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## Homework Statement

Not exactly a homework problem but I tried to predict the spin and parity of (the ground states of)

##^{89}Sr##,##^{97}Zr## and ##^{137}Ba##

using the shell model and my results seem to differ from the tables.

## Homework Equations

Parity

##\pi = (-1)^l##

Figure 4 seems to have the same values as the diagram in my book (Krane)

http://courses.chem.indiana.edu/c460/documents/SEC9ShellModel.pdf

I also found another diagram where some of the energy levels had switched place:

https://www.eng.fsu.edu/~dommelen/quantum/style_a/ntsm.html

## The Attempt at a Solution

##^{89}Sr## have ##51## neutrons. Looking at diagram the unpaired neutron is in the ##1g_{7/2}## state. The parity is then ##(-1)^4=1## so we have ##7/2^+##.

##^{97}Zr## have ##57## neutrons. The unpaired neutron is according to the diagram in an ##1g_{7/2}## state so we have ##7/2^+##.

##^{137}Ba## have ##81## neutrons. The unpaired neutron is then in a ##1h_{11/2}## state. We then have ##11/2^-##.

If however I look up the values in table I have:

##^{89}Sr \; \; 5/2^+##

##^{97}Zr \; \; 1/2^+##

##^{137}Ba \; \;3/2^+##.

I'm wondering why I get different values? I suspect I have the wrong diagram, so far every prediction I did with odd number of protons have worked out but not all the ones for neutrons. Is there a difference?