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author | prashantsinalkar | 2020-04-14 10:19:27 +0530 |
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committer | prashantsinalkar | 2020-04-14 10:23:54 +0530 |
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tree | 2b1df110e24ff0174830d7f825f43ff1c134d1af /Nuclear_Physics_by_D_C_Tayal/9-Nuclear_Models.ipynb | |
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diff --git a/Nuclear_Physics_by_D_C_Tayal/9-Nuclear_Models.ipynb b/Nuclear_Physics_by_D_C_Tayal/9-Nuclear_Models.ipynb new file mode 100644 index 0000000..43f145f --- /dev/null +++ b/Nuclear_Physics_by_D_C_Tayal/9-Nuclear_Models.ipynb @@ -0,0 +1,432 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 9: Nuclear Models" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.11: Quadrupole_and_magnetic_moment_of_ground_state_of_nuclides.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa9.11 : : Page-394 (2011)\n", +"clc; clear;\n", +"R_0 = 1.2e-015; // Distance of closest approach, metre\n", +"// Mass number of the nuclei are allocated below :\n", +"N = rand(4,1)\n", +"N(1,1) = 17; // for oxygen\n", +"N(2,1) = 33; // for sulphur\n", +"N(3,1) = 63; // for copper\n", +"N(4,1) = 209; // for bismuth\n", +"for i = 1:4\n", +"\n", +" if N(i,1) == 17 then\n", +" printf('\n For Oxygen : ')\n", +" I = 5/2; // Total angular momentum\n", +" l = 2; // Orbital angular momentum\n", +" mu = -1.91; // for odd neutron and I = l+1/2\n", +" Q = -3/5*(2*I-1)/(2*I+2)*(R_0*N(i,1)^(1/3))^2*10^28; // Quadrupole moment of oxygen, barn\n", +" printf('\n The value of magnetic moment is : %4.2f \n The value of quadrupole moment is : %6.4f barn', mu, Q);\n", +" elseif N(i,1) == 33 then\n", +" printf('\n\n For Sulphur : ')\n", +" I = 3/2; // Total angular momentum\n", +" l = 2; // Orbital angular momentum\n", +" mu = 1.91*I/(I+1); // for odd neutron and I = l-1/2\n", +" Q = -3/5*(2*I-1)/(2*I+2)*(R_0*N(i,1)^(1/3))^2*10^28; // Quadrupole moment of sulphur, barn\n", +" printf('\n The value of magnetic moment is : %5.3f \n The value of quadrupole moment is : %6.4f barn', mu, Q); \n", +" elseif N(i,1) == 63 then\n", +" printf('\n\n For Copper : ')\n", +" I = 3/2; // Total angular momentum\n", +" l = 1; // Orbital angular momentum\n", +" mu = I+2.29; // for odd protons and I = l+1/2\n", +" Q = -3/5*(2*I-1)/(2*I+2)*(R_0*N(i,1)^(1/3))^2*10^28; // Quadrupole momentum of copper, barn\n", +" printf('\n The value of magnetic moment is : %4.2f \n The value of quadrupole moment is : %6.4f barn', mu, Q);\n", +" elseif N(i,1) == 209 then\n", +" printf('\n\n For Bismuth : ')\n", +" I = 9/2; // Total angular momentum\n", +" l = 5; // Orbital angular momentum\n", +" mu = I-2.29*I/(I+1); // for odd protons and I = l-1/2\n", +" Q = -3/5*(2*I-1)/(2*I+2)*(R_0*N(i,1)^(1/3))^2*10^28; // Quadrupole momentum of bismuth, barn\n", +" printf('\n The value of magnetic moment is : %4.2f \n The value of quadrupole moment is : %5.3f barn', mu, Q);\n", +" end\n", +"end\n", +"\n", +"// Result\n", +"// For Oxygen : \n", +"// The value of magnetic moment is : -1.91 \n", +"// The value of quadrupole moment is : -0.0326 barn\n", +"\n", +"// For Sulphur : \n", +"// The value of magnetic moment is : 1.146 \n", +"// The value of quadrupole moment is : -0.0356 barn\n", +"\n", +"// For Copper : \n", +"// The value of magnetic moment is : 3.79 \n", +"// The value of quadrupole moment is : -0.0547 barn\n", +"\n", +"// For Bismuth : \n", +"// The value of magnetic moment is : 2.63 \n", +"// The value of quadrupole moment is : -0.221 barn " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.12: Kinetic_energy_of_iron_nucleus.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa9.12 : : Page-395 (2011)\n", +"clc; clear;\n", +"h_cut = 1.054571628e-34; // Redued planck's constant, joule sec\n", +"a = 1e-014; // Distance of closest approach, metre\n", +"m = 1.67e-27; // Mass of each nucleon, Kg\n", +"KE = 14*%pi^2*h_cut^2/(2*m*a^2*1.6e-13); // Kinetic energy of iron nucleus, MeV\n", +"printf('\nThe kinetic energy of iron nuclei = %5.2f MeV', KE);\n", +"\n", +"// Result\n", +"// The kinetic energy of iron nuclei = 28.76 MeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.14: Electric_quadrupole_moment_of_scandium.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa9.14 : : Page-396 (2011)\n", +"clc; clear;\n", +"R_0 = 1.2e-15; // Distance of closest approach, metre\n", +"j = 7/2; // Total angular momentum\n", +"A = 41; // Mass number of Scandium\n", +"Z = 20; // Atomic number of Calcium\n", +"Q_Sc = -(2*j-1)/(2*j+2)*(R_0*A^(1/3))^2; // Electric quadrupole of Scandium nucleus, Sq. m\n", +"Q_Ca = Z/(A-1)^2*abs(Q_Sc); // Electric quadrupole of calcium nucleus, Sq. m\n", +"printf('\nThe electric quadrupole of scandium nucleus = %4.2e square metre \nThe electric quadrupole of calcium nucleus = %4.2e square metre', Q_Sc, Q_Ca);\n", +"\n", +"// Result\n", +"// The electric quadrupole of scandium nucleus = -1.14e-029 square metre \n", +"// The electric quadrupole of calcium nucleus = 1.43e-031 square metre " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.16: Energy_of_lowest_lying_tungsten_states.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa9.16 : : Page-398 (2011)\n", +"clc; clear;\n", +"h_cut_sqr_upon_2f = 0.01667; // A constant value, joule square per sec cube\n", +"for I = 4:6\n", +" if I == 4 then\n", +" E = I*(I+1)*h_cut_sqr_upon_2f;\n", +" printf('\nThe energy for 4+ tungsten state = %5.3f MeV', E);\n", +" elseif I == 6 then\n", +" E = I*(I+1)*h_cut_sqr_upon_2f; \n", +" printf('\nThe energy for 6+ tungsten state = %5.3f MeV', E); \n", +" end\n", +"end\n", +"\n", +"// Result\n", +"// The energy for 4+ tungsten state = 0.333 MeV\n", +"// The energy for 6+ tungsten state = 0.700 MeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.1: Estimating_the_Fermi_energies_for_neutrons_and_protons.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa9.1 : : Page-389 (2011) \n", +"clc; clear;\n", +"h_cut = 1.054e-034; // Reduced Planck's constant, joule sec\n", +"rho = 2e+044; // Density of the nuclear matter, kg per metre cube\n", +"V = 238/rho; // Volume of the nuclear matter, metre cube\n", +"// For neutron\n", +"N = 238-92; // Number of neutrons\n", +"M = 1.67482e-027; // Mass of a neutron, kg\n", +"e = 1.602e-019; // Energy equivalent of 1 eV, J/eV\n", +"E_f = (3*%pi^2)^(2/3)*h_cut^2/(2*M)*(N/V)^(2/3)/e; // Fermi energy of neutron, eV \n", +"printf('\nThe Fermi energy of neutron = %5.2f MeV', E_f/1e+006);\n", +"// For proton\n", +"N = 92; // Number of protons\n", +"M = 1.67482e-027; // Mass of a proton, kg\n", +"e = 1.602e-019; // Energy equivalent of 1 eV, J/eV\n", +"E_f = (3*%pi^2)^(2/3)*h_cut^2/(2*M)*(N/V)^(2/3)/e; // Fermi energy of neutron, eV \n", +"printf('\nThe Fermi energy of proton = %5.2f MeV', E_f/1e+006);\n", +"\n", +"// Result\n", +"// The Fermi energy of neutron = 48.92 MeV\n", +"// The Fermi energy of proton = 35.96 MeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.3: General_propeties_of_a_neutron_star.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa9.3 : : Page-390 (2011)\n", +"clc; clear;\n", +"h_cut = 1.0545e-34; // Reduced Planck's constant, joule sec\n", +"G = 6.6e-11; // Gravitational constant, newton square metre per square Kg \n", +"m = 10^30; // Mass of the star, Kg\n", +"m_n = 1.67e-27; // Mass of the neutron, Kg\n", +"R = (9*%pi/4)^(2/3)*h_cut^2/(G*(m_n)^3)*(m_n/m)^(1/3); // Radius of the neutron star, metre\n", +"printf('\nThe radius of the neutron star = %3.1e metre', R);\n", +"\n", +"// Result\n", +"// The radius of the neutron star = 1.6e+004 metre " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.4: Stability_of_the_isobar_using_the_liquid_drop_model.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa9.4 : : Page-391 (2011)\n", +"clc; clear;\n", +"A = 77; // Mass number of the isotopes\n", +"Z = round (A/((0.015*A^(2/3))+2)); // Atomic number of stable isotope\n", +"// Check the stability !!!!!\n", +" if Z == 34 then\n", +" printf('\nSe( %d,%d) is stable \nAs (%d,%d) and Br(%d,%d) are unstable', Z, A, Z-1, A, Z+1, A);\n", +" elseif Z == 33 then\n", +" printf('\nAs( %d,%d) is stable \nSe (%d,%d) and Br(%d,%d) are unstable', Z, A, Z+1, A, Z+2, A);\n", +" elseif Z == 35 then\n", +" printf('\nBr( %d,%d) is stable \nSe (%d,%d) and As(%d,%d) are unstable',Z,A,Z-2,A,Z-1,A); \n", +"end\n", +"\n", +"// Result\n", +"// Se( 34,77) is stable \n", +"// As (33,77) and Br(35,77) are unstable " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.5: Energy_difference_between_neutron_shells.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa9.5 : : Page-391 (2011)\n", +"clc; clear;\n", +"m_40 = 39.962589; // Mass of calcium 40, atomic mass unit\n", +"m_41 = 40.962275; // Mass of calcium 41, atomic mass unit\n", +"m_39 = 38.970691; // Mass of calcium 39, atomic mass unit \n", +"m_n = 1.008665; // Mass of the neutron, atomic mass unit\n", +"BE_1d = (m_39+m_n-m_40)*931.5; // Binding energy of 1d 3/2 neutron, mega electron volts\n", +"BE_1f = (m_40+m_n-m_41)*931.5; // Binding energy of 1f 7/2 neutron, mega electron volts\n", +"delta = BE_1d-BE_1f; // Energy difference between neutron shells, mega electron volts\n", +"printf('\nThe energy difference between neutron shells = %4.2f MeV', delta);\n", +"\n", +"// Result\n", +"// The energy difference between neutron shells = 7.25 MeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.7: Angular_frequency_of_the_nuclei.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa9.7 : : Page-392 (2011)\n", +"clc; clear;\n", +"h_cut = 1.0545e-34; // Reduced Planck's constant, joule sec\n", +"R = 1.2e-15; // Distance of closest approach, metre\n", +"m = 1.67482e-27; // Mass of the nucleon, Kg\n", +"// For O-17\n", +"for A = 17:60 // Mass numbers\n", +"if A == 17 then\n", +"omega_O = 5*3^(1/3)*h_cut*17^(-1/3)/(2^(7/3)*m*R^2); // Angular frequency of oxygen \n", +"// For Ni-60\n", +"elseif A == 60 then\n", +"omega_Ni = 5*3^(1/3)*h_cut*60^(-1/3)/(2^(7/3)*m*R^2); // Angular frequency of nickel\n", +"end \n", +"end \n", +"printf('\nThe angular frequency for oxygen 17 = %4.2e \nThe angular frequency for nickel 60 = %4.2e', omega_O, omega_Ni);\n", +"\n", +"// Result\n", +"// The angular frequency for oxygen 17 = 2.43e+022 \n", +"// The angular frequency for nickel 60 = 1.60e+022 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.9: Angular_momenta_and_parities.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa9.9 : : Page-393 (2011)\n", +"clc; clear;\n", +"Z = rand(5,1);\n", +"N = rand(5,1);\n", +"E = string (rand(5,1));\n", +"// Elements allocated\n", +"E(1,1) = 'Carbon'\n", +"E(2,1) = 'Boron'\n", +"E(3,1) = 'Oxygen'\n", +"E(4,1) = 'Zinc'\n", +"E(5,1) = 'Nitrogen'\n", +"Z(1,1) = 6; // Number of proton in carbon nuclei\n", +"Z(2,1) = 5; // Number of proton in boron nuclei\n", +"Z(3,1) = 8; // Number of proton in oxygen nuclei\n", +"Z(4,1) = 30; // Number of proton in zinc nuclei\n", +"Z(5,1) = 7; // Number of proton in nitrogen nuclei\n", +"N(1,1) = 6; // Mass number of carbon\n", +"N(2,1) = 6; // Mass number of boron\n", +"N(3,1) = 9; // Mass number of oxygen\n", +"N(4,1) = 37; // Mass number of zinc\n", +"N(5,1) = 9; // Mass number of nitrogem\n", +"for i = 1:5\n", +" if Z(i,1) == 8 then\n", +" printf('\nThe angular momentum is 5/2 and the parity is +1 for %s ', E(i,1));\n", +" elseif Z(i,1) == 5 then\n", +" printf('\nThe angular momentum is 3/2 and the parity is -1 for %s', E(i,1));\n", +" end\n", +" if Z(i,1) == N(i,1) then\n", +" printf('\nThe angular mometum is 0 and the parity is +1 for %s', E(i,1));\n", +" end\n", +" if N(i,1)-Z(i,1) == 2 then\n", +" printf('\nThe angular momentum is 2 and the parity is -1 for %s', E(i,1));\n", +" end\n", +" if N(i,1)-Z(i,1) == 7 then\n", +" printf('\nThe angular momentum is 5/2 and the parity is -1 for %s', E(i,1));\n", +" end\n", +"end\n", +"\n", +"// Result\n", +"// The angular mometum is 0 and the parity is +1 for Carbon\n", +"// The angular momentum is 3/2 and the parity is -1 for Boron\n", +"// The angular momentum is 5/2 and the parity is +1 for Oxygen \n", +"// The angular momentum is 5/2 and the parity is -1 for Zinc\n", +"// The angular momentum is 2 and the parity is -1 for Nitrogen " + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |