- Email: [email protected]
Summary: International symposium on nuclear structure physics today May 11–May 14 1993
NUCLEAR PHYSICS A
NuclearPhysicsA570(1994)429cA38c North-Holland, Amsterdam
Summary: International
Symposium
Herman Feshbach” aCenter for Theoretical Physics, Massachusetts
on Nuclear Structure Physics Today
May 11 - May 14 1993
Chung-Li,
Taiwan
Physics, Laboratory for Nuclear Science and Department of 02139 Institute of Technology, Cambridge, Massachusetts
In his letter to me, Prof. Chen asked me to comment upon my sense of the direction of the field of nuclear physics, its robustness and what important unanswered questions lie ahead. I have been thinking for some time about these very issues and let me tell you why. For many years nuclear physics in the U.S. and elsewhere has been under attack particularly by particle physicists. Some major universities, e.g. Berkeley and Cornell have no nuclear physicists on their staff and obviously conduct no nuclear research. I have been personally asked most rudely by at least two Nobel laureates why I am wasting my time and energy in nuclear research. It does very little good to tell these people that they should spend some time looking into what nuclear physicists do and then they would not be so negative. In my opinion particle physics is no more important than nuclear physics. Both operate at the frontiers of our knowledge - both have important things to uncover and discover. The only way to respond is to ask ourselves: can we justify nuclear research to ourselves ? The answer has to be more than the statement that the study of the properties of nuclei and nuclear reactions is fascinating. It is my aim in this report to you to develop an answer to this question. In my answer I will indicate how this conference reflects and contributes to the answer. But before I do this, I cannot resist the temptation to discuss briefly aspects of the future of particle physics. I hope Dr. S. C. Lee, who outlined a policy which would put Taiwanese resources into particle physics and which would be most dangerous to nuclear physics in Taiwan, will read this report. I believe that this policy is, to say the least, misguided and compromises Taiwan’s scientific future. I will show the questions which nuclear physics addresses are every bit as fundamental as those under consideration by particle physics. Indeed particle physicists will neglect or disregard the results obtained for nuclear research at their peril. Particle physicists claim to be in search of the fundamental building blocks, the particles out of which all matter is composed. What is not realized is that it may not be able to combine these particles quantitatively to form matter except possibly in a most qualitative fashion. There is much evidence on behalf of this statement. Quantum electrodynamics is an extremely successful theory. One can compute its consequences with extraordinary accuracy. Calculating the properties of nuclei, assumed to be composed of strongly interacting nucleons starting from the nucleon-nucleon forces turns out to be a formidable task which is accomplished only with the aid of computers and with the close involvement with experiment. Accuracies of the order of a fraction of a per cent can be obtained. But as this conference has shown, unanswered issues remain. The fundamental 037%r474/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved. SSDlO375-9474(94)00119-8
43oc
H. Feshbach I Summary
theory of particle physics is assumed to be &CD. In this case solutions have not been found after many years except for the asymptotic freedom domain where perturbation theory is applicable. Accuracies of the order of 10% are obtained. To obtain results in the non-perturbative domain, the methods now available require a very large computer. Right now an attempt is being made by a consortium of M.I.T. and Brookhaven to obtain a teraflop computer with which it is hoped one can solve QCD equations numerically. If one extrapolates this sequence, it is conceivable that in the limit, the solut;on of the final equations will be forbiddingly difficult. Its solution would require a computer of enormous capability and parenthetically very expensive whose realization may or may not be possible. Parenthetically experiments in the past decade have been unproductive as deviations from the standard theory with its many constants have not been observed. What have particle physicists omitted? In his recent work, my friends Steve Weinberg (he is not one of those who criticize nuclear physics) makes the point that the Schrijdinger equation in principle suffices to explain all of molecular physics. One does not have to verify this in every case. One needs only a few cases. But what he omits in his discussion is the fact that the collective motions of molecules are not obvious results which can be obtained by staring at the Schrijdinger equation. Nuclear physics provides several such examples where collective motion was suggested by experiment and not by looking at the solutions of the many body Schrijdinger equation. We begin the nuclear physics summary with Fig. 1 indicating the contributions of nuclear physics to science and technology. You will note that the arrows from each of these areas to nuclear physics are double headed, indicating that the interaction with nuclear physics goes both ways. We wish, in this talk, to emphasize the area designated by universals. “Universals” refers to contributions which transcend the limits of a given subject providing fundamental principles which inform not only nuclear physics but all areas of science. It is the universals which take nuclear physics research from the parochial albeit fascinating studies of nuclear reactions and structure to the development and formulation of concepts of significance for all of the physical sciences. The universals are most clearly visible as such by showing how discoveries made by nuclear physicists impact on other sciences. Examples are furnished by contributions to this conference. We shall discuss two examples, astrophysics and mesoscopic physics. The close relationship of nuclear and astrophysics is based on the discovery that energy production in the stars is a consequence of nuclear reactions. In one set of reactions four hydrogen nuclei combine to form an alpha particle. The life cycle of a star is intimately connected with these reactions, and the availability of various kinds of nuclei which can be involved. Neutron stars which are the terminal states of many of these life cycles are giant nuclei compressed to small dimensions by the action of gravitational forces. Energy production is accompanied by the emission of neutrinos. Their observation is now the subject of a major research effort whose results will influence our understanding not only of the weak interactions but also of the internal constitution of the stars. Supernova are another result of the combined effect of gravitational and nuclear forces. Their properties are still not completely understood but it is clear that nuclear reactions of the middle weight elements play an important role. Incidentally, the elements beyond iron are formed in super-nova explosions. Many important problems regarding nuclear abundances remain. Some of these were
OTHER SCIENCES ARCHEOLOGY ART HISTORY BIOLOGY CHEMISTRY POLYMERS EARTH SCIENCES MATERIAL SCIENCES ECOLOGY PALEANTOLOGY CHAOS
REACTORS - NEUTRONS APPLICATION TO CONDENSED MATTER, BIOLOGY, CHEMISTRY HIGH T SUPERCONDUCTIVITY
ACCELERATORS ION IMPIANTATION SUPERCONDUCTIVITY SYNCHROTRON RADIATION
Fig. 1: Contributions
of Nuclear
OTHFR PHYSICS ASTROPHYSICS STELLAR ENERGY PRODUCTION SUPERNOVA NEUTRON STARS-PULSARS MESOSCOPIC PHYSICS STRONG INTERACTIONS PARTICLE PHYSICS AND COMPLEXITY, REACTIONS SYMMETRY WEAK INTERACTIONS CHAOS
UNIVERSALS
Physics
$8 r
432~
H. Feshbach I Summary
outlined by Thielmann in his review paper entitled “Astrophysical Abundance and Nuclear Properties.” The various nuances in nuclear structure are important. One hopes to be able to determine what astrophysical conditions must have been to produce the present A particularly important reaction which leads to the formation of 160, abundances. The results were presented by M. Gai. ‘%(a, 7) 160 has bee n studied experimentally. The collision of light heavy ions, e.g. “j0 + 160 with energies below the Coulomb barrier These were discussed in this conference by are of obvious importance for astrophysics. S. C. Wu. Finally, the problems of solar neutrinos and neutrino oscillations were reviewed by W. Haxton. A second area where nuclear physics and nuclear physics concepts play an important role is mesoscopic physics, defined as the physics of systems which are so small that the methods used in discussing macroscopic systems are no longer adequate while the number of constituents are too large for the system to be considered as elementary. Nuclei are obvious examples of such systems. There is thus no surprise that concepts developed by nuclear research are used in the analysis of such systems. For example in the case of metallic clusters commented on by Arima and Iachello, the concept of a mean field (i.e. the shell model) is found to be valid. The electrons in the cluster are assumed to move in a mean field which has the Wood-Saxon form! Using this mean field one can explain the magic numbers (in this case the number of atoms forming a cluster which is especially stable). One can expect that these systems may be deformed (there is some experimental evidence for this), that the system might vibrate. Electron-cluster scattering may show nuclear type phenomena. One can expect at least the validity of the optical model to prevail. One could also speculate that IBM type symmetries may be present. What is being pointed to here is the universals of the major modes of motion that are exhibited generally by complex systems even though the interparticle forces are very different. Chaos offers another example of the relevance of nuclear physics. On the one hand there is the statistical interpretation of the energy spacing of low energy neutron resonances proposed originally by Wigner. The Wigner spacing distribution has been proposed as evidence for quantum chaos. At higher particle energies chaos appears in the form of fluctuations in the energy dependence of cross section called Ericson fluctuations. Both of these phenomena have been observed in the conductivity of small metallic particles and in the energy levels of Rydberg atoms. What the researchers in this field still have to learn from nuclear physics is the importance of energy averaging which in the nuclear case leads to the optical model. In this conference this general case is the subject of Zelevansky’s paper. The mean field (shell model) is one of the important discoveries of nuclear physics. The existence of a mean field in spite of the strong nucleon-nucleon interaction was a great surprise, and as I have emphasized earlier is one of the universals of complex systems. The mean field is a dynamical construct. It can be deformed thereby producing the familiar vibrational and rotational nuclear spectra. However the application of the mean field to nuclear structure is still incomplete. Analysis, which makes significant use of experimental data, has successfully explained the energies, the spins, etc. of the levels of the nuclei up through the s-d shell as exemplified by the work of Brown and Wildenthal. But beyond that there are difficulties which grow with mass number although as this conference reports an attack is being mounted on the p-f shell. The essential barrier that hinders the
H. Feshbach I Summary
433c
application of the shell model to these heavier nuclei, is the astronomically large number of shell model states which have to be diagonalized with respect to the residual interaction which must be added to the mean field to complete the nuclear Hamiltonian. In fact it is apparent that such a diagonalization, even if it were possible, would be a fruitless endeavor as most of the levels obtained in this way would be of little interest. The issue then is how can one select out of these many levels those which are of interest. An example is the rotational states of nuclei. These, theoretically, were not uncovered by solving the many body Schrodinger equation using the shell model as a starting point although a relationship to the mean field was established later. Of overriding importance is the formulation and exploration of principles which will select those states which reveal significant aspects of the complex system, the nucleus. These principles are very likely to be of universal importance in the sense defined earlier. The earliest discussions used atomic, molecular as well as the charged liquid drop models. In this conference emphasis upon the use of symmetry to formulate possible models The first such attempt was that of Wigner who used the SU(4) of nuclear structure. model to discuss the properties of light nuclei. The application of symmetry to discuss collective motion in the heavier nuclei is the thought behind the Interacting Boson Model (IBM). Iachello has applied similar ideas to molecular physics while Dover and Feshbach have employed symmetry to discuss the hyperon-nucleon interaction and hypernuclei. This conference was concerned with %ne tuning” and extensions of the IBM model. Arima and Yoshinaga in their reviews of recent programs have emphasized the importance of adding the effects of the g bosons to those of the traditional s and d bosons. Number conservation was found to be essential. Yoshida discussed the extension to odd-odd nuclei. Leviatan discussed the possibility that the Hamiltonian is not symmetric while some subset of the wavefunctions are. He refers to this possibility as partial dynamic symmetry. Talmi reviewed the seniority and generalized seniority models. He finds that two body seniority is good for repulsive pair T = 1 states whereas it is not valid for attractive T = 0 states. Other symmetries were discussed by Feng (Dynamic Symmetry and Fermions) while Rowe and Gupta looked into the possibility that quantum groups may be relevant to nuclear physics. This writer has pointed to the application of symmetry to collective states in the continuum, such as the giant and isobar analog resonances. One group of talks were concerned with the extension of the shell model to the p-f shell. The caution voiced earlier that there are many states and that relatively few are interesting because they correspond to collective motion. The “simplest” such state is the ground state so that some calculations focus on it with the hope that the properties of the low lying levels will be revealed as well. One of the procedures used, and described by Guidry employs a truncation of the available states (prior to diagonalization) dictated by symmetry. Vallieres introduces the Monte Carlo method using e-OH as a weighting function. For large values of p one obtains the properties of the ground state. Vallieres also makes use of the permutation group. Special techniques were discussed by Ching Teh-Li (maximum decoupling) and by Cheng Li Wu (pair field approach to the shell model). Barrett reverting to pre-war issues proposes the direct calculation of the binding energy
434c
H. Feshbach I Summary
of the light nuclei (A = 2 -+ 7) using the two particle nuclear reaction matrix based on the Reid soft core potential. This avoids the divergence problems which have bedeviled the attempt to obtain the residual potential by higher order corrections to the G-matrix. As an aside let me say that I believe that convergence problems are inevitable for the reaction matrix would then be required to describe the sharp close collisions of the nuclear nucleons. I speculate that convergence would be improved if an appropriate averaging procedure was used. The properties of the relatively recently discovered superdeformed nuclear states is another expression of the mean field. Dudek, K. S. Tanaka, and Bes make comments on this phenomenon. Tanaka points to an SU(3) (a la Eliott) symmetry emphasizing the importance of spin-orbit coupling. Bes describes a general theory (which I won’t attempt to summarize) from which he obtains not only superdeformed states but also an explanation of the unexpected identical superdeformed spectra observed for neighboring nuclei. The use of a temperature concept was introduced into mesoscopic physics by Weisskopf who described nuclear evaporation in 1937. Y. Tzeng discussed the related equation of state for nuclear matter determined semi-empirically, adducing evidence for a phase transition. The contribution of the A excitation of the nucleon to nuclear forces makes it necessary to include the A as a nuclear constituent. Vary presented a shell model calculation for 160, 40Ca and 56Ni which included the A-nucleon interaction. A softer equation of state was obtained as might be expected. We turn next to nuclear reactions. This was not featured at this conference on nuclear structure. However it is worthwhile mentioning it to round out the picture of nuclear physics research. Nuclear reactions are the major source of information with respect not only to nuclear structure but also with respect to the nature of the nuclear Namiltonian. Nuclear reactions probe the nucleus but beyond that as we shall see it is a major source of new phenomena, as many of the collective states are revealed in reaction experiments. An example of its usefulness is illustrated by the contribution to this meeting by II. Lee whose title is “Nuclear Structure Studies and Intermediate Energy Probes.” By using different probes, electrons, muons, pions and kaons, one obtains different views of the probed nucleus. Putting these views together provides us with an integrated picture not accessible with just a single probe. The concepts and phenomena which nuclear reaction studies have discovered include compound nuclear resonances, prompt reactions such as the optical model and direct reactions, doorway states and giant resonances, multi-step reactions of both the direct and compound type. Processes which have been described include multiple scattering by a mesoscopic system, particle exchange between two such systems, inelastic scattering, and production processes of pions, kaons, gamma rays. A principal concept which has emerged from this research is that of energy averaging or alternately the existence of differing time scales. These can be explored by choosing appropriate experimental parameters. The energy resolution, AE is the key. When AE is relatively large we are dealing with prompt reactions, as seen in direct reactions and the optical model. When the energy resolution is very good, it may become possible to see compound nuclear resonance. One can envisage energy resolution which lie between these two limits. Such energy resolutions permit the
observation of a doorway state resonance (in this case an isobar analog resonance) as illustrated in Fig. 2. The upper half gives the s2Mo(p,p) cross section at several angles taken with good resolution. We see only fluctuations. However upon energy averaging by using poorer energy resolution one obtains the bottom curve showing a beautiful resonance dependence on energy. Note that the above developments were made without using accurately determined nucleon-nucleon potentials. Success is a consequence of the existence of the “universals” which as we have alluded to earlier are largely independent of the interparticle forces. As the potentials became better known, the challenge of correlating the semi-empirical results with those which could be obtained from the nucleon-nucleon potential presents itself. In the middle sixties, this calculation was performed by G. E. Brown and Tom Kuo. Their results can be compared with semi-empirical results obtained by Brown and Wildenthal using a method originally devised by Talmi. Using two forms of the potential, the Paris and Bonn, Kuo in his presentation to this meeting points out that agreement with Brown and Wildenthal is best for the Bonn potential because its tensor term is weak. Kuo also discusses evidence from hypernuclei and concludes that the Niejmegen potentials are not as good as the Julich potential. Of course much of this uncertainty would be reduced if particle physicists had derived the baryon-baryon potential from first principles as they promised to do many years ago and many times. We turn next to presentations regarding the weak interactions made by Haxton, Faessler and Ball. Nuclear physics has played a leading role in the study of the weak interactions. The study of parity conservation by Wu et al has been followed by its observation in the baryon-baryon interaction. Recent experiments using electron scattering from nuclei will test the “standard theory.” The research reported by Haxton relies on the use of nuclei as detectors of neutrinos in this case from the sun and from super nova. Ga and Cl detectors measure different portions of the solar neutrino spectrum. Detection of neutrinos emitted in super-nova explosions e.g. 1987A have been made so that a neutrino based astronomy appears to be in prospect. The resolution of the solar neutrino issue will have significant impact on significant fundamental questions such as the validity of the MSW process, the mass of the neutrino and the solar model. Faessler described his analysis of double p decay and its relation to the Majorana neutrino (not radiated in double p decay) and the Dirac neutrino commonly used in single p decay. He finds nuclear properties, e.g. ground state correlations to be important. Finally two new facilities of particular importance to nuclear spectroscopy were discussed.; Olsen described the production of a beam of radioactive nuclei at Oak Ridge, expected to be available by 1995. In this facility, the radioactive nuclei are produced in a cyclotron and then injected into a tandem. Ball described the accompanying experimental program which will focus on proton rich nuclei approaching the proton drip line. Predictions have been made of large deformations, nuclei with exotic shapes. The 2 = N nuclei up to “‘Sn will be produced and studied. Gai pointed to importance of neutron rich nuclei such as ‘Li, “Li, ‘lBe, “Be, etc. The Gammasphere, being built at Berkeley, is designed to be an efficient detector of y decay. A similar instrument is under construction by Great Britain and France, called the Eurogam. Another, the Euroball, is projected to be built to succeed the Eurogam.
436~
H. Feshbach
I Summary
1 I I 5.2
!
I 5.3
Li.4
Proton energy WV)
I
:
I
I
I
I
I
I
I
I
I
I
I
I
I
I
26 m i
26-
X ;
24-
z ;
22-
p
20 -
1 16 16 -
5.0
5.2
5.4
5.6
Incident proton energy (MN)
Fig. 2: The “MO (p,p) reaction. The results shown in the figure at the top were taken with excellent energy resolution; those in the lower figure with poorer energy resolution.
These instruments will be used to study the superdeformed nuclei and the interesting puzzle of identical super-deformed bands from neighboring nuclei. L. Y. Lee presented a discussion of these instruments. This report reveals the great diversity of nuclear physics research, even though there are many topics which could not be included. Problems are attacked with different probes, with differing nuclei which provide a variety of examples. Using sensitive detectors, many experimental situations can be realized. It is the synergism of these studies which leads to a fundamental understanding of nuclei and nuclear reactions and thereby to mesoscopic systems.
NuclearPhysicsA570(1994)429cA38c North-Holland, Amsterdam
Summary: International
Symposium
Herman Feshbach” aCenter for Theoretical Physics, Massachusetts
on Nuclear Structure Physics Today
May 11 - May 14 1993
Chung-Li,
Taiwan
Physics, Laboratory for Nuclear Science and Department of 02139 Institute of Technology, Cambridge, Massachusetts
In his letter to me, Prof. Chen asked me to comment upon my sense of the direction of the field of nuclear physics, its robustness and what important unanswered questions lie ahead. I have been thinking for some time about these very issues and let me tell you why. For many years nuclear physics in the U.S. and elsewhere has been under attack particularly by particle physicists. Some major universities, e.g. Berkeley and Cornell have no nuclear physicists on their staff and obviously conduct no nuclear research. I have been personally asked most rudely by at least two Nobel laureates why I am wasting my time and energy in nuclear research. It does very little good to tell these people that they should spend some time looking into what nuclear physicists do and then they would not be so negative. In my opinion particle physics is no more important than nuclear physics. Both operate at the frontiers of our knowledge - both have important things to uncover and discover. The only way to respond is to ask ourselves: can we justify nuclear research to ourselves ? The answer has to be more than the statement that the study of the properties of nuclei and nuclear reactions is fascinating. It is my aim in this report to you to develop an answer to this question. In my answer I will indicate how this conference reflects and contributes to the answer. But before I do this, I cannot resist the temptation to discuss briefly aspects of the future of particle physics. I hope Dr. S. C. Lee, who outlined a policy which would put Taiwanese resources into particle physics and which would be most dangerous to nuclear physics in Taiwan, will read this report. I believe that this policy is, to say the least, misguided and compromises Taiwan’s scientific future. I will show the questions which nuclear physics addresses are every bit as fundamental as those under consideration by particle physics. Indeed particle physicists will neglect or disregard the results obtained for nuclear research at their peril. Particle physicists claim to be in search of the fundamental building blocks, the particles out of which all matter is composed. What is not realized is that it may not be able to combine these particles quantitatively to form matter except possibly in a most qualitative fashion. There is much evidence on behalf of this statement. Quantum electrodynamics is an extremely successful theory. One can compute its consequences with extraordinary accuracy. Calculating the properties of nuclei, assumed to be composed of strongly interacting nucleons starting from the nucleon-nucleon forces turns out to be a formidable task which is accomplished only with the aid of computers and with the close involvement with experiment. Accuracies of the order of a fraction of a per cent can be obtained. But as this conference has shown, unanswered issues remain. The fundamental 037%r474/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved. SSDlO375-9474(94)00119-8
43oc
H. Feshbach I Summary
theory of particle physics is assumed to be &CD. In this case solutions have not been found after many years except for the asymptotic freedom domain where perturbation theory is applicable. Accuracies of the order of 10% are obtained. To obtain results in the non-perturbative domain, the methods now available require a very large computer. Right now an attempt is being made by a consortium of M.I.T. and Brookhaven to obtain a teraflop computer with which it is hoped one can solve QCD equations numerically. If one extrapolates this sequence, it is conceivable that in the limit, the solut;on of the final equations will be forbiddingly difficult. Its solution would require a computer of enormous capability and parenthetically very expensive whose realization may or may not be possible. Parenthetically experiments in the past decade have been unproductive as deviations from the standard theory with its many constants have not been observed. What have particle physicists omitted? In his recent work, my friends Steve Weinberg (he is not one of those who criticize nuclear physics) makes the point that the Schrijdinger equation in principle suffices to explain all of molecular physics. One does not have to verify this in every case. One needs only a few cases. But what he omits in his discussion is the fact that the collective motions of molecules are not obvious results which can be obtained by staring at the Schrijdinger equation. Nuclear physics provides several such examples where collective motion was suggested by experiment and not by looking at the solutions of the many body Schrijdinger equation. We begin the nuclear physics summary with Fig. 1 indicating the contributions of nuclear physics to science and technology. You will note that the arrows from each of these areas to nuclear physics are double headed, indicating that the interaction with nuclear physics goes both ways. We wish, in this talk, to emphasize the area designated by universals. “Universals” refers to contributions which transcend the limits of a given subject providing fundamental principles which inform not only nuclear physics but all areas of science. It is the universals which take nuclear physics research from the parochial albeit fascinating studies of nuclear reactions and structure to the development and formulation of concepts of significance for all of the physical sciences. The universals are most clearly visible as such by showing how discoveries made by nuclear physicists impact on other sciences. Examples are furnished by contributions to this conference. We shall discuss two examples, astrophysics and mesoscopic physics. The close relationship of nuclear and astrophysics is based on the discovery that energy production in the stars is a consequence of nuclear reactions. In one set of reactions four hydrogen nuclei combine to form an alpha particle. The life cycle of a star is intimately connected with these reactions, and the availability of various kinds of nuclei which can be involved. Neutron stars which are the terminal states of many of these life cycles are giant nuclei compressed to small dimensions by the action of gravitational forces. Energy production is accompanied by the emission of neutrinos. Their observation is now the subject of a major research effort whose results will influence our understanding not only of the weak interactions but also of the internal constitution of the stars. Supernova are another result of the combined effect of gravitational and nuclear forces. Their properties are still not completely understood but it is clear that nuclear reactions of the middle weight elements play an important role. Incidentally, the elements beyond iron are formed in super-nova explosions. Many important problems regarding nuclear abundances remain. Some of these were
OTHER SCIENCES ARCHEOLOGY ART HISTORY BIOLOGY CHEMISTRY POLYMERS EARTH SCIENCES MATERIAL SCIENCES ECOLOGY PALEANTOLOGY CHAOS
REACTORS - NEUTRONS APPLICATION TO CONDENSED MATTER, BIOLOGY, CHEMISTRY HIGH T SUPERCONDUCTIVITY
ACCELERATORS ION IMPIANTATION SUPERCONDUCTIVITY SYNCHROTRON RADIATION
Fig. 1: Contributions
of Nuclear
OTHFR PHYSICS ASTROPHYSICS STELLAR ENERGY PRODUCTION SUPERNOVA NEUTRON STARS-PULSARS MESOSCOPIC PHYSICS STRONG INTERACTIONS PARTICLE PHYSICS AND COMPLEXITY, REACTIONS SYMMETRY WEAK INTERACTIONS CHAOS
UNIVERSALS
Physics
$8 r
432~
H. Feshbach I Summary
outlined by Thielmann in his review paper entitled “Astrophysical Abundance and Nuclear Properties.” The various nuances in nuclear structure are important. One hopes to be able to determine what astrophysical conditions must have been to produce the present A particularly important reaction which leads to the formation of 160, abundances. The results were presented by M. Gai. ‘%(a, 7) 160 has bee n studied experimentally. The collision of light heavy ions, e.g. “j0 + 160 with energies below the Coulomb barrier These were discussed in this conference by are of obvious importance for astrophysics. S. C. Wu. Finally, the problems of solar neutrinos and neutrino oscillations were reviewed by W. Haxton. A second area where nuclear physics and nuclear physics concepts play an important role is mesoscopic physics, defined as the physics of systems which are so small that the methods used in discussing macroscopic systems are no longer adequate while the number of constituents are too large for the system to be considered as elementary. Nuclei are obvious examples of such systems. There is thus no surprise that concepts developed by nuclear research are used in the analysis of such systems. For example in the case of metallic clusters commented on by Arima and Iachello, the concept of a mean field (i.e. the shell model) is found to be valid. The electrons in the cluster are assumed to move in a mean field which has the Wood-Saxon form! Using this mean field one can explain the magic numbers (in this case the number of atoms forming a cluster which is especially stable). One can expect that these systems may be deformed (there is some experimental evidence for this), that the system might vibrate. Electron-cluster scattering may show nuclear type phenomena. One can expect at least the validity of the optical model to prevail. One could also speculate that IBM type symmetries may be present. What is being pointed to here is the universals of the major modes of motion that are exhibited generally by complex systems even though the interparticle forces are very different. Chaos offers another example of the relevance of nuclear physics. On the one hand there is the statistical interpretation of the energy spacing of low energy neutron resonances proposed originally by Wigner. The Wigner spacing distribution has been proposed as evidence for quantum chaos. At higher particle energies chaos appears in the form of fluctuations in the energy dependence of cross section called Ericson fluctuations. Both of these phenomena have been observed in the conductivity of small metallic particles and in the energy levels of Rydberg atoms. What the researchers in this field still have to learn from nuclear physics is the importance of energy averaging which in the nuclear case leads to the optical model. In this conference this general case is the subject of Zelevansky’s paper. The mean field (shell model) is one of the important discoveries of nuclear physics. The existence of a mean field in spite of the strong nucleon-nucleon interaction was a great surprise, and as I have emphasized earlier is one of the universals of complex systems. The mean field is a dynamical construct. It can be deformed thereby producing the familiar vibrational and rotational nuclear spectra. However the application of the mean field to nuclear structure is still incomplete. Analysis, which makes significant use of experimental data, has successfully explained the energies, the spins, etc. of the levels of the nuclei up through the s-d shell as exemplified by the work of Brown and Wildenthal. But beyond that there are difficulties which grow with mass number although as this conference reports an attack is being mounted on the p-f shell. The essential barrier that hinders the
H. Feshbach I Summary
433c
application of the shell model to these heavier nuclei, is the astronomically large number of shell model states which have to be diagonalized with respect to the residual interaction which must be added to the mean field to complete the nuclear Hamiltonian. In fact it is apparent that such a diagonalization, even if it were possible, would be a fruitless endeavor as most of the levels obtained in this way would be of little interest. The issue then is how can one select out of these many levels those which are of interest. An example is the rotational states of nuclei. These, theoretically, were not uncovered by solving the many body Schrodinger equation using the shell model as a starting point although a relationship to the mean field was established later. Of overriding importance is the formulation and exploration of principles which will select those states which reveal significant aspects of the complex system, the nucleus. These principles are very likely to be of universal importance in the sense defined earlier. The earliest discussions used atomic, molecular as well as the charged liquid drop models. In this conference emphasis upon the use of symmetry to formulate possible models The first such attempt was that of Wigner who used the SU(4) of nuclear structure. model to discuss the properties of light nuclei. The application of symmetry to discuss collective motion in the heavier nuclei is the thought behind the Interacting Boson Model (IBM). Iachello has applied similar ideas to molecular physics while Dover and Feshbach have employed symmetry to discuss the hyperon-nucleon interaction and hypernuclei. This conference was concerned with %ne tuning” and extensions of the IBM model. Arima and Yoshinaga in their reviews of recent programs have emphasized the importance of adding the effects of the g bosons to those of the traditional s and d bosons. Number conservation was found to be essential. Yoshida discussed the extension to odd-odd nuclei. Leviatan discussed the possibility that the Hamiltonian is not symmetric while some subset of the wavefunctions are. He refers to this possibility as partial dynamic symmetry. Talmi reviewed the seniority and generalized seniority models. He finds that two body seniority is good for repulsive pair T = 1 states whereas it is not valid for attractive T = 0 states. Other symmetries were discussed by Feng (Dynamic Symmetry and Fermions) while Rowe and Gupta looked into the possibility that quantum groups may be relevant to nuclear physics. This writer has pointed to the application of symmetry to collective states in the continuum, such as the giant and isobar analog resonances. One group of talks were concerned with the extension of the shell model to the p-f shell. The caution voiced earlier that there are many states and that relatively few are interesting because they correspond to collective motion. The “simplest” such state is the ground state so that some calculations focus on it with the hope that the properties of the low lying levels will be revealed as well. One of the procedures used, and described by Guidry employs a truncation of the available states (prior to diagonalization) dictated by symmetry. Vallieres introduces the Monte Carlo method using e-OH as a weighting function. For large values of p one obtains the properties of the ground state. Vallieres also makes use of the permutation group. Special techniques were discussed by Ching Teh-Li (maximum decoupling) and by Cheng Li Wu (pair field approach to the shell model). Barrett reverting to pre-war issues proposes the direct calculation of the binding energy
434c
H. Feshbach I Summary
of the light nuclei (A = 2 -+ 7) using the two particle nuclear reaction matrix based on the Reid soft core potential. This avoids the divergence problems which have bedeviled the attempt to obtain the residual potential by higher order corrections to the G-matrix. As an aside let me say that I believe that convergence problems are inevitable for the reaction matrix would then be required to describe the sharp close collisions of the nuclear nucleons. I speculate that convergence would be improved if an appropriate averaging procedure was used. The properties of the relatively recently discovered superdeformed nuclear states is another expression of the mean field. Dudek, K. S. Tanaka, and Bes make comments on this phenomenon. Tanaka points to an SU(3) (a la Eliott) symmetry emphasizing the importance of spin-orbit coupling. Bes describes a general theory (which I won’t attempt to summarize) from which he obtains not only superdeformed states but also an explanation of the unexpected identical superdeformed spectra observed for neighboring nuclei. The use of a temperature concept was introduced into mesoscopic physics by Weisskopf who described nuclear evaporation in 1937. Y. Tzeng discussed the related equation of state for nuclear matter determined semi-empirically, adducing evidence for a phase transition. The contribution of the A excitation of the nucleon to nuclear forces makes it necessary to include the A as a nuclear constituent. Vary presented a shell model calculation for 160, 40Ca and 56Ni which included the A-nucleon interaction. A softer equation of state was obtained as might be expected. We turn next to nuclear reactions. This was not featured at this conference on nuclear structure. However it is worthwhile mentioning it to round out the picture of nuclear physics research. Nuclear reactions are the major source of information with respect not only to nuclear structure but also with respect to the nature of the nuclear Namiltonian. Nuclear reactions probe the nucleus but beyond that as we shall see it is a major source of new phenomena, as many of the collective states are revealed in reaction experiments. An example of its usefulness is illustrated by the contribution to this meeting by II. Lee whose title is “Nuclear Structure Studies and Intermediate Energy Probes.” By using different probes, electrons, muons, pions and kaons, one obtains different views of the probed nucleus. Putting these views together provides us with an integrated picture not accessible with just a single probe. The concepts and phenomena which nuclear reaction studies have discovered include compound nuclear resonances, prompt reactions such as the optical model and direct reactions, doorway states and giant resonances, multi-step reactions of both the direct and compound type. Processes which have been described include multiple scattering by a mesoscopic system, particle exchange between two such systems, inelastic scattering, and production processes of pions, kaons, gamma rays. A principal concept which has emerged from this research is that of energy averaging or alternately the existence of differing time scales. These can be explored by choosing appropriate experimental parameters. The energy resolution, AE is the key. When AE is relatively large we are dealing with prompt reactions, as seen in direct reactions and the optical model. When the energy resolution is very good, it may become possible to see compound nuclear resonance. One can envisage energy resolution which lie between these two limits. Such energy resolutions permit the
observation of a doorway state resonance (in this case an isobar analog resonance) as illustrated in Fig. 2. The upper half gives the s2Mo(p,p) cross section at several angles taken with good resolution. We see only fluctuations. However upon energy averaging by using poorer energy resolution one obtains the bottom curve showing a beautiful resonance dependence on energy. Note that the above developments were made without using accurately determined nucleon-nucleon potentials. Success is a consequence of the existence of the “universals” which as we have alluded to earlier are largely independent of the interparticle forces. As the potentials became better known, the challenge of correlating the semi-empirical results with those which could be obtained from the nucleon-nucleon potential presents itself. In the middle sixties, this calculation was performed by G. E. Brown and Tom Kuo. Their results can be compared with semi-empirical results obtained by Brown and Wildenthal using a method originally devised by Talmi. Using two forms of the potential, the Paris and Bonn, Kuo in his presentation to this meeting points out that agreement with Brown and Wildenthal is best for the Bonn potential because its tensor term is weak. Kuo also discusses evidence from hypernuclei and concludes that the Niejmegen potentials are not as good as the Julich potential. Of course much of this uncertainty would be reduced if particle physicists had derived the baryon-baryon potential from first principles as they promised to do many years ago and many times. We turn next to presentations regarding the weak interactions made by Haxton, Faessler and Ball. Nuclear physics has played a leading role in the study of the weak interactions. The study of parity conservation by Wu et al has been followed by its observation in the baryon-baryon interaction. Recent experiments using electron scattering from nuclei will test the “standard theory.” The research reported by Haxton relies on the use of nuclei as detectors of neutrinos in this case from the sun and from super nova. Ga and Cl detectors measure different portions of the solar neutrino spectrum. Detection of neutrinos emitted in super-nova explosions e.g. 1987A have been made so that a neutrino based astronomy appears to be in prospect. The resolution of the solar neutrino issue will have significant impact on significant fundamental questions such as the validity of the MSW process, the mass of the neutrino and the solar model. Faessler described his analysis of double p decay and its relation to the Majorana neutrino (not radiated in double p decay) and the Dirac neutrino commonly used in single p decay. He finds nuclear properties, e.g. ground state correlations to be important. Finally two new facilities of particular importance to nuclear spectroscopy were discussed.; Olsen described the production of a beam of radioactive nuclei at Oak Ridge, expected to be available by 1995. In this facility, the radioactive nuclei are produced in a cyclotron and then injected into a tandem. Ball described the accompanying experimental program which will focus on proton rich nuclei approaching the proton drip line. Predictions have been made of large deformations, nuclei with exotic shapes. The 2 = N nuclei up to “‘Sn will be produced and studied. Gai pointed to importance of neutron rich nuclei such as ‘Li, “Li, ‘lBe, “Be, etc. The Gammasphere, being built at Berkeley, is designed to be an efficient detector of y decay. A similar instrument is under construction by Great Britain and France, called the Eurogam. Another, the Euroball, is projected to be built to succeed the Eurogam.
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H. Feshbach
I Summary
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Fig. 2: The “MO (p,p) reaction. The results shown in the figure at the top were taken with excellent energy resolution; those in the lower figure with poorer energy resolution.
These instruments will be used to study the superdeformed nuclei and the interesting puzzle of identical super-deformed bands from neighboring nuclei. L. Y. Lee presented a discussion of these instruments. This report reveals the great diversity of nuclear physics research, even though there are many topics which could not be included. Problems are attacked with different probes, with differing nuclei which provide a variety of examples. Using sensitive detectors, many experimental situations can be realized. It is the synergism of these studies which leads to a fundamental understanding of nuclei and nuclear reactions and thereby to mesoscopic systems.