Research Article
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Year 2020, , 168 - 176, 20.03.2020
https://doi.org/10.36753/mathenot.685084

Abstract

References

  • \bibitem{Yakut} Yakut, H., Guliyev, E., Guner, M., Tabar, E., Zenginerler, Z.: \emph{QPNM calculation for the ground state magnetic moments of odd-mass deformed nuclei: ${}^{157 - 167}{\rm{Er}}$}. Nuclear Physics A. \textbf{888}, 23-33 (2012).
  • \bibitem{Yakut} Yakut, H., Tabar, E., Kuliev, A.A., Zenginerler, Z., Kaplan, P.: \emph{Ground state magnetic properties of odd neutron Dy isotopes}. International Journal of Modern Physics E. \textbf{22} (10), 1350076(13) (2013).
  • \bibitem{Yakut} Yakut, H., Tabar, E., Kuliev, A.A., Guliyev, E.: \emph{The ground-state magnetic moments of odd-mass Hf isotopes}. Central European Journal of Physics. \textbf{12}, 843-850 (2014).
  • \bibitem{Yakut} Yakut, H., Tabar, E., Hoşgör, G.: \emph{Effects of the Isoscalar and Isovector Interaction on the Ground-State Magnetic Moments of the Odd-Mass ${}^{137 - 145}{\rm{Ce}}$ Nuclei}. Canadian Journal of Physics. \textbf{97} (11), 1187-1190 (2019).
  • \bibitem{Tabar} Tabar, E., Yakut, H., Kuliev, A.A., Quliyev, H., Hoşgör, G.: \emph{Magnetic Moments and g factors in odd-mass Ho isotopes}. Chinese Physics C. \textbf{41} (7), 074101 (2017).
  • \bibitem{Tabar} Tabar, E.: \emph{Magnetic properties of ${\rm{K = }}{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}$ states in deformed odd-mass nuclei}. Nuclear Physics A. \textbf{986}, 150-166 (2019).
  • \bibitem{Tabar} Tabar, E.: \emph{A theoretical study on the ground and low-energy magnetic dipole characteristics of ${}^{239}{\rm{Pu}}$ nucleus}. Nuclear Physics A. \textbf{987}, 202-221 (2019).
  • \bibitem{Tabar} Tabar, E.: \emph{A theoretical investigation of the magnetic dipole moment of the ground- and excited-states below 600keV in well-deformed $\begin{array}{l} {}^{183,185}{\rm{W}}{\rm{, }}{}^{185,187}{\rm{Re }} \ and \ {}^{187,189}{\rm{Os}} \end{array}$}. Int. J. Mod. Phys. E \textbf{28}(6), 1950040 (2019).
  • \bibitem{Arima} Arima, A., Horie, H.: \emph{Configuration mixing and magnetic moments of odd nuclei}. Prog. Theor. Phys. \textbf{12}(5), 623–641 (1954).
  • \bibitem{Enguang} Enguang, Z.: \emph{Recent progress in theoretical studies of nuclear magnetic moments}. Chin. Sci. Bull. \textbf{57}(34), 4394–4399 (2012).
  • \bibitem{Shimizu} Shimizu, K., Ichimura, M., Arima, A.: \emph{Magnetic moments and GT-type $\beta $-decay matrix elements in nuclei with a LS doubly closed shell plus or minus one nucleon }. Nucl. Phys. A. \textbf{226}(2), 282–318 (1974).
  • \bibitem{Towner} Towner, I.S., Khanna, F.C.: \emph{Corrections to the single-particle M1 and Gamow-Teller matrix elements}. Nucl. Phys. A. \textbf{339}, 334–364 (1983).
  • \bibitem{Arima} Arima, A.: \emph{A short history of nuclear magnetic moments and GT transitions}. Sci. China Phys. Mech. Astron. \textbf{54}, 188–193 (2011).
  • \bibitem{Bochnacki} Bochnacki, Z., Ogaza, S.: \emph{Spin polarization effect and the magnetic moments of odd-mass deformed nuclei}. Nucl. Phys. \textbf{69} (2), 186–192 (1965).
  • \bibitem{Kuliev} Kuliev, A.A., Pyatov, N.I.: \emph{Spin polarization effects in odd-mass deformed nuclei}. Phys. Lett. B \textbf{28} (7), 443–445 (1969).
  • \bibitem{De Boer} De Boer, J., Rogers, J.D.: \emph{Concerning the magnetic properties of deformed nuclei in region $153 \le A \le 187$}. Phys. Lett. \textbf{3} (6), 304–306 (1963).
  • \bibitem{Bochnacki} Bochnacki, Z., Ogaza, S.: \emph{Spin polarization effect on the fast allowed beta transitions between deformed odd-mass nuclei}. Nuclear Physics A \textbf{102} , 529-533(1967).
  • \bibitem{Kuliev} Kuliev, A.A., Pyatov, N.I.: \emph{Magnetic dipole interactions in deformed nuclei}. Sov. J. Nucl. Phys \textbf{9} (2), 313–323 (1969).
  • \bibitem{Yakut} Yakut, H., Kuliev, A., Guliyev, E.: \emph{Investigations of the gK-factors in the ${}^{175,177,179}{\rm{Hf}}$ isotopes}. AIP Conf. Proc. \textbf{1072}, 258–261 (2008).
  • \bibitem{Yakut} Yakut, H., Kuliev, A.A., Guliyev, E., Yıldırım, Z.: \emph{Intrinsic gK factors of odd-mass ${}^{167 - 179}{\rm{Lu}}$ isotopes}. Pramana–J. Phys \textbf{73}, 829-837 (2009).
  • \bibitem{Yakut} Yakut, H.: Nadir toprak deforme çekirdeklerinde kolektif dipol seviyelerinin elektrik ve manyetik dipol özelliklerinin incelenmesi. Ph.D. thesis. Sakarya University (2009).
  • \bibitem{England} England, J., Grant, I., Griffith, J., Evans, D., Eastham, D., Newton, G., Walker, P.: \emph{Isotope shifts and hyperfine splitting in ${}^{144 - 154}{\rm{Sm I}}$ }. Journal of Physics G: Nuclear and Particle Physics, \textbf{16} (1), 105–123 (1990).
  • \bibitem{Letokhov} Letokhov, V., Mishin, V., Sekatsky, S., Fedoseyev, V., Alkhazov, G., Barzakh, A., Denisov, V., Starodubsky, V.: \emph{Laser spectroscopic studies of nuclei with neutron number $N < 82$ (Eu, Sm and Nd isotopes)}. Journal of Physics G: Nuclear and Particle Physics, \textbf{18} (7), 1177–1173 (1992).
  • \bibitem{Kaplan} Kaplan, M., Blok, J., Shirley, D.: \emph{Magnetic Moment of ${\rm{S}}{{\rm{m}}^{145}}$ and Attenuation Following the Decay of Oriented ${\rm{S}}{{\rm{m}}^{145}}$}. Phy.Rev. \textbf{184} (4), 1177–1180 (1969).
  • \bibitem{Woodgate} Woodgate, G.K.: \emph{Hyperfine structure and nuclear moments of samarium}. The Royal Society, Proc. R. Soc. Lond. A, \textbf{293}, 117-144 (1966).
  • \bibitem{Childs} Childs, W.J., Goodman, L.S.: \emph{Reanalysis of the Hyperfine Structure of the $4{{\rm{f}}^6}6{{\rm{s}}^{{2^7}}}F$ Multiplet in $^{147,149}{\rm{Sm}}$, Including Measurements for the ${}^7{F_6}$ State}. Physical Review A, \textbf{6} (4), 2011-2021 (1972).
  • \bibitem{Soloviev} Soloviev, V.G.: \emph{Microscopic description of vibrational states in deformed nuclei}. Prog. Part. Nucl. Phys. \textbf{28} (C), 49-74 (1992).
  • \bibitem{Soloviev} Soloviev, V.G. Sushkov, A.V., Shirikova, N.Y.: \emph{Gamma-ray transitions between excited states in ${}^{168}{\rm{Er}}$}. J. Phys. G: Nucl. Part. Phys. \textbf{20}, 113-134 (1994).
  • \bibitem{Soloviev} Soloviev, V.G. Sushkov, A.V., Shirikova, N.Y.: \emph{Description of low-lying vibrational and two-quasiparticle states in ${}^{166}{\rm{Er}}$}. Phys. Rev. C. \textbf{51}(2), 551-558 (1995).
  • \bibitem{Malov} Malov, L.A., Nesterenko, V.O., Soloviev, V.G.: \emph{Low-energy octupole resonances in deformed nuclei}. J. Phys. G: Nucl. Phys. \textbf{3}(9), 219-222 (1977).
  • \bibitem{Pyatov} Pyatov, N.I., Salamov, D.I.: \emph{Conservation laws and collective excitations in nuclei}. Nukleonika. \textbf{22}(1), 127-140 (1977).
  • \bibitem{Bohr} Bohr, A., Mottelson, B.: Nuclear structure. Vol. 1, Benjamin, New York and Amsterdam (1969).
  • \bibitem{Soloviev} Soloviev, V.G., Sushkov, A.V., Shirikova, N.Y.: \emph{Low-lying magnetic dipole strength in ${}^{163}{\rm{Dy}}$}. Phys. Rev. C. \textbf{53}, 1022-1024 (1995).
  • \bibitem{Luenberger} Luenberger, D.G.: Optimization by Vector Space Methods. John Wiley Sons. New York (1969).
  • \bibitem{Bussotti} Bussotti, P.: \emph{On the Genesis of the Lagrange Multipliers}. Journal of Optimization Theory and Applications \textbf{117}, 453–459 (2003).
  • \bibitem{Bauske} Bauske, I., Arias, J.M., Brentano, P.Von., Frank, A., Friedrichs, H., Heil, R.D., Herzberg, R.D., Hoyler, F., Van Isacker, P., Kneissl, U.: \emph{First observation of scissors mode states in an odd-mass nucleus}. Phy. Rev. Lett. \textbf{71}, 975-978 (1993).
  • \bibitem{Raman} Raman, S., Nestor, C.W., Tikkanen, P.: \emph{Transition probability from the ground to the first-excited ${2^ + }$ state of even–even nuclides}. Atomic Data and Nuclear Data Tables \textbf{90}, 1-128 (2001).
  • \bibitem{Soloviev} Soloviev, V.G.: Theory of complex nuclei. Pergamon Press New York (1976).
  • \bibitem{Stone} Stone, N.J.: \emph{Table of nuclear magnetic dipole and electric quadrupole moments}. Atomic Data and Nuclear Data Tables \textbf{78}, 75-176 (2005).
  • \bibitem{Bow} Bow, Y.F.: \emph{Magnetic dipole transition probabilities of deformed odd-mass nuclei}. Phys. Rev. C \textbf{2}(5), 1608–1611 (1970).
  • \bibitem{Soloviev} Soloviev, V.G.: Theory of atomic nuclei: Quasiparticles and phonons. Institute of Physics Publishing Bristol and Philadelphia (1992).
  • \bibitem{balas} Balasubramanian, K.: \textit{Computational enumeration of colorings of hyperplanes of hypercubes for all irreducible representations and applications}, J. Math. Sci. Model., \textbf{1}(3), 158 - 180 (2018).
  • \bibitem{Li} Li, R.: \textit{Energy conditions for Hamiltonian and traceable graphs}, Univers. J. Math. Appl. \textbf{2}(1), 33-35 (2019).
  • \bibitem{than}Thangamuthu, M., Thippan, j.: \textit{Numerical solution for Hybrid fuzzy differential equation by fifth order Runge-Kutta Nystrom method}, J. Math. Sci. Model., \textit{2}(1), 39-50 (2019).
  • \bibitem{Fujita} Fujita, Jun-I., Ikeda, K.: \emph{Existence of isobaric states and beta decay of heavier nuclei}. Nucl. Phys. \textbf{67}(1), 145–1771 (1965).
  • \bibitem{Gabrakov} Gabrakov, S.I., Kuliev, A.A., Pyatov, N.I.: \emph{${0^ + }$ and ${1^ + }$ unlike particle-hole states in deformed odd-odd nuclei and ß-strength functions}. Phys. Lett. B. \textbf{36}(4), 275-277 (1971).
  • \bibitem{Kuliev} Kuliev, A.A., Akkaya, R., Ilhan, M., Guliyev, E., Salamov, C., Selvi, S.: \emph{Rotational-invariant model of the states with ${{\rm{K}}^\pi }{\rm{ = }}{{\rm{1}}^ + }$ and their contribution to the scissors mode}. Int. JMod. Phys. E \textbf{9}(3), 249-261 (2000).
  • \bibitem{Kuliev} Kuliev, A.A., Guliyev, E., Gerçeklioglu, M.: \emph{The dependence of the scissors mode on the deformation in the ${}^{140 - 150}{\rm{Ce}}$ isotopes}. J. Phys. G: Nucl. Phys. \textbf{28}(3), 407-414 (2002).
  • \bibitem{Guliyev} Guliyev, E., Ertugral, F., Kuliev, A.A.: \emph{Low-lying magnetic dipole strength distribution in the $\gamma $-soft even-even ${}^{130,136}{\rm{Ba}}$}. Eur. Phys. J. A. \textbf{23}(7), 313-320 (2006).
  • \bibitem{Guliyev} Guliyev, E., Kuliev, A.A., Ertugral, F.: \emph{Low-lying dipole excitations in the deformed even-even isotopes ${}^{154,160}{\rm{Gd}}$}. Acta. Phys. Pol. B. \textbf{40}(3), 653-656 (2009).
  • \bibitem{Guliyev} Guliyev, E., Kuliev, A.A., Ertugral, F.: \emph{Systematic investigation of the low-energy dipole excitations in ${}^{176,178,180}{\rm{Hf}}$ within rotational, translational and Galilean invariant quasiparticle RPA}. Nucl. Phys. A. \textbf{915}, 78-89 (2013).
  • \bibitem{Zenginerler} Zenginerler, Z., Guliyev, E., Kuliev, A.A., Yakut, H., Soluk, G. : \emph{Systematic investigation of the low-lying dipole excitations in even-even ${}^{124,136}{\rm{Ba}}$ isotopes}. Eur. Phys. J. A. \textbf{49}(9), 1-7 (2013).
  • \bibitem{Tabar} Tabar, E., Yakut, H., Kuliev, A.A.: \emph{Magnetic dipole response of the ${}^{169}{\rm{Tm}}$ nucleus}. Nuclear Physics A. \textbf{981}, 130-146 (2019).
  • \bibitem{Tabar} Tabar, E., Yakut, H., Kuliev, A.A.: \emph{Low-energy dipole strength in even–even ${}^{152,164}{\rm{Dy}}$ isotopes within the quasiparticle random phase approximation including symmetry restoring interactions}. Nuc.Phy. A \textbf{979}, 143-164 (2018).
  • \bibitem{Tabar} Tabar, E., Yakut, H., Kuliev, A.A.: \emph{Microscopic description of low-lying M1 excitations in odd-mass actinide nuclei}. Nuc.Phy. A \textbf{957}, 33–50 (2017).
  • \bibitem{Tabar} Tabar, E., Yakut, H., Kuliev, A.A.: \emph{Microscopic description of ground state magnetic moment and low-lying magnetic dipole excitations in heavy odd-mass ${}^{181}{\rm{Ta}}$ nucleus}. Inter. J. Modern Phy. E- Nuclear Physics \textbf{25}(8), 1650053 (2016).

Numerical Analysis of the Ground-State Magnetic Moments of ${}^{143,145,147}{\rm{Sm}}$ Isotopes

Year 2020, , 168 - 176, 20.03.2020
https://doi.org/10.36753/mathenot.685084

Abstract

The explanation of the ground state magnetic properties of odd-mass nuclei is very informative in understanding of the complex structure of the deformed nuclei. The ground-state magnetic moments of most of the odd-A deformed nuclei have been measured by various experimental studies and there are numerous studies in the literature. However, many of the theoretical studies on magnetic moments and spin polarization effects affecting them are far from explaining these measured values. In this paper, the magnetic moments and effective spin g factors of 143,145,147Sm isotopes in the lanthanides region of the periodic table were investigated within the framework of the Quasiparticle-Phonon Nuclear Model (QPNM) for the first time. Spin-spin interaction parameters (χ) were determined by comparing theoretical and experimental values of magnetic moments of the related isotopes and it was determined that these interactions were found to have an isovector character (q = -1). It has been observed that the ground-state structures of the studied isotopes are weakly affected by quasiparticlephonon interactions and the contribution of these interactions ( values) to the ground-state wave functions is quite small (around 0.01%). Theoretical explanation of the renormalization of spin gyromagnetic factor is one of the most important problems of nuclear structure physics. The results obtained in this study for the effective spin gyromagnetic factor also agree with the phenological value .



References

  • \bibitem{Yakut} Yakut, H., Guliyev, E., Guner, M., Tabar, E., Zenginerler, Z.: \emph{QPNM calculation for the ground state magnetic moments of odd-mass deformed nuclei: ${}^{157 - 167}{\rm{Er}}$}. Nuclear Physics A. \textbf{888}, 23-33 (2012).
  • \bibitem{Yakut} Yakut, H., Tabar, E., Kuliev, A.A., Zenginerler, Z., Kaplan, P.: \emph{Ground state magnetic properties of odd neutron Dy isotopes}. International Journal of Modern Physics E. \textbf{22} (10), 1350076(13) (2013).
  • \bibitem{Yakut} Yakut, H., Tabar, E., Kuliev, A.A., Guliyev, E.: \emph{The ground-state magnetic moments of odd-mass Hf isotopes}. Central European Journal of Physics. \textbf{12}, 843-850 (2014).
  • \bibitem{Yakut} Yakut, H., Tabar, E., Hoşgör, G.: \emph{Effects of the Isoscalar and Isovector Interaction on the Ground-State Magnetic Moments of the Odd-Mass ${}^{137 - 145}{\rm{Ce}}$ Nuclei}. Canadian Journal of Physics. \textbf{97} (11), 1187-1190 (2019).
  • \bibitem{Tabar} Tabar, E., Yakut, H., Kuliev, A.A., Quliyev, H., Hoşgör, G.: \emph{Magnetic Moments and g factors in odd-mass Ho isotopes}. Chinese Physics C. \textbf{41} (7), 074101 (2017).
  • \bibitem{Tabar} Tabar, E.: \emph{Magnetic properties of ${\rm{K = }}{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}$ states in deformed odd-mass nuclei}. Nuclear Physics A. \textbf{986}, 150-166 (2019).
  • \bibitem{Tabar} Tabar, E.: \emph{A theoretical study on the ground and low-energy magnetic dipole characteristics of ${}^{239}{\rm{Pu}}$ nucleus}. Nuclear Physics A. \textbf{987}, 202-221 (2019).
  • \bibitem{Tabar} Tabar, E.: \emph{A theoretical investigation of the magnetic dipole moment of the ground- and excited-states below 600keV in well-deformed $\begin{array}{l} {}^{183,185}{\rm{W}}{\rm{, }}{}^{185,187}{\rm{Re }} \ and \ {}^{187,189}{\rm{Os}} \end{array}$}. Int. J. Mod. Phys. E \textbf{28}(6), 1950040 (2019).
  • \bibitem{Arima} Arima, A., Horie, H.: \emph{Configuration mixing and magnetic moments of odd nuclei}. Prog. Theor. Phys. \textbf{12}(5), 623–641 (1954).
  • \bibitem{Enguang} Enguang, Z.: \emph{Recent progress in theoretical studies of nuclear magnetic moments}. Chin. Sci. Bull. \textbf{57}(34), 4394–4399 (2012).
  • \bibitem{Shimizu} Shimizu, K., Ichimura, M., Arima, A.: \emph{Magnetic moments and GT-type $\beta $-decay matrix elements in nuclei with a LS doubly closed shell plus or minus one nucleon }. Nucl. Phys. A. \textbf{226}(2), 282–318 (1974).
  • \bibitem{Towner} Towner, I.S., Khanna, F.C.: \emph{Corrections to the single-particle M1 and Gamow-Teller matrix elements}. Nucl. Phys. A. \textbf{339}, 334–364 (1983).
  • \bibitem{Arima} Arima, A.: \emph{A short history of nuclear magnetic moments and GT transitions}. Sci. China Phys. Mech. Astron. \textbf{54}, 188–193 (2011).
  • \bibitem{Bochnacki} Bochnacki, Z., Ogaza, S.: \emph{Spin polarization effect and the magnetic moments of odd-mass deformed nuclei}. Nucl. Phys. \textbf{69} (2), 186–192 (1965).
  • \bibitem{Kuliev} Kuliev, A.A., Pyatov, N.I.: \emph{Spin polarization effects in odd-mass deformed nuclei}. Phys. Lett. B \textbf{28} (7), 443–445 (1969).
  • \bibitem{De Boer} De Boer, J., Rogers, J.D.: \emph{Concerning the magnetic properties of deformed nuclei in region $153 \le A \le 187$}. Phys. Lett. \textbf{3} (6), 304–306 (1963).
  • \bibitem{Bochnacki} Bochnacki, Z., Ogaza, S.: \emph{Spin polarization effect on the fast allowed beta transitions between deformed odd-mass nuclei}. Nuclear Physics A \textbf{102} , 529-533(1967).
  • \bibitem{Kuliev} Kuliev, A.A., Pyatov, N.I.: \emph{Magnetic dipole interactions in deformed nuclei}. Sov. J. Nucl. Phys \textbf{9} (2), 313–323 (1969).
  • \bibitem{Yakut} Yakut, H., Kuliev, A., Guliyev, E.: \emph{Investigations of the gK-factors in the ${}^{175,177,179}{\rm{Hf}}$ isotopes}. AIP Conf. Proc. \textbf{1072}, 258–261 (2008).
  • \bibitem{Yakut} Yakut, H., Kuliev, A.A., Guliyev, E., Yıldırım, Z.: \emph{Intrinsic gK factors of odd-mass ${}^{167 - 179}{\rm{Lu}}$ isotopes}. Pramana–J. Phys \textbf{73}, 829-837 (2009).
  • \bibitem{Yakut} Yakut, H.: Nadir toprak deforme çekirdeklerinde kolektif dipol seviyelerinin elektrik ve manyetik dipol özelliklerinin incelenmesi. Ph.D. thesis. Sakarya University (2009).
  • \bibitem{England} England, J., Grant, I., Griffith, J., Evans, D., Eastham, D., Newton, G., Walker, P.: \emph{Isotope shifts and hyperfine splitting in ${}^{144 - 154}{\rm{Sm I}}$ }. Journal of Physics G: Nuclear and Particle Physics, \textbf{16} (1), 105–123 (1990).
  • \bibitem{Letokhov} Letokhov, V., Mishin, V., Sekatsky, S., Fedoseyev, V., Alkhazov, G., Barzakh, A., Denisov, V., Starodubsky, V.: \emph{Laser spectroscopic studies of nuclei with neutron number $N < 82$ (Eu, Sm and Nd isotopes)}. Journal of Physics G: Nuclear and Particle Physics, \textbf{18} (7), 1177–1173 (1992).
  • \bibitem{Kaplan} Kaplan, M., Blok, J., Shirley, D.: \emph{Magnetic Moment of ${\rm{S}}{{\rm{m}}^{145}}$ and Attenuation Following the Decay of Oriented ${\rm{S}}{{\rm{m}}^{145}}$}. Phy.Rev. \textbf{184} (4), 1177–1180 (1969).
  • \bibitem{Woodgate} Woodgate, G.K.: \emph{Hyperfine structure and nuclear moments of samarium}. The Royal Society, Proc. R. Soc. Lond. A, \textbf{293}, 117-144 (1966).
  • \bibitem{Childs} Childs, W.J., Goodman, L.S.: \emph{Reanalysis of the Hyperfine Structure of the $4{{\rm{f}}^6}6{{\rm{s}}^{{2^7}}}F$ Multiplet in $^{147,149}{\rm{Sm}}$, Including Measurements for the ${}^7{F_6}$ State}. Physical Review A, \textbf{6} (4), 2011-2021 (1972).
  • \bibitem{Soloviev} Soloviev, V.G.: \emph{Microscopic description of vibrational states in deformed nuclei}. Prog. Part. Nucl. Phys. \textbf{28} (C), 49-74 (1992).
  • \bibitem{Soloviev} Soloviev, V.G. Sushkov, A.V., Shirikova, N.Y.: \emph{Gamma-ray transitions between excited states in ${}^{168}{\rm{Er}}$}. J. Phys. G: Nucl. Part. Phys. \textbf{20}, 113-134 (1994).
  • \bibitem{Soloviev} Soloviev, V.G. Sushkov, A.V., Shirikova, N.Y.: \emph{Description of low-lying vibrational and two-quasiparticle states in ${}^{166}{\rm{Er}}$}. Phys. Rev. C. \textbf{51}(2), 551-558 (1995).
  • \bibitem{Malov} Malov, L.A., Nesterenko, V.O., Soloviev, V.G.: \emph{Low-energy octupole resonances in deformed nuclei}. J. Phys. G: Nucl. Phys. \textbf{3}(9), 219-222 (1977).
  • \bibitem{Pyatov} Pyatov, N.I., Salamov, D.I.: \emph{Conservation laws and collective excitations in nuclei}. Nukleonika. \textbf{22}(1), 127-140 (1977).
  • \bibitem{Bohr} Bohr, A., Mottelson, B.: Nuclear structure. Vol. 1, Benjamin, New York and Amsterdam (1969).
  • \bibitem{Soloviev} Soloviev, V.G., Sushkov, A.V., Shirikova, N.Y.: \emph{Low-lying magnetic dipole strength in ${}^{163}{\rm{Dy}}$}. Phys. Rev. C. \textbf{53}, 1022-1024 (1995).
  • \bibitem{Luenberger} Luenberger, D.G.: Optimization by Vector Space Methods. John Wiley Sons. New York (1969).
  • \bibitem{Bussotti} Bussotti, P.: \emph{On the Genesis of the Lagrange Multipliers}. Journal of Optimization Theory and Applications \textbf{117}, 453–459 (2003).
  • \bibitem{Bauske} Bauske, I., Arias, J.M., Brentano, P.Von., Frank, A., Friedrichs, H., Heil, R.D., Herzberg, R.D., Hoyler, F., Van Isacker, P., Kneissl, U.: \emph{First observation of scissors mode states in an odd-mass nucleus}. Phy. Rev. Lett. \textbf{71}, 975-978 (1993).
  • \bibitem{Raman} Raman, S., Nestor, C.W., Tikkanen, P.: \emph{Transition probability from the ground to the first-excited ${2^ + }$ state of even–even nuclides}. Atomic Data and Nuclear Data Tables \textbf{90}, 1-128 (2001).
  • \bibitem{Soloviev} Soloviev, V.G.: Theory of complex nuclei. Pergamon Press New York (1976).
  • \bibitem{Stone} Stone, N.J.: \emph{Table of nuclear magnetic dipole and electric quadrupole moments}. Atomic Data and Nuclear Data Tables \textbf{78}, 75-176 (2005).
  • \bibitem{Bow} Bow, Y.F.: \emph{Magnetic dipole transition probabilities of deformed odd-mass nuclei}. Phys. Rev. C \textbf{2}(5), 1608–1611 (1970).
  • \bibitem{Soloviev} Soloviev, V.G.: Theory of atomic nuclei: Quasiparticles and phonons. Institute of Physics Publishing Bristol and Philadelphia (1992).
  • \bibitem{balas} Balasubramanian, K.: \textit{Computational enumeration of colorings of hyperplanes of hypercubes for all irreducible representations and applications}, J. Math. Sci. Model., \textbf{1}(3), 158 - 180 (2018).
  • \bibitem{Li} Li, R.: \textit{Energy conditions for Hamiltonian and traceable graphs}, Univers. J. Math. Appl. \textbf{2}(1), 33-35 (2019).
  • \bibitem{than}Thangamuthu, M., Thippan, j.: \textit{Numerical solution for Hybrid fuzzy differential equation by fifth order Runge-Kutta Nystrom method}, J. Math. Sci. Model., \textit{2}(1), 39-50 (2019).
  • \bibitem{Fujita} Fujita, Jun-I., Ikeda, K.: \emph{Existence of isobaric states and beta decay of heavier nuclei}. Nucl. Phys. \textbf{67}(1), 145–1771 (1965).
  • \bibitem{Gabrakov} Gabrakov, S.I., Kuliev, A.A., Pyatov, N.I.: \emph{${0^ + }$ and ${1^ + }$ unlike particle-hole states in deformed odd-odd nuclei and ß-strength functions}. Phys. Lett. B. \textbf{36}(4), 275-277 (1971).
  • \bibitem{Kuliev} Kuliev, A.A., Akkaya, R., Ilhan, M., Guliyev, E., Salamov, C., Selvi, S.: \emph{Rotational-invariant model of the states with ${{\rm{K}}^\pi }{\rm{ = }}{{\rm{1}}^ + }$ and their contribution to the scissors mode}. Int. JMod. Phys. E \textbf{9}(3), 249-261 (2000).
  • \bibitem{Kuliev} Kuliev, A.A., Guliyev, E., Gerçeklioglu, M.: \emph{The dependence of the scissors mode on the deformation in the ${}^{140 - 150}{\rm{Ce}}$ isotopes}. J. Phys. G: Nucl. Phys. \textbf{28}(3), 407-414 (2002).
  • \bibitem{Guliyev} Guliyev, E., Ertugral, F., Kuliev, A.A.: \emph{Low-lying magnetic dipole strength distribution in the $\gamma $-soft even-even ${}^{130,136}{\rm{Ba}}$}. Eur. Phys. J. A. \textbf{23}(7), 313-320 (2006).
  • \bibitem{Guliyev} Guliyev, E., Kuliev, A.A., Ertugral, F.: \emph{Low-lying dipole excitations in the deformed even-even isotopes ${}^{154,160}{\rm{Gd}}$}. Acta. Phys. Pol. B. \textbf{40}(3), 653-656 (2009).
  • \bibitem{Guliyev} Guliyev, E., Kuliev, A.A., Ertugral, F.: \emph{Systematic investigation of the low-energy dipole excitations in ${}^{176,178,180}{\rm{Hf}}$ within rotational, translational and Galilean invariant quasiparticle RPA}. Nucl. Phys. A. \textbf{915}, 78-89 (2013).
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There are 56 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mehmet Güner 0000-0002-3843-9436

Publication Date March 20, 2020
Submission Date February 5, 2020
Acceptance Date March 23, 2020
Published in Issue Year 2020

Cite

APA Güner, M. (2020). Numerical Analysis of the Ground-State Magnetic Moments of ${}^{143,145,147}{\rm{Sm}}$ Isotopes. Mathematical Sciences and Applications E-Notes, 8(1), 168-176. https://doi.org/10.36753/mathenot.685084
AMA Güner M. Numerical Analysis of the Ground-State Magnetic Moments of ${}^{143,145,147}{\rm{Sm}}$ Isotopes. Math. Sci. Appl. E-Notes. March 2020;8(1):168-176. doi:10.36753/mathenot.685084
Chicago Güner, Mehmet. “Numerical Analysis of the Ground-State Magnetic Moments of ${}^{143,145,147}{\rm{Sm}}$ Isotopes”. Mathematical Sciences and Applications E-Notes 8, no. 1 (March 2020): 168-76. https://doi.org/10.36753/mathenot.685084.
EndNote Güner M (March 1, 2020) Numerical Analysis of the Ground-State Magnetic Moments of ${}^{143,145,147}{\rm{Sm}}$ Isotopes. Mathematical Sciences and Applications E-Notes 8 1 168–176.
IEEE M. Güner, “Numerical Analysis of the Ground-State Magnetic Moments of ${}^{143,145,147}{\rm{Sm}}$ Isotopes”, Math. Sci. Appl. E-Notes, vol. 8, no. 1, pp. 168–176, 2020, doi: 10.36753/mathenot.685084.
ISNAD Güner, Mehmet. “Numerical Analysis of the Ground-State Magnetic Moments of ${}^{143,145,147}{\rm{Sm}}$ Isotopes”. Mathematical Sciences and Applications E-Notes 8/1 (March 2020), 168-176. https://doi.org/10.36753/mathenot.685084.
JAMA Güner M. Numerical Analysis of the Ground-State Magnetic Moments of ${}^{143,145,147}{\rm{Sm}}$ Isotopes. Math. Sci. Appl. E-Notes. 2020;8:168–176.
MLA Güner, Mehmet. “Numerical Analysis of the Ground-State Magnetic Moments of ${}^{143,145,147}{\rm{Sm}}$ Isotopes”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, 2020, pp. 168-76, doi:10.36753/mathenot.685084.
Vancouver Güner M. Numerical Analysis of the Ground-State Magnetic Moments of ${}^{143,145,147}{\rm{Sm}}$ Isotopes. Math. Sci. Appl. E-Notes. 2020;8(1):168-76.

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