Hot spot effect in subatomic physics
Encyclopedia
Hot spots in subatomic
physics are regions of high energy density or temperature in hadronic or nuclear matter.
, which consist of nucleon
s, as well as to nucleons themselves, which are made of quark
s and gluon
s, Other manifestations of finite sizes of these systems are seen in scattering of electron
s on nuclei and nucleons. For nuclei in particular finite size effects manifest themselves also in the isomeric shift
and isotopic shift
.
, which in its turn occurs if the thermal conductivity
in the medium is sufficiently small.
The notions of equilibrium and heat
are statistical. The use of statistical methods assumes a large number of degrees of freedom. In macrosocopic physics this number usually refers to the number of atoms or molecules, while in nuclear and particle physics it refers to the energy level density.
Indications of the transition between local and global equilibrium in strong interaction particle physics started to emerge in the 1960s and early 1970s. In high-energy strong interactions equilibrium is usually not complete. In these reactions, with the increase of laboratory energy one observes that the transverse momenta of produced particles have a tail, which deviates from the single exponential Boltzmann
spectrum, characteristic for global equilibrium. The slope or the effective temperature of this transverse momentum tail increases with increasing energy. These large transverse momenta were interpreted as being due to particles, which “leak” out before equilibrium is reached. Similar observations had been made in nuclear reactions and were also attributed to pre-equilibrium effects. This interpretation suggested that the equilibrium is neither instantaneous, nor global, but rather local in space and time. By predicting a specific asymmetry in peripheral high-energy hadron reactions based on the hot spot effect Richard M. Weiner
proposed a direct test of this hypothesis as well as of the assumption that the heat conductivity in hadronic matter is relatively small. The theoretical analysis of the hot spot effect in terms of propagation of heat was performed in Ref.
In high energy hadron reactions one distinguishes peripheral reactions with low multiplicity and central collisions with high multiplicity. Peripheral reactions are also characterized by the existence of a leading particle which retains a large proportion of the incoming energy. By taking the notion of peripheral literally Ref.2 suggested that in this kind of reaction the surface of the colliding hadrons is locally excited giving rise to a hot spot, which is de-excited by two processes: 1) emission of particles into the vacuum 2) propagation of “heat” into the body of the target (projectile) wherefrom it is eventually also emitted through particle production. Particles produced in process 1) will have higher energies than those due to process 2), because in the latter process the excitation energy is in part degraded. This gives rise to an asymmetry with respect to the leading particle, which should be detectable in an experimental event by event analysis. This effect was confirmed by Jacques Goldberg in K- p→ K- p π+ π- reactions at 14 GEV/c. This experiment represents the first observation of local equilibrium in hadronic interactions, allowing in principle a quantitative determination of heat conductivity in hadronic matter along the lines of Ref.3 . This observation came as a surprise, because, although the electron proton scattering experiments had shown beyond any doubt that the nucleon had a finite size, it was a-priori not clear whether this size was sufficiently big for the hot spot effect to be observable, i. e. whether heat conductivity in hadronic matters was sufficiently small. Experiment4 suggests that this is the case.
had suggested that propagation of heat in nuclear matter could be studied in central collisions and Sin-Itiro Tomonaga
had calculated the corresponding heat conductivity. The interest in this phenomenon was resurrected in the 1970s by the work of Weiner and Weström who established the link between the hot spot model and the pre-equilibrium approach used in low energy heavy ion reactions. Experimentally the hot spot model in nuclear reactions was confirmed in a series of investigations some of which of rather sophisticated nature including polarization measurements of protons and gamma rays. Subsequently on the theoretical side the link between hot spots and limiting fragmentation and transparency in high energy heavy ion reactions was analyzed and “drifting hot spots” for central collisions were studied.
With the advent of heavy ion accelerators experimental studies of hot spots in nuclear matter became a subject of current interest and a series of special meetings was dedicated to the topic of local equilibrium in strong interactions. The phenomena of hot spots, heat conduction and preequilibrium play also an important part in high-energy heavy ion reactions and in the search for the phase transition to quark matter.
s) are a possible physical mechanism for the creation of hot spots in nuclear interactions. Solitons are a solution of the hydrodynamic equations characterized by a stable localized high density region and small spatial volume. They were predicted to appear in low-energy heavy ion collisions at velocities of the projectile slightly exceeding the velocity of sound (E/A ~ 10-20 MeV; here E is the incoming energy and A the atomic number). Possible evidence for this phenomenon is provided by the experimental observation that the linear momentum transfer in 12C induced heavy-ion reactions is limited.
Subatomic particle
In physics or chemistry, subatomic particles are the smaller particles composing nucleons and atoms. There are two types of subatomic particles: elementary particles, which are not made of other particles, and composite particles...
physics are regions of high energy density or temperature in hadronic or nuclear matter.
Finite size effects
Hot spots are a manifestation of the finite size of the system: in subatomic physics this refers both to atomic nucleiAtomic nucleus
The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...
, which consist of nucleon
Nucleon
In physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...
s, as well as to nucleons themselves, which are made of quark
Quark
A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s and gluon
Gluon
Gluons are elementary particles which act as the exchange particles for the color force between quarks, analogous to the exchange of photons in the electromagnetic force between two charged particles....
s, Other manifestations of finite sizes of these systems are seen in scattering of electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s on nuclei and nucleons. For nuclei in particular finite size effects manifest themselves also in the isomeric shift
Isomeric shift
The isomeric shift is the shift on atomic spectral lines and gamma spectral lines, which occurs as a consequence of replacement of one nuclear isomer by another. It is usually called isomeric shift on atomic spectral lines and Mössbauer isomeric shift respectively...
and isotopic shift
Isotopic shift
The isotopic shift is the shift in atomic spectra which occurs when one nuclear isotope is replaced by another. If the spectra have also hyperfine structure the shift refers to the center of gravity of the spectra. There are two effects which contribute to this shift:*The mass difference. This...
.
Statistical methods in subatomic physics
The formation of hot spots assumes the establishment of local equilibriumThermodynamic equilibrium
In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium, and chemical equilibrium. The word equilibrium means a state of balance...
, which in its turn occurs if the thermal conductivity
Thermal conductivity
In physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....
in the medium is sufficiently small.
The notions of equilibrium and heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...
are statistical. The use of statistical methods assumes a large number of degrees of freedom. In macrosocopic physics this number usually refers to the number of atoms or molecules, while in nuclear and particle physics it refers to the energy level density.
Hot spots in nucleons
Local equilibrium is the precursor of global equilibrium and the hot spot effect can be used to determine how fast, if at all, the transition from local to global equilibrium takes place. That this transition does not always happen follows from the fact that the duration of a strong interaction reaction is quite short (of the order of 10−22 - 10−23 seconds) and the propagation of “heat”, i.e. of the excitation, through the finite sized body of the system takes a finite time, which is determined by the thermal conductivity of the matter the system is made of.Indications of the transition between local and global equilibrium in strong interaction particle physics started to emerge in the 1960s and early 1970s. In high-energy strong interactions equilibrium is usually not complete. In these reactions, with the increase of laboratory energy one observes that the transverse momenta of produced particles have a tail, which deviates from the single exponential Boltzmann
Ludwig Boltzmann
Ludwig Eduard Boltzmann was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics...
spectrum, characteristic for global equilibrium. The slope or the effective temperature of this transverse momentum tail increases with increasing energy. These large transverse momenta were interpreted as being due to particles, which “leak” out before equilibrium is reached. Similar observations had been made in nuclear reactions and were also attributed to pre-equilibrium effects. This interpretation suggested that the equilibrium is neither instantaneous, nor global, but rather local in space and time. By predicting a specific asymmetry in peripheral high-energy hadron reactions based on the hot spot effect Richard M. Weiner
Richard M. Weiner
Richard M. Weiner is a professor of theoretical physics at the University of Marburg in Marburg, Germany and an associate of the Laboratoire de Physique Théorique at Paris-Sud 11 University in Orsay, France.-Biography:...
proposed a direct test of this hypothesis as well as of the assumption that the heat conductivity in hadronic matter is relatively small. The theoretical analysis of the hot spot effect in terms of propagation of heat was performed in Ref.
In high energy hadron reactions one distinguishes peripheral reactions with low multiplicity and central collisions with high multiplicity. Peripheral reactions are also characterized by the existence of a leading particle which retains a large proportion of the incoming energy. By taking the notion of peripheral literally Ref.2 suggested that in this kind of reaction the surface of the colliding hadrons is locally excited giving rise to a hot spot, which is de-excited by two processes: 1) emission of particles into the vacuum 2) propagation of “heat” into the body of the target (projectile) wherefrom it is eventually also emitted through particle production. Particles produced in process 1) will have higher energies than those due to process 2), because in the latter process the excitation energy is in part degraded. This gives rise to an asymmetry with respect to the leading particle, which should be detectable in an experimental event by event analysis. This effect was confirmed by Jacques Goldberg in K- p→ K- p π+ π- reactions at 14 GEV/c. This experiment represents the first observation of local equilibrium in hadronic interactions, allowing in principle a quantitative determination of heat conductivity in hadronic matter along the lines of Ref.3 . This observation came as a surprise, because, although the electron proton scattering experiments had shown beyond any doubt that the nucleon had a finite size, it was a-priori not clear whether this size was sufficiently big for the hot spot effect to be observable, i. e. whether heat conductivity in hadronic matters was sufficiently small. Experiment4 suggests that this is the case.
Hot Spots in nuclei
In atomic nuclei, because of their larger dimensions as compared with nucleons, statistical and thermodynamical concepts have been used already in the 1930s. Hans BetheHans Bethe
Hans Albrecht Bethe was a German-American nuclear physicist, and Nobel laureate in physics for his work on the theory of stellar nucleosynthesis. A versatile theoretical physicist, Bethe also made important contributions to quantum electrodynamics, nuclear physics, solid-state physics and...
had suggested that propagation of heat in nuclear matter could be studied in central collisions and Sin-Itiro Tomonaga
Sin-Itiro Tomonaga
was a Japanese physicist, influential in the development of quantum electrodynamics, work for which he was jointly awarded the Nobel Prize in Physics in 1965 along with Richard Feynman and Julian Schwinger.-Biography:...
had calculated the corresponding heat conductivity. The interest in this phenomenon was resurrected in the 1970s by the work of Weiner and Weström who established the link between the hot spot model and the pre-equilibrium approach used in low energy heavy ion reactions. Experimentally the hot spot model in nuclear reactions was confirmed in a series of investigations some of which of rather sophisticated nature including polarization measurements of protons and gamma rays. Subsequently on the theoretical side the link between hot spots and limiting fragmentation and transparency in high energy heavy ion reactions was analyzed and “drifting hot spots” for central collisions were studied.
With the advent of heavy ion accelerators experimental studies of hot spots in nuclear matter became a subject of current interest and a series of special meetings was dedicated to the topic of local equilibrium in strong interactions. The phenomena of hot spots, heat conduction and preequilibrium play also an important part in high-energy heavy ion reactions and in the search for the phase transition to quark matter.
Hot spots and solitons
Solitary waves (solitonSoliton
In mathematics and physics, a soliton is a self-reinforcing solitary wave that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium...
s) are a possible physical mechanism for the creation of hot spots in nuclear interactions. Solitons are a solution of the hydrodynamic equations characterized by a stable localized high density region and small spatial volume. They were predicted to appear in low-energy heavy ion collisions at velocities of the projectile slightly exceeding the velocity of sound (E/A ~ 10-20 MeV; here E is the incoming energy and A the atomic number). Possible evidence for this phenomenon is provided by the experimental observation that the linear momentum transfer in 12C induced heavy-ion reactions is limited.