Electric quadrupole transition in neutron rich $^{32-42}$S-isotopes with different model spaces

Document Type : Research Paper


Department of Physics, College of Science, University of Baghdad, Iraq


The electromagnetic properties of some even neutron rich Sulfur-isotopes ${ }^{32-42} \mathrm{~S}$ are studied through the electric quadrupole transition $\left(0_{1}^{+} \rightarrow 2_{1}^{+}\right)$. In particular, excitation energies $E_{x}$, occupancies, electric quadrupole moments $Q$, transition strengths $B(E 2)$, deformation parameters $\beta_{2}$ and the coulomb inelastic electron scattering form factors are calculated for the adopted isotopes within the framework of shell model. The shell model calculations are performed with full $s d$-model space, $p s d$ - and $s d p f$ - cross shell, using different interactions. The results are based on $s d b a$ and $p s d m k$ interactions for sulfur with $N \leq 20$, while sdpfk and $s d p f u$ interactions are dependent for sulfur with $N>20$. The core polarization effects $(C P)$ are included through the Boher-Mottelson $(B-M)$ and standard $(S T)$ effective charges to obtain a reasonable description of the electric quadrupole moments and C2 form factors. The results of $p s d m k$ and $s d b a$-interactions fail to reproduce the measured $B(E 2)$ strengths and deformation $\beta_{2}$ for ${ }^{32-36} \mathrm{~S}$, except for ${ }^{36} \mathrm{~S}$ nucleus is close to the measured value. The results for ${ }^{38-42} \mathrm{~S}$ with both $s d p f k$ and $s d p f u$ interactions nicely confirm the measured values of $B(E 2)$ strengths and deformation $\beta_{2}$ within the experimental error. The influence of the nuclear deformation parameter $\beta_{2}$ on the location of the diffraction minima of $\mathrm{C} 2$ form factors are also indicated.


[1] A.N. Bohr and B.R. Mottelson, Nuclear Structure (in 2 volumes), World Scientific Publishing Company, 1998.
[2] B.A. Brown, R. Radhi and B.H. Wildenthal, Electric quadrupole and hexadecupole nuclear excitations from the
perspectives of electron scattering and modern shell-model theory, Phys. Rep. 101 (1983), no. 5, 313–358.
[3] B.A. Brown, A. Arima and J.B. McGrory, E2 core-polarization charge for nuclei near 16O and 40Ca, Nuclear
Phys. A 277 (1977), no. 1, 77–108.
[4] B.A. Brown, A. Etchegoyen and N.S. Godwin, WDM rae, WA Richter, WE Ormand, EK Warburton, JS Winfield,
L. Zhao, and CH Zimmerman, Tech. Rep. MSU-NSCL-1289, National SuperConducting Cyclotron Laboratory,
[5] P.J. Brussaard and P.W.M. Glaudemans, Shell-model applications in nuclear spectroscopy, North-Holland Publishing Company, 1977.
[6] T. Forest Jr and J. Dirk Walecka, Electron scattering and nuclear structure, Adv. Phys. 15 (1966), no. 57, 1–109.
[7] T.W. Donnelly and J.D. Walecka, Electron Scattering and Nuclear Structure, Ann. Rev. Nuclear Sci. 25 (1975),
no. 1, 329–405.
[8] T.W. Donnelly and I. Sick, Elastic magnetic electron scattering from nuclei, Reviews of modern physics 56 (1984),
no. 3, 461.
[9] J.P. Elliott and T.H.R. Skyrme, Centre-of-mass effects in the nuclear shell-model, Proc. Royal Soc. London. Series
A. Math. Phys. Sci. 232 (1955), no. 1191, 561–566.
[10] T. Glasmacher, B.A. Brown, M.J. Chromik, P.D. Cottle, M. Fauerbach, R.W. Ibbotson, K.W. Kemper, D.J. Morrissey, H. Scheit and D.W. Sklenicka, Collectivity in 44S, Phys. Lett. B 395 (1997), no. 3-4, 163–168.
[11] J.P. Glickman, W. Bertozzi, T.N. Buti, S. Dixit, F.W. Hersman, C.E. Hyde-Wright, M.V. Hynes, R.W. Lourie,
B.E. Norum and J.J. Kelly, Electron scattering from Be 9, Phys. Rev. C 43 (1991), no. 4, 1740.
[12] .K Kaneko, Y. Sun, T. Mizusaki and M. Hasegawa, Shell-model study for neutron-rich sd-shell nuclei, Phys. Rev.
C 83 (2011), no. 1, 014320.
[13] E. Kwan, C.Y. Wu, N.C. Summers, G. Hackman, T.E. Drake, C. Andreoiu, R. Ashley, G.C. Ball, P.C. Bender and
A.J. Boston, Precision measurements of the B (E1) strengths in 11Be, Fission and Properties of Neutron-Rich
Nuclei, World Scientific, 2014, pp. 678–681.
[14] B. Longfellow, D. Weisshaar, A. Gade, B.A. Brown, D. Bazin, K.W. Brown, B. Elman, J. Pereira, D. Rhodes and
M. Spieker, Quadrupole collectivity in the neutron-rich sulfur isotopes S 38, 40, 42, 44, Phys. Rev. C 103 (2021),
no. 5, 054309.
[15] D.J. Millener and D. Kurath, The particle-hole interaction and the beta decay of 14B, Nuclear Phys. A 255 (1975),
no. 2, 315–338.
[16] F. Nowacki and A. Poves, New effective interaction for θhω shell-model calculations in the sd-pf valence space,
Phys. Rev. C 79 (2009), no. 1, 014310.
[17] T. Otsuka, A. Gade, O. Sorlin, T. Suzuki and Y. Utsuno, Evolution of shell structure in exotic nuclei, Rev. Mod.
Phys.92 (2020), no. 1, 015002.
[18] B. Pritychenko, M. Birch, B. Singh and M. Horoi, Tables of E2 transition probabilities from the first 2+ states in
even–even nuclei, At. Data Nucl. Data Tables 107 (2016), 1–139.
[19] R.A. Radhi, A.A. Alzubadi and A.H. Ali, Magnetic dipole moments, electric quadrupole moments, and electron
scattering form factors of neutron-rich s d-p f cross-shell nuclei, Phys. Rev. C 97 (2018), no. 6, 064312.
[20] R.A. Radhi, Z.A. Dakhil and N.S. Manie, Microscopic calculations of quadrupole moments in Li and B isotopes,
Eur. Phys. J. A 50 (2014), no. 7, 1–9.[21] S. Raman and C.W. Nestor, Jr., and P. Tikkanen, At. Data Nucl. Data Tables 78 (2001), no. 1, 43.
[22] W.A. Richter, S. Mkhize, and B Alex Brown, sd-shell observables for the USDA and USDB Hamiltonians, Phys.
Rev. C 78 (2008), no. 6, 064302.
[23] H. Sagawa and B.A. Brown, E2 core polarization for sd-shell single-particle states calculated with a skyrme-type
interaction, Nuclear Phys. A 430 (1984), no. 1, 84–98.
[24] A. Saxena, A. Kumar, V. Kumar, P.C. Srivastava and T. Suzuki, Ab initio description of collectivity for sd shell
nuclei, Hyperfine Interact.240 (2019), no. 1, 1–8.
[25] H. Scheit, T. Glasmacher, B.A. Brown, J.A. Brown, P.D. Cottle, P.G. Hansen, R. Harkewicz, M. Hellstr¨om,
R.W. Ibbotson and J.K. Jewell, New region of deformation: The neutron-rich sulfur isotopes, Phys. Rev. Lett.
77 (1996), no. 19, 3967.
[26] O. Sorlin and M.-G. Porquet, Nuclear magic numbers: New features far from stability, Prog. Part. Nuclear Phys.
61 (2008), no. 2, 602–673.
[27] N.J. Stone, Table of nuclear magnetic dipole and electric quadrupole moments, At. Data Nuc. Data Tables 90
(2005), no. , 75–176.
[28] L. Jo Tassie and F.C. Barker, Application to electron scattering of center-of-mass effects in the nuclear shell
model, Phys. Rev. 111 (1958), no. 3, 940.
[29] Y. Utsuno, T. Otsuka, B.A. Brown, M. Honma, T. Mizusaki and N. Shimizu, Shape transitions in exotic Si and
S isotopes and tensor-force-driven Jahn-Teller effect, Phys. Rev. C 86 (2012), no. 5, 051301.
[30] T.R. Werner, J.A. Sheikh, M. Misu, W. Nazarewicz, J. Rikovska, K. Heeger, A.S. Umar and M.R. Strayer,
Ground-state properties of exotic Si, S, Ar and Ca isotopes, Nuclear Phys. A 597 (1996), no. 3, 327–340.
[31] B.H. Wildenthal, B.A. Brown and I. Sick, Electric hexadecupole transition strength in S 32 and shell-model
predictions for E4 systematics in the sd shell, Phys. Rev. C 32 (1985), no. 6, 2185.
[32] S.-G. Zhou, Structure of exotic nuclei: a theoretical review, arXiv preprint arXiv:1703.09045 (2017).
Volume 13, Issue 2
July 2022
Pages 3127-3137
  • Receive Date: 06 November 2021
  • Revise Date: 20 February 2022
  • Accept Date: 19 March 2022