Week 10: Lecture 49: Experimental evidence for fusion reactions powering the Sun

So uh in this lecture I will talk about uh the experimental evidences for fusion reactions powering the sun. Of course we will uh revisit the nutrinos solar neutrinos. So we will also of course look at some of the reactions of astrophysical interest uh towards the end. Uh in between I'll also perhaps say what is the future of solar neutrino experiments although I think there is no slide but I'll just say it. Okay. So solar neutrinos uh of course as we know nutrinos are proposed by pi it's just a recap uh but since they have a very small interaction cross-section uh they offer a unique probe into the sun's core. Now Bruno Ponteorvo uh had uh uh proposed that we detect these nutrinos by a radiochemical method. uh this was in 1946 when he was uh at the chalk river laboratories in Canada. So he proposed that the nutrino interacts with the chlorine 37 produces an electron and then 37 argon. The 37 argon you could remove and then count it separately in a proportional counter. Alvarez independently also proposed using 37 chloride about three years later but there he proposed using sodium chloride. So these are the three people involved. Pi of course was the one who proposed the nutrino. Bruno Ponttoor who proposed the radiochemical reaction. Uh and then Lelvar is also proposed another I mean the same reaction but involving a different compound and those are the references below. uh uh Lu Alvarez reference I have not given that is I think a Lawrence Berkeley report or something like that uh maybe I will add it when I finally give the final version of the slides okay so just a little bit of history which we didn't uh do in the earlier uh lectures uh Ray Davis and John Ball uh when they thought of using the chlorine as a target for neutrinos uh in particular solar neutrinos they wrote to Bruno Ponteorvo this is a different era where uh whether he was going to follow up and uh when Bruno Ponttooro said no I'm not intending to do this experiment because by then I think he had also left for Russia uh so then they decided to put up a proposal so they put up a proposal to the Brook Haven National Lab where Ray Davis was and John Ball of course I think was at that time also uh in Princeton So uh initially there was a negative response from the authorities in Brook National Lab. Basically it was Gulhabar uh who said that no I mean this is uh this is too much to expect to detect solar nutrinos on the other hand and why should we do that? I mean it's such a tiny cross-section. what uh won the day, what what uh convinced him was that they later said that you know you can actually get a handle on the PP uh you know chain of uh fusion reactions once you uh measure these nutrinos that actually convinced Maurice Goldber and he gave them a green signal. Davis decided to use the safer perch chloride rather than carbon tetrachloride. So C2 CL4 and of course he borrowed this idea came out of the Alvarez uh you know paper or report that you can use an inert gas to flush out 37 argon. Indeed you can use normal argon uh which has very small amounts of course of R137 and then count it in a low back by ground setup. So eventually he set up a 600 ton tank in the Homestake gold mine uh in uh Dakota in the state of South Dakota I think at a depth of about 1 and a half kilometers and then he made a series of measurements lasting about 25 years. uh ultimately leading up to the solar neutrino problem and that solar neutrino problem of course had a huge input from John Beall because uh this was a you know a singles experiment so to speak in the sense that you you just counted the number of argon atoms and then inferred what is the solar neutino flux. Uh so in these sort of measurements they can be uh you know errors systematic errors and in particular uh those uh due to the cross-sections involved due to the mechanisms you know plasma physics involved in the solar interiors and so on. However, he managed to, you know, keep at it and uh also the experimenters uh reduced the errors on the uh relevant uh nuclear reaction fusion reaction cross-sections and then ultimately this error was down to about 20% 20 to 25%. And so when uh Davis saw the shortfall in solar neutrinos uh Bakall was quite confident that this could not be uh you know due to our imperfect knowledge of the plasma physics all of the or indeed nuclear reactions and so on. It has to do with the fundamental properties of the nutrino and ultimately he was proven right. So the solar neutino spectrum as calculated by bakall and his uh you know people who came after him. So this is one of those references. Uh they improved on these solar standard solar model as it came to be known and this is from a 2017 reference much after John Ball passed away. And this is the you know you have the PP neutrinos you have the berillium 7 nutrinos burillium electron capture decay going to the ground state of lithium 7. This is to the first excited states of lithium. So there are two lines and then there are the CNO nutrinos 13 nitrogen 15 oxygen 17 florine and so on. [snorts] But there is also the uh boronate uh nutrino spectrum a continuum which uh which is going up to high energies and in fact this these nutrinos are the ones which contribute uh significantly to the uh chlorine detector of Davis. Uh so this is a summary again we have seen this in some previous lecture. So in terms of uh solar neutrino units uh you have something like 7.7 in these units which is uh a theoretical uh prediction whereas you actually measure 2.56 similarly for the kamio day you expect uh one in those units and you actually see about 0.55 uh super K of course improved the error bars and you know we got 46 plus minus just about 10% or so. Uh then there are the galax the gallium based detectors and here again you see a shortfall 128 solar neutron units whereas it's about 71 for both the sage and the galax and the go experiment. uh snow of course solved this problem in the sense that uh you expected one uh in some units and uh the in the charge current channel they saw 35 whereas if you put together all the neutrinos the flux of sum of the fluxes of all nutrinos then you get 1.01 which is very close to which is within errors agrees with what you expect. Okay. So the fact that we have we have nutrinos coming out from the sun that you can detect them with fairly good precision means that our model of the sun uh is fairly good and uh there is a detector built specifically to look at berillium 7 nutrinos in the real time rather than radiochemical detector which integrates the flux over a period of a month or thereabouts. So they measured this uh this was the key thing which they had aimed at but incidentally of course they also had evidence for PP nutrinos the low energy nutrinos up to 420 KV or so. So the berilium 7 nutrinos gives a compton-like spectrum uh ending at about 200 odd KV below the berilium 7 line electron capture line and uh this is quite prominent you don't need uh you can just see the spectrum and see the evidence for the minimum cells so they they measured the flux to within uh you know 10% or so even better than that and this is the nature reference Of course when they improved on their analysis and so on they even could uh they claimed evidence for the CNO nutrinos which are only a 1% level as compared to the PP nutrinos or the PP cycle sorry the yeah the PP cycle nutrinos so there are two basic cycles PP cycle which contributes about 99% of the nutrino flux and uh the CNO which is relatively much smaller contribution of about 1% So, so they found the evidence for CNO neutron this is in red by doing a detailed analysis of all the background the vertex distribution and is in that uh and uh they the claim is that they have evidence for this. So they say that the this paper of 2020 says that the absence of CNO neutrinos is ruled out at five sigma but the presence has only a lower confidence of about 3.5 sigma. Okay. So we know what now powers the sun. Uh and uh now of course we'll take a look at some of the nuclear properties and reactions of astrophysical interests not only in the sun but also in other stars. Okay. So of course for that you need tools and both theoretical and experimental tools. So first of all of course you need accelerators and we have looked at uh the kinds of accelerators that there are for for measuring nuclear cross-sections of astrophysical interest the DC accelerators are preferable because the energy is known very precisely and uh the cross-sections at low energies change very rapidly as you go down cross-section goes down very much uh is proportional to I mean this is kind of exponential dependence. So the RF accelerators uh you can only use for other properties of the nuclei which are involved uh not for cross-sections as much but for decay properties mass measurements and so on because the energy width of the beams coming out of RF accelerators is rather large. Of course, there are these cooling devices. So, there are storage rings where you can cool it. But operating this at low energy is is a very challenging thing and so nobody has actually built uh things which have been used for nuclear reaction cross-sections at low energy. However, there is an idea of course that you could circulate high energy beams which are much more easy to in terms of manipulating them and then you have two beams one going slightly slower than the other and so on. But these are you know a little futuristic as of now there is no such uh uh you know two ring uh accelerator or storage ring where such measurements can be carried. So generally speaking, DC accelerators for low energy cross-sections, RF accelerators for decay properties, mass measurements and so on. Once you produce those uh nuclei which are more often than not off the stability line, the detectors that you use are the same detectors that we have seen before. Gas detectors, centilation detectors, semiconductor detectors, gas or liquid time projection chambers. uh then electromagnetic and hydron calorie meters also cryogenic bometers. Now the theoretical methods for reactions and extraction of cross-sections. So what we need is of course uh direct measurements and then from there we can extract the cross-section. You can even compute it and there there are methods like the R matrix method if you there are resonances involved and so on and then there are indirect methods of both measurement as well as uh theoretical methods which so-called asytoic normalization constant method and the coolum breakup method. So you start out with let's say suppose you want to measure berillium 7 p gamma radiative capture of a proton berium 7 then you start out with a boronate beam which is of course uh is available in some of these rion beam facilities and then you break it up into seven berillium plus proton and look at the angular distribution energy momentum distribution and from there you can infer what the capture so you use u you know detailed balance to infer the inverse cross-section and c is uh basically relies on transfer reactions where since these transfer reactions are peripheral in nature the absolute magnitude of the wave function of the particle that is transferred if you measure that uh at forward angles for instance measuring these transfer reactions forward angles of course you fit the whole thing but you you extract a absolute radial part of the wave function which is the the outer part is the one which is relevant and then from there you can compute the reaction cross-section for the capture process. Uh the advantage of these indirect methods is of course that the transfer cross-sections in they are mediated by the strong interaction. They are very large they are in tens of millibans. Whereas if you look at the radiative capture cross-section in the uh area in the region of interest in around the gamma energy or somewhat higher then they are of the order of even you know nanobonds to pico bands and sometimes even smaller. Okay. So we'll see examples of that. So first of all let's talk about the basic properties of nuclei whether a nucleus which you think should be there in the in the chain of reactions that build up these nuclei in stars whether they exist or not uh because they might decay on a time scale of 10us 24 seconds. If that is so if they're not stable against uh the last particle be it proton or neutron then of course uh you you don't need to consider them uh right um I mean directly at least uh then we need to know the binding energy we need to know its half-life the decay channels or the branching ratios and so on many of these unstable nuclei are actually produced through the fragmentation reactions in accelerators which have energies of the order of hundreds of me to GV per nucleon. Uh so these are available in many accelerators. Now gsi has such a machine operating for last 10 or more years. The uh radioactive uh ion beam factory at rican that also has been working for again the last 10 years or so. Spiral 2 at ganil uh in France. Then the national superconducting uh lab at uh Michigan State University in the US and the FRIB the fragmentation rare ion beam facility which is coming up in uh Michigan State University at the same place as the NSCL uh which involves coupled cyclutrons rapid high high duty cycle and so on. So the reactions that are of most interest are the reactions which involve protons and helium 4. But also there is interest in dutarium, duterron and helium 3 induced reactions. These are needed for stellar nucleiosynthesis calculations relevant to the stellar core temperatures. Okay. [snorts] The measurements of a cross-section around the gamma energy is possible with stable beams and targets. Uh however with radioactive ion beams or rare ion beams as they are now called uh it becomes difficult to measure these cross-sections which are very tiny around the gamma energy. We'll come to what the gamma energy is uh because we don't have our technology is not good enough to get uh highly intense beams or at least the beams of the requisite intensity uh with the you know the targets that we have. So, so of course this could be done in inverse kinematics. You can have a unstable beam uh and uh hitting a proton or helium target but we don't have those intensities of the ultimately because what is important is the product of the beam intensity and the target thickness. Okay. So if you don't have enough intensity then we cannot do these measurements at gamma energies but of course you can do them at higher energy than extrapolate. So that is where this uh uh the method that I talked about earlier using transfer reactions and A and C uh to extract the so-called S factor or the extrapolated uh behavior of the cross-section at uh gamma or near gamma energies. Okay. So we also of course need neutron cross-section because as we will see in the rapid neutron capture process uh you need neutron cross-section of course neutron beams primary beams are not available. You have to make do with secondary beams. So you have to have some charged particle uh beam which interacts with the target. Charged particles of course can be accelerated. So then you produce neutrons and then these neutrons can be uh made to uh interact with the target and then you look for the products. So some of these can be measured at the so-called neutron time of flight facility at sun. Okay. So direct cross-sections can be done at higher energies and then you have to extrapolate to gamma energies uh which involving unstable beams at least. uh so then you could miss resonances in that process okay indirect measurements as I've already said uh using transfer uh cross-sections of tens of millib bands nuclear structure information the low energy can behavior can be extracted at best of course you get 10% accuracy sometimes it is worse than that but uh quite often uh a cross-section measurement even with 20 or 50% error bar is better than having no cross-section measurement at all. Okay? Because sometimes the theory can go wrong by even up to a factor of 10. So that's a,000% inaccuracy. So of course any measurement is good. Whatever best can be done uh should be done. Radiative capture cross-sections can be inferred as I said already from culum dissociation. That means you have a projectile breaking up into a proton plus uh the residue or alpha plus residue and then you work back and uh use the principle of detailed balance to get the cross-section. So these coolum dissociation processes are done at energies of about 50 to 100 m per nucleon or sometimes even higher and then they are useful uh when the projectile target is unstable. So boronate break up and so on. And you can do that on a heavy target. So that provides a large coolum field. So large virtual photon field which enables you to make this process measurable. If you use a light target then of course there are not just uh coolum but also nuclear processes and since then the cross-sections or the amplitudes are comparable then you have a hard time in deciphering the coolum process or the amplitude from the coolum process. Okay. Now let's see what this gamma peak means. Okay. So what is plotted here is the relative probability of a fusion let's say cross-section for example I mean it could also be some other process uh I mean even the transfer processes actually governed by the kulum interaction so in any case the fusion this is what is typically plotted here is a fusion cross-section in some units uh versus energy in the center of mass. So uh the since tunneling is involved through the coolum barrier the cross-section rises as you go up in energy. Okay. On the other hand in a star at a certain temperature T the number of particles uh of a given energy which could cause these nuclear reaction that keeps falling with energy. Okay. Now if you fold these two together, multiply these two together, then you get a form factor like this and uh there is a peak here and this was recognized by George Gamma and so this was uh the so-called gamma peak and uh of course the cross-section goes in this way. You can actually parameterize it such that you remove the exponential dependence uh of this uh cross-section. Uh so s of e by e exponential minus 2 pi ea where this 2 pi ea is given by the product of the two zeds the projectile and target the reduced mass mu by e to the power of half. Okay, so these are just some numbers to tell you. For instance, the proton plus 7 billium case. The coolum barrier is about 2 and a half m. The sun's core temperature is about 15 million kelvin and the KBT is about 1.3 K. Okay, so this is it. Sun has a temperature uh or or KBT corresponding to 1.29 K. So this these are related 15 million and 1.29 K. Now just as a aside George Gamma who was indeed a I mean unique uh scientist in the sense that he was a polymath apart from being the first to apply quantum mechanics to alpha decay. Uh this is the first instance of quantum mechanics being applied to any real problem. So he applied it to alpha decay. He proposed the liquid drop model of the nucleus. He thought of the origin of the universe and and the big bang name of course came from H oil but uh that it starts out from a very tiny size in principle even a point size and then you know expands rapidly and so on and then ultimately give uh then the beta decay he has contribution the so-called gamotella transitions which is uh delta t equal to zero I mean Sorry delta t equal to + -1 and delta j equal to 0 + -1 or 0 + - 1 uh nucleiosynthesis uh genetic coding which is a very different area from this right so you know you have these four things that code the DNA and he found that you know 20 combinations lead to the amino acids that we know and then of course he was a great science popularizer the most popular book I think would 1 2 3 infinity. Okay. So the gamma peak energy E 0 and the width are in terms of with some small approximation very reasonable approxim approximation it's just about 0.5 KT time Z projectile Z target times a reduced mass number the whole this to the power of half and the whole thing to the power of 2/3 and the width of this gamma peak is some constant here again ZP Z TA reduced to the power of half and uh KT to the^ of 5x6 for example in the carbonarbon system at a temperature of about 10 the 9 in some of these stars that actually have carbon and produce magnesium and so on this E 0 is of the order of 2.3 M okay the NZ chart of nuclei known and unknown is given here so the dashed you know locus here is where we expect particle stable nuclei to exist and these blue the the red ones are the uh you know stable ones or stable plus the uh nuclei which we have produced in accelerators and reactors and so on. The black ones are the stable nuclei. If you look carefully, there are these black dots. They are the stable nuclei. And the red and blue ones are the ones which we have seen uh in various kinds of experiments. And blue is the one which does a beta minus decay because neutron rich and red is the one which does a beta plus decay or electron capture decay. Uh that is shown here on the upper side. They are the and then the alpha decay nuclei are shown here in green light green and spontaneous fish nuclei are in green darker green which is somewhere here these are the heavy nuclei okay so neutron number on this axis and proton number on this axis okay so the kinds of particle detectors that we use and also recoil mass separator I'll have vision to tell you something about that so as I already said we have gas detectors And they operate just there's three modes are given here but there are other modes as well the so-called uh you know so there is avalanche there's a streamer mode but I broadly speaking ionization proportional avalanche modes cintillation counter some examples are given here sodium iodide berium fluoride lanthon bromide plastic cintilators then liquid cintilators also which have the pul shift discrimination property semiconductor detectors silicon high purity germanmanium even diamond nowadays is used and then there There are other detectors as well the 53 semiconductor 62 semiconductors. Then there are cryogenic bometers and [snorts] then we have veto detectors uh detectors which detect cosmic muons and then you can if you have an event in your detector then you can uh veto those events with these cosmic muon veto detectors. So that if there is a coincidence coincident signal you know that it has come actually from a cosmic muon. So you reject those and as long as the cosmic muons are not too many in number they will not uh take away your real events. Okay, they will not reduce. Uh there are also arrays of detectors. One example is the so-called taps array which consists of uh many actually this even this is an early number this uh many more detectors now but there are smaller arrays of BF2 detectors which have been used in experiments of astrophysical interest then there are these so-called recoil mass separators which have uh electric and magnetic field suitably placed so that you can select out a particular mass. You also have gas field recoil mass separators for very high efficiency and especially for super heavy element searches. Okay. The targets used normally for stable beams and stable targets or even enriched targets. We have solid targets. they're self-supporting or sometimes they are even backed by something which is very heavy so that the beam sees a huge coolum barrier in that backing and so it doesn't contribute to any reaction. Uh on the other hand, you can also then cool the target because you have very intense beams hitting the target and these targets are usually prepared by evaporation using resistive heating or you can use ion sputtering or you can use electron beam heating uh and you know you use for instance ion sources which are on a low voltage deck uh and you can actually implant these uh you know some beams uh some uh targets onto a backing. Then there are gas jet targets. You can have windowless gas jet target. You can have supersonic flows uh such that you have about 10^ the 19 atoms per square centimeter over 2 mm by 2 mm uh closed loop for isotypically enriched gases. So it does is not pumped out into the air but it is a closed loop. So you have 99% recovery and you can also have a target come gas detector. Okay, in some cases the impur reduction is extremely important such as the carbon 13 impur when you are looking at this reaction alpha plus carbon 12 going to gamma plus 16 oxygen. Now this is just a formula I think I will not say anything more here because when we work out some problems uh then we will look at that maybe for assignments this will be useful. Okay. So this is an example of a gas jet target. It's a supersonic gas jet target giving thicknesses up to 10^ the 19 mm. Uh in the measured size was about 4 to 5 mm at full width at half maximum. The pressure at which this uh jet is uh released from this and then sorry from here and then it expands and then goes into this uh inner receiver and then outer receiver. That's about 30 bar of pressure here. Okay. Uh with so much of gas of course you have to have differential pumping and these are very uh you know high volume high rate pumps and uh you know okay this is a technology by itself. Uh makes a these pumps make a large sound. So that has to be uh you know has to be reduced uh by suitable techniques such that microphonics doesn't contribute to detectors which are measuring these low rate events but these these things have been done. So for instance the helium 3 helium 3 2p reaction which involves as I mentioned some time earlier all charged particles in the initial and final states has been measured near solar gamma energy. Okay. So for instance this is a measure of the uh the s factor which you can extract from the cross-section. So this is the the gamma peak and now these experiments from uh the grandaso uh collaboration the luna collaboration uh they have been able to measure this even below the gamma peak. Of course at the lowest point the errors are large because you have only a few counts. uh so in any case so they also see that there is a tendency for this cross-section the S factor to rise above what you expect and that is because uh if you have shielded nuclei then uh then you can get a slightly larger cross-section because as the charged particle comes in it is able to go a little closer to the nucleus than otherwise where there to be no shielding okay so similarly the S factor for a radiative capture cross-section alpha plus D going to lithium 6. This is important from the big bang nucleiosynthesis and this has been measured with a very large high purity germanium detector and uh this is the schematic of that setup. Uh so the Nuna measurements these are the red ones here they actually measured uh at the relevant energies and uh where there were only just upper bounds they actually got uh the cross-section measurement okay down to about.1 100 KV or so this is an interesting reaction this is uh is very important in uh both in the cenocycle as well as in stars that make nuclei that have much larger fraction of CNO cycle in them. And uh for instance here the gammaray energy spectrum is shown. This is the laboratory background. Okay. And these are the uh this is the peak that you see. Uh of course this is done in by the Luna collaboration. So the background is suppressed because it is about uh 1 one and a half kilometer or so uh in a in a tunnel below a mountain. So the cosmic neon spectrum doesn't contribute very much. And uh you see that this uh so this is 2 hp gamma and this is the 14 nitrogen p gamma that is this one here at around uh 7.4 4 me or so peaking and then there are other reactions. Okay. So in this reaction they have again measured a little below the gamma peak and with fairly low error bars. This uh reaction was also interesting because an earlier measurement was off by a factor of two as compared to later measurement. In fact, in between these two measurements, there's an indirect measurement which said that uh this the earlier measurement was could be off by a factor of two and then of course that measurement the direct measurement was actually carried out in transasso and they confirmed what the indirect measurement said and uh they actually measured this uh to be about half of what was measured earlier. So uh coming to this uh the earlier measurements were all examples of direct measurements. One of the indirect measurements involves using transfer reactions. I've already said that. And uh the advantage of this method is that sigma transfer is much greater than sigma radiative capture. And this makes it much easier to especially if you are talking about radioactive or rare ion beams. You can do this in inverse kinematics and the accuracy even though it is only limited to 10% as I said is still very useful very useful. And this is from one of my talks that I gave more details in this. Okay. So I'll just very briefly describe a measurement that we did for the S factor of 7 berillium plus proton going to 8 boron plus gamma. So this is the first radioactive ion beam in India that is developed uh at the NSC now called the IUC in Delhi. And we measured this cross-section uh the transfer cross-section at 0° essentially but also within a certain band of angles. And the ancillary measurement was that we measured the elastic scattering cross-section to get a hold on the optical model parameters. So this is a setup. This is a recoil mass separator called HIA. This is the focal plane detector setup. So the recoil mass separator selects out the seven berillium beam from the seven lithium bombarding a hydrogen in a myar target which is rotating so as to make it not burn up. And uh then the berillium 7 that is produced is selected uh in the magnet here which has a pair of slits and you actually get a physical separation between the uh lithium 7 and burillium 7 and enough to get a very pure beam greater than 99.9% pure beam of 7 burillium. And then you again focus it uh at the end of this uh recoil mass facility where you have a target of uh uh dutarium and then you also have a detector. So you have a combination you have both the target as well as the detector and this measurement uh so the elastic cross-section varies like this as a function of angle d sigma by d omega as a function of theta and there are these fits from various kinds of potentials and the best one uh you use and also you can vary some of these parameters. So and then this is the transfer cross-section. essentially are looking at this cross-section but also a little bit on at higher angles in the center of mass. So we did this with various kinds of potentials in the for the dutron for the uh neutron and the bound state potential of the proton in the boron 8 and you know we we did many calculations about 80 calculations and then we plotted these S factors that were extracted. Uh so that gave a one measure at least of systematic errors involved in this. Uh and then this is a plot of the S factors from various kinds of measurements. And uh this the measurement that we did agrees with the uh the direct P gamma measurement and does not actually agree with another measurement which uh was very high is almost like 28 uh EV ban from a Chinese measurement again using a radioactive ion beam of uh berium 7. But they had a uh a kind of cocktail in which the main this 7 beam was only I think about 30% or so. So it could be that there are errors because of that and also because of the less intensity of the beam whereas we had a intensity of about 3,000 particles brillium 7s per second. So we extracted this and this is competitive with other methods. Uh the error being about again 10% or so. uh the main the another important point was that this is useful for the P gamma S factors with unstable nuclei with a precision of 10%. I think this we have emphasized in our paper here. Okay. So in summary we have looked at the PP and CNO fusion reaction chains in the core of the sun. The solar nutrino detection both validates the SSM and unveils a hither to unknown property of nutrino oscillation. This also we have discussed in earlier lecture. Uh so the shortfall uh can be accounted for if you have neutral oscillations. But basically the standard solar model is good. That is what these measurements show. And then we have just seen a brief uh view of what are the how do you measure these nuclear reaction cross-sections of interest to nuclear astrophysics. Okay. Thank you. >> [bell and music] [music]