 So previously we are studying about MOSBIR spectroscopy and we have found that if I want to have a MOSBIR spectroscopy we actually need to have a source and that has to be bound to a solid matrix otherwise we cannot have that MOSBIR effect due to the recoil. So we want to have a recoil less environment and for that I need to graft our source in a solid matrix. Similar thing should be also happening to the sample. So this is the source, this is the sample that I am going to look into and at the end we have a detector and what is actually happening they are all put on a stage where the detector and the sample typically are actually bolted so they do not move. However, the source is put on a wheel where you can actually move it backward or forward and you can also even measure its velocity plus V means it is coming towards the sample minus V means it is going around the sample. And what happens it actually gives the gamma ray and then depending on whether it is absorbing or not you can detect it in the detector. So what happens what we found that there are different possibilities are there depending on what is the sample absorbance feature. So this is energy versus absorbance and say this is the source one and the source energy I can modulate by changing the velocity because I can include a Doppler effect of that and depending on that there are say like five different condition if I think about say 1, 2, 3, 4, 5 and in the fifth condition it says that it actually matched perfectly with the absorbance feature of the sample and then if I want to plot it with respect to percentage of transmittance of gamma ray that has been detected in the detector versus the velocity I am moving. So what I am going to see that it is going to have a feature like this. So say this is number one point position where is nothing is happening, number two position a little bit of happening due to this overlap, number three is the maximum because everything is absorbed, number four again a very little overlap and number five again no overlap. So that is how the signal typically looks like for a MOSBus spectroscopic. So that we have gone into the details of it and I found out we found out like how it is happening. Now the question is why the source and sample although they are exchanging their energy between i equal to three half and i equal to half for the source and i equal to half to i equal to three half for the sample why they are not really matching why they are a little bit different for the sample and source and the answers is lying on the effect of electron density on the nucleus and last day we have gone into the details out of four different orbitals that you can have SPDF among them only the s orbital can have some finite possibility to present inside a nucleus and if you remember we have gone through this thing called radial distribution function and from there we figure it out that yes there is a finite possibility for only the s orbitals and you can look into the wave functions how it is given and you can find for the s orbitals if r equal to zero value if I put that means that nucleus the wave function doesn't vanishes it does vanish for TD and F but for s orbitals it doesn't vanish so there is a finite possibility that your electron is actually staying inside the nucleus and that we have found and with respect to that we try to figure it out okay the s orbital can be there so what is the effect of the s orbital on the nucleus and over there we assume this is my nucleus and this is the electron density that we are having around the nucleus this is the nucleus and this is the electron density and over there only the s electron density can be present inside this and over here if I have two assumptions basically they are two different parts of the same assumption first is that the nucleus is spherical and the second thing is the radius of the nucleus is r then what we are going to have we are going to have something called a monopole interaction a monopole interaction is a columbic interaction because there is a positive charge present in that nucleus which is going to get affected by the electron density present into it and that can be represented by this Hamiltonian so previously when we talk about Hamiltonian we think about what is the effect of nucleus on the electron now we are looking in the other way looking what is the effect of electron on nucleus so the Hamiltonian says that what you are going to have is the following 2 by 5 power 5 this are coming for the condition that we have assumed that nucleus is spherical so that way this particular terms are coming then comes the z square is for the nucleus charge then psi 0 square that is the electron density inside the nucleus into r square okay r is the radius of the nucleus so over here the ze so let me go to the next slide so again I am writing this full equation 2 by 5 by z square psi 0 square into r square over here the term ze is actually coming for the nuclear charge where z you can see it is nothing but the atomic number that mean how many protons are present that is going to give you the positive charge psi 0 square give you the electron density inside the nucleus and actually it is given by minus e into psi 0 square so those e and this e over here that is why you get a e square term and this negative term is actually getting cancelled because you are talking about a monopole so first you have to start with a negative term over here but which is getting cancelled with the negative charge of the electron so they are getting cancelled so you have a positive term altogether so that is the Hamiltonian of a case electron density effect on the nucleus right so now here comes the issue so you have a ground state and electronic state so say we are talking about iron 57 system from now on so ground state means i equal to half excited state means i equal to 3 half so if there is no case electron density present no matter what system I am taking I am going to get the same energy gap between the excited state and the ground state if there is no effect of the electronic state no effect of the s electrons but in reality there is so there is s electrons have finite possibility that it is actually penetrating into the nucleus so that is why the ground state and excited state is not going to be same they are going to change their energy and as they are going to change their energy the energy gap is not going to be the same so say it is the ideal energy gap what it should be but now my energy gap is this e source and this how much it is changing it depends on how much s electron density you are allowing it to be similarly what is happening in the sample that can be also in a different position so their ground state and excited state for sure but due to the presence of this s electron density the energy gap is not remaining the same so over here what I am trying to say e sample is not equal to e source and that is why we have to balance that energy gap between the sample and source by creating a Doppler effect by moving the source towards or away from the sample and that is happening because of the effect of the s electron density and that is why we have to know how to connect them together how the s electron density can be connected with respect to the energy of the nucleus state so so far we are already having one of the fact over there that this Hamiltonian is giving me an idea that the s electron density has something to say on the nuclear and this nucleus of air is going to be present there now if I say that there are two different systems one is the source and one is the sample so say there is my source and here is my sample and so they are not the same molecular identity they are both iron but not molecularly same say one is iron chloride one is iron sulfate so how much that is going to affect it so that what we can do specifically differentiate that energy with respect to the s electron density and what I am going to get is a difference in energy of the source and sample and that is given by this equation 4 by 5 z is square r square delta r by r psi 0's sorry psi 0 square of sample minus psi 0 square of source so let us go slowly what do I mean by this particular equation this equation is saying that if you have a sample and source and if there is an energy difference present between the energy gap of the source and sample so this delta value is nothing but what it is saying that say this is my ground state and excited state so what I am basically drawing the ground state and excited state you have the difference for the source and say the sample is different so say this is e source and this is e sample so this delta value is a function of this e sample minus e source okay so that is what I am trying to figure it out over here and that is given by this term delta what is the actual name of that I will come into a little bit later but this delta value defines what will be the difference of energy between the sample and source and what are the parameters that is going to be different over here so if we look into here what are the parameters that is going to be differ at these two terms one is this one and one is this one so first come into this particular term psi 0 square sample minus psi 0 square source what is giving it basically it is saying what is the difference of s electron density inside the nucleus so if you can measure the s electron density between the sample and also there's a density inside the source whatever the difference is that is going to be this particular term and say your source and samples are actually basically the same thing this terms becomes 0 and you will not see any difference between the source and sample in it okay so that is given by this particular term now what is delta r by r now that is very interesting what it is actually given delta r value is that difference in the radius in the excited state minus ground state so what it is saying that when you are changing the nuclear state from i half to i three half is it always true that the nucleus remaining almost same can it also change its nuclear radius and the answer is yes it can change its nuclear radius it can shrink down or it can expand if it expands that means excited state radius will be higher than the ground state so delta r will be a positive term but if it shrinks down that means excited state is smaller than the ground state it will be negative term and over here this delta r by r term defines what are the changes you are seeing with respect to the nuclear size so it is a change in the nuclear size or nuclear radius and this term depends on the particular atom you are taking because depending on the particular atom or isotope I should say particular isotope say like 57 iron in the case of 57 iron this value is negative why because in case of 57 the excited state radius that means that i equal to 3 by 2 is actually smaller in size than in the ground state i equal to half so that is why this value will be negative so these are the two parameters that can be changed during the transition one is the a-selectron density difference one is the change in the radii of the system any question so far please go ahead so this is very important like what are the changes can happen that can affect that the excited state and the ground state energy cap can be different from source to sample and what you found there are two important factors one is this delta r by r and one is this difference in the a-selectron density now delta r by r can be changed but that has minimal effect with respect to what is happening around the nucleus whether the electron density is changing increasing that doesn't matter it only says that the delta r by r whether it will be positive or negative for iron it is negative if you go for 119 it is positive so this value becomes positive that means in this case of 119 the excited state has a higher radii compared to the ground state that's all so it actually defines what will be the the signature of it like it's a negative or positive however it doesn't really matter too much what will be the absolute value of it it just defined it is will be positive or negative but the absolute value will be depend on the difference between the sample and source a-selectron density okay so that is why the electron density or a-selectron density can matter and can affect that the value can be different okay and that is why if I go back a little bit over there you can see the sample and the source will be different and that is why we are actually have to move the source back and forth so to match the sample because the source and sample cannot be same all the time due to the change in the a-selectron density so now if I want to find out if I have an iron what should be the trend of this change which side I should move around that will be totally dependent on this particular value of the a-selectron density so that will be our concern from now on so this one a-selectron density that I am going to look into now how the a-selectron density can matter so again I am taking iron as an example so if I look into iron there are 26 electrons if I start from the atomic state of the iron atom so say I am taking a iron atom a single iron atom in gaseous state with 26 electrons what would be the electronic configuration you are doing that from 7 standard right now it is so it will be 1s2 2s2 2p6 3s2 3p6 and 3d8 that we actually write it down right so sorry if I did it correctly so let me write down 2 2 4 10 12 16 electron 10 15 8 huh so that is the 26 electrons you can have over there however when I am writing it I am writing at 3d8 but previously you guys have probably studied it is 3d6 4s2 right because we are so writing 4s2 so over here you have to understand it depends on which particular condition I am talking about if it is an iron atom in gaseous state in such a way that this iron atom is not interacting with anything else then only it can be 3d6 4s2 any other condition even in metallic state it is going to have a configuration of 3d8 4s0 why because it depends on the energy of the orbitals so say I am looking into two different state one is the atomic gaseous state and one in a molecular interaction when the atom is following a molecule so in the atomic condition what happens the 4s orbital has lower energy than 3d so that is why 4s orbital get accumulated first so that is why we get over here 4s2 3d6 however as you start forming the molecules the d orbitals have better overlap higher interaction so it gets stabilized on the other hand 4s orbital is not so much so it gets higher in energy so in a molecule 3d has lower energy compared to 4s so that is why it goes to 3d8 4s0 system okay and that is why we are going to look into this configuration mostly