The basis functions of the translation invariant shell model are used to construct the ground state nuclear wave functions of 3 H. The used residual two-body interactions consist of central, tensor, spin orbit and quadratic spin orbit terms with Gaussian radial dependence. The parameters of these interactions are so chosen in such a way that they represent the long-range attraction and the short-range repulsion of the nucleon-nucleon interactions. These parameters are so chosen to reproduce good agreement between the calculated values of the binding energy, the root mean-square radius, the D-state probability, the magnetic dipole moment and the electric quadrupole moment of the deuteron nucleus. The variation method is then used to calculate the binding energy of triton by varying the oscillator parameter which exists in the nuclear wave function. The obtained nuclear wave functions are then used to calculate the root mean-square radius and the magnetic dipole moment of the triton.
De-Shalit, A. and Talmi, I. (2013) Nuclear Shell Theory. Academic Press, New York.
Bargman, V. and Moshinsky, M. (1961) Group Theory of Harmonic Oscillators. I. The Collective Modes. Nuclear Physics , 18, 697-712. https://doi.org/10.1016/0029-5582(60)90438-7
Kramer, P. and Moshinsky, M. (1966) Group Theory of Harmonic Oscillators (III). States with Permutational Symmetry. Nuclear Physics , 82, 241-274. https://doi.org/10.1016/0029-5582(66)90001-0
Ring, P. and Schuck, P. (1980) The Nuclear Many-Body Problem. Springer Verlag, New York. https://doi.org/10.1007/978-3-642-61852-9
Vanagas, V.V. (1971) Algebraic Methods in Nuclear Theory. Mintis, Vilnius.
Doma, S.B. (2002) Single Particle Schrödinger Fluid and Moments of Inertia of Deformed Nuclei. Journal High Energy Physics and Nuclear Physics , 26, 836-842.
Doma, S.B., Kharroube, K.A., Tefiha, A.D. and El-Gendy, H.S. (2011) The Deformation Structure of the Even-Even p-and sd Shell Nuclei. Alexandria Journal of Physics , 1, 1-13.
Doma, S.B. (2003) The Single Particle Schrodinger Fluid and Moments of Inertia of Deformed Nuclei. Bulgarian Journal of Physics , 30, 117-124.
Doma, S.B. and Amin, M.M. (2009) Single Particle Schrödinger Fluid and Moments of Inertia of the Even-Even Uranium Isotopes. The Open Applied Mathematics Journal , 3, 1-6. https://doi.org/10.2174/1874114200903010001
Doma, S.B. and El-Gendy, H.S. (2018) A Nuclear Phenomenological Study of the Even-Even Thorium Isotopes. International Journal of Modern Physics E , 27, Article 1850040. https://doi.org/10.1142/S0218301318500404
Hammad, M.M., Yahia, M.M., Motaweh, H.A. and Doma, S.B. (2020) Critical Potentials and Fluctuations Phenomena with Quartic, Sextic, and Octic Anharmonic Oscillator Potentials. Nuclear Physics A , 1004, Article 122036. https://doi.org/10.1016/j.nuclphysa.2020.122036
Hammad, M.M., Shetawy, H.E., Aly, A.A. and Doma, S.B. (2019) Nuclear Supersymmetry and Dual Algebraic Structures. Physica Scripta , 94, Article 105207. https://doi.org/10.1088/1402-4896/ab2442
Hammad, M.M., Yaqut, A.S.H., Abdel-Khalek, M.A. and Doma, S.B. (2021) Analytical Study of Conformable Fractional Bohr Hamiltonian with Kratzer Potential. Nuclear Physics A , 1015, Article 122307. https://doi.org/10.1016/j.nuclphysa.2021.122307
Blatt, J.M. and Weisskopf, V.F. (1979) Theoretical Nuclear Physics. Springer-Verlag, New York. https://doi.org/10.1007/978-1-4612-9959-2
Doma, S.B. (2003) Study of Nuclei with A = 5 on the Basis of the Unitary Scheme Model. International Journal of Modern Physics E , 12, 421-429. https://doi.org/10.1142/S021830130300134X
Doma, S.B. and El-Zebidy, A.F.M. (2005) Cluster-Cluster Potentials for the Lithium Nuclei. International Journal of Modern Physics E , 14, 189-195. https://doi.org/10.1142/S0218301305002989
Doma, S.B. (1985) Unitary Scheme Model Study of 4 He with the Gogny, Pires and Detourreil Interaction. Helvetica Physica Acta , 58, 1072-1077.
Doma, S.B., El-Zebidy, A.F.M. and Abdel-Khalik, M.A. (2006) The Mean Lifetime of the β -Decay and the Nuclear Magnetic Dipole Moment for Nuclei with A = 7. Journal of Physics G : Nuclear and Particle Physics , 34, 27. https://doi.org/10.1088/0954-3899/34/1/002
Doma, S.B. and El-Gendy, H.S. (2018) Unitary Scheme Model Calculations of the Ground and Excited State Characteristics of 3 H and 4 He. Journal of Physics Co m munications , 2, Article 065005. https://doi.org/10.1088/2399-6528/aac79f
Doma, S.B., El-Nohy, N.A. and Gharib, K.K. (1996) The Ground-State Characteristics of Deuteron Using Gaussian Potentials. Helvetica Physica Acta , 69, 90-104.
Doma, S.B., El-Gendy, H.S. and Hammad, M.M. (2020) Large Basis Unitary Scheme Model Calculations for the Mirror Nuclei with A = 7. Chinese Journal of Physics , 63, 21-35. https://doi.org/10.1016/j.cjph.2019.10.026
Doma, S.B. (2002) Ground State Characteristics of the Light Nuclei with A ≤ 6 on the Basis of the Translation Invariant Shell Model by Using Nucleon-Nucleon Interactions. Chinese Physics C , 26, 941-948.
Doma, S.B. (2012) Unitary Scheme Model Calculations of A = 6 Nuclei with Realistic Interactions. International Journal of Modern Physics E , 21, Article 1250077.
Ericson, T.E.O. and Rosa-Clot, M. (1983) The Deuteron Asymptotic D-State as a Probe of the Nucleon-Nucleon Force. Nuclear Physics A , 405, 497-533. https://doi.org/10.1016/0375-9474(83)90516-X
Ericson, T.E.O. (1984) The Deuteron Properties. Nuclear Physics A , 416, 281-298. https://doi.org/10.1016/0375-9474(84)90467-6
Rodning, N.L., Madison, W.U. and Knutspn, L.D. (1990) Asymptotic D-State to S-State Ratio of the Deuteron. Physical Review C , 41, 898-909. https://doi.org/10.1103/PhysRevC.41.898
Zheng, D.C., Vary, J.P. and Barrett, B.R. (1994) Large-Space Shell-Model Calculations for Light Nuclei. Physical Review C , 50, 2841-2849. https://doi.org/10.1103/PhysRevC.50.2841
Carlson, J. and Pandharipande, V.R. (1981) A Study of Three-Nucleon Interaction in Three-and Four-Body Nuclei. Nuclear Physics A , 371, 301-317. https://doi.org/10.1016/0375-9474(81)90069-5
Friar, J.L. (1987) Results of Recent Calculations Using Realistic Potentials, Few-Body Problems in Particle, Nuclear, Atomic, and Molecular Physics. Proceedings of the XIt h - European Conference on Few - Body Physics , Fontevraud, 31 September-5 August 1987, 51-63. https://doi.org/10.1007/978-3-7091-8956-6_4