics (AMD). The observed candidates for the α clusterstate of 22Ne are understood as the molecular-orbital states and α+18O di-nuclei states.The presence of the molecular-orbital states in the O and F isotopes and the drasticreduction of their excitation energy near the neutron-drip line are predicted.

1. Introduction

The successful description of neutron-rich Be isotopes based on the molecular-orbitalpicture [1–3] suggests a new type of binding mechanism and the exotic clustering peculiarto N�=Z nuclei. But such cluster states with covalent neutrons are known only for Beisotopes at present. Therefore, the exploration of the molecular-orbital states in heaviersystem and the investigation of their nature are of interest and importance to show theuniversality of a novel clustering in neutron-rich nuclei.

We have investigated the ground and excited states of 22Ne and neutron-rich O and Fisotopes by AMD to study the α-clustering and molecular-orbitals in these isotopes. SinceAMD does not assume any cluster structure and is capable to systematically investigatenuclear spectra including highly excited states, it serves the purpose of the present study.For the detail of AMD framework, readers are directed to the references [3–5].

2. Results and Discussions

Experimentally, more than thirty years ago, W. Scholz et al. [6] firstly reported thesignificant α clustering of several states lying below α threshold energy, but the theoreticalinterpretation has not been established yet. Recently, besides those states, the α+18O di-nuclei states lying above the threshold that were predicted by the cluster model calculation[7] are observed [8–10]. Thus, the cluster states of 22Ne are reported at two energy region, afew MeV below and above the α threshold energy, suggesting more complicated clusteringaspects than Be isotopes.

Figure 1 summarizes observed and calculated (AMD) [5] ground and excited rotationalbands with prominent α clustering. It is noted that AMD calculation also reproduces

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other known excited states that are suppressed in this figure. We have obtained twogroups of α cluster bands; three bands starting below the α threshold and two above thethreshold. The former corresponds to the states reported by W. Scholz et al. [6], whilethe latter corresponds to the references [8–10]. The neutron single particle orbitals revealnature of the rotational bands of the former group (Kπ=0+

2 , 0−1 , 1−). Figure 2 shows thecore nucleus density and the neutron single particle orbitals in the Kπ = 0−1 band. Here,two neutrons occupy each orbital. One can confirm the prominent α clustering in thisband and the neutron orbitals from No. 1 to 5 are well confined within the clusters (α and16O). Only the most weakly bound two neutrons (valence neutrons, No. 6) are orbitingaround the α+16O cluster core and covalently bound. This valence neutron orbital is thecomplete analog of the σ molecular-orbital in Be isotopes. It is also noted that all ofthe Kπ=0+

2 , 0−1 , 1− rotational bands have the α+16O cluster core and neutron(s) in theσ-orbital, while the ground band that does not show α clustering has no neutron in σorbital. Therefore, the neutron(s) in the σ orbital induces the clustering of the core. AMDcalculation reproduces the observed α reduced with amplitude and we can convince thepresence of the molecular-orbital states in 22Ne.

By the similar analysis of the neutron motion, it is found that the latter group (Kπ=0+3 ,

0−2 ) have two valence neutrons orbiting only around 16O cluster. Therefore, these bandsare understood as α+18O di-nuclei states. This interpretation agrees with the observations[8–10] and cluster model calculations [7]. Again, AMD reproduces the observed energies,moment of inertia and α reduced width amplitude of these bands.

0

2

4

6

8

10

12

14

16

18

20

22

24

26

01 2 3 4 5 6 7 8 9

excita

tio

n e

ne

rgy [

Me

V]

J

exp (negative-parity)

hybrid-GCM (positive-parity)

ground band

hybrid-GCM (negative-parity)

exp (positive-parity)

22Ne α cluster bands

molecular orbital

bands

α+18O molecular

bands

Kπ=0+

Kπ=0+

Kπ=0+

Kπ=0-

Kπ=1-

Kπ=0-

1

2

1

3

2

α+18O threshold

Figure 1. Calculated and observed ro-tational bands of 22Ne.

Figure 2. Matter (solid line) and neu-tron single particle (color) densities ofKπ=1− band.

The same calculation have been performed for O and F isotopes [11] and we havepredicted similar molecular-orbital states in these isotopes. Recently, several cluster statesare observed in 18,20O [12] and they can be the candidate of the predicted molecular-orbitalstates. In the case of F isotopes, we have found the presence of the molecular-orbital states

M. Kimura et al. / Nuclear Physics A 834 (2010) 482c–484c 483c

throughout the isotope chain and the drastic reduction of their excitation energies. Figure3 shows the excitation energies of the band head states that have a proton hole in p-shell.19F has an famous α cluster state at 0.11 MeV in which one proton in p-shell is excitedinto sd-shell. The addition of neutrons in sd-shell to this state (red line) reduces the αclustering of the core and increases the excitation energies, since the valence neutronssd-shell does not favor strong deformation caused by the clustering of the core. On thecontrary, the addition of valence neutrons in σ molecular-orbital (green and blue lines)switches on the α clustering of the core. These states are understood as the molecular-orbital states and it must be noted that their excitation energies are greatly reduced

toward neutron-drip line. This drastic re-duction is closely related to the breaking ofthe neutron magic number N=20 and under-stood as follows. Around the neutron-dripline, the intruder orbital from pf -shell comesdown close to sd-shell. The point is that thisorbital have a large overlap with or is almostidentical to the σ molecular orbital. There-fore, near the drip line, the excitation of va-lence neutrons to σ molecular-orbital doesnot cost much energy and it induces the αclustering . Furthermore, the strong defor-mation caused by α clustering reduces thesingle particle energy of σ molecular-orbital.

0

2

4

6

8

10

12

14

5/2+ 5/2+ 5/2+ 5/2+1/2+

1/2-

1/2-1/2-

1/2-

1/2- 1/2-

1/2-

1/2-

1/2-

1/2-

1/2-1/2-

3/2+

3/2+3/2+

3/2+3/2+

5/2+

19F 21F 23F 25F 27F 29F

excita

tio

n e

ne

rgy [M

eV

]

proton hole

with

neutron σ1 config.

proton hole

proton hole

with

neutron σ2 config.

Figure 3. Excitation energies of theband head states with a proton hole.

3. Summary

We have studied the α-clustering and molecular-orbitals of 22Ne and F isotopes basedon AMD. It is shown that the molecular-orbital states with covalent neutrons and theα+18O di-nuclei states appear in 22Ne The presence of the molecular-orbital states in Fisotopes and the drastic reduction of their excitation energy are predicted.

REFERENCES

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