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Nuclear Chemistry Question

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Please see the attachment.

i) Give the expression for the energy levels of a nucleus exhibiting collective quadrup vibrations, taking care to explain the symbols used.

State the spin and parity of the first excited state expected in a nucleus exhibiting colle quadrupole vibrations and a nucleus exhibiting collective octupole vibrations.

What are the spin and parity of the ground state of 16O (Z=8)? Justify your answer.
The energy and spin/parity of the fire three excited states in 16O are:
6049 keV (0+), 6130 keV (3-) and 6917 keV (2+).
State which of these can be associated with each of quadrupole and octupole vibrations.

The octupole vibrational state decays to the ground state of 16I by gamma-decay.
Which electromagnetic multipole(s) contribute to the gamma-decay of the octupole vibrational state in 16O? Justify your answer.

ii) What is meant by the term 'isospin'? Give values for the isospin and isospin-projection quantum numbers for a neutron and a proton.

Give the expressions for the isospin projection T_Z for a nucleus (Z,A) and for all the possible values of total isopin T.

Compute in a table the values of T_Z and all possible balues of T for the A=16 isobars 16N (Z=7), 16O (Z=8) and 16F (Z=9).

Give the likely value for the total isospin of the ground state T_gs of each of these nuclei.

What are the corresponding multiplets? Represent these multiplets on an energy level diagram labelled with the A = 16 isobars and their T and T_Z values.

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Solution Summary

Answers to each of the questions, including expressions, value of isospin, and multiplets are given in the attached Word document.

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I've done most of them and have included references for you to read and clarify. Please see the attachment.

The energy levels of electric quadruple vibrations is given by,
EN = (N+5/2)ħω where N is the number of phonons, ħ is a constant and ω is the angular momentum.
(http://physics-database.group.shef.ac.uk/phy303/phy303-3.html)

An alternate formula is found at this website
http://www.eng.fsu.edu/~dommelen/quantum/style_a/ntcs.html

The spin and parity of the first excited state for quadruple vibration is 2 and + while that for octupole vibration is 3 and -. So 0+  2+ and 0+  3-

For quadrupole parity π = (-1)2 = +1 while for octupole π = (-1)3 = -1

(http://www.phys.unsw.edu.au/PHYS3050/pdf/Nuclear_Models.pdf)

For 16O8, you can look at the ...

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