Phys4440 nuclear models

Physics 4440, Homework
Nuclear Models:
In order to do this homework you will need to log on to the National Nuclear Data Center (NNDC).

Once you are on the home page of the NNDC site, click on "Nuclear Structure and Decay Databases" and then select ENSDF. You should find yourself on the page below.

http://www.nndc.bnl.gov/ensdf/

Example:
You can select data on a particular isotope, for example ¹⁷O by entering 17O in the quick search box. Then check off the first box labelled "ADOPTED LEVELS, GAMMAS". On the bottom of the page click on the HTML button as below.

Get selected ENSDF datasets:

html

At the top of the page are various graphical displays for the level schemes: JPEG PDF PS. You can select one of these to see the level scheme.
If you scroll down the page you will also see text data giving you the energies of the states, the spin and parity, the life time of the state, references, the isospin T=(N-Z)/2, and the magnetic moment in nuclear magnetons. From the table or the graphical level schemes you can see that the ground state spin of 5/2+ is consistent with the shell model predictions. The first excited state is 1/2+, which is also consistent with the shell model expectations. The 2nd excited state is 1/2-, which no longer follows the simple shell model scheme so the nucleons have rearranged themselves in a different fashion. There should be a large component in the wave function for the 1/2- state of a neutron moving up to the d5/2 level where it couples with another neutron to produce a combined spin 0. This leaves a hole in the 1p1/2 state which would give the right spin and parity for the state.

0.0	5/2+	stable	A B C D F I J K L M O P QRST UV	T=1/2; µ=-1.89379 9 (1989Ra17)
870.7310	1/2+	179.2 ps 18	A C D F I J K L M O P QR T UV
3055.3616	1/2-	0.08 ps +6-4	A C D F I K L O P QR T V
3842.84	5/2-	≤18 fs	C D F G I K L M P QRST V

1) Shell Model
Check the following nuclei ³He, ³H,¹⁵O,⁴¹Ca,⁴³Ca,⁴⁵Ca,⁴⁷Ca,⁴⁹Ca,⁵¹Ca, ⁶⁷As, ⁶⁹As, ⁷¹As.
Make a table for them listing the spin-parity combination, the magnetic moment in nuclear magnetons, and the quadrupole moment in barns.

a) Does the shell model give the expected spin-parities for these nuclei?
b) What is the orbital angular momentum for the Ca and As isotopes?
c) Does the magnetic moment for the Ca and As isotopes follow the expected trend predicted by the shell model? Give the evidence from the data to support your conclusion.