IntroductoryNuclearPhysics

Introductory Nuclear Physics (Kenneth Krane)

Very solid. Learned a lot
No other field of science comes readily to mind in which theory encompasses so broad a spectrum, from the most microscopic to the cosmic, nor is there another field in which direct applications of basic research contain the potential for the ultimate limits of good and evil.
Nuclear physics lacks a coherent theoretical formulation that would permit us to analyze and interpret all phenomena in a fundamental way; atomic physics has such a formulation in quantum electrodynamics, which permits calculations of some observable quantities to more than six significant figures. As a result, we must discuss nuclear physics in a phenomenological way, using a different formulation to describe each different type of phenomenon, such as a decay, /3 decay, direct reactions, or fission. In place of a single unifying theory there are islands of coherent knowledge in a sea of seemingly uncorrelated observations.
nuclear sizes are of order 1-10 fm
Nuclear Kinetic energies in the nucleas are of order 10 MeV which is small compared to their rest energies, so we can use nonrelativistic QM.
The list of instructions needed to build an exact replica of a French colonial house or a ’57 Chevy is relatively short; the list of instructions necessary to characterize all of the mutual interactions of the 50 nucleons in a medium weight nucleus could contain as many as 50! or about terms!
To a considerable extent, we can describe a nucleus by a relatively small number of parameters: electric charge, radius, mass, binding energy, angular momentum, parity, magnetic dipole and electric quadrupole moments, and energies of excited states. These are the static properties of nuclei that we consider in this chapter. In later chapters we discuss the dynamic properties of nuclei, including decay and reaction probabilities. To understand these static and dynamic properties in terms of the interaction between individual nucleons is the formidable challenge that confronts the nuclear physicist.
One remarkable conclusion is obvious- the central nuclear charge density is nearly the same for all nuclei.

Thus the number of nucleons per unit volume is roughly constant:
The nuclear skin thickness is ~ fm (~2fm)
In a heavy nucleus like Pb, the muonic 1s orbit has its mean radius inside the nuclear radius R; the effect of the nuclear size is a factor of 2 in the transition energies, a considerable improvement over the factor of le-4 o 1e-6 to in electronic transitions.
Even though these measurements of the nuclear charge radius use very different techniques, they all give essentially the same results: the nuclear radius varies with mass number as R_o A^(1/3), with R_o , = 1.2 - 1.25 fm.
the charge and matter radii of nuclei are nearly equal, to within about 0.1fm
The measurement of nuclear masses occupies an extremely important place in the development of nuclear physics.
The nuclear reaction method allows us to determine the masses of unstable nuclides whose masses cannot be measured directly.
Electronic binding energies are of order 10-100 keV in heavy atoms, while atomic mass energies are of order A x 1000 MeV; thus to a precision of about 1 part in l o 6 we can neglect them
The average binding energy of most nuclei is, to within 10%, about 8 MeV per nucleon. Second, we note that the curve reaches a peak near A = 60, where the nuclei are most tightly bound. This suggests we can “gain” (that is, release) energy in two ways-below A = 60, by assembling lighter nuclei into heavier nuclei, or above A = 60, by breaking heavier nuclei into lighter nuclei.

The most obvious term to include in estimating B/A (binding energy per nucleon) is the constant term, since to lowest order B ~ A. The contribution to the binding energy from this “ volume” term is thus B = a_v A where a_v, is a constant to be determined, which should be of order 8 MeV. This linear dependence of the binding energy per nucleon is in fact somewhat surprising, and gives us our first insight into the properties of the nuclear force. If every nucleon attracted all of the others, then the binding energy would be proportional to A ( A - l),or roughly to A2. Since B varies linearly with A , this suggests that each nucleon attracts only its closest neighbors, and not all of the other nucleons.
For even A, the pairing term gives two parabolas, displaced by 2 delta. This permits two unusual effects, not seen in odd-A decays: (1) some odd-2, odd-N nuclei can decay in either direction, converting a neutron to a proton or a proton to a neutron; (2) certain double beta decays can become energetically possible, in which the decay may change 2 protons to 2 neutrons.
of the hundreds of known (stable and radioactive) even-2, even-N nuclei, all have spin-0 ground states.
Thus all odd-parity static multipole moments must uanish electric dipole, magnetic quadrupole, electric octupole ( L = 3), and so on.
Ordinary magnetic interactions of matter (ferromagnetism, for instance) are determined by atomic magnetism; only in very special circumstances can we observe the effects of nuclear magnetism
Not only is the proton value (for magnetic moments) far from the expected value of 2 for a point particle, but the uncharged neutron has a nonzero magnetic moment!
In nuclei, the pairing force favors the coupling of nucleons so that their orbital angular momentum and spin angular momentum each add to zero.
The nucleon-nucleon force includes a repulsive term, which keeps the nucleons at a certain average separation.
the deuteron should be what the hydrogen atom is for atomic physicists. Just as the measured Balmer series of electromagnetic transitions between the excited states of hydrogen led to an understanding of the structure of hydrogen, so should the electromagnetic transitions between the excited states of the deuteron lead to an understanding of its structure. Unfortunately, there are no excited states of the deuteron- it is such a weakly bound system that the only “excited states” are unbound systems consisting of a free proton and neutron.
though beams of neutrons are readily available, targets of free neutrons are not.
The Interaction between Two Nucleons Consists to Lowest Order of an Attractive Central Potential The Nucleon - Nucleon Interaction is Strongly Spin Dependent This observation follows from the failure to observe a singlet bound state of the deuteron and also from the measured differences between the singlet and triplet cross sections.

The Nucleon- Nucleon Interaction Becomes Repulsive at Short Distances
We postulate a physical mechanism for the nucleon-nucleon force that will yield potentials similar to those that have already proven to be successful in calculations. A successful mechanism is that of the exchange force. There are two principal arguments in support of the presence of exchange forces in nuclei. The first comes from the saturation of nuclear forces. The experimental support for saturation comes from the relatively constant nuclear density and binding energy per nucleon as we go to heavier nuclei. A given nucleon seems to attract only a small number of near neighbors, but it also repels at small distances to keep those neighbors from getting too close. We encounter exactly the same sort of behavior in molecules. When we bring two atoms together to form a diatomic molecule, such as one with covalent bonding, electrons are shared or exchanged between the two atoms, and a stable molecule forms with the atoms in equilibrium separated by a certain
In summary, both the saturation of nuclear forces and the strong backward peak in np scattering are explained by exchange forces. In the former case, “something” is exchanged between nucleons to produce a sort of saturated bond. In the second case, “something” is exchanged between nucleons and actually changes their character.
In the early development of classical physics, objects were said to interact by means of ‘‘action at a distance.” Somehow one object mysteriously transmitted through space its force on the other object. The great development in nineteenth-century theoretical physics was the introduction of the concept of fields, according to which one object establishes throughout space a force field (electro-magnetic and gravitational fields are examples) and the second object interacts only with the field, not directly with the first object. Maxwell showed in the case of electromagnetism how the fields were transmitted through space. The major development of twentieth-century physics is quantum mechanics, according to which all exchanges of energy must occur in bundles of a discrete size. The classical field is smooth and continuous, and to bring classical field theory into agreement with quantum theory, the field itself must be quantized. That is, according to quantum field theory, the first object does not set up a classical field throughout space but instead emits field quanta. The second object can then absorb those field quanta (and reemit them back to the first object). The two objects interact directly with the exchanged field quanta and therefore indirectly with each other.
For a spin-1/2 neutron to turn into a spin-1.2 proton, it is clear that the exchanged particle must have integral spin (0 or 1) and must carry electric charge.
hbar x c = 200 MeV fm hc = 1240 evnm
The lightest of the mesons, the pi-meson or simply pion, is responsible for the major portion of the longer range (1.0 to 1.5 fm) part of the nucleon-nucleon potential. At shorter ranges (0.5-1.0 fm), two-pion exchange is probably responsible for the nuclear binding; at much shorter ranges (0.25 fm) the exchange of w mesons ( m = 783 MeV) may contribute to the repulsive core whereas the exchange of p mesons (m = 769 MeV) may provide the spin-orbit part of the interaction. The differing masses for the charged and neutral pions may explain the possible small violation of charge independence we discussed previously.
We the following approach for nuclei. We choose a deliberately oversimplified theory, but one that is mathematically tractable and rich in physical insight. If that theory is fairly successful in accounting for at least a few nuclear properties, we can then improve it by adding additional terms. A successful model must satisfy two criteria: (1) it must reasonably well account for previously measured nuclear properties, and (2) it must predict additional properties that can be measured in new experiments.
The so-called “magic numbers” (Z or N = 2, 8, 20, 28, 50, 82, and 126) represent the effects of filled major shells, and any successful theory must be able to account for the existence of shell closures at those occupation numbers.
The shell model, despite its simplicity, is successful in accounting for the spins and parities of nearly all odd-A ground states, and is somewhat less successful (but still satisfactory) in accounting for magnetic dipole and electric quadrupole moments. The particular application of the shell model that we have considered is known as the extreme independent particle model. The basic assumption of the extreme independent particle model is that all nucleons but one are paired, and the nuclear properties arise from the motion of the single unpaired nucleon.
we must consider two types of collective structure, for the nuclei with A < 150 seem to show one set of properties and the nuclei with 150 -=A < 190 show quite a different set. The nuclei with A < 150 are generally treated in terms of a model based on vibrations about a spherical equilibrium shape, while nuclei with A between 150 and 190 show structures most characteristic of rotations of a nonspherical system. Vibrations and rotations are the two major types of collective nuclear motion. The collective nuclear model is often called the “liquid drop” model, for the vibrations and rotations of a nucleus resemble those of a suspended drop of liquid and can be treated with a similar mathematical analysis.
the spherical vibrational model gives us quite an accurate picture of the structure of these nuclei. Rotational motion can be observed only in nuclei with nonspherical equilibrium shapes. deformed nuclei are found in the mass ranges 150 < A < 190 and A > 220 (rare earths and actinides).
The rotational behavior is thus intermediate between a rigid object, in which the particles are tightly bonded together, and a fluid, in which the particles are only weakly bonded. (We probably should have guessed this result, based on our studies of the nuclear force. Strong forces exist between a nucleon and its immediate neighbors only, and thus a nucleus does not show the long-range structure that would characterize a rigid solid.)
The deformed nuclei exist only in regions far from filled neutron and proton shells. Just as the cooperative effect of a few nucleon pairs outside of a filled shell was responsible for the microscopic structure of the vibrations of spherical nuclei, the cooperative effect of many valence nucleon pairs can distort the “core” of nucleons until the equilibrium shape becomes strongly deformed.
The radioactive decays of natually occuring minearals containing uranium and thorium are in large part responsible for the birth and study of nuclear physics. These decays have half-lives that are of the order of the age of the Earth

The radioactive decays of naturally occurring minerals containing uranium and thorium are in large part responsible for the birth of the study of nuclear physics. These decays have half-lives that are of the order of the age of the Earth, suggesting that the materials are survivors of an early period in the creation of matter by aggregation of nucleons; the shorter-lived nuclei have long since decayed away, and we observe today the remaining long-lived decays. Were it not for the extremely long half-lives of U238 U235, we would today find no uranium in nature and would probably have no nuclear reactors or nuclear weapons.
The probability to converta target particle from stable to radioactive is about 10e-10/s. Event if the reaction is allowed to proceed for hours, the absoulte number of converted target particles is small. We can therefore regaurd the number of target particles as constant.
Beta decay can occur in three possible ways each of which must involve another charged particle to conserve electric charge
Gamma emission is observed in all nuclei that have excited bound states (A > 5) and usually follows alpha and beta since those decays will often lead to excited states in the daughter nucleus. The 1/2 life for gamma emmission is usually quite short 10e-9s
The Earth and the other planets of our solar system formed about 4.5 × 10⁹ y ago out of material rich in iron, carbon, oxygen, silicon, and other medium and heavy elements. These elements in turn were created from the hydrogen and helium that resulted from the Big Bang some 15 × 10⁹ y ago. During the 10 × 10⁹ y from the Big Bang until the condensation of the solar system, the hydrogen and helium were "cooked" into heavier elements in stellar interiors, novas, and supernovas; we are made of the recycled debris of these long dead stars. Most of the elements thus formed were radioactive, but have since decayed to stable nuclei. A few of the radioactive elements have half-lives that are long compared with the age of the Earth, and so we can still observe their radioactivity. This radioactivity forms the major portion of our natural radioactive environment, and is also probably responsible for the inner heating of the terrestrial planets.
Most long-lived natural radioactive elements observed today originate with the very heave elements, which have no stable isotopes at all. There are four independent decay chains. The decay processes will tend to concentrate the nuclei in the longest-lived member of the chain, and if the lifetime of that nuclede is at least of the order of the age of the Earth, we will observe that activity today.
In general the radioactive elements are tightly bound to the minerals and are not hazardous to our health, but all of the natural radioactive series involve the emission of a gaseous radioactive element, radon. This element, if formed deep within rocks, normally has little chance to migrate to the surface and into the air before it decays. However, when rocks are fractured, the radon gas can escape (in fact the presence of radon gas has in recent years been observed as a precursor of earthquakes). There is also the possibility of escape of radon from the surface of minerals, and particularly those that are used in the construction of buildings.
To make a workable solid detector, however, we must satisfy two contradictory criteria: (1) The material must be able to support a large electric field, so that the electrons and ions can be collected and formed into an electronic pulse, and little or no current must flow in the absence of radiation, so that the background noise is low. (2) Electrons must be easily removed from atoms in large numbers by the radiation, and the electrons and ionized atoms must be able to travel easily through the material.
To increase the probability for photon emission and to reduce self-absorption of the light, small amounts of impurities called activators are added to the crystal. A commonly used activator is thallium, and so these detectors are indicated as, for instance, NaI(Tl). The activator provides states in the energy gap and the light emission takes place between the activator states. In the case of NaI, the wavelength of maximum emission is shifted from 303 nm in pure NaI to 410 nm in NaI(Tl). Absorption at this energy cannot occur in NaI(Tl), because the activator ground states are not populated, and the change in wavelength from the ultraviolet to the visible gives a better overlap with the maximum sensitivity of most photomultiplier tubes.
The energy resolution of a detector is deteremined by the square root of the number of ionizing events.
There must therefore be a special reason that nuclei choose a emission over other possible decay modes. In this chapter we examine this question and study the a decay process in detail.
Geiger and Nuttall noticed that a emitters with large disintegration energies had short half-lives and conversely. The theoretical explanation of this Geiger-Nuttall rule in 1928 was one of the first triumphs of quantum mechanics.
Beta decay provides a convenient way for an unstable nucleus to “slide down” the mass parabola (Figure 3.18, for example) of constant A and to approach the stable isobar.
In contrast with alpha decay, progress in understanding beta decay has been achieved at an extremely slow pace, and often the experimental results have created new puzzles that challenged existing theories.
The degree to which a transition is forbidden depends on how far we must take the expansion of the plane wave to find a nonvanishing nuclear matrix element.
ft value gives us a way to compare the beta-decay probabilities in different nuclei.
As in the case of alpha decay, there is an enormous range of half-lives in beta decay -ft values range from about 1e3 to le20 s.
A superior method (of determining m_nu) uses the shape of the beta spectrum near the upper limit. Thus at the endpoint dN/dp -+ 0 if m_nu = 0, while dN/dp -+ inf. if m_mu> 0.
Putting in all of the numerical factors, the resulting cross section is 1.2e-19 b = 1.2e-43 cm2. We can appreciate this incredibly small cross section (compare with the low-energy nucleon-nucleon scattering cross section of 20 b!) by evaluating the probability for a neutrino to be captured in passing through a typical solid, which contains of the order of 1e24, protons per cm3. The neutrino has a reaction cross section of about 1e-43 cm2 for each proton it encounters, and in passing through 1 cm3 of material a neutrino will encounter about 1e24, protons. The net reaction probability is (1e-43cm2)(1e24, cm-3) = 1e-19 cm-1; that is, the reaction probability is about 1e-19 for each cm of material through which the neutrino passes. To have a reasonable probability to be captured, the neutrino must pass through about 1e19 cm of material, or about 10 light-years. No wonder it took 25 years to find one!
Since our goal is not to test the invariance of the laws of nature to physicists standing on their heads, we must have some way more clearly to identify the reflected process. One way is to assume the decaying particle A to have a spin vector that is pointing in a specific direction.

Most alpha and beta decays, and in fact most nuclear reactions as well, leave the final nucleus in an excited state. These excited states decay rapidly to the ground state through the emission of one or more y rays, which are photons of electromagnetic radiation like X rays or visible light. Gamma rays have energies typically in the range of 0.1 to 10 MeV, characteristic of the energy difference between nuclear states, and thus corresponding wavelengths between 1e4 and 100 fm.

The actual y-ray energy is thus diminished somewhat from the maximum available decay energy Delta E. This recoil correction to the energy is generally negligible, amounting to a 1e-5 correction that is usually far smaller than the experimental uncertainty with which we can measure energies. There is one circumstance in which the recoil plays an important role; this case, known as the Mossbauer effect.
For low-energy y rays, the recoil energy is less than 1 eV and has a negligible effect. High-energy y rays (such as the 5-10-MeV radiations emitted following neutron capture) give recoils in the range of 100 eV, which may be sufficient to drive the recoiling atom from its position in a solid lattice. Effects of this sort are known as radiation damage and have an important place in the study of solids.
For gamma radation: (1) The lower multipolarities are dominant- increasing the multipole order by one unit reduces the transition probability by a factor of about 1e-5. A similar effect occurs in atoms, in which the most common transitions are dipole. (2) For a given multipole order, electric radiation is more likely than magnetic radiation by about two orders of magnitude in medium and heavy nuclei.
A classical electromagnetic field produced by oscillating charges and currents transmits not only energy but angular momentum as well. IF we surround the charges and currents with a large spherical absorbing shell, the shell can be made to rotate by the absorbed radiation. When we go over to the quantum limit, we can preserve the proportionality if each photon carries a definite angular momentum. The multipole operator of order L includes the factor Y_LM(theta,phi), which is associated with an angular momentum L. We therefore conclude that a multipole of order L transfers an angular momentum of Lh per photon.
To determine the multipole order of the y radiation, we must measure the angular distribution of the radiation, and to distinguish electric from magnetic radiations, it is necessary to do additional measurements, such as to measure the polarization of the radiation.
In nuclear radiation, there is minimal overlap between the emission and absorption lines, and thus little probability of resonant excitation. Contrast this with the case of atomic radiation. Optical transitions have energies of a few eV; the recoil correction in Hg would be 2.7 x eV and there would be almost complete overlap between the profile of the source and absorber transitions. Atomic resonant absorption experiments are thus relatively easy to perform.
Except for a very small energy region between 1.019 and 1.147 MeV, there is a one-to-one correspondence (for a given T,) between Tb and theta. That is, keeping the incident energy fixed, choosing a value of theta to observe the outgoing particles automatically then selects their energy.
For a typical nucleus of radius R = 6 fm, the geometrical area piR2 is about 100 fm2 = 1 b; for neutron capture by 135Xe,the cross section is about le6 b, while for other much more improbable reactions the cross section may be measured in millibarns or microbarns.
As the uncharged member of the nucleon pair, the neutron plays a fundamental role in the study of nuclear forces. Unaffected by the Coulomb barrier, neutrons of even very low energy (eV or less) can penetrate the nucleus and initiate nuclear reactions. On the other hand, the lack of Coulomb interaction presents some experimental problems when using neutrons as a nuclear probe: energy selection and focusing of an incident neutron beam are difficult, and neutrons do not produce primary ionization events in detectors (neutrons passing through matter have negligible interactions with the atomic electrons).
The stable isotope of beryllium, 9Be, has a relatively loosely bound neutron (1.7 MeV binding energy).
Because neutrons produce no direct ionization events, neutron detectors must be based on detecting the secondary events produced by nuclear reactions, such as (n, p), (n, a),(n, y), or (n, fission), or by nuclear scattering from light charged particles, which are then detected.
One of the useful features in studying neutron capture y rays is that the primary radiation is almost completely unselective in populating the lower excited states-no strong selection rules based on nuclear structure will forbid primary decays to any particular excited state. Thus if, for instance, the capture state has I’ = 4, we expect dipole radiation to populate directly all spin 3, 4, and 5 states.
Neutron interferometery, done 50 years after de Broglie's work and after the introduction of the Schrodinger equation, is the first to demonstrate that the Schrodinger equation and the laws of quantum mechanics apply to gravitational fields.
Fission results primarily from the competition between the nuclear and Coulomb forces in heavy nuclei. Although any nucleus will fission if we provide enough excitation energy, as a practical matter the process is important only for heavy nuclei (thorium and beyond).
The best choice for a moderator is the lightest nucleus, to which the neutron transfers the largest possible energy in an elastic collision. Carbon is a reasonable choice because it is available as a solid, thus with a high density of scattering atoms, and is inexpensive and easy to handle.
It is estimated that a coal-burning power plant operating at 1000 MW annually releases into the atmosphere 23 kg of uranium and 46 kg of thorium, along with their radioactive decay products, most notably radon. The radiation exposure to the general population from coal-burning power plants is several times that of nuclear power reactors. We know far more about the risks of exposure to radioactive fission products than we know about the effects of this radioactive release from coal-burning power plants.
fusion has several obvious advantages over fission: the light nuclei are plentiful and easy to obtain, and the end products of fusion are usually light, stable nuclei rather than heavy radioactive ones. There is one considerable disadvantage, however: before light nuclei can be combined, their mutual Coulomb repulsion must be overcome.
this process is called thermonuclear fusion Because the thermal energy is used to overcome the Coulomb barrier that inhibits fusion,
The most elementary fusion reaction, p +p -> 2He, is not possible, owing to the instability of 2He
The fusion of four protons ultimately to form 4He (in several steps) is responsible for the thermonuclear energy released in stars similar to the sun.
The product ZaZX will ultimately appear in an exponential barrier penetration probability, and so the fusion cross section is extremely sensitive to the Coulomb barrier.
The mean solar radiation reaching the Earth is about 1.4e3 W/m2, which (if distributed uniformly in space) means the sun's total output is about 4e26W. Each fusion reaction produces about 25 MeV, and thus there must be about 1e38 fusion reactions per second, consuming 4e38 protons per second. At this rate, the sun can be expected to continue to burn its hydrogen fuel for another 1e1O y.
Stars begin life as a mixture of hydrogen and 24% (by weight) helium. As the original gas cloud collapses, the individual atoms exchange their gravitational potential energy for kinetic energy, thereby increasing the temperature of the cloud. Eventually, the temperature is high enough that the protons can overcome the repulsive Coulomb energy, and fusion reactions can begin. The outward pressure from the radiation released in fusion effectively halts the gravitational collapse, and the star enters an equilibrium phase (like our Sun) that may last 1e1O y.

When a star's hydrogen fuel is depleted, gravitational collapse can begin again, and eventually a higher temperature is reached (perhaps 1-2 e8 K, compared with 1e7 K for the present Sun) where the Coulomb barrier for 4He-4He fusion can be overcome. The increased ignition temperature results in a larger radiation pressure, which expands the outer envelope of the star's surface by a large factor, perhaps by a factor of 100 or 1000. The apparent energy density of the surface decreases, and the star appears at a lower effective surface temperature. This is the red giant stage.
We know that 12^C is plentiful in the universe, but the calculated rates of 2a +8Be and 8Be +a -+12C are not sufficient to produce the observed large abundances of 12C, as was first realized by Fred Hoyle in the early 1950s. The Q value for 12Be +a -> 12C is 7.45 MeV, and Hoyle argued that the large production of 12C requires this reaction to occur readily, which in turn requires a resonance to account for what must be an increase in the cross section at this energy. He made this suggestion to W. A. Fowler, whose research group at Cal Tech began in the 1950s an extended program concerning the study of nuclear reactions of astrophysical importance. The Cal Tech group discovered the 12C resonance corresponding to an excited state at 7.65 MeV, just above the energy predicted by Hoyle
Once 12C is formed, other a-particle reactions become possible.
When the helium fuel begins to be exhausted, gravitational collapse sets in again (only if the star is sufficiently massive-otherwise the gravitational force is not strong enough to oppose the “degeneracy pressure” of the electrons that are reluctant to have overlapping wave functions). The star then heats up enough to ignite 12Cand l6 0burning, which permits other reactions.
the abundances of the elements formed by a capture ( Z = even) are far greater (an order of magnitude or more) than the neighboring odd-2 elements. Notice also the dramatic (6 orders of magnitude) drop for elements below C; these elements are not formed in the stellar processes discussed SO far.
Two processes are responsible for the formation of the vast majority of the stable isotopes of the nuclei beyond A = 60. The first process, in which neutron capture occurs only on a long time scale, leaving time for all intervening beta decays to occur, is called the s (for slow) process. The second process, which does not leave time for any but the most short-lived decays, is called the r (for rapid) process.

Stars are an s process Supernova is belived to be an r-process but there is as yet no general agreement on this hypothesis, The experimental evidence for the production of r-process nuclei is firm, and we will therefore accept that somewhere in the universe is a source (supernova, neutron star, etc.) that is capable of producing the necessary fluxes.

IntroductoryNuclearPhysics

Introductory Nuclear Physics (Kenneth Krane)

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