- Email: [email protected]
Introductory note
Introductory Note D. H. WILKINSON University of Sussex, Brighton BNI 9RH, U.K.
We know that we may, to a rather good first approximation, think of the atomic nucleus as a collection of neutrons and protons that individually move smoothly under an effective over-all field of force built up out of all the mutual attractions that the nucleons have for each other. This is the shell model of the nucleus; it satisfactorily accounts for ground-state quantum numbers throughout the periodic table and, when elaborated by introduction of the statedependence of the nucleon-nucleon interactions, also accounts for the excitation spectra and dynamical properties of those nuclei, at the moment up to A = 40, that are sufficiently simple to permit of detailed computation; beyond A = 40 the account remains eminently satisfactory within a narrowing compass associated with the need, owing to computational complexities, to truncate the set of effectivelyparticipating nucleons. We also know that we may, on occasion, think of the nucleus as indulging in collective motions, rotations and vibrations, that may or may not distinguish between neutrons and protons; some of these collective motions may be pictured as involving all the nucleons of the nucleus in particularly simple ways: the giant resonances. Although the shell and collective models appear to be so different they are intimately connected. Sometimes the connection is an extremely simple one; thus the collective picture of the giant electric dipole resonance of a doubly-closedshell nucleus such as 160 or 40Ca is of all the neutrons and all the protons vibrating collectively in anti-phase with each other, all the nucleons therefore being obviously and explicitly involved; but the shell model description of this identical motion involves merely the excitation of a single nucleon from the topmost filled major shell to the next major shell; the collectivity of the first picture is found in the second through the representation of the single-nucleon excitation as the coherent superposition of all possible excitations between the two major shells in question and through the effect of the Pauli principle in involving the nucleons of the low-lying "undisturbed" shells in an implicit but essential way be preventing the downwards excitation of nucleons which would contribute negatively to the net absorption strength. The connection between the pictures is that of a mathematical identity. Sometimes the connection between the shell and collective pictures is much more complicated as in, for example, the rotational bands of the nuclei of the (2s,ld)-shell around A = 20-30 but here also the collective picture arises naturally from the full shell model treatment, in this case not even involving excitations out of the major shell that describes the ground state; no collectivity, as such, needs to be separately injected into the shell model to generate the collective motions. I have gone over this familiar ground at some length to emphasize that traditional nuclear structure physics, although tremendously detailed and tremendously
P.P.N.P. V O L
4 ~- A ~
2
Introductory
Note
rich is, nevertheless, superficial in depending on only a small fraction of the totality of the nucleons of the nucleus for its description even when it may seem to involve them all. One might also add that traditional nuclear structure physics does not involve the putting of nuclear matter into novel conditions of pressure or densit~ the nucleus in the excited states traditionally investigated remains of essentially the same central density as in its ground state and the fall-off of density through the nuclear surface is also in no essential way changed. If we were able to bring about significant density increases in nuclei a different nuclear physics would certainly be revealed. We should not even be able to assume the continued validity of the shell model on account of the increased importance of the strong short-distance interactions that tend to break down the simple orbital motions, to disrupt the tranquility of the Fermi sea. But even assuming the continued good offices of the shell model, which must hold up to certain point, the details of the nuclear physics would change if only because the effective interactions between nucleons in given orbitals would change both absolutely in terms of the effective interactions in a given spectroscopic state and also relatively in terms of the relative strengths of interactions in different spectroscopic states on which nuclear spectroscopy depends so critically. Nuclear structure will be a function of nuclear density. However, significant changes of nuclear density could have more radical effects than merely presenting us with another axis along which to determine nuclear structure. Missing from the traditional account of nuclear structure is explicit regard for the mechanisms through which the forces that hold the nucleus together arise. Pions and other mesons are exchanged between nucleons and, in those exchanges, may raise nucleons into excited baryonic resonance isobar states and may also engender particle - anti-particle pairs. The effects of those processes are difficult to disentangle from the overall nuclear properties and, to a considerable degree, are subsumed into the effective forces through which the detailed account of nuclear structure given by the shell model is parameterized. Those processes have, however, received considerable theoretical study as surmnarized, for example, in the 1976 Erice School "The Mesonic Interface between Nuclear Structure and Particle Physics" and in the recent book that Mannque Rho and I edited, "Mesons in Nuclei"; they are certainly strongly density-dependent: we can obviously expect the abundance of nucleon isobars to increase rapidly at higher nuclear density and this in turn will rapidly enhance the role of the manybody forces; the role of the mesonic and isobar effects themselves will also rapidly expand and we shall no longer be able to incorporate them in a perturbative way into an initial wave-function that refers only to nucleons; with further increase of density a full field-theoretical description of the nucleus will be upon us. However, before we get to this point a more-radical revision of the nuclear scene may be needed. As it now clearly recognized, nuclear matter at high density must undergo a phase change or phase changes, associated with the condensation of pions and other mesons. Pion condensation rides on the back of the ~ - i s o b a r which acts as a catalyst for the generation of more and more pions as short-range effects become encouraged by the higher nuclear density. Such generation of high pion densities is now thought to be unlikely at normal nuclear densities but probably at densities increased by only a factor of two or so. Another widelydiscussed possibility at high densities is the so-called Lee-Wick regime, a cooperative phenomenon involving the ~ - m e s o n or its mock-up out of pions. At one time thought possibly to constitute a "basement" state of nuclear matter, of energy less than the "ground" state and of much higher density, but cut off from it by a barrier that would make it very difficult to attain, this Lee-Wick regime is now thought rather to obtain at energies significantly higher than the ground
Introductory Note
5
state but nevertheless to impress a significant inflection, or possibly even a deep minimum, into the energy/density curve of nuclear matter. A further high-density phenomenon about which, at the moment, we scarcely know how to speculate, is the possible explicit coming into play of quark degrees of freedom. At sufficiently-high densities nuclear matter must, we presume, become quark matter with the dissolving of the bags around the individual nucleons. However, well below such ultimate densities we may rather confidently anticipate that multi-quark entities formed by the temporary fusion of nucleons and mesons will become important particularly, of course, for "hard" encounters where very high momenta are transferred. What have the two points that I have been making about the superficiality of the information about the nucleus available from our traditional approaches to it, and the possibility of novel modes of organization of nuclear matter at high densities, to do with heavy ions at high energies? Quite simply that in the energetic collision between heavy ions, especially at small impact parameters, deep penetration of nuclear matter by nuclear matter must be expected to take place so that a profound re-arrangement of that matter, involving a large fraction of the participant nucleons in a non-trivial matter, may be anticipated and also that we might expect high densities to be built up as more and more nucleons from the remoter parts of the colliding nuclei pile into the region of the collision while those already there are not able to get out of the way in time. To be sure, there may be considerable difficulty in our knowing from the debris of such collisions what has gone on in their course. This means that we must investigate, most carefully, the possible consequences of such collisions looked at from all available "traditional" viewpoints as well as from the novel but conventional viewpoints that reasonably suggest themselves simply on account of the novel circumstances and also from unconventional viewpoints to which we would not be led by a mere extrapolation, into the novel regime, of considerations with which we are already familiar. We shall be seeking to learn something new about the behaviour of nuclear matter and we can do this only by finding, resulting from the collisions in question, final states differing from those to which our preconceptions would have led us. The Erice school, to which this note is a preface, was devoted to looking at heavy ion collisions from as wide a range of viewpoints, conventional and unconventional, as possible so as to map out as broad a spectrum of expectations as we are able at the present time. In this pursuit of the unknown by novel methods, theory and experiment must go hand in hand so that the school laid considerable emphasis on what we already know, not oniy to guide us into the most profitable directions for our developing understanding but also to indicate those directions of experimental exploration most likely to throw up qualitative challenges to that understanding. The emphasis of the School was on the move into the unknown offered by the energetic collisions of heavy ions. Such collisions are able, in their gentler, more peripheral, modes, also to bring us valuable information of traditional type to do with spectroscopic factors for few-nucleon transfer and so on but with this, optical model potentials and so on, we were not at all concerned. We did, however, as a complement to the problems of nuclear matter, concern ourselves with one aspect of the unknown that can be approached only through heavy ions and that is not even nuclear in its content: the quantum electrodynamical phenomena, particularly the spontaneous generation of positrons, made possible by the intense electric fields generated by the close putting-together of two heavy nuclei.
We know that we may, to a rather good first approximation, think of the atomic nucleus as a collection of neutrons and protons that individually move smoothly under an effective over-all field of force built up out of all the mutual attractions that the nucleons have for each other. This is the shell model of the nucleus; it satisfactorily accounts for ground-state quantum numbers throughout the periodic table and, when elaborated by introduction of the statedependence of the nucleon-nucleon interactions, also accounts for the excitation spectra and dynamical properties of those nuclei, at the moment up to A = 40, that are sufficiently simple to permit of detailed computation; beyond A = 40 the account remains eminently satisfactory within a narrowing compass associated with the need, owing to computational complexities, to truncate the set of effectivelyparticipating nucleons. We also know that we may, on occasion, think of the nucleus as indulging in collective motions, rotations and vibrations, that may or may not distinguish between neutrons and protons; some of these collective motions may be pictured as involving all the nucleons of the nucleus in particularly simple ways: the giant resonances. Although the shell and collective models appear to be so different they are intimately connected. Sometimes the connection is an extremely simple one; thus the collective picture of the giant electric dipole resonance of a doubly-closedshell nucleus such as 160 or 40Ca is of all the neutrons and all the protons vibrating collectively in anti-phase with each other, all the nucleons therefore being obviously and explicitly involved; but the shell model description of this identical motion involves merely the excitation of a single nucleon from the topmost filled major shell to the next major shell; the collectivity of the first picture is found in the second through the representation of the single-nucleon excitation as the coherent superposition of all possible excitations between the two major shells in question and through the effect of the Pauli principle in involving the nucleons of the low-lying "undisturbed" shells in an implicit but essential way be preventing the downwards excitation of nucleons which would contribute negatively to the net absorption strength. The connection between the pictures is that of a mathematical identity. Sometimes the connection between the shell and collective pictures is much more complicated as in, for example, the rotational bands of the nuclei of the (2s,ld)-shell around A = 20-30 but here also the collective picture arises naturally from the full shell model treatment, in this case not even involving excitations out of the major shell that describes the ground state; no collectivity, as such, needs to be separately injected into the shell model to generate the collective motions. I have gone over this familiar ground at some length to emphasize that traditional nuclear structure physics, although tremendously detailed and tremendously
P.P.N.P. V O L
4 ~- A ~
2
Introductory
Note
rich is, nevertheless, superficial in depending on only a small fraction of the totality of the nucleons of the nucleus for its description even when it may seem to involve them all. One might also add that traditional nuclear structure physics does not involve the putting of nuclear matter into novel conditions of pressure or densit~ the nucleus in the excited states traditionally investigated remains of essentially the same central density as in its ground state and the fall-off of density through the nuclear surface is also in no essential way changed. If we were able to bring about significant density increases in nuclei a different nuclear physics would certainly be revealed. We should not even be able to assume the continued validity of the shell model on account of the increased importance of the strong short-distance interactions that tend to break down the simple orbital motions, to disrupt the tranquility of the Fermi sea. But even assuming the continued good offices of the shell model, which must hold up to certain point, the details of the nuclear physics would change if only because the effective interactions between nucleons in given orbitals would change both absolutely in terms of the effective interactions in a given spectroscopic state and also relatively in terms of the relative strengths of interactions in different spectroscopic states on which nuclear spectroscopy depends so critically. Nuclear structure will be a function of nuclear density. However, significant changes of nuclear density could have more radical effects than merely presenting us with another axis along which to determine nuclear structure. Missing from the traditional account of nuclear structure is explicit regard for the mechanisms through which the forces that hold the nucleus together arise. Pions and other mesons are exchanged between nucleons and, in those exchanges, may raise nucleons into excited baryonic resonance isobar states and may also engender particle - anti-particle pairs. The effects of those processes are difficult to disentangle from the overall nuclear properties and, to a considerable degree, are subsumed into the effective forces through which the detailed account of nuclear structure given by the shell model is parameterized. Those processes have, however, received considerable theoretical study as surmnarized, for example, in the 1976 Erice School "The Mesonic Interface between Nuclear Structure and Particle Physics" and in the recent book that Mannque Rho and I edited, "Mesons in Nuclei"; they are certainly strongly density-dependent: we can obviously expect the abundance of nucleon isobars to increase rapidly at higher nuclear density and this in turn will rapidly enhance the role of the manybody forces; the role of the mesonic and isobar effects themselves will also rapidly expand and we shall no longer be able to incorporate them in a perturbative way into an initial wave-function that refers only to nucleons; with further increase of density a full field-theoretical description of the nucleus will be upon us. However, before we get to this point a more-radical revision of the nuclear scene may be needed. As it now clearly recognized, nuclear matter at high density must undergo a phase change or phase changes, associated with the condensation of pions and other mesons. Pion condensation rides on the back of the ~ - i s o b a r which acts as a catalyst for the generation of more and more pions as short-range effects become encouraged by the higher nuclear density. Such generation of high pion densities is now thought to be unlikely at normal nuclear densities but probably at densities increased by only a factor of two or so. Another widelydiscussed possibility at high densities is the so-called Lee-Wick regime, a cooperative phenomenon involving the ~ - m e s o n or its mock-up out of pions. At one time thought possibly to constitute a "basement" state of nuclear matter, of energy less than the "ground" state and of much higher density, but cut off from it by a barrier that would make it very difficult to attain, this Lee-Wick regime is now thought rather to obtain at energies significantly higher than the ground
Introductory Note
5
state but nevertheless to impress a significant inflection, or possibly even a deep minimum, into the energy/density curve of nuclear matter. A further high-density phenomenon about which, at the moment, we scarcely know how to speculate, is the possible explicit coming into play of quark degrees of freedom. At sufficiently-high densities nuclear matter must, we presume, become quark matter with the dissolving of the bags around the individual nucleons. However, well below such ultimate densities we may rather confidently anticipate that multi-quark entities formed by the temporary fusion of nucleons and mesons will become important particularly, of course, for "hard" encounters where very high momenta are transferred. What have the two points that I have been making about the superficiality of the information about the nucleus available from our traditional approaches to it, and the possibility of novel modes of organization of nuclear matter at high densities, to do with heavy ions at high energies? Quite simply that in the energetic collision between heavy ions, especially at small impact parameters, deep penetration of nuclear matter by nuclear matter must be expected to take place so that a profound re-arrangement of that matter, involving a large fraction of the participant nucleons in a non-trivial matter, may be anticipated and also that we might expect high densities to be built up as more and more nucleons from the remoter parts of the colliding nuclei pile into the region of the collision while those already there are not able to get out of the way in time. To be sure, there may be considerable difficulty in our knowing from the debris of such collisions what has gone on in their course. This means that we must investigate, most carefully, the possible consequences of such collisions looked at from all available "traditional" viewpoints as well as from the novel but conventional viewpoints that reasonably suggest themselves simply on account of the novel circumstances and also from unconventional viewpoints to which we would not be led by a mere extrapolation, into the novel regime, of considerations with which we are already familiar. We shall be seeking to learn something new about the behaviour of nuclear matter and we can do this only by finding, resulting from the collisions in question, final states differing from those to which our preconceptions would have led us. The Erice school, to which this note is a preface, was devoted to looking at heavy ion collisions from as wide a range of viewpoints, conventional and unconventional, as possible so as to map out as broad a spectrum of expectations as we are able at the present time. In this pursuit of the unknown by novel methods, theory and experiment must go hand in hand so that the school laid considerable emphasis on what we already know, not oniy to guide us into the most profitable directions for our developing understanding but also to indicate those directions of experimental exploration most likely to throw up qualitative challenges to that understanding. The emphasis of the School was on the move into the unknown offered by the energetic collisions of heavy ions. Such collisions are able, in their gentler, more peripheral, modes, also to bring us valuable information of traditional type to do with spectroscopic factors for few-nucleon transfer and so on but with this, optical model potentials and so on, we were not at all concerned. We did, however, as a complement to the problems of nuclear matter, concern ourselves with one aspect of the unknown that can be approached only through heavy ions and that is not even nuclear in its content: the quantum electrodynamical phenomena, particularly the spontaneous generation of positrons, made possible by the intense electric fields generated by the close putting-together of two heavy nuclei.