Study of the Shell Evolution Effect on the Nuclei around the 78Ni Core Structure

Year 2019, Volume: 9 Issue: 2, 109 - 113, 27.12.2019

Nadjet Laouet , Fatima Benrachı Habiba Guerraıche Karima Benhızıa

https://doi.org/10.17678/beuscitech.633561

Abstract

	Bitlis Eren Universıty  Journal of scıence and technology 00 (2013) 000–000
	Available online at www.dergipark.ulakbim.gov.tr/beuscitech/   Journal of Science and Technology                                                                   E-ISSN 2146-7706

 

Study of the shell evolution effect on the nuclei structure around the ⁷⁸Ni core 

 

Nadjet Laouet * , Fatima Benrachi, Habiba Guerraiche, Karima Benhizia

LPMPS Laboratory, Frères Mentouri Constantine-1, 25107,Constantine Algeria

A R T I C L E  I N F O Article history: Received 00 December 0000 Received in revised form 00 January 0000 Accepted 00 February 0000   Keywords: Nuclear shell model Doubly magic core 78Ni Monopole interaction Nuclear structure properties NuShellX@MSU code

A B S T R A C T The interactions between the core which is anymore inert and the valence nucleons play a very important role in the interpretation of nuclear properties far from stability. The work done in this study is based on the calculations of energy spectra and electromagnetic properties for even-even isotones with N=52, in the 78Ni region. Based on the interaction jj45apn with the space model jj45pn, we have realized some modifications considering the monopole interaction and a new interaction called jj45am is introduced. The calculations are performed in the framework of the nuclear shell model using the NuShellX@MSU code. The shell evolution, studied by estimating the effective single particle energies in this region, show an important influence on the nuclear structure properties. The obtained results using the new interaction jj45am are in good agreement with the experimental data, and better than those given by the original one jj45apn.    © 2017. Turkish Journal Park Academic. All rights reserved.

 1. Introduction

Nuclei close to doubly magic cores that are in the
limit of the nuclear chart are good candidate to test new theoretical
predictions in order to explain the experimental observations in such systems.
Experimental studies and spectroscopic calculations, in these regions, can
prove and expect new phenomena as the disappearance of some habitual magic
numbers and the appearance of new ones (Dobaczewski et al., 1994; Otsuka et
al., 2005). These observations may result from the so-called shell evolution. ⁷⁸Ni
is one of the best exotic doubly magic cores, which is considered as the
closest core to the neutron drip-line. This region offers best opportunity to
develop a comprehensive understanding of shell evolution.

In this context, we have studied N=52 isotones, which
cover a large range from the neutron drip line to the neutron one near 78Ni
core. Indeed, there are few experimental data in the considered mass region.
⁷⁸Ni is an exotic nucleus that situated in the limit of nuclear chart and it is
very difficult to study experimentally. The two neutrons in N=52 isotones are
situated on d_5/2 shell for low excitation
energies. For high ones, one or two neutron can move to other orbits. These
isotones have been studied by (Czerwinski et al., 2013). In their work, the ⁸⁶Se
and ⁸⁸Kr nuclei have been investigated following,
respectively, spontaneous fissions of ²⁴⁸Cm and ²⁵²Cf
by means of prompt-g
-ray-spectroscopy methods using the Gamma sphere Ge array (Czerwinski et al.,
2013). In addition, they have predicted the Energies of the first 2⁺
and 4⁺ levels in the ⁸²Zn nucleus using
systematics shown in Figure 1, that presents the calculated excitation
systematics in comparison with the available experimental data (see (Czerwinski
et al., 2013) for more details).

                                                                                                                

Figure 1. Calculated
excitation systematic in comparison with the available experimental data
(Czerwinski et al., 2013).

2. Theoretical framework

One of the most
important phenomena used to study such nuclear systems is the monopole effect; which
has been focused on after the discovering of new nuclei more and more exotic
and the appearance of unexpected observation as the appearance of new magic
numbers, as a result of shell evolution (Cortes and Zuker, 1979; Sorlin and
Porquet, 2008).

This effect comes
from the interactions between the core and the valence nucleons (Otsuka et al.,
2010; Smirnova et al., 2010). In this approximation, a nuclear system can be
presented in terms of a monopole and a multipole Hamiltonians. 

                                                         
(1) 

The monopole part is expressed as a function of single
particle energies e_s,
occupation n_st, isospin T_st operators, and V_j
which presents an energy average over the spin J (Poves and Zuker,
1981; Otsuka et al.,2010):

                                                              (2)  

The TBMEs of the using interaction are modified taking
in consideration the proton-proton, neutron-neutron and proton-neutron monopole
effects for even-even nuclei in the ⁷⁸Ni region and a new
interaction is introduced.

3. Results and discussions

For our
calculations, we have used jj45pn as a single particle state (SPS).
The single particle energies (SPE) were taken from the experimental data
and from Grawe et al., for some shells (Grawe et al., 2007; nndc.bnl.gov, 2019).
The used interaction is obtained starting from jj45apn original one,
based on the G matrix for ¹³²Sn region (Jensen et al., 1995; Rejmund et al., 2016), considering
the monopole effect.

One of the well-known codes, the NuShellX@MSU
is used to carry out the spectroscopic calculations achieved in this work. It
presents a development of NuShellX code; which contains a set of
computed codes written by Rae (Brown and Rae, 2014). The calculation results in
comparison with the experimental data are reported in Figure 2.

Figure 2. Calculated energetic spectra using jj45apn and jj45am
interactions in comparison with the available experimental data (nndc.bnl.gov,
2019).

These spectra are used to plot the energetic
systematics for N=52 isotones with Z=30-50. The results are shown
in Figure 3:

Figure 3. Calculated systematics by means of  jj45am
(right) in comparison with the experimental ones (left), in N=52 isotones.

For the
experimental energies (left), the spectra show a peak for Z=38 isotope. The
peak is clear for 4⁺, 6⁺ and 8⁺ states. The
available data for 2⁺ and 4⁺ states show also a peak for
Z=50. These two peaks are clear in the calculated systematics (right). The peaks
is clear for all excited states.

The explanation of
the Z=50 peak is clear as this charge number is a habitual magic number. The other
peak in Z=38 is a sign of a possible new magic number which can be a result of
shell evolution in ⁷⁸Ni.

4. Conclusions

This work
is based on the energetic spectra calculations, for even-even N=52 isotones,
with two neutrons and few protons in their valence spaces. The calculations are
realized in the framework of the nuclear shell model, by means of NuShellX@MSU
nuclear structure code. Using the jj45apn original interaction of the
code, we carried out some modifications based on the monopole interaction to
get jj45am one.

Most of the calculated spins and
parities of the studied nuclei are in agreement with the experimental ones. The
excited states calculated using the elaborated interaction jj45am are
close to the available experimental data, in comparison with those calculated
using the original interaction without monopole terms, which are underestimated
in this case. The calculated results give a prove of the magic nature of the number
Z=38. This may give an important indication of the monopole interaction
consideration role on the explanation of spectroscopic properties. 

Acknowledgements

Authors of this article thanks to the organizers
of the “XII. International Conference on Nuclear Structure Properties NSP 2019,
October 11^th-13^th 2019, Bitlis-Turkey’, for the
organization and the support provided during the conference. Special thanks are
owed to B. A. Brown for his help in providing us theNuShellX@MSU code (Linux
Version).

References

     Dobaczewski, J., Hamamoto, I., Nazarewicz , W., and Sheikh, J. A. 1994. Nuclear Shell Structure at Particle Drip Lines. Physical
Review Letters 72, 981-984.          Otsuka, T., Suzuki, T., Fujimoto, R., Grawe, H., and Akaishi, Y. 2005. Evolution of Nuclear Shells due to the Tensor Force. Physical
Review Letters 95, 232502 1-4.

    Smirnova, N. A., Bally, B., Heyde, K., Nowacki, F., and Sieja K. 2010. Shell evolution and nuclear forces. Physics Letters B 686,
109-113.

    Cortes, A., and Zuker, A. P. 1979. Self-Consistency and many
body monopole forces in shell model calculations. Physics Letters 84B, 25-30.

     Czerwinski, M. et al. 2013. Yrast excitations in the
neutron-rich N = 52 isotones. Physical Review C 88, 044314 1-13.

    Sorlin, O.,  and Porquet, M. G. 2008. Nuclear Magic numbers: New
features far from stability. Progress in Particle and Nuclear Physics 61,
602-673.

    Otsuka, T., Suzuki, T., Holt, J. D., Schwenk, and A.,
Akaishi, Y. 2010. Three-body forces and the limit of oxygen isotopes. Physical
Review Letters 105, 021501 1-5.

    Poves, A., and Zuker, A. P. 1981. Theoretical spectroscopy
and the FP shell. Physics Reports, 70, 235-314.

    https://www.nndc.bnl.gov/ensdf/endf/xundl.jsp.

    Grawe, H., Langanke, K., and Martinez-Pinedo, G. 2007.
Nuclear structure and astrophysics. Reports on Progress in Physics, 70,
1525-1585.

     Hjorth-Jensen, M., Kuo, T.T.S., Osnes, E. 1995.
Realistic effective interaction for nuclear systems. Physics Reports, 261,
125-270.

      Rejmund, M. et al., 2016. Structural changes at large
angular momentum in nuclear rich ^121-123Cd. Physical Review C 93, 024312 1-6,
2016.

    Brown, B. A., andRae, W.
D. M. 2014. The Shell-Model Code NuShellX@MSU. Nuclear Data Sheets 120,
115-118.

Keywords

Nuclear shell model, Doubly magic core 78Ni, Monopole interaction, Nuclear structure properties, NuShellX@MSU code

References

• Dobaczewski, J., Hamamoto, I., Nazarewicz , W., Sheikh, J. A., 1994. Nuclear Shell Structure at Particle Drip Lines. Physical Review Letters 72, 981-984.
• Otsuka, T., Suzuki, T., Fujimoto, R., Grawe, H., Akaishi, Y., 2005. Evolution of Nuclear Shells due to the Tensor Force. Physical Review Letters 95, 232502 1-4.
• Smirnova, N. A., Bally, B., Heyde, K., Nowacki, F., Sieja K., 2010. Shell evolution and nuclear forces. Physics Letters B 686, 109-113.
• Cortes, A., Zuker, A. P., 1979. Self-Consistency and many body monopole forces in shell model calculations. Physics Letters 84B, 25-30.
• Czerwinski, M. et al., 2013. Yrast excitations in the neutron-rich N = 52 isotones. Physical Review C 88, 044314 1-13.
• Sorlin, O., Porquet, M. G., 2008. Nuclear Magic numbers: New features far from stability. Progress in Particle and Nuclear Physics 61, 602-673.
• Otsuka, T., Suzuki, T., Holt, J. D., Schwenk, A., Akaishi, Y., 2010. Three-body forces and the limit of oxygen isotopes. Physical Review Letters 105, 021501 1-5.
• Poves, A., Zuker, A. P., 1981. Theoretical spectroscopy and the FP shell. Physics Reports, 70, 235-314.
• https://www.nndc.bnl.gov/ensdf/ensdf/xundl.jsp.
• Grawe, H., Langanke, K., Martinez-Pinedo, G., 2007. Nuclear structure and astrophysics. Reports on Progress in Physics, 70, 1525-1585.
• Hjorth-Jensen, M., Kuo, T.T.S., Osnes, E., 1995. Realistic effective interaction for nuclear systems. Physics Reports, 261, 125-270.
• Rejmund, M. et al., 2016. Structural changes at large angular momentum in nuclear rich 121-123Cd. Physical Review C 93, 024312 1-6, 2016.
• Brown, B. A., Rae, W. D. M., 2014. The Shell-Model Code NuShellX@MSU. Nuclear Data Sheets 120, 115-118.