# Nuclear Chemistry Question

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 Preview

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 ...

#### Solution Summary

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