- #1

Marioweee

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- Homework Statement
- See below

- Relevant Equations
- See below

The independent particle energies for protons and neutrons around the

exotic doubly magic core 132Sn are shown in the figure below, where

π refers to protons and ν to neutrons.

Using the nuclear shell model and using this figure as a guide, answer

to the following questions:

a)Estimate Jπ for the lowest energy states of 132Sb. From graph determine the ground state energy of 132Sb with respect to

to 132Sn.

b)In 132Sb the analogous isobaric state (IAS) ##|Sb_{IAS}>## of the ground state of 132Sn ##|Sn_{g.s}>## is given by the decay ##|Sb_{IAS}>=T^{+}|Sn_{g.s}>##

where the operator ##T^{+}=\sum_{i}t^{+}_{i}## and ##t_{i}## exchange a neutron for a proton. Write the quantum numbers of spin, parity, isospin and third component of isospin for the IAS in 132Sb and try to estimate its energy with respect to the ground state of 132Sn using some macroscopic model.

-----------------------------------------------

a) 132Sb has p=51 and n=81. According to the order of filling the layers, all of them will be complete until ##\pi g_{9/2}## and ##\nu h_{11/2}##. We have an unpaired neutron and proton in ##\pi g_{7/2}## and ##\nu d_{3/2}##. It is this unpaired proton and neutron that will give us the possible spins in the ground state of 132Sb. The possible states are: $$J^{\pi}=(2)^+, (3)^+, (4)^+, (5)^+$$. Would this reasoning be correct?

As for the energy of the ground state of 132Sb from the graph, the truth is that I do not know how it would be done.

b)I am also a bit lost on this question. All I know is that the third isospin component of 132Sb is ##T_z=\dfrac{Z-N}{2}=-15## and therefore the isospin has to be between ##15<= T <= A/2=66##.

Any suggestions on how to continue? The truth is that I do not understand very well what is being asked of me either, since I am not very familiar with the concept of analogous isobaric state and I do not find much information on the matter either.

exotic doubly magic core 132Sn are shown in the figure below, where

π refers to protons and ν to neutrons.

Using the nuclear shell model and using this figure as a guide, answer

to the following questions:

a)Estimate Jπ for the lowest energy states of 132Sb. From graph determine the ground state energy of 132Sb with respect to

to 132Sn.

b)In 132Sb the analogous isobaric state (IAS) ##|Sb_{IAS}>## of the ground state of 132Sn ##|Sn_{g.s}>## is given by the decay ##|Sb_{IAS}>=T^{+}|Sn_{g.s}>##

where the operator ##T^{+}=\sum_{i}t^{+}_{i}## and ##t_{i}## exchange a neutron for a proton. Write the quantum numbers of spin, parity, isospin and third component of isospin for the IAS in 132Sb and try to estimate its energy with respect to the ground state of 132Sn using some macroscopic model.

-----------------------------------------------

a) 132Sb has p=51 and n=81. According to the order of filling the layers, all of them will be complete until ##\pi g_{9/2}## and ##\nu h_{11/2}##. We have an unpaired neutron and proton in ##\pi g_{7/2}## and ##\nu d_{3/2}##. It is this unpaired proton and neutron that will give us the possible spins in the ground state of 132Sb. The possible states are: $$J^{\pi}=(2)^+, (3)^+, (4)^+, (5)^+$$. Would this reasoning be correct?

As for the energy of the ground state of 132Sb from the graph, the truth is that I do not know how it would be done.

b)I am also a bit lost on this question. All I know is that the third isospin component of 132Sb is ##T_z=\dfrac{Z-N}{2}=-15## and therefore the isospin has to be between ##15<= T <= A/2=66##.

Any suggestions on how to continue? The truth is that I do not understand very well what is being asked of me either, since I am not very familiar with the concept of analogous isobaric state and I do not find much information on the matter either.

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