Study of N = 16 shell closure within RMF+BCS approach

TL;DR

This study uses the RMF+BCS approach to analyze the N=16 shell closure in even-even nuclei, confirming strong shell effects in light isotopes like 22C and 24O and contrasting results for higher Z isotones.

Contribution

It provides a detailed theoretical investigation of N=16 shell closure using RMF+BCS, aligning with recent experimental findings and highlighting differences across isotones.

Findings

Strong shell closure at N=16 in 22C and 24O

Large energy gap between neutron states 2s1/2 and 1d3/2

Agreement with experimental data for light isotopes

Abstract

We have employed RMF+BCS (relativistic mean-field plus BCS) ap- proach to study behaviour of N = 16 shell closure with the help of ground state properties of even-even nuclei. Our present investigations include sin- gle particle energies, deformations, separation energies as well as pairing energies etc. As per recent experiments showing neutron magicity at N = 16 for O isotopes, our results indicate a strong shell closure at N = 16 in 22C and 24O. A large gap is found in between neutron 2s1/2 and 1d3/2 states for 22C and 24O. These results are also supported by a sharp increase in two neutron shell gap, zero pairing energy contribution and with excellent agreement with available experimental data. Moreover, our calculations of N = 16 isotones are however found at variance for higher Z isotones like 36Ca, where experiments show high lying first excited 2+ state indicating shell closure at N = 16.

Equations

$$\mathcal{L}$$

$$H_{\mu \nu }$$

$$G_{\mu \nu }^a$$

$$F_{\mu \nu }$$

Full text

\PACS

21.10.-k, 21.10.Ft, 21.10.Dr, 21.10.Gv, 21.10.-n, 21.60.Jz

1 Introduction

Emergence of new shell closures and disappearance of conventional shell closures throughout the periodic chart have opened various theoretical and experimental treatments in understanding the behaviour of nuclei with neutron-to-proton ratio. It has also been established that shell structure influences the locations of the neutron and proton drip lines and the stability of matter. Appearance of new magic numbers N = 16 in the 24O [1, 2] and the emergence of an N = 32 sub-shell closure in 52Ca [3] are some of the examples of changes in shell structure. In this paper we have investigated N = 16 shell closure with the use of Relativistic Mean Field plus BCS approach [4, 5].

2 Relativistic Mean-Field Theory

Our RMF calculations have been carried out using the model Lagrangian density with nonlinear terms both for the ${\sigma}$ and ${\omega}$ mesons [5].

[TABLE]

where the field tensors $H$, $G$ and $F$ for the vector fields are defined by equation (1)

[TABLE]

and other symbols have their usual meaning. Based on the single-particle spectrum calculated by the RMF described above, we perform a state dependent BCS calculations and continuum is replaced by a set of positive energy states generated by enclosing the nucleus in a spherical box. For further details of these formulations we refer the readers to ref. [5].

3 Results and Discussion

The results of single particle energy of N = 16 isotonic chain calculated using RMF with TMA force parameter [6] have been shown in Fig. 1. A large variation in the energies of states 2s1/2, 1d5/2 and 1d3/2 is clearly seen moving from proton rich to neutron rich (right to left). It is evident from Fig 1 that moving towards proton deficient side 2s1/2 state creates a substantial gap with 1d3/2 state specially for Z = 6 and Z = 8 resulting development of new shell closure N = 16 in 22C and 24O. This gap is around 3.5 MeV and 3.3 MeV for 22C and 24O respectively as can be seen in figure. This kind of reorganization is also observed from the calculations with other parameters NL3 and PK1 (not shown here). It is gratifying to note here that our results are showing doubly magic character of 24O as observed in recent experiments [1, 2] and in addition the same shell closure N = 16 is also observed in 22C. On the other side, for larger Z, 2s1/2 and 1d3/2 states are found with very small gap giving no sign for N = 16 shell closure. This result is not in accord with experimental investigations showing shell closure at N = 16 due to high lying 2+ state for 36Ca [7] along with 30Si and 32S [8]. Further investigations are required for consistent description of isotonic chain in terms of parameters, pairing and isospin.

To get into more insight, we have plotted two neutron shell gap (S2n (N, Z)

• S2n (N+2, Z)) in lower panel of Fig. 2, for C and O isotopes calculated by RMF+BCS approach using TMA force parameter [6] along with experimental shell gap for O isotopes [8]. One can observe abrupt increase in shell gap for conventional shell closure at N = 8. In the same way another rise in two neutron shell gap can be seen moving from N = 14 to N = 16 for both C and O isotopes. This rise which is in accord with experiments [8] supports occurrence of new spherical shell closure at N = 16 for 22C and 24O both. Further, in upper panel of Fig. 2, we have shown paring energy contribution for both C and O isotopes. For doubly magic nuclei pairing energy vanishes and indeed it vanishes for 12C, 14C, 22C and 14O, 16O, 24O for N = 6, 8 and 16 respectively. The result in upper panel of Fig. 2 again fortify shell closure at N = 16 for 22C and 24O and general validity of RMF approach.

Acknowledgements

Authors are grateful to Prof. H. L. Yadav, BHU, India for his kind guidance and support. One of the authors (G. Saxena) gratefully acknowledges the support provided by SERB (DST), Govt. of India under the young scientist project YSS/2015/000952 and International Travel Grant.