Consider the following oxygen isotopes ( { }^{15} mathrm{O},{ }^{16} mathrm{O} ) and ( { }_{mathrm{n}}^{mathrm{T}} mathrm{O} ) in thein ( rac{5^{-}}{2}, 0^{+} )and ( rac{3^{+}}{2} ). The total binding energies of ( { }_{71}^{12} 0,{ }_{70}^{15} 0 ) and ( { }_{10}^{15} ) (forc) ( 31.7625 mathrm{MeV}, 111.9521 mathrm{MeV} ) and ( 127,620 mathrm{MeV} ), respectively. 1. Inferpet these states according to the shell model ing govive the shell-model configurations of these nuclei that are consistent with the obsefod ofin-parities assigmments. 3. Calculate approximately the excitation cnergy at which you count the first excited state of ( { }_{15}^{15} 0 ) and to. Make any comments you find useful. 4. Knowing that the first excited sanagh ( mathrm{F}_{0} mathrm{O} ) is located ar ( 0.87 mathrm{MeV} ) relative to its ground state, deduce the energy position of theswo first empty neutron subuhell of ( { }^{16} 0 ) 5. Plot to scale the energy pgrinengof the fist rwo levels of empty neutrons in ( { }_{5}^{15} 0 ). relative to yienground state. Plot to scale on the Figure of question (5), the energy positions of the last yodevits of empty protons in 40. 7. Hew do yop interpret the difference in binding energy between the nuclet of ( { }^{17} 0 ) and ( { }_{3}^{17} mathrm{~F} ) in Their ground state? Deduce the radius of the homogeneous sphere equivalent to these nuclei. Is it acgeptable? 8. Compare the excitation energy of the fina excited sate of ( { }^{17} mathrm{O} ) with that of the finst excited state of ( { }^{17} mathrm{~F} ) and explain why this leads you to think that the root-mean-square radius of the single about the wave functions of the shell-modet?

Consider the following oxygen isotopes 1115O,10160 and 1n17O in their and 127,620MeV, respectively. 1. Inferpet these states according to the shell model finf give the shell-model configurations of these muclei that ane consistent with the obsefped ofin-parities assignments. 2. Compute the spin and parity for the finstoveited atite of 15H and 17O. 3. Calculate approximately the excitation energy at which you count the first excited state of 15150 and 170. Make any comments you fief uscful. deduce the energy position of theswo first empty neutron subuhell of 160 5. Plot to seale the energy pgsintingof the fist rwo levels of empty neutrons in 5016. relative to yiegrotind state. Plor to scale on the Figure of question (5), the energy positions of the last youleshls of empty protons in 160. Their ground state? Deduce the radius of the homogeneous sphere equivalem to these nuclet is it acoppuble? 8. Compare the excitation energy of the fins excited state of 170 with that of the finst excited state of 17F and explain why this leads you to think that the root-mean-square radius of the single 1717 proton is greater in the state 31 than in the state 25. Is this consisteat with what you know about the wave functions of the sluell- model