 So the idea of this today's lecture is to tell you more. How atoms interact. I'm coming from a Helmholtz Institute in Jena. This is very roughly speaking half the way from Munich to Berlin. It's a small university town and we are associated also to this university. I divided into two parts. A short one at the beginning where I tried to give you a small view what I understand from an atomic theory side about the theory and the computation in a certain sense in a nutshell. And you're all aware of course of the first three processes. We should get a feeling what type of processes do we have to interact with atoms or ions in our case. Of course you all know spontaneous emission as well as the stimulated emission and the photo ionization. This means Einstein's photoelectric effect. It is clear if you stimulate with a light field then you can stimulate the emission or the absorption and you know from lasers of course that basically in this case you get photon fields which have which share the same properties like the incoming with respect to phase frequency polarization all this stuff. The spontaneous emission is also of course you are aware that this is a very important process but it is much harder to understand because it occurs even without an ambient electromagnetic field and of course we have first to find the relation how it is related to us. But these are only a few of the possible processes. You can also have something like photon scattering which stands here for Rayleigh and Compton scattering which means the elastic or the inelastic scattering of x-rays or gamma rays by atoms or molecules or a particular case Thompson scattering which can be considered as a low energy limit of Compton scattering that you say is a momentum transfer which you make by absorbing or by scattering a photon becomes negligible with respect to the energy to the rest energy of the atom who absorbs. But of course you have even more processes like multi photon excitation and ionization processes or also multi photon decay processes which is the signature of a known linear electron photon interaction that the signal increases known linear quadratically or even in a higher power with the intensity of the photon field but this appears also under certain circumstances with respect to the decay and which is then associated with the spontaneous processes. There are more like ionization or electron impact excitation and ionization and we can add even if we go to higher energies something like of course pair production the creation of particles and anti particles from the internal interaction of light with matter the creation basically of electron-positron pairs in the first instance or even if we go further to something like Dalebrook scattering which is really a process which can be understood only in the framework of quantum electrodynamics if we in addition to the quantized atom also also quantize electromagnetic field of course in practice the distinction in the discussion of this different atomic and electron photon interaction processes and one could add certainly a few more here of course also depends on the community and I try to relate my talk a little bit also what I have seen yesterday with with respect to your poster but to make it short what is the aim of atomic theory is of course said starting from a wide range of many body methods and techniques the central goal is in ab initio atomic structure and collision theory to describe not only the electronic level structure of course also these but also the properties and the dynamical behavior on the basis of the many electron Schrodinger equation or by applying even slightly more advanced techniques this is certainly not what I will tell today we restrict mainly to this part or even to the phenomenological side first of all one has to get a feeling because until the present this has turned out to be a really ambitious task with a lot of surprises if it really comes to detail on the other hand atomic theory is this theory which is considered as a playing ground in order to understand new many body techniques and many of the techniques which are nowadays used for molecules solid state also they have been in the first instance tested with regard to atoms one of the idea of course today is also to to train and to talk with you together about physical intuition because this is typically beneficial or at least helpful in this sense in going ahead Yuri very nicely explained yesterday how you come to many electron wave function what are the central steps I take a slightly general view at the beginning said in order to understand the interaction of atoms and one could generalize it of course also to molecules but we are here in a framework of atoms and ions and plasmas mainly is one should have a good feeling about the hierarchy of atomic interaction it is obvious the first two parts the nuclear potential and the electron-electron interaction this is basically what forms you an atom and without this we would not need to talk about atoms or ions but then as you saw yesterday in Yuri's lectures the orbit interaction starts to play an important role and if you go from light elements towards medium and heavy elements of course also relativistic contributions you have to recognize that the electrons they move faster and faster as heavier the nuclear charge in particular the inertial electrons and we often say that the 1s or the casual electron in something like uranium it has already about 65 to 70 percent of the speed of light and it is obvious that in this case you have really a relativistic description and you have the need for relativistic effects which phenomenologically comes in two ways one of them is of course you have currents the electrons orbit around the nucleus you have a small current and with these currents you have associated a magnetic moment as you know from classical mechanics the interaction of these classical moments leads basically to something like spin-spin interactions as well as you have a retardation which is indicated here that the interaction is not with the position which is at this given time but it is felt in a retarded way because you have to take into account that you don't have an instantaneous interaction among the electrons but you have a retardation if you really become comparable with the speed of light up to now one is on the level set up to this what is everything in this yellow box one is in principle able to include self-consistency to describe this in a nice fashion including more or less independent whether it is necessary also the relativistic contribution but as it was indicated yesterday already and if i want to point out further today of course you have also still the interaction with the radiation field and this is something which you feel in this spontaneous emission but also see in the context of course of shifts with regard to energy levels which associated with the quantum electrodynamic effects and if you look even closer you will recognize that you see the properties of the nucleus known as the hyperfine structure as well as if you look even closer you would start to see the electric and magnetic distributions inside of the nucleus and you can turn the view around that in order to understand something about the nuclei one often uses nowadays precise laser spectroscopy in order to deduce out of this so-called isotope shifts which basically has two components one of the different fields which arises from the nuclear potential which arises basically from the composition of protons and neutrons inside of the of the nucleus as well as an effect which is called the mass or the mass polarization which is not an inherent interaction which would appear on the Hamiltonian but which is a consequence basically of the conservation of momentum that one and which appears basically is in a very similar manner within a given Hamiltonian you would also see something like this so in order to talk about different processes one should have a good idea about this hawaiki and up to which point you should include it into your description it is not at all wise in atomic theory to start immediately from the most complete theory this would be in our case quantum electrodynamics but even 80 years after development of quantum mechanics we are not much better than that we are able to deal with hydrogen and even hydrogen only basically up to a two photon exchange in the QED picture with respect to set alpha to the force power as you see one is very much limited and one has to learn from this hawaiki and this gives us also to the models while we are used to describe the electronic structure of the atoms and ions in a quantum mechanical sense that of course we say these are quantum systems and we need to describe them in terms of wave functions of energy levels all what was yesterday explained based on a more or less well-defined atomic Hamiltonian the interaction of the atoms with the radiation field is hardly described in a quantized manner here we use a trick and I will explain this in a minute in more detail that the radiation is in almost all cases described by a classical field and the purpose is that of course it would be much too cumbersome to try to deal everything right from the beginning the only exception is where one leaves this is typically in quantum optics where you have to deal with the interaction of individual atoms with individual photons like for instance in cavity QED where you can have a control of one or few photons in a cavity interacting in a well-defined way with one or a few atoms where I am now by using this semi-classical treatment of course we are able to describe a large number of problems but only for surprise that we have to incorporate in an ad hoc manner and I will explain this this quantum effects the coupling to the electromagnetic field which for instance is responsible for spontaneous emission in this way that we have to add it in our talk treatment and as I said a full treatment one point which I typically like to make at this point that apart from this hierarchy of the interaction you should also be aware about the hierarchy of time scales of course you all know if we talk about optical fluorescence or near ultraviolet fluorescence typical lifetimes range in the order of nanoseconds or part of nanoseconds in which is comparable for instance with the folding time of proteins but if we if we go down in time we see that we will enter of course not also the molecular decrease of freedom like the rotations and vibrations but also that we come to basically to the time scale of the electronic motion and this is responsible for the adjoinization and this explains to you also why for light elements at least you have here typically a dominance of the adjoinization in comparison to the coupling to the radiation field as long as you don't have of course driving fields and this is also the reason why the atomic time unit you know it is just 24 utter seconds this is related basically to the motion of the electron of course these numbers all arise from the hydrogen atom but of course are characteristic also for many other systems okay just to conclude this first part of course i don't need to tell you too much about the need of having a good atomic theory and also an accurate atomic theory the majority of posters which i saw yesterday came from the first three this regard to astrophysical as well as plasma physical interpretation and diagnostics also a couple of posters regarded to uv lithography but i would like to make you aware that there has been perhaps not as large as this first three communities there are further communities which are highly dependent basically on a good atomic description and also on the way how we understand the coupling basically to external fields and particle collision this is one of them is atomic clocks where one has enormous precision achieved perhaps knows that in this type of laser spectroscopy they get an incredible accuracy of 8 10 12 digits of accuracy to determine transition frequency frequency comp as just as a keyword and here one becomes sensitive not only with respect to all this detailed interaction in saharaiki but one become may become even sensitive to the black body radiation to the coupling basically to blanks law in this particular case another community is the search for heavy and super heavy elements which is going on originally from the 60s in order to find the island of stability beyond set equivalent 114 116 they didn't determine that's the beginning now it is obvious that this very stable island will not exist but nevertheless the idea is to complete or to extend further this nuclear chart the chart of nuclear isotopes where meanwhile in the order of 3000 nuclei are known and of course need to be also characterized and only small fraction perhaps 10 to 15 percent of these isotopes are stable or reasonable stable all the others are way too active and decay often in very short time this is related also to nuclear physics said they want to use atomic type of spectroscopy in order to derive information about the nuclear properties like the nuclear spines or the nuclear moments of course it's also related to surface and environmental physics but what i wouldn't like to make you aware here in this context just that it is also of course associated with fundamental physics to use this low energy physics to understand signatures about new physics that go beyond the standard model also in this case one need precise data and this can be considered to some extent as a competition or as an alternative to high energy physics to turn like physics as well as of course related to the foundation so this basically is a framework why it is worse to look in particular into this coupling and this brings me to the second topic which i now want to explain in much further detail with regard to the interaction of atoms in weak fields i restrict myself to weak fields where we have the situation that's a radiation field for instance or the field which is associated with the collision in the sense of a linear visual potential are so weak in comparison to the internal fields which is felt by the electron in its motion around the nucleus that it doesn't affect the electronic structure so that we can still talk about the level structure as it was explained yesterday the first what we of course should look at if we talk about weightative transitions the coupling of atoms to the radiation field refers to the well known Einstein coefficient or to the spontaneous emission or spontaneous and stimulated emission which is represented by this A and B and it was indeed a genius idea of Einstein it was 1917 well before the development of quantum mechanics said he put up this statistical model and considered a two level atoms of a two level atom or two level model of the atom where he say we have just the atom which can occupy levels e1 and e2 with occupation numbers n1 and n2 and can we somehow understand this strange process of spontaneous emission the interaction to a radiation field if there is no radiation field in our classical perception around and of course as you see here what happens is you can of course excite stimulated excites this is basically absorb photons as well as spontaneously emit this a to one as a B to one and this is of course the stimulated processes they should be related to something what is known as the spectral energy density or in a more simplified way is a number of useful photons a number of photons per volume and in particular for frequency range which helps you to excite a particular transition we all know that of course the line widths of atomic transition or ionic transition are pretty small so you have to fit with your frequency range quite well to the frequency which is needed to make an excitation just to show you very briefly Einstein's argumentation at this point was that of course the change the loss of atoms in the level two is just the gain in the level one related per time interval and of course you can immediately lie down while the stimulated emission and the stimulated absorption are associated with the spectral density as the spontaneous process occurs in addition and this helps us to give us basically a relation between the emission and the absorption probabilities interesting if there's no fields this means this row of omega is equivalent zero this right two terms basically becomes zero and you immediately see that's a well-known weightative decay law that basically is associated by a constant which appears here as the inverse lifetime or which is just the Einstein a coefficient of course in equilibrium we have the situation said neither and dn2 by dt or dn1 changes and we immediately get by just using this formula this relation between the stimulated absorption and the spontaneous and stimulated emission process as a ratio which can be resolved now together by using basically a statistical consideration with regard to this Boltzmann constant the idea what Einstein brought in in addition of course it's the so-called principle of detailed balance said it the process with respect to two levels should be independent with respect to the processes for the other levels so that we can consider them independently and which means now that instead of one a coefficient we typically have to sum over all this Einstein a coefficient with regard to lower lying levels the decay possibility and this together given in the inverse of course still gives us the lifetime basically of such an atomic level if we can use this relation here above in order to determine also the ratio between the spontaneous and the stimulated emission or absorption probabilities together with this statistical factor as well as with Einstein's power law with regard to radiation and if we put this together Einstein found as I said well before the development of quantum mechanics said basically we have a key how we can describe this process of this spontaneous emissions spontaneous coupling in terms of the stimulated process as you see here in front of it appears a factor apart from some other constant like h bar and c appears a factor omega ij to the third power and this is also why in some fields of atomic physics basically the spontaneous processes are important one like in the optical region or an even ultra-red or x-ray region but where said it is pretty unimportant if one goes for instance to measures to microwave fields because then you have a several order of magnitude lower frequency and if you take it to the third power it is well understandable that all these effects basically can be neglected but I want to make you aware of course this is only one contribution which determines the line widths here again with respect to this orange sodium lines is the two line which was discussed yesterday in Yuri's lecture that if we compare for this particular line the natural line widths with line widths which is given by the motion under standard condition here for a temperature of 500 kelvin we see first of all that this natural line width is pretty small it is in the order of 0.1 gigahertz if you combine these numbers and put them together this relative ratio while the Doppler widths becomes as large for a temperature of 500 kelvin which is certainly not yet a hot plasma in the relation of 12 gigahertz so we have here two or sometimes even more orders of magnitude and it would require a very cold atom beam or even cold gases in the sense of cooling them down in order to make these widths comparable so far we have the lucky situations that we know how this is spontaneous and the stimulated processes are related of course what we need in order to understand this we need basically to understand how we can describe it and this was of course also related to Einstein's assumption said these coefficients Einstein A and B coefficients they are properties of the atom so that's the overall interaction and you know it perhaps from from rb oscillation from driving field is always decomposed or the factorizes into a part which is determined by the atoms these are exactly these coefficients basically the coupling strengths as well as the the properties of the field and how to obtain now what we call transition probabilities or this lifetimes if we have to sum up then of course to give you just a sketch here said we have a radiation field which is time dependent which introduces a time dependent interaction and we have the atomic structure and of course we need to take into account this atom field coupling and again there are two possibilities in order to deal with it the first one which is the preferred one in atomic and in particular also in plasma physics is the semi-classical consideration that we quantize the atom but that we deal with in classical electromagnetic field while in the QED picture we would have to quantize both but for surprise that the theory becomes really elaborate and cumbersome and people have tested it for individual transition but it would be lead completely out of control if you really describe more complex atoms within this framework there's no chance to to keep this type of treatment feasible just to indicate what are the limitations of our semi-classical description as i said this is the way that we are talk somehow remember this Einstein relation and take it over in order to describe all the time if we deal with the coupling with a radiation field we know from our classical consideration how to deal with a or the semi-classical consideration how to deal with a coupling for the stimulated processes and we take in addition this ad hoc manner this spontaneous processes into account of course in classical fields the relative importance of this spontaneous emission is reduced if we have in addition also driving field and it would be even more reduced if we have strong fields which is not the topic of this today's lectures also strong in the sense that you really come in with intensities which have are much which are comparable or much larger in the field strengths than this regard to the internal atomic fields but how to deal now this is a classical description you perhaps remember in this case you have to replace your atomic Hamiltonian p squared over 2m this momentum by the canonical momentum which is given by p plus e times a where a is the spatial part of the four potential this phi is basically the time component or the representation of the often of the Coulombic part of the potential in most cases if we now start from this type of Hamiltonian you see that in addition to the atomic case which you know all from your quantum mechanic lecture we got a term where we have p dot a and a dot p which if we consider both as operators we should be careful not to combine them but if we have a classical field of course this is nothing else in a multiplication operator and we combine this immediately to 2p dot a and in particular we would also have a term which is a squared but to make this story short basically we divide our Hamiltonian into an atomic Hamiltonian something very familiar to us and where we understood from the yesterday lecture how to determine the level structure as well as an atomic field interaction and one can put these pieces together usually one makes a plane wave expansion but what i want to point out at this is only that you have now in the framework of time dependent perturbation theory the possibility to deal with this atom under the inclusion of this time dependent a dot p this a is here time dependent we make time dependent perturbation theory and if you remember the general framework then of course we end up with Fermi's rule and what we achieved at this moment is that we can relate the stimulated processes and the coefficients which describes the stimulated processes as a property of the atom basically to a so-called transition matrix element what is here inside is nothing still than this a dot p term by making this special ansatz as well as of course the transition from an initial state to i to some final state j and because we talk about the probability we have of course here not the matrix element as itself but the modulus square of this matrix element and now one can of course what one has to do one has to analyze basically this type of transition amplitude or this type of matrix element to understand how the atom couples with respect to the to the light field here it is written all for a single electron system like atomic hydrogen but one can more or less easily generalize it by saying that of course in a many particle electron the momentum of each at electron interacts of course with the radiation field so what we have to do is basically we have to to deal with this type of transition matrix element of course our surroundings our also our daily experience is based more or less purely on electric dipole interaction that of course in this frequency range which we are used to have optical frequencies but also ultraviolet and of course in particular also for all lower frequency range we can say that basically the atomic radius is much much smaller than basically the typical variation of the field over a single wavelength for this particular example of visible light lambda 500 nanometers you can easily estimate that an atom is about thousand to ten thousand times smaller since this wavelength which means that all the electron basically sees at a given time the same field and does it what does it mean from a mathematical viewpoint we can from this exponential factor e to the i k r make an expansion and simply use the first term constant field which is felt by all the electron this is a dipole approximation that over the size of the atom the light field is constant and then you can analyze these matrix elements I will not go into these details at this point just say that what one has to use is now the symmetry properties of the wave function like it was explained yesterday and that one has to use that of course an atom is spherical symmetric system so it has a well defined total momentum it has a well defined projection as well as of course a parity with respect to reflection of all the coordinates with regard to the origin this piece you know from hydrogen and the same applies for all atoms at least to a very good approximation as long as you are not considering something like parity known conserving interaction but they come on a very tiny level 10 to the minus 7 10 to the minus 8 degree if at all and so what one has to do at this point is basically is this spontaneous one can express this spontaneous emission now in terms of these just of these matrix elements where it becomes clear said for optical transitions this is a very important process but said it goes down due to this scaling which we had before between a and the stimulated as stimulated b coefficients with regard to lower frequency and we also see more or less immediately because of this omega 3 we have basically a set to the third power so increases this importance of this spontaneous processes increases with the third power in the nuclear charge this is just the leading term if we go back from this expansion of the exponential factor we can discuss also of course higher multiples in a minute I just want to make you aware that this is only half of the discussion that we know the coupling strengths also expressed basically in terms of these Einstein coefficients and which we would call this is the knowledge of the transition probabilities the second part is of course how are these levels populated and if you think on a plasma of course here comes into play statistical methods that you or the statistical considerations that you have to to get a model how your levels are populated in the atomic in the case of atomic spectroscopy this is typically associated with the with the excitation process so the excitation together with the coupling to the radiation field determines how much you will see from this line what is a very nice tool which helps you to understand basically is the selection rules that one says if we use simply the symmetry of the wave function in detail this looks sometimes a bit technical and I will not do this in all this technical detail but of course one simple argument for instance if we look at this electric dipole term is said if we basically make a reflection of r goes to minus r then out of the symmetry of the hydrogenic wave function and something similar you would find also for the multi-electron cases that basically you get a factor minus 1 to the 2l plus 1 which means that an electric dipole transition this dominant part in the in the in the electron photon operator can only be act if you have a transition from an even to an odd parity state in all other cases it could not combine these levels you would get more or less matrix elements which are identical zero with respect to this part of the electron photon interaction also said delta l which is equivalent this plus or minus one of course it is odd and if one goes through these technical details one would see that basically in order to understand this transition probabilities this coupling to the radiation field said it can be typically factorized in a part which you really have to calculate basically the evaluation of radial integrals which determines the intensity plus what I often call a geometrical factor which is basically given by the angular part of this wave function and which can also differ a little bit in the size but this is much less than what it comes in from this radial part so this radial part really determines basically the strength of the coupling and what can be done for the electric dipole approximation can of course now be can now be continued to discuss the next terms apart from the dipole term is this i k dot r which gives rise both to the so-called magnetic dipole as well as to the electric electric quadrupole rotation and here again one can benefit from the symmetries of this of the wave function in order to understand under which circumstances we have a known vanishing contribution how is this election rules act in this particular case election rules first of all it's always related to the symmetry of the wave function second what you should be aware selection rules are almost never strict in atomic physics it's always strict only with certain parts of the electron photon coupling so you you find exception i will discuss it later on said how they come into play it only shows you the hierarchy of the interaction and you for instance we are in the magnetic dipole is still related to a vector operator this basically the magnetic moment of the electron as a transition operator we have the situation set for electric quadrupole which both comes out of these terms we are now related to a second order tensor operator basically to the quadrupole operator which shows who remember classical field theory electromagnetic fields you have it of course also in the multipole expansion of the electromagnetic field if you put these details together you understand however and this is the main message from using this selection rules that's the electric dipole relative to the magnetic dipole relative to the electric quadrupole and one could go on to higher orders by including higher orders from this expansion it scales roughly like one through alpha squared where alpha is the fine structure constant so you know right from the beginning this magnetic dipole or electric quadrupole is typically suppressed by four five orders of magnitude of course one should be taking a certain care about this statement under certain circumstances you will see that this is not immediately given by this factor but this is a scaling with regard to the coupling of this field and before I I still have a few minutes I can discuss here these dipole transitions in many electron atoms here not much need to be said it becomes more technical and it would be impossible to give this sketch just in order to see that this symmetry always faltered within a few lines first of all one should deal with the decomposition of this into spherical tensors this is done something like here that basically you have an representation of the dipole transition operator which is now written in terms of spherical tensors still a sum over all the individual operators for the electrons one to n in a many electron system as well as of course now decomposed into the radial component times basically functions which transforms themselves like the spherical harmonics and of course the spherical harmonics are one set this basically sets of physical quantities which transforms themselves like the spherical harmonics are considered as spherical tensors and they are usually helpful to immediately or to simplify the evaluation for these many electron atoms but to come back to the physics what does it mean now if we consider just this simple hydrogenic quotient diagram or energy level diagram of course this electric dipole it need to connect levels of different parity and where this delta j is just zero or plus minus one so the electric dipole transition is from ps like you know or from dp or sp also stuff where you just have a change in the parity as well as a change in delta j by zero or plus minus one the magnetic dipole in contrast it can relate also levels of the same parity so for instance two s to one s can decay via a magnetic dipole it is much much weaker for standard uh understand that condition as well as we have the situation that we have by m one because we have three half and one half to combine it is both possible and magnetic dipole as well as an electric quarter pole which again has the same parity of the initial and final states but will have of course the possibility to connect also levels with delta j up to two and this can be continued even though in the known relativistic theory one typically stops with the magnetic and the electric quarter poles if one wants to go beyond and there are many reasons to do so it is usually more helpful to use such a multiple expansion in the relativistic regime where you don't have any more this p dot a term multiplied of course with the electric charge but this is now replaced by alpha dot a alpha is the dirac matrices vector the dirac matrices so it becomes now operators with a four times four representation which itself acts of course on a four component spinor so doing this we are well in in the middle of the relativistic theory i will not touch this explicitly but i want to make you aware that this would be the way in order to include also higher multiples and i discuss in the second part of my lecture how this is that there are exist many situations where this is useful just to show you here how it scales you see that while the electric dipole scales with the third power in the nuclear charge the scaling of the magnetic dipole as well as electric quarter pole is quite also magnetic quarter pole is quite differently here shown for the blue lines the magnetic quarter pole scales with the eighth power and the m one with the tens power so that if you go along for instance the hydrogenic sequence from neutral hydrogen to something like hydrogenic uranium which can be investigated in nice detail at storage rings for instance then of course you will have the situation that some of the processes which are completely negligible in one region of the periodic table becomes really essential and important in the other but with regard to this election rules as i said they are never strict they are only strict with respect to certain parts of the electron photon coupling operator we still have the same rules like here said if you have electric uh multiple in general you need basically a change in the parity no you need a change in depending minus n to the l as a electric dipole you need electric quarter pole you don't need and and so on whereas with the magnetic it is just the other way around magnetic dipole don't need a change in the parity and electric quarter pole magnetic quarter pole would need so it is often a competition to the electric dipole and still you can express it said basically in this so-called triangular delta said the total angle of the initial and of the final state together with the multipolarity of the photon field this is represented by this l it should fulfill the triangular rule it must be possible to form out of these three integers and and and triangle okay perhaps i i simply say two words more what i wanted to say is the suspected scaling rules with nuclear charge set that you see that you have a very different scaling with respect to the electric multipole magnetic dipole electric dipole magnetic dipole as well as the magnetic quarter pole and we will see later on in our discussions this is only one way that it couples once with the rejection fields there are also higher-order process so called higher-order processes like e1 e1 or two e1 processes which scales with a six power or something of course also the decay of e1 m1 for instance in in volume like ions the lowest level beyond of the 2s squared thing let as a zero ground state is the 2s to p this was one example which uh Yuri Yester calculated the 2s to p triplet p zero and this triplet p zero because it's a zero to zero transition it cannot decay by a single photon at least as long as there's no nuclear spin and in this case you have to use something like an such an electric dipole magnetic dipole as a leading term in this on the other hand you understand that all these are only part of an expansion which tells you an hawaiki in the interaction but in most cases not a very strict rule and with this one i want to conclude let's come back five times uh five times uh five parts ten and i will tell you in the second part more thank you