Large Scale Shell Model Calculations of the Negative-Parity States Structure in 24Mg Nucleus
Keywords:PSDPF, negative-parity states, electron scattering, shell model, form factors, 24Mg
The negative-parity states of 24Mg nucleus are investigated within the shell model. We are based on the calculations of energy levels, total squared form factors, and transition probability using the p-sd-pf (PSDPF) Hamiltonian in a large model space (0 + 1) hW. The comparison between the experimental and theoretical states showed a good agreement within a truncated model space. The PSDPF-based calculations successfully reproduced the data on the total squared form factors and transition probabilities of the negative-parity states in 24Mg nucleus. These quantities depend on the one-body density matrix elements that are obtained from the PSDPF Hamiltonian. The wave functions of radial one-particle matrix elements calculated with the harmonic-oscillator potential are suitable to predict experimental data by changing the center-of-mass corrections.
P.J. Davies et al. Toward the limit of nuclear binding on the N = Z line: Spectroscopy of 96Cd. Phys. Rev. C 99, 021302 (2019).
Eunja Ha, Myung-Ki Cheoun, H. Sagawa. Eff ects of the Coulomb and the spin-orbit interaction in a deformed mean fi eld on the pairing correlations in N = Z nuclei. Phys. Rev. C 99, 064304 (2019).
T. Inakura, S. Mizutori. Rod-shaped rotational states in N = Z even-even nuclei from 12C to 32S. Phys. Rev. C 98, 044312 (2018).
H. Morita, Y. Kanada-En'yo. Low-energy Gamow-Teller transitions in deformed N = Z odd-odd nuclei. Phys. Rev. C 98, 034307 (2018).
E. Ha, M.-K. Cheoun, H. Sagawa. Spin singlet and spin triplet pairing correlations on shape evolution in sd-shell N = Z Nuclei. Phys. Rev. C 97, 024320 (2018).
K. Kaneko, Y. Sun, G. de Angelis. Enhancement of high-spin collectivity in N = Z nuclei by the isoscalar neutron-
proton pairing. Nucl. Phys. A 957, 144 (2017).
I. Wiedenh¨over, A.H. Wuosmaa, R.V.F. Janssens, C.J. Lister, M.P. Carpenter, H. Amro, P. Bhattacharyya, B.A. Brown, J. Caggiano, M. Devlin, A. Heinz, F.G. Kondev, T. Lauritsen, D.G. Sarantites, S. Siem, L.G. Sobotka, A. Sonzogni. Identifi cation of the Iп = 10+ yrast rotational state in 24Mg. Phys. Rev. Lett. 87, 142502 (2001).
I. Wiedenh¨over, A.H. Wuosmaa, R.V.F. Janssens, C.J. Lister, M.P. Carpenter, Janssens, R.V.F. Amro, H. Caggiano, J. Heinz, A. Kondev, F.G. Lauritsen, T. Siem, S. Sonzogni, A. Bhattacharyya, P. Devlin, M. Sarantites, D.G. Sobotka. Measurement and analysis of quadruple (ayy) angular correlations for high spin states of 24Mg. Nucl. Phys. A 682, 22 (2001).
E.S. Diff enderfer, L.T. Baby, D. Santiago-Gonzalez, N. Ahsan, A. Rojas, A. Volya, I. Wiedenh¨over, A.H. Wuosmaa, M.P. Carpenter, R.V.F. Janssens, C.J. Lister, M. Devlin, D.G. Sarantites, L.G. Sobotka, Y. Utsuno, M. Horoi. High-spin spectrum of 24Mg studied through multiparticle angular correlations. Phys. Rev. C 85, 034311 (2012).
M. Bouhelal, F. Haas, E. Caurier, F. Nowacki, A. Bouldjedrib. Negative-parity intruder states of the neutron-rich N = 20, Z = 14-16 isotones: a 1 ~ w shell model description. Acta. Phys. Pol. B 40, 639 (2009).
P. Marley, D.G. Jenkins, P.J. Davies, A.P. Robinson, R. Wadsworth, C.J. Lister, M.P. Carpenter, R.V.F. Janssens, C.L. Jiang, T.L. Khoo, T. Lauritsen, D. Seweryniak, S. Zhu, S. Courtin, F. Haas, D. Lebhertz, M. Bouhelal, J.C. Lighthall, A.H. Wuosmaa, D. O'Donnell. High-resolution spectroscopy of decay pathways in the 12C(12C,y) reaction. Phys. Rev. C 84, 044332 (2011).
D.G. Jenkins, M. Bouhelal, S. Courtin, M. Freer, B.R. Fulton, F. Haas, R.V.F. Janssens, T.L. Khoo, C.J. Lister, E.F. Moore, W.A. Richter, B. Truett, A.H. Wuosmaa. y-ray spectroscopy of the A = 23, T = 1/2 nuclei 23Na and 23Mg: High-spin states, mirror symmetry, and applications to nuclear astrophysical reaction rates. Phys. Rev. C 87, 064301 (2013).
M. Bouhelal, F. Haas, E. Caurier, F. Nowacki, A. Bouldjedri. PSDPF interaction to describe the 1 ~ w intruder
states in sd shell nucleiNucl. Phys. A 864, 113 (2011).
M. Bouhelal, F. Haas, E. Caurier, F. Nowacki, A. Bouldjedri. PSDPF interaction to describe the 1ћ? intruder states in sd shell nucleiNucl. Phys. Rev. C 96, 044304 (2017).
R. S. Lubna, Vandana Tripathi, S.L. Tabor, P.-L. Tai, K. Kravvaris, P.C. Bender, A. Volya, M. Bouhelal, C.J. Chiara, M.P. Carpenter, R.V.F. Janssens, T. Lauritsen, E.A. McCutchan, S. Zhu, R.M. Clark, P. Fallon, A.O. Macchiavelli, S. Paschalis, M. Petri, W. Reviol, D.G. Sarantites. Intruder confi gurations of excited states in the neutron-rich isotopes 33P and 34P. Phys. Rev. C 97, 044312 (2018).
S. Aydin, M. Ionescu-Bujor, G.Tz. Gavrilov, B.I. Dimitrov, S.M. Lenzi, F. Recchia, D. Tonev, M. Bouhelal, F. Kavillioglu, P. Pavlov, D. Bazzacco, P.G. Bizzeti, A.M. Bizzeti-Sona, G. de Angelis, I. Deloncle, E. Farnea, A. Gadea, A. Gottardo, N. Goutev, F. Haas, T. Huyuk, H. Laftchiev, S. Lunardi, Tz.K. Marinov, D. Mengoni, R. Menegazzo, C. Michelagnoli, D.R. Napoli, P. Petkov, E. Sahin, P.P. Singh, E.A. Stefanova, C.A. Ur, J.J. Valiente-Dob'on, M.S. Yavahchova. High-spin states and life-times in 33S and shell-model interpretation in the sd -fp space. Phys. Rev. C 96, 024315 (2017).
B. Fu, M. Seidlitz, A. Blazhev, M. Bouhelal, F. Haas, P. Reiter, K. Arnswald, B. Birkenbach, C. Fransen, G. Friessner, A. Hennig, H. Hess, R. Hirsch, L. Lewandowski, D. Schneiders, B. Siebeck, T. Steinbach, T. Thomas, A. Vogt, A. Wendt, K. Wolf, K.O. Zell. y-ray spectroscopy of 33P and 33S after fusion-evaporation reactions. Phys. Rev. C 94, 034318 (2016).
A. Radhi, Ali A. Alzubadi, A.H. Ali. Magnetic dipole moments, electric quadrupole moments, and electron scattering form factors of neutron-rich sd- pf cross-shell nuclei. Phys. Rev. C 97, 064312 (2018).
B.A. Brown, A. Etchegoyen, W.D. Rae, N.S. Godwin, W.A. Richter, C.H. Zimmerman, W.E. Ormand, J.S. Winfi eld. MSU-NSCL Report No. 524, 1985 (unpublished).
S. Cohen, D. Kurath. Spectroscopic factors for the 1p shell. Nucl. Phys. A 101, 1 (1967).
B.A. Brown, W.A. Richter. New "USD" Hamiltonians for the sd shell. Phys. Rev. C 74, 034315 (2006).
E.K. Warburton, B.A. Brown. Eff ective interactions for the 0p1s0d nuclear shell-model space. Phys. Rev. C 46, 923 (1992).
S. Nummela, P. Baumann, E. Caurier, P. Dessagne, A. Jokinen, A. Knipper, G. Le Scornet, C. Mieh'e, F. Nowacki, M. Oinonen, Z. Radivojevic, M. Ramdhane, G. Walter, J. Ayst¨o. Spectroscopy of 34?35Si by B decay: sd -fp shell gap and single-particle states. Phys. Rev. C 63, 044316 (2001).
A.A. Al-Sammarraie, F.I. Sharrad, H.A. Kassim. Nuclear structure for 24Mg within sd-shell model space Hamiltonians. Armenian Journal of Physics 8, 170 (2015).
R.E. Tribble, G.T. Garvey, J.R. Comfort. Particle-hole nature of the two lowest 3-states in 24Mg. Phys. Lett. B 44, 366 (1973).
R.B. Firestone. Nuclear Data Sheets for A = 24. Nucl. Data Sheets 108, 2319 (2007).
F.I. Sharrad. Binding energy and B(E2; 4+1→ 2+1) calculations for nuclei with A = 20. AIP Conf. & Proc. 1528, 376 (2013).
H. Zarek, S. Yen, B.O. Pich, T.E. Drake, C. F. Williamson, S. Kowalski, C.P. Sargent. Inelastic electron scattering to
negative-parity states of 24Mg. Phys. Rev. C 29, 1664 (1984).
A.A. Al-Sammarraie, M.L. Inche Ibrahim, M.A. Saeed, F.I. Sharrad, H.A. Kassim. Inelastic electric and magnetic
electron scattering form factors of 24Mg nucleus: Role of g-factors. Int. J. Mod. Phys. E 26, 1750032 (2017).
B.A. Brown. Lecture Notes in Nuclear Structure Physics (Michigan State Univ., 2011).
A.A. Al-Sammarraie, F.I. Sharrad, N. Yusof, H.A. Kassim. Longitudinal and transverse electron-nucleus scattering form factors of 25Mg. Phys. Rev. C 92, 034327 (2015).
B.A. Brown, B.H. Wildenthal, C.F. Williamson, F.N. Rad, S. Kowalski, Hall Crannell, J.T.O' Brien. Shell-model analysis of high-resolution data for elastic and inelastic electron scattering on 19F. Phys. Rev. C 32, 1127 (1985).
H. Chjandra, G. Sauer. Relativistic corrections to the elastic electron scattering from 208Pb. Phys. Rev. C 13, 245 (1976).
L.J. Tassie, F.C. Barker. Application to electron scattering of center-of-mass eff ects in the nuclear shell model. Phys. Rev. 111, 940 (1958).
D. Branford, N. Gardner, I.F. Wright. Evidence for negative-parity rotational bands in 24Mg. Phys. Lett. 36, 456 (1971). https://doi.org/10.1016/0370-2693(71)90528-4
A. Johnston, T.E. Drake. A study of 24Mg by inelastic electron scattering. J. Phys. A: Math., Nucl. Gen. 7, 898 (1974) (un available online). https://doi.org/10.1088/0305-4470/7/8/004
B.T. Lawergren, A.T.G. Fergusono, G.C. Morrision. States with T = 1 in 20Ne, 24Mg and 28Si. Nucl. Phys. A 108, 325 (1968). https://doi.org/10.1016/0375-9474(68)90095-X
B.T. Lawergren, A.T.G. Fergusono, G.C. Morrision. States with T = 1 in 20Ne, 24Mg and 28Si. Nucl. Phys. A 108, 325 (1968).
How to Cite
License to Publish the Paper
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.